Cricket and Football in Pensnett in the 19th Century


The 19th century was of course the great era for the development of mass participation sports in England. At the start of the century the laws of cricket, the major summer sport, had been codified by the M.C.C. and the game developed over our period from one based on clubs and informal societies, playing “friendly” if competitive games, to one based on counties, with the highly competitive County Championship being finally established in 1890. Locally in 1889 the Birmingham and District Cricket League, the oldest in the world, was formed, consisting of seven teams from Birmingham and the Black Country.  The major winter sports were of course all variations of football, and the century saw the codification of the rules of association football, rugby union and rugby league. Again most of the games were “friendlies” but competition came through a number of cup competitions – the FA cup from 1871 and locally the Birmingham Senior cup from 1876, and later through leagues – the Football league itself from 1888 and the local Birmingham and District league from a year later.

Cricket in Pensnett

The information on what sports were played in Pensnett in the latter half of the nineteenth century is limited, but a little can be gleaned from local newspapers. It seems that there was a cricket team from the 1850s onwards, and several football teams from the 1880s. A cricket match between Pensnett Victoria and Kingswinford is recorded from 1859, with a win for the former.  The scorecard is given below. Note that this is a one-day game yet featured two innings from each side – the pitches were of course not prepared, and the batsman’s task was more than a little difficult.

Pensnett Victoria versus Kingswinford scorecard 1859

Over the course of the following decades, further matches are recorded against a range of local sides- for example Wednesbury, Brierley Hill Amateurs, West Bromwich Peep O’Day, Netherton, Droitwich, Bridgnorth and Oldbury.  The press mentions of the club cease after a notice of a General Meeting was published in March 1875 – either because the club ceased to function or because it simply stopped sending match reports to the newspapers. Reports resume about 15 years later with a small number of matches reported between1889 and 1894. Victoria was not the only Pensnett team however. A Pensnett Albion team was reported in 1864, and for a brief period in the early 1880s there also seems to have been a Pensnett Vicarage cricket team, which played three matches in 1881 winning the first but losing the last two by large margins. Also, in 1887 a match between Pensnett Oak Farm and Smethwick Eagle Works is recorded. Most of these were again two innings matches, with scores being typically low at around 30 or 40 per innings.

An interesting variant was the “single wicket match” and a report on such a match (between Pensnett Victoria and Brierly Hill Amateur) is given below. It is not clear what the rules were for this game, but clearly it involved two players a side which batted sequentially. Cricket, Jim, but not as we know it.

Report of single wicket match between Pensnett Victoria and Brierley Hill Amateur in 1867

Pensnett Football Teams

A Pensnett football team existed from the early 1880s and fielded both first and second teams, playing at a ground near Lenches Bridge. The first recorded match was in 1881 against Brierley Hill. Numerous further matches are recorded between 1882 and 1885 including some with the major teams in the area – for example with Stourbridge Standard first and second teams (the forerunner of the current Stoubridge club), Dudley, and West Bromwich Albion second team, as well as against more local teams such as Brockmoor Harriers and Lower Gornal Excelsior. As far as it is possible to tell most of these matches in the early days were ”friendlies”. The only competitive match that was recorded was in 1883, where Pensnett beat St John’s Swifts of Birmingham 6-1 in a “cup tie”, but the nature of the competition is not clear.

After 1885 the situation becomes somewhat confused with a paucity of press reports, and the ones that do appear refer to different teams – Pensnett Rovers, Pensnett Junior, Pensnett Villa and Commonside Unity. A Pensnett Victoria team appears in 1889, at the same time as the reappearance of the cricket club. A court case of 1892 over payment for a field at Lenches Bridge on which to play both football and cricket, refers to the Pensnett Victoria Football and Cricket Club – possibly a refoundation of the former club (BNA 1892). Again, most of the football matches that were played in the later period were friendlies, but more competitive games also took place. In 1889 the local newspapers give quite full details of the Pensnett Charity cup – a knockout competition for around twenty local teams, including Pensnett Juniors, Brockmoor Harriers, Kingswinford White Star and Kingswinford Rovers.

The situation changed however in1899 with the formation of the Brierley Hill and District Football League, in which Pensnett Victoria played. A late season league table is shown below. This really marked the end of the era of friendlies, and from this point on the structure of the game became league based, and much more familiar to modern eyes.

Brierley Hill League Table 31st March 1900

It was mentioned above that the Pensnett football ground was at Lenches bridge in both the early 1880s and early 1890s,  possibly on the Kingswinford side of the bridge, just outside the parish where the land was available and flat enough to accommodate a suitable pitch – see the extract from the 1882 OS map below with possible sites marked. Clearly in the early 1890s, the cricket ground was there as well, and that may well also have been its location in the 1860s and 1870s.

