There are major efforts underway to “decarbonize” the GB rail network. One way of pursuing this goal is to reduce traction energy costs which would contribute to decarbonization either directly through the reduction in fossil fuel use, or indirectly through the reduction in the use of electricity produced from non-renewable sources. In this post, I will attempt to show that the train aerodynamic drag reduction due to the use of slab rather than ballasted track may result in significant fuel and energy savings for an entire train fleet that would contribute to the decarbonization agenda and that could radically change the overall business case for the installation of slab track, which is currently only used in specific circumstances. It will be seen that the argument is very speculative in places, but perhaps strong enough to warrant further investigation. We begin in the next section with an introduction to train resistance.
The specification of train resistance is required for the assessment of energy consumption, train timing etc. Now train resistance is, very broadly, composed of mechanical (rolling) resistance and aerodynamic resistance, and is conventionally described by the Davis equation given in equation (1).
Here v is the train speed and a, b and c are constants. The first two terms are taken to be the mechanical resistance, and the last term is taken to be the aerodynamic resistance. The aerodynamic resistance is thus proportional to the square of train speed and becomes progressively more important as train speed increases. The parameters a, b and c are usually obtained from coast down tests on (ideally) straight, level section of track, in which trains coast from top speed to zero and acceleration, speed and distance are measured. A quadratic curve is then fitted to data. Typical examples of tests sites in the UK are given in figure 1 and a typical set of results in figure 2. Note that this figure and most of those that follow are taken from the recent book “Train Aerodynamics – Fundamentals and Applications” by myself and a number of colleagues. Note also that it is also possible to estimate the aerodynamic component of resistance from wind tunnel tests and CFD calculations, but there are significant technical issues (mainly due to the inability of both techniques to model full length trains) and thus in what follows we consider only data from full scale measurements.
The coefficient c is related to the aerodynamic drag coefficient CD by the simple expression of equation (2).
Here A is the frontal area of the train and r is the density of air. The drag coefficient for a wide range of trains is shown in figure 3 (from ???).
Very broadly, for any individual train class, the drag coefficient in linearly proportional to train length, and can be represented by the simple form of equation (3).
Here L’ is an effective train length (the length of the train minus the length of the nose and tail sections) and p is the wetted perimeter of the train envelope. The values of the parameters K1and K2 are given in table 1 for the train types shown in figure 3.
Breakdown of Aerodynamic drag
Figure 4 shows how the components of aerodynamic drag for high speed trains from the work of two different authors. Whilst there is some variability between the results it can be seen that the drag of the underbelly and bogies contributes 20 to 50% of the overall drag and skin friction drag on the train side and roof contributes 30% to 40%. An important point to appreciate is that the underbody drag includes drag due to the track roughness – energy needs to be used to overcome the aerodynamic resistance of the track itself. This point does not seem to have been well appreciated in the past.
Referring back to equation (3), K2is a friction coefficient for train, combining theeffect of skin friction on side and roof and bogie and underbody drag. As can be seem from figure 3, values of 0.004 are typical for high speed trains (but note the quality of fit is not terribly good).
Friction coefficients can be obtained directly from measurements of the velocity profile on the side and beneath the train and then fitting of logarithmic profile to the data. This process is somewhat difficult and subjective, but has nonetheless been attempted by a number of authors in the past. Table 2 shows the values for skin friction on the side of the train that have been obtained, and table 3 shows values for the underbody of trains.
Typical values of the former are 0.0015 and typical values for the latter for ballasted track are 0.03. The higher values for underbody coefficient are of course to be expected because of the roughness of the train underbelly. For slab track the one set of data available gives a significantly lower value of the underbody friction coefficient of 0.01.
If we assume that, for high speed trains, skin friction values of 0.0015 and underbody drag of 0.03 and assume that the former acts over 90% of the wetted perimeter and the latter over 10% these weights give a value of K2 of 0.00435 which is consistent with drag compilation value from table 1 of 0.004 and result in a drag coefficient of 1.4 for a 200m high speed train. If underbody drag reduced to 0.01 by use of slab track, the same calculation leads to drag coefficient of 0.81 – a staggering 40% decrease. A rule of thumb that is often applied is that a drag coefficient reduction of x% results in an energy saving of 0.4x% suggests 40 x 0.4 % which suggest a potential reduction in fuel use of 16%.
Now many assumptions have been made in the above analysis, perhaps the most significant being the value of friction coefficient for slab track, which is based on one set of experimental results only. Thus the argument that significant fuel cost reductions might be a possibility through the use of slab track more widely, is at best suggestive but I would suggest merits further investigation. The question arises as to whether such energy savings have the potential to change the business case for slab track, which is in general only currently used for very specific situations such as tunnels, poor ground conditions etc. I would thus suggest a preliminary investigation that addresses the question of what reduction in drag coefficient would actually be required to change business case for slab track? As both infrastructure and trains would be involved, a system approach would be required here. If further investigation of the business case shows that it is worth pursuing these ideas, the next stage would be to conduct coastdown tests with the same train over ballasted and slab track. A long straight level section of slab track would thus be required. Does such a section of track exist in the UK?
This post addresses the issue of the use of what has become known as the “Chinese Hat” gust model. The use of this title has become increasingly problematic over recent years for obvious reasons, and I will no longer use it, but will instead refer to the “CEN extreme gust model” in what follows.
The CEN extreme gust model
In a number of situations in wind engineering, some sort of deterministic (as opposed to stochastic) gust model is required in order to determine structural response. One such case is in the determination of the risk of overturning of road or rail vehicles in high winds. A methodology of this type is set out in CEN (2018), where an extreme gust model is described. This model was originally developed in wind loading studies for wind turbines as a time dependent gust to be applied to calculate wind turbine loading at one fixed location (Bierbooms and Cheng, 2002). As such, it is perfectly adequate and a good representation of an average extreme gust in high wind conditions. In the methodology of CEN however, it is re-interpreted as a stationary spatially varying gust. This must be regarded as a very significant assumption for which, in my view, there is little justification. Nonetheless the formulation has proved useful practically and we begin by considering it in a little more detail.
For a wind normal to the track, the extreme gust formulation is given by equation (1) on Box 1. Note that the “characteristic frequency” of the gust is calculated from standard wind engineering methods for temporally, rather than spatially, varying gusts. Equation (1) is a generalised form of that given in CEN (2018) to remove some of the constants that tie the expression to a particular location and topography through specific values of peak factor and the turbulence intensity (the ratio of the standard deviation to the mean velocity). The time dependence is recovered through the passage of the train passing through this gust at a speed v = xt to give equation (2). It can be seen that the gust thus has a maximum value of (1+ peak factor x turbulence intensity) when t = 0 and decreases to unity for small and large times. It is symmetrical about t = 0. The velocity relative to the train is then found by the vector addition of this gust velocity with the vehicle velocity to give a time varying value.
To enable the gust profile to be specified, the characteristic frequency f is required. This is specified in equations (3) to (5). These equations are again in a more generalized form than given in CEN (2018), where a value of the upper limit of integration is fixed at 1 Hz, together with an implicit value of the turbulence length scale of around 75m. The genesis of the 4.18 factor is however not clear to me. Equation (3) shows that the calculation of the characteristic frequency is thus based on the calculation of the zero-crossing rate of temporal fluctuations through the use of the velocity spectrum. Again, note that these parameters describe a time varying rather than a spatially varying velocity, and their use is not formally consistent with a spatially varying gust. From equations (3) to (5), it can be seen that the normalized characteristic frequency is a function of the normalized upper limit of integration. A numerical solution of these equations was carried out and the following empirical line fitted to the results for a value of the latter greater than 1.5 (which is the realistic range) – equation (6). From equations (2) and (6) we thus obtain equation (7). Although the overall methodology cannot be regarded as wholly sound, equation (7) does (in principal) significantly simplify its use and also allows the implicit wind parameters in the method to be explicitly defined.
Is there a better methodology?
It can be seen from the above that the CEN methodology thus does not fully describe a typical gust as seen by a moving train, which would vary both spatially and temporally, and can at best be regarded as an approximation, although its practical utility must be acknowledged. Ideally, if such an approach is to be used, a gust that varies both in space and time is really required. Such a gust was used in the SNCF route assessment method of Cleon and Jourdain (2001), where the shape of the gust is appropriately described as a rugby ball. This method was however for very specific wind characteristics and does not seem to have found widespread use. Thus in this post, we investigate the possibility of developing a spatially and temporally varying gust, that can be expressed in a simple form (ideally similar to equation (2)) for practical use.
Towards a new model
In this section we will draw on experimental results for extreme gust characteristics in both temporal and spatial terms to construct a simple, if empirical model, that fulfills the function of the CEN (2018) model without the theoretical drawbacks.
We consider first the full-scale experimental data analysed by Sterling et al (2006) which used conditional sampling to determine the average 99.5th percentile gust profile for four anemometers on a vertical mast with heights between 1m and 10m. These results thus give the time variation in gust speed as the gust passes the anemometers. They showed that the gust profiles could be well approximated by the formula shown in equation (8) (Box 2). The parameter G in this equation is the equivalent of the peak factor multiplied by the turbulence intensity in equation (2) and for these measurements was 0.786. n was -0.096, and the value of m depended upon whether t was greater or less than zero. For t < 0, i.e. on the rising limb, m was 0.1, whilst for t> 0, on the falling limb, m was 0.2. The gust shape was thus asymmetric with a maximum at t = 0. This curve was a good fit to all the gust profiles throughout the height range. In what follows we will use a rather different curve fit expression to the same data, more consistent with that used in CEN (2018) – equation (9). It was found that the best fit value of b was equal to 0.5 for all t, whilst the best fit values of a were 0.49 for the rising gust and 0.37 for the falling gust. This expression thus describes the temporal variation of wind speed as a gust passes through the measuring point
To describe the lateral spatial variation of the gust profile, we use the data of Baker (2001) who presents conditionally sampled peak events for pressure coefficients along a 2m high horizontal wall. This data allows the lateral extent of the gusts to be determined, from the variation of the time varying pressure coefficient divided by the mean value of the coefficient and then assuming that the gust velocity variation can be found from equation (10). The spatial variations of velocity were then fitted by a curve of the form of equation (11). g was found to be 6.16 and d was found to be 0.7.
On the basis of the above expressions one can thus write the expression of equation (12), which describes the variation of the gust velocity in both space and time. The movement of the train through the gust can again be allowed for by letting x = vt (equation (13)).
Box 3 sets out the formulations of the CEN extreme gust model and the model derived here. In some ways they are similar in form, with an exponential formula that is primarily a function of normalized time. Whilst the CEN model is symmetric around t = 0, the new model has a degree of asymmetry because of the different values of the curve fit parameters for t < 0 and t > 0. However an examination of the new model suggest that the asymmetric term may be small, and thus Box 3 also shows an approximate version of the new model where this term is neglected.
Figure 1 shows a comparison of these three models for the following parameter values – peak factor = 3.0; turbulence intensity = 0.25; train speed = 75m/s; mean wind speed = 25m/s; turbulence length scale = 75m, upper frequency of integration = 1.0Hz. It can be all three models are similar in form, showing a sharp peak at t = 0. The full and approximate forms of the new model are almost indistinguishable, showing that the approximation suggested above is valid. The main difference is that the CEN model has a much greater spread in time than the new model. This difference persists whatever input parameters are chosen.
At this point it is necessary to consider again the genesis of the models – the CEN model resulted from an application of a time varying gust model as a spatially varying gust model, whilst the new model was developed based on measured temporal and spatial gust values. As such, I would expect the latter to be more accurate. The broad spread of the CEN gust may result from an application of the time varying along wind statistics to a cross wind spatial gust. Since it is known that that longitudinal integral scale is several times larger than the lateral integral scale, this would result in a wider spread of the gust than would be realistic. This is to some extent confirmed by the period of the two gusts – around 2s for the CEN gust and around 0.8s for the new model. For a train speed of 75m/s, this corresponds to gust widths of 150m and 60m – roughly approximating to the expected the longitudinal and lateral turbulence integral scales.
In this post I have looked again at the CEN extreme gust method and raised concerns about its fundamental assumptions. I have also developed an equivalent, but perhaps more rigorous, methodology based on experimental data for wind conditions at ground level. This strongly suggests that the CEN gusts are spatially larger than they should be, which suggests its long term use should be reviewed. However, when used to compare the crosswind behaviour of individual trains, rather than in an absolute sense, it is probably quite adequate.
CEN, 2018. Railway Applications d Aerodynamics d Part 6: Requirements and Test Procedures for Cross Wind Assessment. EN 14067-6:2018.