1882 Ordnance Survey map – possible football (and cricket?) ground locations shown as brown circles

The players

From the match reports in the newspapers, it is possible to identify the names of some of those who played for the cricket and football teams. In principle it is then possible, through the use of census information, to find out a little more about these individuals. I say “in principle” because it is not always easy. Often only surnames or initials are published and these can’t be unambiguously identified with specific individuals. That being said, it has been possible to identify with some certainty seventeen individuals who played for the cricket team between 1859 and 1872, and seven of those who played for the football team between 1882 and 1883. In terms of their profession, both sets of players reflect the make up of the area at the time, with a mix of skilled and unskilled industrial workers, and a few from other trades. For example, the seventeen cricket players included labourers, miners, boiler and chain makers, engineers and shopkeepers and the same mix can be seen in the football players.  The three cricketers from the 1859 scorecard who can be identified are the opener batsman, Joseph Bache (27) who was a chemist and druggist on High St, John Caswell (18) who was an engine fitter from Chapel St., and William Caswell (19) who was a chain maker from Tansey Green. The two Pensnett players who took part in the double wicket match in 1867 described above were William Yates (23) an Ironworks labourer from John St in Brierley Hill, and Thomas Baker (37) a coal miner from Chapel St. The other point that emerges from these considerations is that by no means all the players came from the parish of Pensnett itself. Of the seventeen cricketers identified, seven came from neighbouring parishes (Kingswinford, Brierley Hill and Brockmoor) and of the football players, only one came from Pensnett (the captain, Albert Colley (25), a timber merchant from Bradley Street) with the rest again coming from neighbouring parishes.


Finally, two other points are worthy of note before we end. Firstly, whilst the football played by the various teams in Pensnett was at what might be called junior level, the senior level of the game was played just outside the parish. Brierley Hill Alliance was formed in 1887 from a merger of Brockmoor Harriers and Brockmoor Pickwick and, before they moved to their Cottage Street Ground in Brierley Hill in 1888, played on the Labour in Vain ground in Brockmoor, a few hundred yards out of Pensnett parish. They went on to join the Birmingham League in 1890 and remained there, with some success, up to their eventual demise in 1981. Secondly, the name of Pensnett Victoria is not confined to the football and cricket teams. In 1880 a few matches played by a Pensnett Victoria Quoits team are reported. However, most newspaper mentions of the name refer to performances of the Pensnett Victoria Saxhorn band. If the reader, like me, doesn’t know what a Saxhorn is, then Wikipedia has the answer.

Some thoughts on ventilation and pathogen concentration build up

Modeling airflow scenarios in classrooms
Covid spread from CFD studies


Up till recently most attention had been focused on the spread of Covid-19 by near field transmission – being in close proximity to an infected person for a certain amount of time, and rather ad hoc social distancing rules have been imposed to attempt to reduce transmission. However, there is another aspect of transmission – the gradual build up of pathogen concentrations in the far field in enclosed spaces due to inadequate ventilation. The importance of this mode of transmission is beginning to be recognised – see for example a recent seminar hosted by the University of Birmingham. The main tool that seems to have been used for both near and far field dispersion is Computational Fluid Dynamics (CFD) – see the graphic above from the University of Minnesota for example. Now whilst such methods are powerful and can produce detailed information, they are very much situation specific and not always easy to generalise. This post therefore develops a simple (one could even say simplistic) method for looking at the far field build up of pathogens in an enclosed space, in a very general way, to try to obtain a basic understanding of the issues involved and arrive at very general conclusions.

The model

We begin with equation (1) below. This is a simple differential equation that relates the rate of change of concentration of pathogen in an enclosed volume to the pathogen emitted from one or more individuals via respiration and the pathogen removed by a ventilation system. This assumes that the pathogen is well mixed in the volume and is a simple statement of conservation of volume.

From the point of view of an individual, the important parameter is the pathogen dose. This is given by equation (2) and is the volume of pathogen ingested over time through respiration. The respiration rate here is assumed to be the same as that of the infected individual.

Equations (1) and (2) can be expressed in the normalised form of equations (3) and (4) and simply solved to give equations (5) and (6).

Equations (5) and (6) are plotted in figures 1 and 2. Note that an increment of 1.0 in the normalised time in this figure corresponds to one complete air change in the enclosed volume. It can be seen that after around three complete air changes the concentration of pathogen reaches an equilibrium value and the dose increases linearly, whatever the starting concentration. To the level of approximation that we are considering here we can write the relationship between normalised dose and time in the form of equation (7), which results in the non-normalised form of equation (8).