Cleon, L., Jourdain, A., 2001. Protection of line LN5 against cross winds. In: World Congress on Rail Research, Köln, Germany.
Sterling M, Baker C, Quinn A, Hoxey R, Richards P, 2006, An investigation of the wind statistics and extreme gust events at a rural site, Wind and Structures 9, 3, 193-216, http://dx.doi.org/10.12989/was.2006.9.3.193
This post arises out of a discussion with a number of colleagues on the issue of train overturning, in particular Mr Terry Johnson and Dr Dave Soper. Their (perhaps inadvertent) contribution to the development of the ideas set out below is gratefully acknowledged, although the responsibility for any inadequacies and errors must remain mine.
In recent decades a great deal of research has been carried out to investigate the safety of trains in high cross winds, primarily to determine the wind speeds at which overturning will occur, and the risk of a wind induced accident (Baker et al, 2019). This usually takes the form of the determination of the aerodynamic forces and moment coefficient for a particular train, the use of these coefficients to determine the cross wind characteristic (CWC) – effectively a plot of accident wind speed against vehicle speed – and then some sort of risk analysis on the route over which the train will run. The first two steps are usually the concern of train manufacturers and are undertaken when the design of the train, at least in terms of overall shape and size, is fairly well advanced. The third step is usually the concern of the infrastructure operator. One question that is not often asked however is whether there is a “best” design for a train to minimise the risk of a wind induced accident, and thus to maximise safety. This has been addressed to some extent by a number of recent investigations that used a combination of CFD methods to calculate the forces and moments on a train, and optimisation methods to consider the effect of changes to train geometry. It is not however clear as to what should be the objective function of such optimisation – for example a number of different force or moment coefficients for a range of different yaw angles could be chosen. This post addresses this issue though an analysis of accident risk and investigates the aerodynamic parameters required to minimise this risk
2. Aerodynamic force and moment coefficients
In a recent book (Baker et al, 2019) the author suggests a way of parameterising train aerodynamic force and moment data that seems to have a wide validity. This is set out in Box 1 below, in which the formulation for lee rail rolling moment coefficient is given, and is illustrated for a specific case. It applies equally well to side and lift force coefficient data. It can be seen that the form of the rolling moment / yaw angle curve is specified by four parameters – the coefficients at yaw angles of 30 and 90 degrees and exponent shape factors that describe the shape of curve, n1 and n2. Figure 1 shows a comparison of this methodology with side force coefficient data from the CEN codes (CEN, 2018) and the AeroTRAIN project (Paradot et al, 2015) as given in Baker et al (2019). All this data was obtained in a consistent way, with an STBR ground simulation in low turbulence wind tunnels. The agreement can be seen to be in general good and gives some confidence in the use of the parameterisation in what follows. The biggest discrepancy is in the transition region between the high and low yaw angle regimes, but it will be seen that this is not particularly critical to the argument that follows.
3. Crosswind characteristics
The method used to specify the crosswind characteristic is also taken from Baker et al (2019) and is set out in Box 2. Using this methodology, the CWC are functions of n1 and n2, the ratio of the moment coefficients at yaw angles of 90 and 30 degrees, and what is defined as a characteristic wind speed, which is itself a function of train and track parameters. Box 2 gives the formulation for flat straight track, with a wind angle normal to the track – a fuller form can be found in Baker et al (2019). A comparison of this method with the results from CEN (2018) and Paradot et al (2015) is given in figure 2, again from Baker et al (2019). Agreement can be seen to be good, and this gives further confidence in the use of the methodology in what follows.
Box 2 also indicates how the accident risk can be calculated for a specific reference site using the Weibull distribution to specify wind speed probabilities. We assume a section of railway of a specified length, with specified values of the Weibull parameters and a typical service pattern, and we then express the CWCs as a plot of train speed against the probability that a wind induced accident will occur in the section, rather than accident wind speed. This enables us to better address the question as to what is a “good” vehicle in cross wind terms, as it will highlight the relative importance in risk terms of different vehicle speed ranges.
Figure 3 shows the calculated CWC, expressed as both an accident wind speed plot and as a risk plot, for what we will take as our base case. The parameters for this case are shown in the figure. The plot of accident wind speed against vehicle speed shows a reduction in the former as the latter increases, as would be expected. There is a break in gradient, at the point of transition between the low yaw angle (at high speed) and high yaw angle (at low speed) formulations of Box 2. Figure 2 shows that this is quite typical of the calculated CWCs from Paradot et al (2015). The plot of site risk against vehicle speed shows an increase in risk with the vehicle speed. At the vehicle speed of 350 km/hr the logarithmic risk is around -8 (but remember that this absolute value is completely arbitrary). The risk falls by an order of magnitude as the speed decreases through the low yaw angle range to around 100 km/h, with an increased rate of fall for low speeds, where the high yaw angle formulation becomes relevant.
Figures 4 to 7 show the effect on the CWCs of changing the parameters for the moment characteristics. As the low yaw angle exponent n1 is varied between 1.3 and 1.7, there are variations of about half a magnitude in risk for the higher train velocities, although this varies through the speed range. This parameter is typically around 0.9 to 1.1 for lorries, 1.2 to 1.4 for blunt nosed trains, 1.4 to 1.6 for streamlined trains, and 1.7 to 2.0 for trailing vehicles. As the high yaw angle exponent n2 is varied, the variations in accident velocity and risk are confined to the low speed range as would be expected, although here the variations in risk can be several orders of magnitude. As the lee rail rolling moment coefficient at 30 degrees is varied between 3 and 5, there can be seen to be very significant variations in both accident wind speeds and risk throughout the speed range. For variations in the lee rail rolling moment coefficient at 90 degrees only the low speed accident wind speeds and risk levels are affected as would be expected. From these graphs it can be concluded that the risk of an overturning accident will be reduced for high vehicle speeds if n1 increases and the lee rail rolling moment coefficient at 30 degrees decreases; and for low vehicle speeds if n2 increases (becomes less negative) and the lee rail rolling moment at 90 degrees decreases. Of the parameters the 30 degree coefficient produces most change in accident wind speeds and risk levels across the speed range, and is perhaps where most design effort should be concentrated.
Now let us consider specific trains. Table 1 shows, for the CEN (2018) and AeroTRAIN (Paradot et al, 2015) trains, the maximum train speed, the values of the four parameters that define the rolling moment characteristic, the characteristic velocity, and the risk at the maximum operating speed. Those shaded red indicate values that would increase risk significantly above the average, and those shown in green indicate values that would decrease risk significantly the average. It can be seen that of these trains the ICE3, IR and Silbering has the “best” values of rolling moment coefficient. For the ICE3 this is presumably due to the nose shape, resulting in low levels of lift and side force, and thus rolling moment. For the IR and Silberling however, these low values are due to the lack of underbody blockage, at least as modelled in the wind tunnel tests. The ICE3 values of n1 and n2 are around the average, whilst those for the IR and Silberling are low, and would thus tend to increase risk. The worst train in terms of rolling moment coefficients is the double deck M6BX. The IC4, RevCo and ZTER also have high values of the coefficient at 90 degrees.
The risk at the maximum speed for the all trains, with one exception, is between -7.3 and -8.4 i.e. it varies by one order of magnitude. The ICE3, TGV, ZTER and IR have the lowest risk and the M6BX the highest for the standard site. This risk variation is perhaps less than would be expected, and is partly caused by the reduction in risk with the reduction in maximum operating speed. The outlier from the range of -7.3 to -8.4 is the ADR, which has a low value of -9.1, which is due to its high mass and high resulting characteristic velocity.
From the above, it can be seen that for high speed trains, the aerodynamic parameter that most affects the overturning risk is the lee rail rolling moment coefficient in the low yaw angle range, characterised by the value at 30 degrees. In these terms the ICE3 shape is “best”. However this does not necessarily apply for lower speeds, when the higher yaw angle range becomes of importance. These points being made there are some important caveats.
The overturning wind speed and thus accident risk depends upon a range of parameters as well as the aerodynamic characteristics. Train mass is particularly important.
Similarly the infrastructure characteristics are important, and accident wind speed and risk will be affected by can’t and topography.
Perhaps most importantly, the level of risk is determined by the nature of the train operation itself – if speed limits are imposed in high winds, it is quite possible that the most important aerodynamic characteristics will move from those in the low yaw angle range to those in the high yaw angle range.
One further point is of interest. In Baker at al (2019) the head pressure pulse magnitudes and wake slipstream gust velocities are tabulated for orange of trains. Of those trains included, the Velaro (i.e. the ICE3) has both the lowest pressure pulse magnitude and the lowest slipstream gust velocities, suggesting that the nose / tail shape of this train has considerable aerodynamic advantages.
Baker, C., Johnson, T., Flynn, D., Hemida, H., Quinn, A., Soper, D., Sterling, M. (2019) Train Aerodynamics – Fundamental and Applications, Elsevier.
CEN, 2018. Railway applications — Aerodynamics — Part 6: Requirements and test procedures for cross wind assessment. EN 14067-6:2018.
Paradot, N., Gregoire, R., Stiepel, M., Blanco, A., Sima, M. et al., 2015. Crosswind sensitivity assessment of a representative Europe-wide range of conventional vehicles. Proceedings of the Institution of Mechanical Engineers. Part F Journal of Rail and Rapid Transit 229 (6), 594-624.
In a post of January 2020, I attempted to collate the numerous train aerodynamics research papers that had appeared since myself and my fellow authors began to write the book “Train Aerodynamics – Fundamentals and Applications” (hereafter referred to as TAFA) in mid-2018. I considered these papers under the application headings that were defined in TAFA – train drag, loads on structures etc. In this post I want to look at a subset of these papers, but consider them in rather a different way. Specifically I will consider a number of papers that used various CFD approaches to investigate a range of issues. One of the major benefits of CFD methods is that they can, in principle, give details of the entire flow fields around the trains that are studied and I will thus try to assess what information can be obtained from these papers to assist our basic understanding of the flow around trains. In what follows I will make no comments at all on the methodology used in the papers, assuming that these have been validated by the publication procedures, but will rather consider only the results in order to assess the flow field. I will use the framework outlined in TAFA, for various flow regions – nose region, boundary layer region, underbody region, wake region and cross wind effects. The papers that I will use are given in table 1. Note that most (but not all) of these papers come from Chinese institutions and are thus (naturally) mainly concerned with the variants of the Chinese High Speed Train (CRH2).
Two studies in particular give useful information concerning the pressure pulse around train noses – those of Wang et al (2019) and Dong et al (2019) both for a CRH2C train. The former investigates the effect of bogie complexity on a three-coach train, whilst the latter investigates the effect of bogie fairings on a two-coach train. Neither bogie complexity or fairings however affect the flow around the nose to any extent. Usefully both authors give data for the two TSI positions of 0.2m (termed trackside) and 1.4m (termed platform) above top of rail (ATOR) at various distances from the centre of the track (COT). In TAFA Table 5.1 typical values of peak-to-peak pressure coefficient for high-speed trains at 1.4m ATOR are within the range 0.15 to 0.20. At this position Wang et al give values of 0.18 and Dong et al a value of 0.14, which are broadly consistent with TAFA. Both papers also give useful information on how the peak-to-peak values vary with distance from the centre of the track – see the graphs of figure 1. There is a difference between the two sets of data which is not easily explicable, as the calculation conditions and set up are similar. Dong et al also give pressures on the track centre line, with a value of peak-to-peak pressure coefficient of 0.78 at the height of the top of the rail, 0.66 at 0.05m below the top of the rail and 0.52 at 0.23m below the top of the rail. The last value is similar to the value of 0.48 reported in TAFA Figure 5.19 for track bed pressures under the Class 373 Eurostar.
Figure 1 Nose pressure transients
Both papers also give data that enables the peak of the dimensionless nose velocity transient to be determined. Similar data can be obtained from the work of Chen et al (2019a) who investigated the effects of different nose lengths on an idealized high-speed train model. The results are shown in figure 2 for the heights of 0.2m and 1.4m above the top of rail. The data from Chen et al is for a 7.5m nose length. Although this parameter is not tabulated in TAFA, figure 5.2 gives a value of 0.08 at 0.2m above the top of rail, which is consistent the data from the more recent papers. There is again no obvious reason for the difference between the results of Dong et al and Wang et al. The data for Chen et al for a 7.5m nose is close to that of Wang et al at 0.10. For the 5m and 10m nose lengths the values are 0.12 and 0.09.
Figure 2. Nose velocity transients
Boundary layer region
In addition to the three papers mentioned in the last section (Chen et al, 2019a; Dong et al, 2019; and Wang et al, 2019), the papers by Li et al (2019) and Wang et al (2018) also give information on the nature of the flow in the boundary layer region along the train side and roof. Li et al (2019) considered the effect of the coupling between two units, comparing the results found for a single 6 coach unit, and those for two coupled three-coach units, both with CRH2 geometry. Wang et al (2018) used a two-coach model of a more generic high-speed train shape to study the effects of bogies on the flow. All five papers gave slipstream velocity time histories that were in principle directly comparable, and could also be compared with the full-scale data for high-speed trains in TAFA chapter 5. The results are plotted in figure 3, with the normalised velocity values being given at the centre of each coach. The accuracy for the data from the published papers is not high, as I have taken the information from small-scale figures, but it should nonetheless suffice. Specifically the following sets of data are shown on the graph.
Chen et al (2019a) – 7.5m nose length
Dong et al (2019) – Complex bogie
Li et al (2019) – Single unit
Wang et al (2018) – Full model
Wang et al (2019) – No bogie fairings
In general it seems that the slipstream velocities around the CFD models increase much quicker along the train than for the full-scale data, and thus there is much more rapid boundary layer growth in the CFD calculations. There is much scatter however, and some of this growth may be due to the specific model configuration used. For example the Wang et al (2019) data was for the case with no bogie fairings, which might be expected to lead to a rapidly growing boundary layer. That being said, one would actually expect a more rapidly growing boundary layer at model scale than at full scale for trains such as those considered here. For smooth high speed trains, where the analogy with a flat plate boundary layer is appropriate, the ratio of boundary layer thickness to distance from the nose of the train can be expected, very broadly, to be proportional to (Reynolds number based)-0.2. For a model scale of 1/8 and roughly full scale train speeds, which is the case for most of the calculations considered here, this suggests that at any point on the train, the scaled up boundary layer thickness for the computations should be about 1.5 times the actual full scale size, all other things being equal. For trains with blunter noses, or for freight trains, the size of the boundary layer will be more influenced by local separations and model scale and full-scale values should be more consistent.
Figure 3. Normalised velocity at 3m from COT and 0.2m above TOR
The growth of the boundary layer has been measured by Chen et al (2019a) in terms of the classic boundary layer parameters of displacement and momentum thickness and form parameter. His results for the displacement thickness on the side of the train are shown in figure 4 below for both the trackside and the platform cases, and also on the roof of the train. For the train side case, the boundary layer thicknesses from full-scale measurements of the ICE1 are also shown (from TAFA figure 5.12). These can be seen to be somewhat above those of Chen et al (2019a) which is perhaps not surprising as the blunt nosed ICE1 will cause a significant boundary layer thickening near the front of the train. For both the side and the roof results of Chen the form parameter is around 1.25 to 1.3, somewhat nearer to the classical boundary layer value than the ICE1 values of 1.15.
Figure 4 Boundary layer displacement thickness along side of train and roof
Figure 5 again shows the data for Chen et al (2019a) for the train roof, but this time showing the momentum thickness in order to enable a comparison to be made with a comparison with the results of Li et al (2019). The results can be seen to be similar if not identical.
Figure 5 Boundary layer momentum thickness along the roof of the train
In terms of overall boundary layer thickness, Gao et al (2019) and Niu et al (2018b) show contour plots around the train section. The figures shown are too small to take meaningful numbers from, but do indicate the thickening of the boundary layer close to the bogie region, and a slight thinning over the roof of the train. Wang et al (2019) provide rather more information of boundary layer thickness, and the development of the boundary layer down the side of their models is shown in figure 6, in terms of bogie position. These values are consistent with the displacement and momentum thicknesses shown above, being about an order of magnitude greater than the displacement and momentum thicknesses.
Figure 6 Boundary layer thickness along the side of the train
Wang et al (2019) also give data for the velocity profiles at the side of the train (figure 7). These show the boundary layer extending to 3 to 4.4m from COT, which whilst broadly consistent with the various full-scale data sets in TAFA (figure 5.11), are perhaps somewhat thicker than the full scale results given there.
Figure 7 Boundary layer velocity profiles
Finally the individual datasets in some of the papers give useful information of the effect of different train geometries. These are summarised in table 2, which shows the normalised slipstream velocities at 3m from the centre of the track and 0.2m above TOR for the last coach of the train for Chen et al (2019a) (different nose lengths); Li et al (2019) for single and double units; and Wang et al (2019) for bogie fairings. The most noticeable effect is that of the gap between the units in double unit formations.
Table 2. Effect of train modifications on normalised velocity (3m from COT, 0.2m above TOR at the centre of the last coach).
Perhaps the most significant paper to consider the flow beneath trains was that of Paz et al (2019) who looked at a novel method of specifying ground conditions that was much more realistic than current methodologies. This involved the scanning of the ballast and sleeper profiles of real track, with all the inherent irregularities and using this as the bottom boundary condition in CFD simulations. They showed that this methodology produced velocity profiles under long trains that conformed well with full-scale experiments, and that results in much more turbulent and chaotic flows than conventional ground simulations. This has obvious implications for the movement of ballast beneath trains. It seems to me that this paper sets the standard for proper ground simulations beneath trains in the future
A number of other papers looked at specific issues to do with the flow underneath the train, but it is difficult to draw any general conclusions from them, partly because they were addressing very localized effects and partly because they in general used short trains where the flows beneath the trains were not fully developed – for example Dong et al (2019) used a 2 car model when investigating different ground simulations; Gao et al (2019) used a three car model to look at bogie effects on the wake flow; Liu et al (2018) used a 1.5 car model to investigate snow accumulation on bogies; and Wang et al (2019) used a 3 car train to investigate the effect of bogie fairings. Whilst all these results are interesting in their own right, their application is very specific to the cases considered.
A number of authors considered the wake flow of high-speed trains in some detail, looking at the effect of various geometric changes on the nature of the wake. In all cases the broad structure of the wake was similar to that found by many investigations in the past – a pair of counter-rotating longitudinal vortices. The investigations came to a number of conclusions as to the effect of geometric variations on the strength of this vortex pair as follows.
Chen et al (2019a) found that the flow pattern for the shortest of the three train noses they used (5m) created a different wake topology to that with the 7.5m and 10m noses, and higher slipstream velocities.
Gao et al (2019) showed that the precise position of the rear bogies had a noticeable, if not major effect upon wake topology.
Li et al (2019) looked at the different wakes for single and multiple unit trains, They found that the wakes were similar in the two cases, but that for the double unit was more unsteady, reflecting the greater unsteadiness in the separating boundary layer at the end of the train due to the inter-unit gap. Overall they suggested however that the vortex pattern was dominated by the separation from underbody structures.
Wang et al (2018) showed that the presence of bogies on train models enhanced the unsteadiness of the flow. However the same dominant wake frequencies appeared with and without bogies, suggesting that whilst the vortex pattern results from the separated shear layer from the train, and has a certain fundamental unsteadiness, this unsteadiness is enhanced by the turbulence from the underbody flow
Wang et al (201), showed, unsurprisingly, that large fairings decrease scale and intensity of wake flow.
Overall these results suggest that the counter-rotating flow behind a high speed train is basically formed from the separating shear layers from the train side and roof boundary layers, but can be significantly modified by high levels of turbulence in the underbody flow. Here a word of caution is appropriate. As noted above, the underbody flow is the most difficult to simulate and really requires long trains and a sophisticated ground simulation, neither of which is usually the case in most CFD calculations. Thus the calculated effects of underbody flow or geometric changes on the wake structure must only be regarded as illustrative. There is a danger of reading too much into the various CFD results with regard to the wake structure. In addition it has been pointed out in TAFA that wake flows are quite sensitive to even small cross winds. Such winds will have length scales of the same approximate size as the vortex scale and it can be expected that in reality the general vortex flow pattern will be significantly distorted by such effects. Care should thus be taken so as not to overanalyze CFD models of wake flows.
These points having been made, it is possible to extract from the various papers values of the average maximum wake flow velocity, and the TSI gust velocity. These values are shown in tables 3 and 4 below for the trackside TSI position 3m from COR and 0.2 ATOR for both single and double units, together with data from TAFA. Very broadly the ensemble mean maximum peak for the CRH2 tests is consistent with the published data, as are the TSI gust measurements, for both single and double units. The ensemble mean maximum for the generic high speed trains than are however lower than the published values.
If one accepts that the wake structure is largely determined by the nature of the separating boundary layer at the end of the train, the fact that the CRH2 results are similar to the full scale results is perhaps a little surprising, in that the train boundary layers seem to grow more rapidly at model scale than at full scale (see above). It may be that this effect is compensated for by two effects; firstly that the model scale trains are shorter than the full scale trains, and thus the boundary layer at the end of the model scale trains will have a scaled thickness similar to that at full scale; and secondly it may be that the wake flow is not overly sensitive to the precise boundary layer characteristics at the end of the train. Nonetheless it does suggest some caution is required in the interpretation of slipstream measurements from reduced scale physical or computational tests for high speed, relatively smooth trains.
Table 3 Wake velocities for single units
Table 4 Wake velocities for double units
Of the papers reviewed, four of them looked at specific crosswind effects
Chen et al (2019b) investigated the effect of nose length on cross wind pressures on the train. These were found to be small except around the nose and the tail.
Guo et al (2019) compared the crosswind behavior of single and double units in terms of cross wind forces and wake characteristics.
Li et al (2018) looked at the effect of crosswinds on pantograph forces, and also presented some useful calculations of train roof boundary layers in crosswinds.
Niu et al (2018a) considered the effects of wind breaks on cross wind forces and wake characteristics.
All the calculations presented in the above papers give details of the inclined vortex wake behind the trains in low yaw angle crosswind conditions, and analyse these wakes in some depth. Now, none of the simulations attempted to reproduce atmospheric turbulence, so they are all unrealistic in this regard. The length scales of atmospheric turbulence near the ground are of the same order of size as the trains and the inclined vortices in the train wake. Thus in reality train wakes will be very disrupted by atmospheric turbulence and the detailed patterns observed in the CFD results will not occur. This suggests that to carry out a detailed analysis of the train wake is to over interpret the results.
Thus in what follows, we do not look at the detailed results in these papers, but rather the results for global force coefficients that can be used to expand the existing database of information on crosswind forces on trains. Force coefficient data is given in Guo et al (2019), Li et al (2018) and Niu et al (2018a). Side force and lift force coefficients are set out in tables 5 to 7, with the reference area taken as 10m2in the conventional way. Two major points arise from these tables.
There is little difference between single and multiple unit crosswind forces, except for the cars near the junction between the two sets.
The windbreak calculations suggest there can actually be significant negative side forces on trains behind wind breaks under some circumstances.
Table 5. Force coefficient data from Guo et al (10 degrees yaw)
Table 6 Pantograph force coefficients from Li et al (2018)
Table 7 Train force coefficients from Niu et al (2018a) (15 degrees yaw, Zero porosity windbreak)
On March 23rd 2020 I was due to give a presentation with the above title to a Transportation Futures workshop at the University of Birmingham. Unfortunately the workshop has been cancelled because of the ongoing corona virus situation. Thus I am posting the slides I would have used here. In order that the file isn’t impossibly large for downloading, the slides are in handout form with the video clips removed. A brief commentary follows.
Slide 1 – Introduction
Slides 2 to 4 – these describe the Bridgewater Place incident in Leeds in 2013 in which a lorry blew over and killed a pedestrian that was the catalysts for much of the recent work that has been carried out. A report on the incident can be found here.
Slide 5 gives typical comfort and safety criteria – the red outline indicates the safety criterion of relevance here.
Slides 6 to 10 illustrate recent work on an EPSRC funded project entitled “The safety of pedestrians, cyclists and motor vehicles in highly turbulent urban wind flows” to investigate wind effects on people. This project involved wind tunnel testing, CFD analysis and the measurements on volunteers in windy conditions, which are reported here. Slide 7 shows a photo of Dr. Mike Jesson of the University of Birmingham who had responsibility for the work with volunteers. Measurements were made with shoe-mounted sensors to measure the volunteer’s walking pattern, and back-mounted sensors to measure acceleration. The results are shown in figures 8 and 9 and summarized in figure 10. The latter shows that at all gusts speeds above 6m/s stride “swing width” variation could be measured in some volunteers, where the volunteers subconsciously adjusted their stride to take account of crosswinds. The frequency of such events rose from around 40% at gust speeds of 6m/s to 100% at gust speeds of around 15m/s. Lateral accelerations of the torso first appeared at about 10m/s and reached a frequency of 100% at 17m/s. Actual instability of volunteers was only rarely recorded, but seemed to begin at gusts of around 15m/s. In general however, there was not enough data to draw firm conclusions. Perhaps typically for such measurements, the period of the project proved to be quite calm in wind terms overall.