Assuming that there is a critical dose, the critical time after which this occurs is then given by equation (9).

Equation (9), although almost trivial, is of some interest. It indicates that the time required for an individual to receive acritical dose of pathogen is proportional to the volume of the enclosure and the ventilation rate. This is very reasonable – the bigger the enclosure and the higher the ventilation, the longer the time required. The critical time is inversely proportional to the concentration of the emission, which is again reasonable, but inversely proportional to the square of the respiration rate. This is quite significant and a twofold increase in respiration rate (say when taking exercise or dancing) results in the time for a critical dose being reduced by a factor of 4, or alternatively the need for ventilation rate to increase by a factor of 4 to keep the critical time constant. Similarly if there are two rather than one infected individuals in the space, then the respiration rate will double, with a reduction in the critical time by a factor of four.


Now consider the implications of this equation for two specific circumstances that are of concern to me – travelling on public transport (and particularly trains) and attending church services. With regard to the former, perhaps the first thing to observe is that there is little evidence of Covid-19 transmission on trains, and calculated risks are low. In terms of the far field exposure considered here, respiration rates are likely to be low as passengers will in general be relaxed and sitting. This will increase the time to for a critical dose. On modern trains there will be an adequate ventilation system, and the time to reach a critical dose will be proportional to its performance. Nonetheless the likelihood of reaching the critical level increases with journey time – thus there is a prima facie need for better ventilation systems on trains that undergo longer journeys than those that are used for short journeys only. For trains without ventilation systems (such as for example the elderly Class 323 stock I use regularly on the Cross City line) has window ventilation only, and in the winter these are often shut. Thus ventilation rates will be low and the time to achieve a critical dose will be small.

See the source image
Class 323 at Birmingham New Street

Now consider the case of churches. Many church buildings are large and thus from equation (9) the critical times will be high. However most church buildings do not possess a ventilation system of any kind, and ventilation is via general leakage. Whilst for many churches this leakage this can be considerable (….the church was draughty to day vicar….), some are reasonable well sealed – this will thus, from equation (9) tend to reduce the critical time. In this case too the respiration rate is important. As noted above the critical time is proportional to the respiration rate squared. As the rate increases significantly when singing, this gives a justification for the singing bans that have been imposed. - Wikimedia Commons
Church interior – Wikipedia Commons

The above analysis is a broad brush approach indeed, and in some ways merely states the obvious. However it does give something of a handle on how pathogen dose is dependent on a number of factors, that may help in the making of relevant decisions. To become really useful a critical dose and initial pathogen concentration need to be specified together with site specific values of enclosed volume, ventilation rate and expected respiration rates. This would give at least approximate values of the time taken to reach a critical dose in any specific circumstance.

Tornadoes and debris

Get the facts about tornadoes - Chronicle Media

The debris trajectory animations of Figures 6 to 11 were provided by Professor Mark Sterling, whose ability to use advanced EXCEL functions seems to be significantly greater than mine. His contribution is much appreciated.

Previous work

In 2017 Mark Sterling and I published the paper “Modelling wind field and debris flight in tornadoes”, which described the integration of a tornado wind field model and the debris flight equations to look at the pattern of compact debris movement in tornadoes of different types. Typical results for falling and flying debris are shown in figure 1 below and give an indication of the complexity of the debris trajectories that were predicted.

Figure 1. Debris Trajectories from 2017 model

Now whilst the tornado wind model that was used in the analysis was a considerable improvement over those that existed at the time, in that it gave a consistent three dimensional velocity formulation, it did however have one major drawback. This was the fact that the vertical velocity component was unbound and increased with height, albeit quite slowly. In a more recent paper in 2020 “The lodging of crops by tornadoes”, we developed an improved model, in which the vertical velocity peaked at a certain height and then decreased at greater heights. In this blog post I will briefly explore  the use of this wind model to predict compact debris flight paths using the same methodology as in the first paper, and in doing so will illustrate the importance of the tornado model on debris trajectory prediction.

The tornado wind model

Figure 2. Velocities from 2020 model

The expressions for the radial, circumferential and vertical velocities in the 2020 model are given in figure 2. Here the velocities are normalized by the maximum circumferential velocity and the radial and vertical distances by the radius at which the maximum velocity occurs. Note that this is different from the 2017 paper where the maximum radial velocity was used for normalization. The parameter K is related to what will be termed the swirl ratio S (the ratio of the maximum circumferential to maximum radial velocity) by a function of the parameter gamma, which is a shape parameter that affects the shape of the radial and vertical profiles. (Unfortunately this web template doesn’t support Greek letters, so I have to spell them out). Figure 3 shows typical velocity profiles for different values of this parameter.  It can be seen that for gamma = 2, the peak of the vertical velocity is at the vortex centre, as in a typical single cell vortex, whilst for higher values it moves away from the centre becoming more like a two cell vortex (but note there is no downflow at the vortex centre in this case.

Debris flight equations

The equations for compact debris flight are given in figure 4. These are the same as in the 2017 paper, although expressed a little differently. The debris velocities (lowercase) in the three directions are again normalized by the maximum tangential tornado velocity. Two dimensionless parameter are identified – the Tachikawa number Ta that relates the flow force on the debris particle to its weight, and a tornado Froude number Fr. Different dimensionless parameters were used in the 2017 paper, because of the different reference velocity that was used

Figure 4. Debris flight equations


Figure 5. Base case parameters

Putting together the velocity equations in figure 2 and the particle flight equations in figure 4, it can be seen that there are four parameter that define debris trajectories – the tornado parameters S, gamma and Fr, and the debris Tachikawa number Ta. In addition any one flight trajectory will be defined, at least in its early stages by the dimensionless values of the radius and height at its release point. If these six parameters are specified then the equations of debris flight can be solved in a straightforward manner.  In what follows we define a base case situation as in figure 5, and then vary each of the parameters around this base case value. We present the results in the animations of figures 6 to 11.Each animation shows four plots – the trajectories projected onto a vertical plane through the tornado centre; the trajectories projected onto a horizontal plane; the trajectories in a rotating plane in the radial and vertical directions, and a plot of the variation of particle kinetic energy with time. The latter acts as a damage indicator of debris flight, but also clearly shows whether or not the solution converges or diverges with time. Note that the dimensionless time shown in the kinetic energy plots is proportional to the time of revolution of the vortex – a time of 2 pi corresponds to one vortex revolution. 


Figure 6. Effect of variations in Tachikawa number

First consider the effect of changing Tachikawa number, Ta – see Figure 6. This represents changes in the nature of the debris. A low value of Ta represents heavy debris and vice versa. It can be seen that at low values of Ta, the debris tracks can reach significant heights and the debris undergoes a diverging motion when viewed in the radius / height plane, with a diverging kinetic energy oscillation. At some point in the trajectory the debris hits the ground and the energy falls to zero. The base case situation at Ta = 100 is still mildly diverging but the trajectory does not intersect the ground plane for the length of the calculation. As Ta increases further, the debris takes up a stable path in the radius / height plane travels around a small circular trajectory, with the kinetic energy converging to a stable value. This suggest that light debris can reach an equilibrium where it is held aloft by the tornado. The position around which the circular motion takes place is around a normalized radius of 1.3 and a normalized height of 0.9. The value of height is much less than calculated in the 2017 paper, reflecting the fact that the vertical velocity does not decrease indefinitely with height for the new model as it did in the old.


Figure 7. Effect of variations in Froude number

The effect of variations in Froude number is shown in Figure 7. The primary effect that increase in Fr has is to increase the centrifugal force on the debris. At low values, the trajectories are stable and similar to that of the base case. As the values increase above 1.0 the oscillations become larger due to the increased centrifugal forces and eventually become unstable, with the trajectories meeting the ground at high values.


Figure 8. Effect of variation in Swirl Ratio

The effects of variations in the Swirl ratio shown in Figure 8 are complex, with diverging trajectories (and ground impact) at both low and high values, and a region of stable trajectories between values of around 1.0 to 1.9. At low values the trajectories are destabilized by the high values of radial velocity, and at high values are destabilized by high values of the circumferential velocity.


Figure 9 Effect of variations in gamma

The change in values of gamma from the one cell form of gamma = 2 to the quasi-two cell form of gamma = 4 shown in Figure 9 results in little change to the debris trajectories from the base case, although the oscillations in the kinetic energy fall as gamma increases.


Figure 10. Effect of variations in radial starting position


Figure 11. Effect of variations in vertical starting position

The debris trajectories remain stable as the normalized radius varies between 1 and 1.9 but outside those limits the trajectories diverge and intersect with the ground (Figure 10). Similarly the trajectories are only stable for normalized values for height between 0.8 and 1.2 (Figure 11). Thus the starting point window for the trajectories to ultimately attain a stable form is quite small.

Concluding remarks

A number of points arise from the results presented above.

  • Even for the simple wind and debris flight formulation adopted, debris trajectories can be quite complex.
  • A comparison of the results obtained with the old and the new wind field model show very considerable differences, due to the different vertical velocity formulation. analysis reveals that the debris trajectories can be specified by a small number of debris and tornado parameters, with the Tachikawa number and the Swirl Ratio being the most significant.
  • There are regions within parameter space for which the debris trajectories become stable – i.e. the debris flies indefinitely.