Slide 11 is a re-iteration of the safety criteria – all work of the type described above needs ultimately to be expressed in very, very simple terms to be useful.
Slides 12 to 14 show the limited work that has been carried out on the effect of cross winds on cyclist safety – wind tunnel and CFD work supervised by Prof Mark Sterling and Dr Hassan Hemida whose pictures are shown in figure 3, to measure the aerodynamic forces on cyclists in cross winds, and some full scale work carried out under the EPSRC project, together with associated calculations of cyclist behavior. This work suffered even more than the pedestrian measurements from lack of suitable wind conditions and the results must be regarded as inconclusive.
Slides 15 and 16 begins the discussion of road vehicles in cross winds, with the latter showing the wind speed restrictions on Skye Bridge.
Slides 17 to 19 illustrate the various methodologies for determining crosswind forces on road vehicles – full scale, wind tunnel and CFD. The former were carried out by Dr. Andrew Quinn, whose photograph is shown on Slide 17. These results lead to the curves of accident wind speed against wind angle shown on slide 19, which can be used to develop wind speed restrictions.
Slides 21 to 24 summarise the study of bridge wind speed restrictions described in another post here. In finalizing restriction strategies operational conditions for specific bridges become very important, and in particular the ease or otherwise of restricting specific types of vehicle and not others.
Slides 25 to 29 briefly describe the wind effect on trains. Methods of determining the aerodynamic forces are illustrated in figure 27, where the University of Birmingham moving model TRAIN rigis shown. These results were obtained by Dr Dave Soper, whose photo is shown on the slide. These forces can be used to calculate the curve of accident wind speed against vehicle speed in slide 28. The practicalities of imposing speed restrictions are illustrated in slide 29.
The overall message of the presentation was that, although investigations to determine the underlying physical processes involved are very important, the translation of the results into practice needs to take account of the sometimes severe operation constraints.
The experiments described in this post involved a large number of colleagues in the development and mounting of instrumentation, the sorting of the data and the analysis and interpretation of the results. Dr Andrew Quinn, Dr Dave Soper, Dr Martin Gallagher and Dr Stefanie Gillmeier of the University of Birmingham, and Mr Terry Johnson of RSSB deserve special mention.The assistance of staff at Network Rail who operated the New Measurement Train is also gratefully acknowledged.
In the previous post I discussed the pressure transients measured on the NMT due to passing trains on the WCML. In this post, I will consider the pressure transients that were measured as the NMT passed through a number of tunnels on that route. These transients can be the source of significant aural discomfort for passengers. The five tunnels that are considered are outlined in Table 1 below. They are arranged in order of length, from the shortest Preston Brook at 71m to the longest, Kilsby, at 2.2km. All are double track tunnels that cater for either fast trains only, or for mixed traffic. They were all built in the 1840s when the line was constructed and are small by today’s standards. Two of them have airshafts.
The pressures that will be presented were measured on the side of the train, although pressure varied little around the circumference in most cases. They were measured against a reference pressure in a leaky reservoir on the train itself, and a small correction was required to relate them to atmospheric pressure. The main unknown was the actual configuration of the NMT at the time the measurements were made. The NMT could run as two power cars plus anything between 3 and 5 coaches between them, giving train lengths of 115m to 161m. The pressure measurement points were 14m from the end of the power car. Also, as these were operational runs, the train speed could vary by several m/s during any one run. Thus the velocities that are given below must only be regarded indicative.
Table 1 Tunnel characteristics
We begin by considering the shortest tunnel – Preston Brook at 71m. Figure 1 shows the pressure transients measured on the NMT for the front car and the rear car, at similar speeds. Both pressure records were obtained from runs in the down (London to Glasgow) direction, as indeed is the case for all the results described below. Consider first the case of the front car. The nose of the train enters the tunnel around 0.3s earlier than the measuring point (distance from nose / train speed) and sets up a compression (positive pressure) wave. This takes approximately 0.2s to travel along the tunnel (tunnel length / speed of sound) and then reflects as an expansion (negative pressure) wave, taking another 0.2s to reach the initial end. Thus the measurement point experiences a short period of positive pressure for about 0.1s, before the expansion wave passes over it causing a dramatic fall in pressure. The pressure then oscillates with a period of around 0.4s to 0.5s as the wave passes back and forth along the tunnel. The measurement point leaves the tunnel before the rear of the train enters.
The situation is somewhat different when the measurements are made at the rear of the train. By the time the measurement point enters the tunnel the initial wave system caused by the train nose will have traversed the tunnel four or five times, and friction will have attenuated its magnitude significantly. From the pressure data shown, it can be seen that the measurement point experiences a small period of positive pressure, before the expansion wave from the rear of the train passes over it causing a sharp drop in pressure. This tail wave then dominates, reflecting from the far end as a compression wave, with again an overall period of about 0.4s to 0.5s. The data from Preston Brook thus shows the pressure variations due to single waves – either the nose wave or the tail wave.
Figure 1 Preston Brooktunnel
Kensall Green tunnel is 290m long, and the train speeds are in general somewhat lower than elsewhere, as trains are accelerating away from Euston. Again, consider the pressures on the leading car first. The front of the train enters the tunnel around 0.25s before the measurement point enters. The nose compression wave will take about 1.8s to travel to the far end of the tunnel and back again. The measurement point first experiences the increase in pressure behind the initial wave, which grows steadily due to wall friction slowing the flow around the train. At around 2s, the expansion wave passes over it and the pressure falls rapidly. This wave reflects back along the tunnel and passes over the measurement point again as an expansion wave at about 3.8s. Now the tail of the train will enter the tunnel somewhere between 3 and 4s after the nose depending on the (unknown) train length. Its effect can be seen from the fact that the regular oscillations up to around 5s are disrupted by interaction between the nose and tail wave systems. For the rear measurement point, the pressure drops initially as the tail expansion wave passes over the measurement point. Thereafter the oscillation pattern is a complex interaction between nose and tail wave systems.
Figure 2 Kensall Greentunnel
Northchurch tunnel (figure 3) is a little longer than Kensall green and the train speeds are somewhat higher. The main difference however is that this tunnel has an airshaft at its mid point. For the front car measurements the nose enters the tunnel at a time of about 1.6s. Although the main nose wave will take around 2s to return to the start of the tunnel at a time of 3.5 to 4s, a smaller reflected wave from the airshaft can be expected to pass over the measurement point before that. This can be seen to be the case, with the pressure at the front measuring point showing a sharp fall as the expansion wave from the airshaft passes over it at a time of around 2.2s. The main expansion wave arrives at about 3.7s. The train tail enters the tunnel two or three seconds after the train nose (depending on the unknown train length) and the resulting expansion wave and its reflections at the airshaft and far end of the tunnel add to the complications. For the rear measurement point, the expansion wave due to the tail passes over it first, and then it is subject to the complex interactions between the reflecting waves. Thus the presence of an airshaft can be seen to considerably complicate the measured pressures.
Figure 3 Northchurchtunnel
Shugborough tunnel passes underneath the former Shugborough estate of the Earl of Lichfield, and its portals are suitably grand (see figure 4). More prosaically, Figure 5 shows the pressure traces for the 700m long Shugborough tunnel, which has no air shafts. In some ways this is the simplest of all the traces. The front measurement point shows the initial compression wave and the gradual increase in pressure due to friction. The initial wave takes about 4s to return to the entrance, whilst the tail of the train enters the tunnel between 3 and 4s after the nose and its expansion wave will pass over the measurement point at about the same time as the reflected nose wave. The sharp drop caused by these waves at about 5s is clear. Thereafter the two wave systems can be seen to be broadly in phase and pass backwards and forwards along the tunnel producing complex peaks and troughs of pressure. The rear measurement point experiences an initial fall in pressure due to the tail expansion wave, and thereafter is subject to the pressure distributions of the complex interacting waves.
Figure 5 Shugborough tunnel
Figure 6 Western portal of Shugborough tunnel
Kilsby tunnel (figure 6) is quite a fascinating construction. When it was built it was the longest tunnel in the world, at 2.225km and has numerous airshafts (table 1). The largest of these, at the 1/3 and 2/3 points are vast, and more like caverns than airshafts. A picture of one of the surface structures for these airshafts is shown in figure 7. In addition there are 10 other open shafts distributed along the tunnel. Recent investigative work by NR has revealed that there are a number of other blind shafts or pumping shafts along the line of the tunnel, and some someway off the line, whose position cannot be precisely determined.
In aerodynamic terms the large airshafts effectively split the tunnel into three, and this is very clear from the pressure records for both the front and rear measurement points in figure 6. Interestingly, the two measurement points on the train may well be in different sections of the tunnel at any one time, and thus subject to completely different pressure wave systems. As with Northchurch the measurements record multiple reflections from the airshafts, and the presence of three or four airshafts in each section results in highly complex flow patterns.
Figure 6 Kilsbytunnel
Figure 7 Kilsby tunnel airshaft
Finally consider the rear car results from Shugborough for a range of train speed (figure 8). The 40.2m/s speed data has already been shown in figure 4 and shows the expected pattern of a steep initial drop due to the passage of the train tail expansion wave and then a series of interacting wave reflections. Similarly the lowest speed 28.2m/s data show the expected pressure wave oscillations. However the mid-speed range 32.3m/s data shows no such oscillations here. It is likely in this case that the initial nose wave returns to the tunnel entrance as the train tale enters and is cancelled out by the tail expansion wave. Such an effect is of course critically dependent upon the precise values of train speed (which are not well specified for these measurements) and tunnel length, but is interesting nonetheless.
Figure 8 Shugborough tunnel pressures for several train speeds.
The experiments described in this post involved a large number of colleagues in the development and mounting of instrumentation, the sorting of the data and the analysis and interpretation of the results. Dr Andrew Quinn, Dr Dave Soper, Dr Martin Gallagher and Dr Stefanie Gillmeier of the University of Birmingham, and Mr Terry Johnson of RSSB deserve special mention.The assistance of staff at Network Rail who operated the New Measurement Train is also gratefully acknowledged.
Between 2011 and 2016, as part of a large project sponsored by the UK Engineering and Physical Sciences Research Council, colleagues at the University of Birmingham made full-scale aerodynamic measurements on the Network Rail New Measurement Train (NMT). This is a Class 43 train, with two power cars and a variable number of coaches, which is used to assess track conditions on main line railways in the UK (figure 1), on a regular two-week cycle. The aerodynamic measurements were mainly directed at measuring crosswind forces, and these results have been reported elsewhere. However during its travels around the country the NMT also detected the pressure transients caused by other passing trains, and by its own passage through tunnels. Whilst this data is of itself reliable and can be located confidently in time and space, it is not always easy to get the precise experimental conditions associated with each set of pressure transients – for example the precise NMT configuration in terms of number of coaches; the wind conditions; type and speed of passing trains etc.. Thus these results are not fully adequate for publication. Nonetheless they are of some interest if properly interpreted, and thus this blog post will present some of these results for open-air pressure transients, and the next will present some results for tunnel transients. The former are important as pressure transients caused by passing trains can cause trains to be suddenly displaced laterally causing passenger discomfort, and can also cause repeated loading on trains and trackside infrastructure, which can contribute to fatigue failure of components or structures. Tunnel pressure transients can be a source of aural discomfort to passengers, particularly in narrow tunnels – and indeed there are locations in the UK where aerodynamic speed limits have been imposed on tunnels.
Figure 1. The New Measurement Train
The results that will be presented were all obtained as the NMT passed up and down the West Coast Main Line between London and Glasgow. This is a 200km/h line, with both four-track sections (two for fast trains and two for slow trains) and two-track sections. It has branches to Birmingham, Manchester and Liverpool. In the four-track sections the NMT always travelled on the fast lines. The services that use the line are as follows.
200 km/h services with limited stops between London, Birmingham, Liverpool, Manchester and Glasgow, using 9 or 11 car Class 390 Pendolino tilting trains (figure 2a)
200 km/h services that connect a range of towns and cities across the country using double unit Class 220 4 car Voyager trains (non-tilting) or Class 221 4 or 5 car Super Voyagers (tilting) (figure 2b), in 8 or 9 car formation. Irregular 4 or 5 coach Class 220/221 units also operate over sections of the WCML route.
Semi-fast and commuter services operated mainly by Class 319 trains (figure 2c) south of Milton Keynes and by Class 350 trains along the whole line (figure 2d). Both of these run in single (4 car) unit or double (8 car) unit configurations. Class 350s can travel at 175 km/h and Class 319s at 160km/h.
A variety of freight services hauled by both electric and diesel locomotives. Perhaps the most common locomotive in use is the Class 66 (figure 2e)
Figure 2 Train types on the WCML
Typical pressure transients measured on the side of the NMT for Class 390s, Class 221s, Class 350s and freight trains are shown in figure 3. It can be seen that
all types of train show a large positive / negative pressure transient as the nose of the passing train passes the measuring point and the passenger trains also show a negative / positive tail peak;
no tail peak can be observed for freight trains;
a large transient can be observed at the gap in the centre of the double unit trains;
between the peaks there is a small negative pressure, and the passage of individual carriages can also be discerned on the pressure traces.
The time between the nose and tail transients can be used to determine the speed of the oncoming train, if the type of train and its length can confidently be specified. This was in general only the case for the Class 390 trains as it was usually not possible to distinguish between the different types of four and five coach trains. The results shown for the Class 350 in figure 3 are one of the few datasets where the train type could be confidently determined.
Figure 3 Train passing pressure transient types
As noted above, it is possible to determine the speed of Class 390 Pendolinos passing the NMT. This allows the dimensionless pressure coefficient to be determined (peak to peak pressure / (0.5 x density of air x velocity of approaching train squared)), which enables the effect of velocity on the peak-to-peak pressures to be removed in a consistent fashion. Pressure coefficient is plotted against train separation in figure 4 below. The train separation is calculated from the track spacing and the train geometry. Here again the data is less than ideal, and it was not possible to find accurate track spacings easily from NR databases. They were thus obtained from large scale digital OS maps, and are only accurate to within about 10cm. It can be seen that, as expected, the pressure coefficients fall with train separation. Perhaps the most notable point is the large variability of the data, which reflects both the uncertainties in track spacing described above, the effects of tilt and curvature and other operational variables. This level of variability is something that needs to be appreciated by both physical and computational models when assessing the engineering significance of their results.
Two other sets of data are shown on figure 4. The first is the pressure on trackside hoardings passed by a Class 390, measured in moving model experiments. These hoardings are about half train height, so one would expect some pressure relief as the disturbed flow passes over the hoarding, and indeed the pressure coefficients lie at the bottom end of the NMT measurements. One data point is also shown for the pressure coefficient measured in free air as a Pendolino passes. This can be seen to be about half the value of the pressure coefficients on the NMT at the same spacing.
Figure 4 Effect of train spacing on peak-to-peak pressure coefficients
Despite not being able to determine train speeds for trains other than the class 390, the pressure data measured on the train is still reliable for all train types, and the overall type of train can be identified. Thus the overall distribution of peak-to-peak pressures can be determined. This is shown in figure 5 for Class 390, 4 or 5 car multiple units and freights trains, and in figure 6 for all train types. The lower cut-off magnitude for a pressure transient to be included was 400 Pa. It can be seen that the Class 390 transients, have a distribution from 400 to 1220 Pa, with the peak being between 1000 and 1200 Pa. The freight train distribution is from 400 to 1000 Pa, with the peak in the 600 to 800 Pa interval, reflecting the fact that, although freight locomotives can be expected to be aerodynamically blunt, they move relatively slowly and the absolute transient magnitude is somewhat less than for the express passenger trains. The four- or five-coach multiple units have a very broad distribution of peak-to-peak values, and the maximum pressure transient values experienced by the NMT are caused by such trains. The maximum peak-to-peak pressures that were measured in the trials (with values of 1449 Pa and 1498 Pa) were both identified as being caused by passing blunt nosed Class 350 units travelling at 46.7 and 47.7 m/s on the smallest centre-to-centre track spacing of 3.2m. These values both exceeded the standard value of 1444 Pa. The equivalent pressure coefficients in both cases were 1.10, somewhat higher than the values shown on figure 4.
This distribution of peaks is of course very specific to the route under consideration and the services that operate on it. However it does suggest that, for a mixed traffic railway such as the WCML, the range of pressure transient loadings on trains themselves is very large, and if any sort of fatigue loading calculation is required, then a suitable distribution such as that shown in figure 6 needs to be determined to give the required loading information. If maximum loads are required, then these are likely to result from passings by higher speed but aerodynamically blunt trains.
Figure 5 Distribution of pressure transients experienced by the NMT by passing train type
Figure 6 Distribution of pressure transients experienced by the NMT for all train types
The book “Train Aerodynamics – Fundamentals and Applications” (hereafter referred to as TAFA) was published in early 2019, but in reality took no account of any material published after June 2018. There has however been a significant number of studies published in the second half of 2018 and 2019, and it seemed worthwhile to try to collate these in some way, and this blog post attempts to do this. Selfishly such a collation might help for any second edition of TAFA that is produced (if the sales warrant it!) but more generally it is hoped that it may prove useful to all those involved in Train Aerodynamics in one way or another in signposting ongoing work around the world.
It should be emphasized at the outset that this collation cannot properly be described as a review. A review (as I have told my graduate students for the last three decades) needs some degree of synthesis of the various reports and papers discussed. This of course requires a number of papers addressing the same issue to be available to synthesise. Looking at papers from a short time period that cover a wide range of subject matter, this is not really possible, so what follows is essentially a brief description of the work that has been carried out in 2018 and 2019, with a few interpretive comments.
We consider the various publications roughly in the order of the Applications described in Part 2 of TAFA – train drag, pressure transient loads, slipstream loads, ballast flight, OHL issues, crosswind studies, tunnel aerodynamics and emerging issues. A brief section is included on train and tunnel ventilation that was not considered in TAFA. Some concluding reflections are included at the end of the post.
In the text, published references are linked directly to their DOI, rather than to a reference list. Those references with no DOI (recent conference publications in the main) are given in a short list at the end of the post. A full reference list can be found here.
One of the major issues in both experimental and computational assessments of train drag is the simulation of the ground, as the nature of this simulation can have a significant effect on the measured force. Niu et al (2018b) present some CFD analyses that usefully address this issue for a number of ground and ballast representations. Overall they show that the effect on measured drag coefficients at zero yaw angle is small (of the order of 2 to 3%) and probably not significant in comparison with the large variation in drag measured at full scale, and in different types of CFD and physical model simulations. Nonetheless the results can give some guidance for the setting up of physical model tests and CFD trials.
There have been a small number of train drag investigations looking at the effect of modifications to different parts of the train on overall drag – nose length, inter-car gaps, bogie position, roof equipment and for freight trains, container spacing. They will be considered in turn below.
Chen et al (2019a), using IDDES, looked at effect of nose lengths of between 5 and 10m on drag on a five-car train. The drag was shown, unsurprisingly, to decrease with nose length. Li et al (2018b) used the k-omega method to investigate the effect of inter car gap length on drag, and showed that gap lengths of less than 80mm full scale had no effect on drag. The k-epsilon CFD work of Gao et al (2019) looked at the effect of changing bogie position on the leading car of a three-car high-speed train. The results indicate that moving the front bogie back 2m from its normal position can reduce the overall drag of the front car by 10% and the overall three-car drag by 6.5%. These drag reductions will of course be a smaller proportion of the overall drag for full-length trains.
Tschepe et al (2019) investigated the drag of roof-mounted insulators through wind tunnel experiments. They observed considerable Reynolds number effects and effects of insulator position on the measured drag (which in aerodynamic terms were in the critical range), and showed that overall drag due to roof elements could be about 5% of overall train drag. Interestingly they found that soft insulators displayed a tendency to flutter, resulting in higher drag than rigid insulators.
Maleki et al (2019) carried out a CFD investigation of the flow around containers using LES. There were major changes in the wake of containers as container spacing increased. Above a certain spacing wake closure occurs with high speed flows impinging on downstream container, resulting in increased drag. They also present potentially useful results for the optimisation of single and double stack container positions for low -drag.
Pressure transients and loads
A small number of investigations have been reported of the pressure transients and loads caused by passing trains. Soper et al (2019) made full scale experiments on the transient pressure loads caused by high speed trains on acoustic barriers, and were able to determine the effect of variations in track distance and the nature of the overall trackside infrastructure on the measured loads. The CEN load correlations were found to represent the results well.
Huang et al (2019) added to the small amount of data available on the loads caused by passing trains through an experimental and compressible CFD study of high speed Maglev trains passing each other, including detailed calculations of the transient pressure field around the train.
Munoz-Paniagua and Garcia (2019) developed an optimization methodology for nose shape to optimize (i.e. minimize) the pressure transients. This involved a large number of CFD runs for different geometries that were used to train a genetic algorithm. It was shown, perhaps unsurprisingly, that nose length and bluntness were the most important parameters in the optimization. They also considered the optimization of nose shape for cross wind performance, which will be discussed further below.
Slipstream velocities and loads
In 2018 and 2019 a significant number of papers have been published that use (in the main) CFD IDDES to calculate trains slipstream and wakes and to look at specific flow effects. These all give a great deal of information concerning the micro-nature of the flow field that it is not always easy to interpret of to put into a bigger picture. They are useful however in helping to build up a picture of the complexity of even the idealised CFD flow fields around trains. As with drag investigations described above, these studies were aimed at assessing the effects of slipstreams of changes to different parts of the train – nose and tail, gaps between double units and bogies.
Chen et al (2019a) looked at the effect of different nose / tail lengths on drag and lift, but also looked at the effect of the slipstream behavior along and behind the train. They found that the TSI slipstream velocities decreased with tail length, with the longitudinal trailing vortices becoming weaker. In a further paper they extended this work to look at the effect of changes in nose length on the slipstreams and wakes in crosswinds (Chen et al, 2019b). Not surprisingly they found that the effect of nose length on the overall flow field was complex and quite difficult to quantify.
Li et al (2019b) looked at the effect of the gap in double unit trains on the development of the slipstream and the wake and showed that the main effect was to increase the boundary layer and wake velocities downstream of the gap.
Two papers from the same group in Changsha (Wang et al, 2019 and Dong et al, 2019) describe aspects of an IDDES investigation of flow around bogies. The first looks at the effect of bogie fairings on the slipstream and wake and, as might be expected, shows that bogie fairings reduce the velocities in the boundary layer and the strength of the longitudinal vorticity in the wake. The second studies the effects of simplifying the geometry of train bogies in CFD simulations. It shows that the effects are mainly felt in the underbody flow region rather than in the wider flow around the train, and offers some suggestions for appropriate degrees of geometric simplification.
Finally the IDDES modelling of Wang et al (2018c) should be mentioned. This is a fundamental study of the effects of bogies on the slipstreams of high-speed trains. The study shows that the generation of the strong spanwise oscillation of the wake, observed especially in the presence of bogies is due to the amplification of a natural instability of the time-mean pair of counter-rotating vortices.
The work in this area has focused on two aspects – the nature of the flow field around the train, and the accumulation of snow in the bogie area.
With regard to the first, two useful studies have been reported that address the issue of the train underbody flow, which of course controls the flight of ballast. The first of these is the thesis by Jönsson (2016), which is somewhat outside the publication time range considered here, but is nonetheless worth mentioning. The author carried out extensive measurements using PIV to measure the flow field beneath 1/50thscale model trains, with different underbody geometries and sleeper layouts. Comparisons were made with full scale and showed that the essential aspects of the underbody flow field could be reproduced. The tests also showed how important train underbody irregularities were in increasing velocities and thus the likelihood of ballast flight. The data was also used in a simple analytical framework similar to (and earlier than, so it takes academic priority!) that included in TAFA.
Also with regard to the underbody flow, Paz et al (2019) consider the nature of ground simulation in CFD trials, and present a method for simulating track and ballast geometries in this region, using scanned profiles of real sleeper and ballast geometries. The results show significant differences between the simulation and the normal flat ground geometries, particularly close to the ballast where higher levels of turbulence were measured. Overall the methodology as set out is potentially of great use in simulations for train authorization purposes.
Two CFD studies, both by the same group have also been carried out to address the related problem of snow accumulation around bogies – one using a discrete phase model and IDDES (Liu et al, 2018) and one using a discrete phase model and URANS (Wang et al, 2018b). A somewhat qualitative validation of the methodology against experiments was carried out. Similar results were obtained using both methods, but the URANS work used considerably less computer resource. Unsurprisingly snow was shown to accumulate in areas of low velocity in the bogie cavity. Overall the results give useful qualitative indications of those aspects of bogie design that could be altered to reduce snow accumulation.