Pollution, Covid and Trains

Voyager at Birmingham New Street

There has been a significant amount of research recently to investigate the air quality in railway stations. Perhaps the major study, with which I was very much involved, involved extensive measurements of the air quality at Birmingham New Street by colleagues at the University of Birmingham (Figure 1). Measurements were made of the oxides of nitrogen (NOX) and particulate matter (PM) and concentrations were measured that were considerably in excess of Environmental Health limits. Typical daily average results are shown in Figure 2. This work informed the efforts by Network Rail to improve the air quality at the station through an improved ventilation system. Further work was carried out by Kings College London and Edinburgh University, under an RSSB contract, to measure NOX and PM at Kings Cross in London and Edinburgh Waverley. Typical results are shown in figure 3 and although these results are not as extreme as the Birmingham measurements, do show some exceedances of environmental health limits. Between them, these three investigations have given a great deal of information on station air quality and informed methods for alleviating the worst of the effects.

Figure 1. Air quality measurements at Birmingham New Street
Figure 2. Daily pollutant levels at Birmingham New Street (red lines show EU limits)
Figure 3 Comparison of pollutant levels at New Street, Kings Cross and Edinburgh Waverley

However, that is not the whole story. There are growing indications that air quality ON trains is also very poor. A study on diesel commuter stock in Canada has shown high levels of ultrafine particles and black carbon within the passenger cabins (Figure 4). In 2016 the BBC reported the measurements made by their reporter Tim Johns  as he commuted into London, which again showed high particulate levels on diesel commuter trains, although not as high as in Black Cabs (Figure 5). Similarly, the BBC in 2019 reported a study by the Committee on the Medical Effects of Air Pollutants which showed very high levels of particulates on the London underground (Figure 6) which resulted in a strong response from the rail unions. These high levels are presumably due to two sources – diesel particulate emissions from trains being ingested into air conditioning systems, and also from ambient particulates in the dirty tunnels of the underground. The levels of particulates measured have significant implications for human health, particularly for those with respiratory conditions.  

Figure 4. Air Quality measurements on Canadian trains
Figure 5. Particulate measurements by BBC Reporter
Figure 6. BBC report on Underground particulate levels

Similarly, some work has been recently reported from Greece that shows elevated levels of both gaseous pollutants and particulate pollutants on diesel trains, both in excess of EU limits (Figure 7). Again this is presumably due to ingestion of diesel emissions by ventilation systems. Hopefully in the near future we will see the results of more quantitative investigations for the UK of on train NOX and particulate concentrations, and of work to investigate the ingestion of external pollutants, both from diesel emissions and dirty environments, by ventilation systems. However current indications are, that, care should be taken in using ventilations systems that draw external air into the train without the use of extensive filtering of the input.

Figure 7. NOX measurements on Greek train (red line is EU limit)

And then along comes Covid-19. The importance of high levels of ventilation on reducing pathogen concentrations and thus the risk of infection is becoming clear – se for example the recent seminar organized by the University of Birmingham. Ideally, very high (airline) levels of air exchange with the outside are required in internal environments, including trains and buses. An interesting illustration of this is provided by the publicity material in figure 8 produced by SNCF in France. I have seen nothing similar for the UK. There is an obvious dichotomy here between the need to reduce external air intake to minimize NOX and PPM ingestion and to keep internal levels of NOX and particulates at an acceptable level, and the need to increase ventilation rates to decrease pathogen levels. Both could be achieved by aggressive filtration of the air drawn through the train. However, this is likely to require major modification to existing trains in Britain, that won’t be cheap. I suspect train ventilation is going to become a major issue in the near future.

Figure 8. SNCF publicity material

A historical curiosity – Fog Cottages

The original Lichfield Trent Valley station

Next to the original Lichfield Trent Valley station (north if the current one – see my blog post at…/lichfield-trent-valley…/ ) the OS map of 1900 shows a row of cottages that the census return names as Fog Cottages as shown in figure 1 below.

Figure 1. Lichfield Trent Valley 1900 OS map

I noticed recently whilst out walking that there is another similarly named row of cottages just beyond Rugeley Trent Valley station. This is not shown on the 1900 map, but is there on the 1920 map, again shown on Figure 2.

Figure 2. Rugeley Trent Valley 1920 OS Map

The Staffordshire Past Track website has a picture of these cottages at… with the following explanation for the name.