Overhead and pantograph systems
Two interesting studies on the dynamics of pantograph and catenary systems were reported in 2018/2019. In the first, Li et al (2018a) describes DDES calculations of the flow around and forces on pantographs on a three car high speed train at yaw angles of 0, 20 and 30 degrees, thus representing a range of cross wind velocities. As might be expected, the flow around the pantographs becomes increasingly complex and turbulent as the yaw angle increases. The aerodynamic forces on the pantograph were found to oscillate around a mean value even at zero yaw, and as the yaw angle increased a range of different dominant frequencies appeared. Whilst these results are doubtless quite specific to the case being considered, and the simulation does not fully reproduce the range of turbulent fluctuations in the atmosphere, they do show the potential for high cross winds to excite a range of pantograph oscillations. This is an area where further work would be of significant interest.
Secondly, Xie and Zhi (2019) report wind tunnel results for the dynamic behavior of catenary systems, including the effect of wire tension on the natural frequency and displacements of the contact wire in a range of cross wind conditions. A large scale if somewhat crude simulation of the near ground atmospheric boundary layer was used. The authors discuss the possibility of resonant oscillations occurring between the train pantograph system and the overhead wire. Deflections of 6cm at mean wind speeds of 17m/s were measured. This is again a topic where further work would be useful – in particular a study of the interaction between pantographs and the overhead wires in high crosswinds would be very interesting and potentially very significant.
The number of new studies on trains in crosswinds has increased significantly in recent years and shows no sign of slowing down. In 2018/19 results of studies have been published on wind conditions near the track, train aerodynamic forces in cyclonic winds, train aerodynamic forces in tornado winds, the effects of wind shelter and full-scale measurement of wheel unloading risk. These will be considered in turn below. It is perhaps worth noting at this point however that many of the CFD calculations described below, even though they give a detailed description of unsteady flow fields, nonetheless do not fully simulate the turbulence structure of the oncoming atmospheric boundary layer. These results thus not fully represent reality, where the flow structures around the train can be expected to be disrupted by the oncoming turbulence. They are nonetheless useful in giving an overall impression of the flow field and the effects of different geometry changes for example.
Zhang at al (2019b) used IDDES, calibrated against wind tunnel tests, to predict the flow speed up over embankments of varying geometry, to enable a rational siting of warning anemometers. This work usefully adds to the data available for the wind speed up over railway embankments. Hu et al (2019) also consider wind characteristics in terms of the nature of the wind relative to a moving vehicle. The analytical framework they have produced is more extensive and rigorous than those developed by earlier authors and has the potential to be used to generate realistic time series of velocity that could be used in overturning calculations.
A number of studies have been reported that enlarge the database of aerodynamic coefficients of trains in cross winds. Noguchia et al (2019) provide experimental and LES data for the crosswind forces and moments on a range of conventional train types on embankments. Guo et al (2019) present the results of IDDES calculations that investigated the difference in cross wind pressures and forces for both a 6 car single unit and a 6 car double unit high-speed train. They also provide extensive discussions of the nature of the wake and the unsteady flow. The effect of the gap between the two units was shown to have a significant effect on the crosswind forces on coaches in the centre of the formation, and also affected the primary frequencies of oscillation. Lin et al (2019) report the results of a benchmark test to measure crosswind forces and moments with two different trains in three different wind tunnels, all of which were carried out to confirm to the CEN guidelines. Systematic differences in results between nominally similar tests are observed, and seem to be associated with blockage and boundary layer effects in the wind tunnels. These results were presented in brief at a conference, and a full write up of the results should prove extremely interesting and is eagerly awaited by the author.
The opimisation work of Munoz-Paniagua and García (2019) has already been mentioned above. As with the pressure transients they found that nose length was the major factor determining the crosswind forces and moments.
The above studies were concerned with trains in cyclonic winds. A couple of studies have been reported where pressures on trains were measured using Tornado Vortex Generators – that of Bourriez et al (2019) with a moving model, and that of Cao et al (2019) with a stationary model. Both these studies have major scaling issues, where the train scale and tornado vortex scale do not match. Nonetheless they give interesting indicative results. Further developments can be expected in this field in the future.
In view of the importance of reducing crosswind forces and moments, the literature describing the effect of wind barriers on trains in cross winds is surprisingly sparse. Recent studies have gone some way to remedy this – Mohebbi et al (2019), Niu et al (2018a), Hashmi et al (2019) used a variety of CFD techniques to investigate the effect of wind fences on train forces; Misu et al (2019) used equivalent wind tunnel tests; He et al (2018) and Flamand et al (2019) both considered train / bridge systems, where the cost to providing shelter on the train in increasing the loads on the bridge were considered. Wu et al (2019) looked at a case where wind shielding effects were undesirable, when a train runs in the wake of a bridge tower. Through the use of a simple low speed moving model rig to measure transient train forces, and a dynamic model of the wind / bridge / vehicle system they concluded that the shielding effect could have an adverse impact on both the running safety and riding comfort of the train.
Finally in terms of assessing safety and risk, two interesting full-scale experimental techniques have been developed. Wei et al (2018) report a method for measuring wheel unloading by making continuous measurement of the accelerations and displacements of the wheel set using relatively simple equipment, rather than the more conventional measurements made by instrumenting the wheels themselves (although such measurements are themselves quite innovative and difficult). The results from full-scale experiments on trains for the derailment and loading coefficients as they move in and out of the shelter provided by wind breaks are impressive and indicate that the methodology may be of some use in the future. Similarly, Lu et al (2019) use measurements from primary suspension. Good agreement with instrumented wheelset data was demonstrated provided a suitable calibration was carried out.
In 2018 and 2019 a number of papers have been published on tunnel aerodynamics, addressing the issues of pressure transients and micro-pressure waves, tunnel velocities and structural loading. We will consider each of these issues in turn.
The work on pressure transients in tunnels has been carried out using both experimental and computational methods. The experimental work of Heine et al (2019) using a moving model rig investigates the effect of wall cavities (for cross passages) on tunnel pressures. These cavities were installed to reduce the pressure load on interconnecting doors, but interestingly the results show that, by creating extra surfaces for pressure waves to reflect from, the pressure loading on the doors can actually increase under certain circumstances.
Iliadis et al (2018) also used a moving model rig to look at pressure transients as blunt freight trains entered a tunnel, with measurements both on the tunnel wall and the train. The major point to emerge is that for certain freight train loading situations, gaps in the train formation can result in significant tunnel entry pressure transients, and the maximum pressure in the tunnel might not always be associated with the entry of the train nose as for passenger trains.
Li et al (2019c) report a k-epsilon CFD investigation of the pressure waves in tunnels with variable cross section, but with sudden transitions between the sections. Unsurprisingly they show that a complex series of pressures results from these transitions, but on the whole the magnitudes of the pressures are reduced from the single area case. Wang et al (2018) describe a similar investigation using k-omega CFD, but with gradually varying area rather than abrupt transitions. The pressure magnitudes are again reduced as would be expected. Both of these also showed that there was the potential for reducing the gradient of the initial pressure wave, which is the main parameter of importance in the generation of micro-pressure waves, using such approaches.
Micro-pressure waves were considered in more detail in the work of Saito (2019) who used the results of moving model rig experiments and a simple analytical formulation of tunnel entry pressures. He investigated the optimum area and length of unvented entrance hoods, and derived some useful design guidelines.
Another method of reducing the strength of micro-pressure waves is to use ballast rather than slab track in tunnels. Fukuda et al (2019) report on the results of full-scale tests where experiments were measured before and after slab track in a tunnel was replaced by ballasted track. Significant reductions in pressure gradient were observed. A simple methodology for predicting these pressure gradient reductions has been derived.
The propagation of micro-pressure waves themselves has been considered by Zhang et al (2018) and Zhang et al (2019a). The former developed straightforward analytical models of pressure magnitudes around the tunnel exit portal, which were calibrated against experimental and CFD data. The latter made measurements of the relatively small pressure amplitudes at the exit of a tunnel simulation using a moving model rig.
In some situations it is necessary to determine the velocity transients in tunnels as well as the pressure transients, particularly when loads on structures or people are required. These issues have been addressed by Jiang et al (2019) who carried out a URANS study of the slipstreams generated by different train types in a double track tunnel, providing a great deal of detailed information concerning the nature of the slipstream variation with height above the ground and distance along the tunnel. The work of Iliadis et al (2019) mentioned above for freight trains, also made such measurements. Kikuchi et al (2019) took a different approach and developed a simple calculation method based on unsteady incompressible flow for the flow over the roof of a train. This method takes into account the unsteady boundary layer development along the train roof, and allows the velocities to be determined that can be used to assess pantograph performance in confined tunnel situations.
Finally a couple of papers have appeared that have addressed the issues of loads on trains and tunnel infrastructure directly. The first, by Lu et al (2018) looked at the fatigue loading caused by the pressure waves due to two high speed trains passing in a tunnel, and involved the use of unsteady k-epsilon CFD and a finite element model of the car body to determine the loads at specific points on the vehicle. Courtine at al (2019) carried out full scale and model scale experiments to analyse designs of “deflectors” to be placed around lorries in the Channel Tunnel, particularly with regard to the effect that they might have on the loads on the soft-sided trailers.
The final chapter of TAFA briefly summarises a number of emerging issues. Of the ones discussed, there are two that have seen further work published in 2018/19 – evacuated tube transport, and snow drifting.
With regard to the former, two investigations have investigated the shock wave formation around such tube trains for very high speed vehicles using different methodologies. Zhou et al (2019) use the compressible Navier-Stokes equation for flow around an axisymmetric body in a tube, whilst Niu et al (2019) use a variety of different CFD methods, and also consider heating of the flow. Both reveal complex shock wave patterns, particularly behind the vehicle, and investigate the choked flow region in particular. Both sets of results serve to emphasise the complexity of the flows around such vehicles and indicate the formidable challenges that still remain before this type of transport can be implemented.
The issue of wind blown sand around railways has been addressed by a group at Torino in Italy. The paper by Raffaele and Bruno (2018) presents an outline of a probabilistic method for assessing the accumulation of sand around railways, while the second by Bruno et al (2018) presents a thorough review of current literature and methodologies. Clearly it is not possible to easily summarise a review paper – suffice it to say that this provides and excellent starting point for those who wish to delve into this subject further.
One area of study that was not included in TAFA, and in retrospect probably should have been, is that of ventilation of tunnels and stations, and the internal ventilation of the trains themselves. The need for such studies is becoming increasingly urgent as the poor air quality in underground stations and on trains becomes more and more apparent. Whilst no attempt will be made to present a full review of this subject here, it is worthwhile to set out the work that has been done in the 2018/19 period at least.
First of all let us consider the ventilation of tunnels and underground stations. Izadi et al (2019) present the results of a unsteady RANS calculation of velocities and pressures in a small number of stations connected by a single tunnel. Pressures and velocities were predicted for a variety of train operating scenarios using both a simple axisymmetric geometry and a more complex three-dimensional geometry. Various fan operating strategies were also discussed. Koc et al (2018) use a simpler one-dimensional approach, but applied to a more complex network of tunnels and stations. A methodology for using ANNs to predict pressures and velocities in complex situations is presented. Zarnaghsh et al (2019) use a finite volume technique to investigate the behavior of tunnel ventilation fans and in particular the interaction between the velocity field produced by trains and those produced by the fans themselves. It was shown that the passage of trains could result in the operating characteristics of the fans moving significantly away from their nominal operating point.
Work on the ventilation of trains has also been reported. Abadi et al (2019) report a CFD k-omega study to improve the performance of a roof mounted ventilation system under crosswind conditions, by varying the inlet geometry. Li et al (2019a) report a DES similar study to investigate the performance of an ACU with roof inlets on a high speed train at different speeds.
Firstly some paper statistics are of interest, but note the figures that follow are somewhat arbitrary in many ways and reflect both the chosen publication dates and the sources consulted. There were 55 items accessed in total, all but one from between mid-2018 to the end of 2019. Of these, 28 were from Chinese institutions, reflecting the fact that research there is driven by the rapid development of the Chinese high-speed rail network, with the rest being spread fairly evenly around Europe, the Middle East and the Pacific Rim. Of the Chinese papers, 18 were from the Central South University at Changsha, 7 from South West Jiaotong University at Chengdu and 3 from elsewhere (although there was some overlap of authorship). In terms of technique used, 30 of the papers were mainly based on CFD studies, although some included experimental verification of one sort or another. Of the Chinese papers 21 were CFD studies, including 16 from Central South University. There was thus a significant imbalance between the use of CFD in China and elsewhere.
The growing use of CFD techniques is thus notable, and in particular the IDDES technique seems to be becoming the most favoured. This growth is wholly understandable and will no doubt continue. Arising from this, it seems to the author that there is a growing need for a small set of freely available well documented validation cases, ideally from full scale experiments for a range of train types, that investigators can use routinely to prove their techniques. At the moment the validations used are somewhat ad hoc, and perhaps a more systematic approach would give greater confidence in the results, and also allow research papers to be reduced somewhat in length, as the details of the validation cases would not be required. It would be interesting to hear from CFD practitioners on such a possibility.
Finally it must be remembered that CFD simulations, in the same way as physical models, can only offer a simplified representation of the flow around full-scale trains, and need to be interpreted in this light. There is a tendency amongst some authors (and I name no names!) to quote numerical results to higher levels of accuracy than is either sensible or useful when the uncertainty of the full-scale situation is considered. Just as with physical model tests, the role of the engineer in interpreting CFD results in terms of the reality of the operating railway is crucial.
References without DOIs
Bourriez F, Soper D, Baker C and Sterling M (2019) Physical model measurement of tornado induced forces on trains, Proceedings of the 15thInternational Conference on Wind Engineering, Beijing
Cao J, Cao S, Ge Y (2019) Experimental investigations of wind load distributions on a high-speed train under tornado-like vortices, Proceedings of the 15thInternational Conference on Wind Engineering, Beijing
Courtine S, Aguinaga S, , Bouchet J-P, Brunel C (2019) Aerodynamic improvement of superstructure interacting with trucks carried in the Channel Tunnel, 15thInternational Conference on Wind Engineering, Beijing
Flamand O, Gattas M, van Stuijvenberg J, te Morsche N, Jongstr B, Knapp G, Benthem J (2019) Improving the wind protection of High Speed trains whilst decreasing wind loads on the supporting bridge, 15thInternational Conference on Wind Engineering, Beijing
Jönsson M (2016) Particle image velocimetry of the undercarriage flow of downscaled train models in a water-towing tank for the assessment of ballast flight, PhD Thesis, Technical University of Hamburg
Lin P, Brambilla E, Rocchi D, Tomasini G (2019) Measurement of the aerodynamic coefficients of high-speed railway vehicles: benchmark between different wind tunnels, 15thInternational Conference on Wind Engineering, Beijing
Misu Y, Takeda S, Nagumo Y, Doi K (2019) Estimation Effectiveness of Windbreak Fences at Rolling Moment on Leeward Rails, 15thInternational Conference on Wind Engineering, Beijing
Raffaele L, Bruno L (2018) Probabilistic assessment of windblown sand accumulation around railways”, Proceedings Italian Conference on wind Engineering
Wu J, Tang Q, Li X (2019) Shielding effect of bridge tower on aerodynamic characteristics and running safety of high-speed train with wind tunnel tests, 15thInternational Conference on Wind Engineering, Beijing
A blog from a previous version of this website – written in 2017
At the time this blog was written, Storm Friederike has just passed over Western Europe and has resulted in a number of deaths and considerable traffic chaos. The BBC reported that
Deutsche Bahn had already suspended rail traffic in North Rhine-Westphalia (NRW), neighbouring Rhineland-Palatinate state and Lower Saxony, when it announced a Germany-wide suspension of long-distance trains. Any regional trains still running have cut their speed because of the strong winds.
A spokesman said it was the “right decision” due to the risk of trees falling on overhead wires and on tracks.
The Dutch Railways (NS) and operator ProRail said overhead power lines had been damaged by the wind, as well as some railway tracks. An alert on the NS website said that “at most, only a few trains” would run throughout the evening.
Trains do occasionally blow over. The first recorded incident was on the Leven viaductin south Cumbria in 1904 when a wooden bodied train blew over on the embankment on the approach to a viaduct. A number of other incidents have occurred around the world in recent years, the latest being in Switzerland where a video has been posted online of a train in the process of being blown over – here and here. Clearly as accidents of this type can have potentially very severe consequences they need to be in some was taken into account by train builders and railway operators in design and practice.
The effect of cross winds on trains (and lorries to some extent) is a research topic that has stayed with me throughout my career. My first involvement with the issue was when I worked for BR Research in the early 1980s in looking at the effects of high winds on the Advanced Passenger Train. The issue arose again when the Channel Tunnel was opened as the very light lorry carrying vehicles were found to be at risk of blowing over in ports. Then, with the advent of high speed trains in the 1990s, considerable effort has been devoted to developing a methodology to ensure that cross wind effects are taken into account in both design and operation – in Europe, Japan, Korea, and most recently in China. There is broad agreement on the methodology that is to be used. It consists of three parts.
An assessment of the aerodynamic loads on the train – usually in the form of graphs of aerodynamic forces and moments against wind angle.
The use of this aerodynamic data in some sort of mathematical model of the effects of wind on the vehicle under consideration to determine a graph of wind speed that will cause and accident against vehicle speed – usually referred to as a Cross Wind Characteristic or Characteristic Wind Curve (CWC).
The use of this CWC together with weather, route and operating data to determine the risk that the train will blow over on the route under consideration.
The design of trains usually considers only the first two steps and the CWC that is obtained is compared with reference CWCs in the train certification process. Train operators clearly need to know the output of the third stage, so they can design suitable risk alleviation systems – eg. slowing trains down, providing protection such as wind breaks etc.
Each of the above steps can have varying levels of complexity.
The assessment of aerodynamic loads can involve physical model tests of different types – using standard low turbulence wind tunnel tests, wind tunnel tests with a simulation of atmospheric turbulence or moving model tests. Embankments and bridges may or may not be modeled. Alternatively the loads can be determined by CFD calculations, again of varying levels of complexity, from simple RANS calculations, through to complex (and resource hungry) DES and LES calculations.
The calculation CWCs needs a simulation of the wind – that can either be the specification of a simple gust velocity, the specification of a spatially and temporally varying ideal gust, or the full specification of a wind time history; and also a simulation of the vehicle system – either a simple one, two or three mass model or the specification of the suspension system with varying levels of complexity. More recently some authors have even used calculations that are coupled with the track dynamics and with the dynamics of a bridge that the train passes over.
Finally the determination of the risk requires detailed wind statistical information that is not always easily available, together with route topographical information – embankment heights, bridge geometries etc.
To my mind one of the most important things about this three part process, and one that is not always appreciated, is that each component has a very different level of precision. The aerodynamic forces and moments can probably be specified to within 5%. The calculation methodology for CWCs, given specific values of the forces and moments, is highly accurate (say to within 1%), whilst the calculation of risk has massive inbuilt uncertainties because of the uncertainties in the meteorological information. Thus usually the risk of a wind induced accident can only be specified to within an order of magnitude i.e. 10-8or 10-9. Thus highly accurate determinations of CWCs are really pointless when the uncertainties in the risk calculations are considered.
Having spent the last 40 years involved with this problem to some degree or other, I would thus like to make the following reflections.
The different aspects of the subject – fluid mechanics, vehicle dynamics, meteorology etc. – make for a fascinating intellectual mix, and have led to the development of a range of complex modeling and analytical techniques. For an academic these challenges are fascinating – but these intellectual challenges can sometimes result in the end points of the process (train certification and risk specification) to be forgotten. I am as guilty of this as anyone of course. As an academic I can argue that my work in this area has enabled progress in other research areas, as indeed it has, but the end goal shouldn’t be forgotten.
The current train certification methodology in the CEN code is essentially a comparative one with CWCs for particular trains being compared with CWCs for trains that are considered safe. As such, accurate values of accident wind velocities are not required, as long as they were derived in the same way as for the reference safe vehicle. The CEN code sensibly goes down this route, and specifies a simple type of wind tunnel test to obtain the force coefficients. However it requires a full multi-body dynamic simulation with an artificial gust simulation, with a complexity that seems inconsistent with the accuracy with which the aerodynamic forces and moments can be specified.
The above multi-body simulation technique can, and has in the recent past, result in game playing that has no relevance to train operation or safety – by marginally changing the suspension parameters in an arbitrary way in the dynamic calculations so that the CWC is above the reference value and thus allowing the train to be certified. There must be doubts about any methodology that allows such things to happen.
Taking the above considerations a little further, there is an increasing tendency in published papers in this area to include as many complications as possible – multiple degrees of freedom of train, track and (if appropriate) bridge; coupling of train movement with the aerodynamic coefficients; very high resolution (and resource usage) CFD calculations. In my view the proper way to use such techniques is to carry out studies to determine the effects of such complex methodologies on overall aerodynamic forces and CWCs (almost always second order) and then to develop a much similar methodology that allows for them in an approximate way that is consistent with the accuracy of the overall process. Just because it is possible, using modern numerical techniques, to make complex calculations, it is not always sensible, or a proper use of resources, to do so.
Finally there is the effect of operation that needs to be taken into account, which brings us back to where we began. In the recent storms, the German and Dutch railway authorities simply stopped train movement, because of worries about debris on the track or trees falling onto overhead wires – not because of worries about trains overturning, as the wind speeds were much too low for that. The same happens in the UK. When high winds are forecast Network Rail and the TOCs first impose a blanket regional 50mph speed limit, mainly so that trains have some hope of reducing speed when debris is blown onto the track. A major problem in this regard seems to be trampolines at the moment – see figure 2 below – and at higher predicted gust speeds of around 65mph, train operation is stopped completely. Also, very often, train movements are blocked by tree fall onto the overhead. Operational reality takes precedence over all the wind tunnel tests, CFD calculations and MDS modeling we can conceive of doing.
The study of the effects of high winds on trains is fascinating and alluring academically, and allows the use of a whole range of fun physical model experiments and challenging computational techniques. But a sense of perspective is required I think – to keep the various methodologies simple enough for reasonably routine use in train certification and route risk assessment; and not to forget the overriding importance of train operational considerations.
This post is based on a talk given by the author at the PWI Midland Technical Seminar – High Speed Rail: The Technical Challenges, on October 19th2017.
When the word “aerodynamics” is used within a railway context, most listeners would immediately think of trains with streamlined front ends whose function is to reduce aerodynamic resistance and thus fuel consumption. This indeed is an important issue for train manufacturers and operators, and, since train aerodynamic resistance varies with (train speed)2, has become of increasing importance in recent years as train speeds increase. However the most aerodynamic effects on the railway are not simply concerned with train design and operation, but are of significant importance to the railway infrastructure as well. These effects include the pressure waves that pass up and down tunnels and affect passengers aural comfort; the sonic booms that are emitted from the end of tunnels on high speed lines; the transient pressures that load trackside structures as trains pass; the high velocity slipstreams flows that can cause problems to passengers waiting on train platforms; the pickup of ballast beneath high speed trains; and a range of disruptive effects caused by high winds.
In the next section, we will briefly consider the tools that are available to the engineer to investigate aerodynamic effects, and then we will proceed to give brief introductions to the effects outlined above.
The available tools
There are essentially four different tools that can be used to investigate aerodynamic effects on train infrastructure – full scale testing; physical model scale testing; computational fluid dynamics (CFD); and the use of codes and standards. We will consider each of these in turn.
Clearly full scale measurements are the preferred type of testing, as these, properly conducted, will actually measure the reality of the situation. There are well established techniques for measuring wind velocities (using a range of anemometers of different types) and pressures (loads) on the infrastructure or the train (using pressure probes and pressure transducers) – see figure 1 for some slipstreams measurements made by BCRRE staff in Germany. However, there are serious practical issues. Setting up measurements requires close liaison with operators, development of safe working practices, possessions to install equipment etc., all of which can be costly and difficult to organize. Full scale tests are very vulnerable to weather conditions, and high winds, which unfortunately tend to come at the most inconvenient time, can make any test results very hard to interpret. To obtain representative data, usually around 20 passes of trains are required, with trains of the same configuration running at close to the same speed, which is of course not always achievable. And of course, very often, information is required for trains or structures that are not yet built, and so full scale testing is not possible. This technique remains the best to use, but these practical issues can often make it impossible to do so.
Figure 1 Slipstream measurements in Germany
Physical model tests can take a variety of forms. The simplest (used to investigate cross wind effects) are standard low turbulence wind tunnel tests. However such tests do not properly reproduce the relative motion between the train and the ground. To model these effects properly it is necessary to use a moving model rig, such as the BCRRE TRAIN Rig based at Derby, which is a 150m long test track, capable of firing 1/25thscale model trains along two tracks at 75m/s (270 km/hr) – see figure 2 below. Such rigs can also be used to measure tunnel pressure transients (the TRAIN rig was originally built by BR Research in the 1980s to investigate transients in the proposed Channel Tunnel); loads on trackside structures; slipstream effects and (most recently) for the measurement of flow beneath trains in ballast pickup studies.