“A postcard view of Fog Cottages, on the Colton Road near Trent Valley Station, Rugeley. They acquired the name Fog Cottages because the end cottage had an alarm bell installed and this was used in foggy conditions to call out the railway men who lived in the cottages to go and place fog detonator alarms on the nearby rails to assist the train drivers.”.

A modern view of the Rugeley Cottages (from Google Street View) is shown in Figure 3 below.

Figure 3. Fog Cottages, Rugeley

The question then arises as to whether the name of Fog Cottages has more widespread use. And the answer is that it does. Mathams and Keshall (2014) present an old photograph of a now demolished set of Fog cottages at Amington, next to the LNWR line north of Tamworth (Figure 4).

Figure 4. Fog Cottages Amington (Mathams and Keshall, 2014)

Rightmove (perhaps one of the more unusual historical sources!)  reveals that there are Fog Cottages at Watford, Collingtree and Althorp Parkin Northamptonshire and at Tring in Hertfordshire (see the Google Street View shots of these in figure 5). There are almost certainly more that I have not identified. All are next to the LNWR line, but only some are near stations or the sites of former stations. On the Amington Cottages Mathams and Keshall write

The LNWR standard cottages were built after 1883 when the design was introduced by Francis Webb, Chief Engineer of the LNWR and later examples – built after 1883/4 – are recognisable by the courses of stepped-out brickwork on the gable ends and under the eaves, and the four red-brick bands which run round the building in line with window sills and lintels, all of which can be seen in the picture below.  Nearly everything (except the slates) came from the LNWR works at Crewe;  bricks, woodwork and metal fittings.  

I can find no mentions of Fog Cottages other than in LNWR territory so it looks as if we have here a specifically LNWR naming policy. But if there are any occurrences away from the LNWR I would be pleased to be told.

A brief look at the incidence of Covid-19 in UK Universities

See the source image

Alarm has been expressed by many commentators at the prevalence of Covid-19 in UK Universities, and on the face of it, the figures do seem to be alarming. For example, the UniCovid UK website that attempts to track the spread of Covid in Universities indicates that, as at October 17th 2020, since the start of term there have been 1650 cases at the University of Manchester and 1522 at the University of Northumbria. This data comes from a variety of sources where it is reported in different ways and needs to be treated with caution, but nonetheless gives a broad indication of the current situation. However these raw figures do not give a real indication of the situation since they do not take into account the size of the institution or the length of time since the start of term, which differs from place to place. To look at this in a little more detail I have carried out the following simple analysis using the UniCovid UK data at October 17th 2020.  I have taken the number of reported cases since the start of term at each institution and divided them by the factor (total student population x days since the start of term / 14). This gives a rough approximation of the proportion of students who might currently be expected to have Covid-19, making the assumption that the illness lasts for 14 days. I am very aware of the other implicit assumptions involved in this calculation (the assumption of constant infection rate,  the neglect of the different demographic profiles of different universities, different rates of testing and so on), but at least it gives a crude normalization of the data. On this basis, the 30 Universities with the highest percentages of students currently with Covid-19 is shown in the table below.

Approximate % of students infected (October 17th 2020)

Now the UniCovid UK web site gives the prevalence of the virus amongst the student age population as between 0.24 and 0.52%. Most of the Universities in the above table lie above the upper bound value, but many not by a great amount (and here the assumptions in the analysis need to be kept in mind). Only twelve exceed a value of greater than 1% of the students having the virus. Whilst for some of these top twelve the situation is clearly very serious, with the proportion of those infected many times the expected levels, the numbers suggest that the issues are localized – and indeed mainly in areas where there are high rates of infection in the wider community.

The Kingswinford Tithe Agreement

The 1840 Fowler Map

In Kingswinford Manor and Parish (KMAP) I have written extensively about the two Fowler Maps of 1822 and 1840 – two large scale maps of the parish that were produced for the landowners  by W. Fowler and Co. and which, together with their Books of Reference that give names of owners and occupiers, give a detailed picture of the life of the parish at that time. When the Staffordshire Tithe Maps were published on line by Staffordshire Fast Track, and described in outline in another blog post, it came as a considerable surprise to me to find that the Kingswinford Tithe Map was actually a version of the 1840 Fowler map, with some added information on tithe rental values and ownership. In this post, I will belatedly (and to my shame as I should have known about this much earlier) consider this new material in the light of the discussion in KMAP, to see what new insights it brings.

Tithes before 1840

The Tithe Commutation Act of 1836 replaced the old tithe system in which a tenth of the produce of the land was given to the church either in kind, or through a cash allocation, with a rental system where a tithe rental charge was allocated for each portion of land. In preparation for the Act, in 1832 the Ecclesiastical Commissioners wrote to the incumbent of every parish in the country asking for details of their income from tithes and other sources. The returns for Kingswinford parish are shown in table 1.

Table 1 Church income 1832

The chapel of St Michael at Brierley Hill had been opened in the 1760s and was staffed by a Perpetual Curate. The new parish church was Holy Trinity at Wordsley, which was built in 1831, when the old parish church of St Mary in Kingswinford village was felt to be too small for the growing population, and was also suffering damage to its fabric due to mining subsidence. The Rector was based at the former whilst the latter was staffed by a Perpetual Curate. It can be seen that the income has three components – tithes and easter offerings, rental from Glebe land (land set aside for the use of the clergy) and other sources. The Perpetual Curates relied on the latter, with the tithe and glebe income going to the Rector. The overall figure for the Rector of £1130 would have made the parish one of the most lucrative in the county (see E Evans 1970, “A History of the tithe system in England 1690-1859 with special reference to Staffordshire”, PhD thesis, Warwick University), and was much sought after by clergy in the eighteenth and nineteenth who often did not take up residence and left all their duties to paid curates, but took most of the income for themselves.

Before the passing of the Act, the collection of tithes would have been an arduous affair, and would usually have been carried out by a paid tithe collector, who would travel around the parish at harvest time to take their due from the landowner, and would also assess and collect a tenth of the other produce of the land – in terms of cattle, sheep, wool etc.. In Kingswinford there were more than a hundred tithe payers, and over two thousand distinct plots of land and tithe collection was obviously a complex affair. In addition, there were a range of extra customary dues that had to be collected, known as moduses. For example, for Kingswinford parish these included a modus of two pence / per acre on all meadow and pasture land; one penny and a halfpenny for a cow and a calf; one penny for a garden; and four pence for a colt. Not all land was treated in the same way – for example the lands enclosed by the Ashwood Hey Enclosure in 1776 were only liable for the tithes of “wool and lamb”. When the difficulties of collecting all that was due are considered, it can be seen that the move to a tithe rental was a major simplification and seems to have been broadly welcomed in the parish.

The Rector and landowners of the parish were keen to move to a new system, and soon after the Act became law they moved quickly to reach a voluntary agreement on tithe rental by June 1838. In many other parishes in the county and elsewhere agreement on tithe rentals could not be reached voluntarily and tithe commissioners imposed a valuation. The results of the agreement are contained within the Tithe Allocation agreement and the associated map. 

The Tithe Allocation agreement

The total area of the parish of Kingswinford was 7319 acres. Of this, 6032 acres (82.5%) was allocated a tithe rental.  The only recipient of tithe rentals was the Rector of the parish, George Saxby Penfold, which was one reason why reaching agreement was straightforward. The total rental allocation was £813. Of those lands that were assessed for no payment, 174 acres was Glebe (i.e. allocated to the Rector, who was not expected to pay the tithe rental to himself, and usually rented to others for farming) and 178 acres was the Corbyn’s Hall estate which was tithe free (see below). The rest of the untithed land was composed of many very small plots of land which presumably had their allocation rolled into nearby tithed land, so as to simplify the allocation and collection procedure. (Note that these figures are taken from summing those that have been transcribed from the Fowler Reference and the Tithe Agreement, and do not quite match the equivalent figures in the tithe agreement, due to  differences in the allocation of plots to different categories. The differences are however small and of no real consequence.)

The fact that Corbyn’s Hall was specified as tithe free is of interest. It is not clear why this is the case but was presumably the result of how the estate was originally established. In KMAP I speculated that the Corbyn’s Hall, Tiled House and Bromley Hall estates were originally one land unit. The fact that the latter two were allocated tithe rentals in the normal way suggests that this might not have been the case. At the time of the tithe allocation map, the extent of the Corbyn’s Hall estate was very similar to that shown on a  1703 map of the estate shown in outline in figure 1 below (again from KMAP), and included the region around Corbyn’s Hall and Shut End, some land in the Tansey green region and a block of land around Standhills.

Figure 1 1703 map of Corbyn’s Hall estate

The way in which tithe rentals were allocated to individual portions of land is not wholly clear from the tithe agreement. The land in the parish seems to have been allocated to a small number of land use categories – arable, meadow and pasture; woodland; and a further miscellaneous category combining mines, road and houses etc. The calculation given in the tithe agreement gives 3486 acres of arable land; 1532 acres of meadow or pasture; 154 acres of woodland; and 1655 acres in the miscellaneous category. A rental / charge per acre was applied to each category other than the miscellaneous for which no charge was allocated. For the arable land this was based on a weighted average of the cost of wheat, barley and oats over the previous few years.  