Figure 2 The BCRRE TRAIN Rig
CFD techniques have seen major advances in recent years, and there have been a large number of applications to investigate railway aerodynamic effects. Most investigators use steady flow methods (usually referred to as RANS – Reynolds Average Navier Stokes – methods), which can be run on desktop workstations with run times of the order of hours or a few days. These methods can be learnt quite easily, and can give an indication of the flow field around trains and railway infrastructure. Whilst they are undoubtedly convenient, they do have significant limitations in that they cannot fully describe the highly transient an unsteady aerodynamic conditions that exist in the railway environment. Thus in recent years unsteady methods such as Detached Eddy Simulation (DES) and Large Eddy Simulation (LES) have come to be used more and more. Whilst these methods can produce a great deal of flow field and loading information (see figure 3 below for exapmle), they are extremely resource intensive. For example recent calculations at Birmingham to measure cross wind effects on trains have used computational grids with more than 50 million cells, which take weeks or months to run on the University supercomputer facility. Such methods are not yet practical for routine use in the train and infrastructure design, although they may well become so in the not too distant future.
Figure 3 DES Simulation of the flow field around a Class 43 HST
Finally we come to codes and standards. In recent years much work has been undertaken by CEN to produce a series of standards entitled “Railway Applications – Aerodynamics EN14067”. There are six parts to this code – Part 1 Symbols and Units; Part 2 Aerodynamics on the Open Track; Part 3 Aerodynamics in tunnels; Part 4 Requirements and test procedures for aerodynamics on open track; Part 5 Requirements and test procedures for aerodynamics in tunnels; Part 6 Requirements and test procedures for cross wind assessment. These standards have aimed to synthesise a great deal of work that has been carried out over recent years, and provide a very valuable resource. At the time of writing revisions are underway on parts 4 to 6, and a further standard on ballast pickup assessment is in the very early stage of development. Various aerodynamic requirements are also set out in the Infrastructure and Rolling Stock TSIs, often referring back to the CEN standards for the methodology.
Tunnel pressure waves and sonic booms
The phenomenon of pressure changes in tunnels is well known. Essentially when a train enters a tunnel a compression wave (pressure increase) passes along the tunnel at the speed of sound. This reflects from the open end of the tunnel as an expansion wave (pressure decrease) and travels back along the tunnel. To complicate matters when the end of the train enters the tunnel this generates and expansion wave which again passes along the tunnel but reflects as a compression wave. These pressure waves can thus bounce from one end of the tunnel to another, resulting in extremely complicated pressure patterns both in the tunnel and on the train itself. The complexity can be compounded by the presence of airshafts which can also cause wave reflections, or by more than one train in the tunnel at the time. On unsealed trains this variable pressure can be very uncomfortable for passengers, and there are some tunnels on the GB network where aerodynamic speed limits are in operation. Most modern trains are sealed of course, and depending on the degree of sealing the pressure transients may or may not be felt by passengers. The CEN codes specify criteria for allowable pressure changes over different periods of time – for example 3kPa in 4 seconds in a single track tunnel. These transients can be quite accurately predicted using very simple one dimensional calculation methods, based on the equations of gas dynamics, and more complex CFD methods are only necessary for very detailed calculations around, say, the inlet to the tunnel. The advantage of the simple methods is that they can be run a large number of times to investigate a wide range of cases i.e. when trains enter the tunnels from both ends, the time lag between the first and the second entering the tunnel can be varied to investigate the worst case scenario.
An associated issue is that of the sonic booms that are emitted form the ends of tunnels on high-speed lines. This was first noticed in Japan in the 1980s as Shinkansen speeds increased through relatively small tunnels. Once observed, its cause was quite quickly established. The compression wave that results from train entry into the tunnel is not an instantaneous pressure rise, but rather a more gradual rise over a short period of time. The pressure wave thus has a spatial gradient. For long tunnels, particularly with ballasted track, the friction of the tunnel wall and track bed tends to steepen the wave significantly. When this wave arrives at the far end of the tunnel, most of the energy is reflected as an expansion wave, but some of the energy propagates outward as a sonic boom, with an intensity that is proportional to the pressure gradient at the exit. The method for minimizing sonic booms is straightforward, although perhaps not intuitive, and involves giving the inlet pressure wave as shallow a gradient as possible, so that even if it does steepen in the tunnel, its gradient at the outlet is still not sufficiently large to cause a strong sonic boom. This is achieved by the use of variable area hoods at the entrance to the tunnel – see figure 4 below for a hood that was tested on the TRAIN Rig at Birmingham as part of the initial HS2 studies.
Figure 4 Tunnel entrance hood to eliminate sonic booms
Aerodynamic loading of trackside structures
As the front of trains pass by trackside structures, they generate a transient pressure wave on the structure with the pressures first increasing and then decreasing. For example figure 5 shows the pressure on the underside of an overbridge as three different trains pass, plotted in dimensionless terms as a pressure coefficient. The peak to peak pressures are not in general that large (around 0.5 to 1kPa in dimensional terms) but, when they are repeated many thousands of times, can lead to fatigue failure of structures such as noise barriers, platform canopies etc. Guidance on allowing for these effects can be found in the CEN codes, based on full-scale tests carried out in Germany in the 1980s. These are of course not directly applicable to the GB situation because of the different loading gauge, so the RSSB have recently commissioned some tests on the TRAIN rig to measure the pressure transients on a variety of structures (hoardings, canopies, overbridges, tressle platforms) using 1/25thscale models, to provide information for a UK National Annex. The data shown in figure 5 is taken from those experiments and shows that the pressure transients caused by a Class 66 locomotive is very much greater than that caused by a Class 158 multiple Unit or the Class 390 Pendolino.
Figure 5 Pressure transients measured on a 10m wide bridge, 4.5 m above the track in TRAIN Rig experiments
As trains move along the track, not only do they generate pressure transients as outlined above, but they also generate high velocities. This velocity field is known colloquially as a slipstream. Along the side of the train (and on the roof) there is a region of flow where the air around the train is moving at the train speed next to the surface of the train (due to friction effects), decaying to zero at some distance away from the train. This region is known as the train boundary layer, and its thickness grows along the train. For passenger trains the boundary layer can be around 1m to 1.5 thick at the end of the train. For freight trains the boundary layer can be much thicker and extend 3 or 4m from the side of the train. In the wake of the train, the flow is very different for passenger and freight trains. For passenger trains the flow within the boundary layer rolls up into longitudinal vortex structures that can extend for tens or hundreds of metres behind the train – and indeed for such trains the highest airflow velocities are usually found in the wake and experienced by passengers on platforms when the train is disappearing into the distance. For freight trains these vortices do not seem to exist, and the flow velocities decay rapidly behind the train. This difference in the flow field is illustrated in figure 6, which shows the average velocities measured at trackside for around 20 train passes, as an ICE2 and a container freight train pass by. It can be seen that the highest velocities for the ICE2 occur in the wake of the train, but for the freight train these occur along the side of the train and the high velocities exists for much longer than for passenger trains. In this figure the air velocities are normalized by train speed, and the normalized freight train air velocities are much higher than those for the passenger train. This implies that the air flow velocities caused by freight trains at their normal operating speed (80 to 100km/h) can be higher than those caused by passenger trains moving much faster. This issue has come to prominence lately because of two incidents in the UK. In the first, at Twyford station, a disabled girl in a pushchair was sucked into the side of a hopper train, and, mercifully, simply bounced of with only a minor injury. In the second an empty pushchair was moved by the slipstream of a passing container train at Nuneaton station and hit the train before bouncing back onto the platform. There is potentially an issue here that needs to be addressed by the industry.
Figure 6. Slipstream velocities measured for a high speed passenger train (ICE2) and a container freight train. (passenger train figure shows velocities at different distances from the side of the 270m long train; container train figure shows velocities for two different container consists for a 600m long train)
As noted above, train slipstream velocities can be measured at full scale, with all the practical difficulties that involves. A methodology is given in the CEN standards, together with limits for allowable velocities at both trackside and on platforms. Over recent years, it has been demonstrated that moving model tests an also be used for slipstream velocity measurements, although careful consideration of scaling effects is required. Standard RANS CFD techniques are not yet suitable for slipstream velocity assessments, because they do not capture the highly transient nature of the flow.
The problem of ballast flight beneath trains is one that has made itself felt very forcibly over recent years, with a variety of (usually unpublicised and unpublished) events occurring on high speed lines, where ballast has been lifted from the track, seemingly by aerodynamic effects, and caused considerable damage to train under bodies and tracks. The phenomenon seems to manifest itself in different ways in different countries. In parts of Europe incidents have occurred in normal weather conditions, where large quantities of quite large ballast have become airborne and caused extensive pitting of train under bodies. In particular this occurred during ICE3 tests in French and Belgium lines in 2003 and 2004, where major damage was caused to the trains, but other incidents have been reported in Italy and Spain. In other parts of France and the Far East, the problem seems to be due to ice particles falling from trains, that then displace ballast that then causes train and track damage. In the UK, the problem appears to be due to smaller ballast particles being lifted onto the track, where they are crushed by either the train that caused the ballast to lift or a following train, leading to pitting of the wheel and rail, and the need for more regular maintenance and shown below. Indeed discussion with operators in the UK suggest that the flight of ballast has been a problem for many years, with long term requirements for extra wheel maintenance through grinding, for the front and rear wheel sets, and regular observations of ballast high up in the underbody equipment during maintenance periods. But without a doubt the most severe issues occur on ballasted high-speed lines when operating around and above 300km/hr.
The causes of ballast pickup are quite complex. Ballast experiences a number of different types of force as trains pass over – mechanical forces due to track vibration and aerodynamic pressure and friction forces. These forces all vary in different ways with train geometry speed, ballast size and packing etc., and these variations probably explain the different ways in which the phenomenon is manifested. This phenomenon has initiated a significant amount of research work around the world, particularly within Europe, through the Aerodynamics in the Open Air (AOA) and AeroTRAIN projects. The thrust of these investigations has been towards developing a method for the certification of new trains, through a standardised testing procedure, based on measuring the flow velocity beneath trains above a standardised track form. More recent tests by the University of Birmingham and the University of Southampton on HS1 have measured mechanical effects and aerodynamic effects simultaneously during the passage of Eurostars in an attempt to understand more fully the physics behind ballast pick up. Southampton University developed the technique of using ballast with accelerometers, data loggers and batteries mounted within the ballast itself – with the data downloaded each evening via a USB port! Alongside these full scale tests, work was carried out to predict the flow beneath the train using physical models on the TRAIN Rig and advanced CFD techniques. The Eurostar model on the TRAIN Rig is shown in Figure 7. It can be seen that the train travelled along the rig upside down under a false floor, to make access easier for instruments. The physical model experiments were in excellent agreement with full-scale results and potentially offer a way for the certification of new train designs, although much further development work is required.
Figure 7 Upside down Eurostar model on the TRAIN Rig for underbody flow measurements
High wind effects
The study of the effects of high winds on trains has a long history dating back to the risk assessment that was carried out to determine the risk of the Advanced Passenger Train blowing over on the West Coast Main Line in the late 1970s. The Rolling Stock TSI specifies that all new high speed trains have to demonstrate that they have sufficient cross wind stability (i.e. they will not overturn) and likewise the Infrastructure TSI requires that a suitable risk assessment is carried out before trains can be certified to run on specific routes. The methods for carrying out these assessments are quite complex and are set out in the TSIs and CEN standards. The risk assessment requires the exposure of routes to high winds to be assessed, and the risks of high wind gusts to be specified.
However the effect of cross winds on railway operation is not of course confined to train design and route risk assessment. In the recent storms in Europe (early 2018), the German and Dutch railway authorities simply stopped train movement, because of worries about debris on the track or trees falling onto overhead wires – not because of worries about trains overturning, as the wind speeds were much too low for that. The same happens in the UK. When high winds are forecast Network Rail and the TOCs first impose a blanket regional 50mph speed limit, mainly so that trains have some hope of reducing speed when debris is blown onto the track. A major problem in this regard seems to be trampolines at the moment (!) and at higher predicted gust speeds of around 65mph, train operation is stopped completely. Also, very often, train movements are blocked by tree fall onto the overhead.
It can be seen from the descriptions of the various issues set out above that there are a wide range of aerodynamic issues that need to be taken into account in railway infrastructure design and operation, as well as in the design of new trains and other rolling stock. One final point is worthy of mention however. It seems to the author that this range of issues is ill served by a simple split between train effects and infrastructure effects, as is, inevitably, fostered by the Rolling Stock and Infrastructure TSI. Aerodynamic effects on the railway are usually a combination of the effects of train movement around and through infrastructure – trackside structures, the track itself, tunnels and so on, and cannot easily be compartmentalized. This is perhaps what makes the subject such a fascinating one for study!