If the tithe rentals for plots of land greater than one acre in size are plotted against the allocated rental (figure 2) it is clear that there were two basic rental allocations – one at around 5s per acre (the green line) and one at around 1s per acre (the red line). In general arable land and high status houses and ground cluster around the green line, and pasture and woodland around the red line. There is considerable scatter about these lines however, which no doubt reflects the specific circumstances of each plot of land and lengthy debates between the landowner and the Rector.  In the area that was enclosed by the Ashwood Hay act, the arable land is also clustered around the lower red line, no doubt reflecting the lower tithes that were prescribed by the act (see above). Most of the land in the miscellaneous category was not allocated a tithe rental.

Figure 2 Tithe Allocation

Table 2. Tithe payers and landowners

In total there were one hundred and twenty six tithe payers, although this involved some duplication due to some individuals being involved in partnerships that were assessed for tithes. Of these one hundred payed less than £5 and sixty six payed less than £1. The fourteen who payed more than £10 are shown in table 2. The cumulative tithe column in the table shows that three quarters of the tithe rental was paid by just thirteen individuals or organisations. The percentage of the tithe that each payed is also given, as is the percentage of the land that they owned (from KMAP, chapter 4). As is to be expected, the figures in these columns correlate quite well, with the percentage of tithe rental being in general greater than the percentage of land, due to the significant proportion of untithed land.

The other major landowners given in KMAP are the Glebe lands, the lands of John and Benjamin Gibbons,, and the Stourbridge Canal Company.  As noted above, the Glebe lands were tithe free and provided the Rector with an income as they were rented out for farming. The Gibbons main holdings were on the tithe-free Corbyn’s Hall estate. It would also seem that when the Stourbridge Canal Company was formed it purchased land without the tithe obligations, and the land it gained in the Fens area from the enclosure of Pensnett Chase was also tithe free.

Reducing train aerodynamic resistance through the use of slab track

Ballastless double track of the type "Rheda 2000" including concrecte slabs and ties/sleepers, rails, and drainage slits.

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.

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).

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.

Figure 2 Typical results for Class 45 and 6 passenger coaches between Thirsk and Northallerton

Drag coefficient

The coefficient c is related to the aerodynamic  drag coefficient CD by the simple expression of equation (2).

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 ???).

Figure 3. Drag coefficient correlation

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).

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.

Table 1 Parameter values

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), K2 is 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.

Table 2 Skin friction coefficients
Table 3 Underbody friction coefficients

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?

Leisure travel by rail after the pandemic

Figure 1 Public transport use in the UK

It is becoming clear that the effect of the Covid-19 pandemic on public transport in the UK is very significant, and is resulting in a major reduction in rail and bus use that looks as if it will persist at least in the short and medium term and also possibly into the long term future. Figure 1, compiled from DfT statistics, shows the seven-day average use of rail and bus over the course of the pandemic, up to 29/9/2020. It can be seen that rail and tube use seems to be plateauing at around 40% of the pre-pandemic values, and bus use at around 60%. The same trend can be seen in other cities around Europe – see figure 2 from the Financial Times, which shows general public transport use. London does however seem to have a greater reduction than other capital cities.

Figure 2 Public transport use in major European cities

The trends shown on figures 1 and 2 do however mask considerable geographical and service type variations. There is evidence that the use of public transport in larger cities has fallen more sharply than in smaller conurbations, and also that travel patterns are changing. Network Rail Chairman Peter Hendy made the following comment at a recent online conference

“It is clear that people’s methodology of working has changed. Many jobs can’t be done from home, but there are lots of people who can work from home and have learned something they didn’t know before and are learning to live in a different way. Leisure travel has returned quicker than work travel. One of the scenarios that we might want to have in our heads is that we might be going back to a situation like the 1950s, when maximum traffic on the railway was on peak summer Saturdays and not in  what we now regard as normal peak hours.”

My personal experience would tend to confirm this – I, and others in my family, have recently travelled on quite heavily loaded services with passengers heading for leisure destinations in the north of England. This trend is also clear in the data from the excellent Centre for Cities website for Birmingham and Bournemouth, shown in figures 3 and 4 below. These show a variety of metrics that indicate how these places are recovering. It is clear that activity in Birmingham, a major commuter hub, remains well below pre-pandemic values, whilst activity in Bournemouth, at least in part a leisure resort, has in general increased.

Figure 3 Centre for Cities data for Birmingham

Figure 4 Centre for Cities data for Bournemouth

In this post I want to consider briefly how the rail network might take into account this leisure market. In pre-nationalisation days and the early days of BR, this market was catered for by excursion traffic from the major centres of population to a range of coastal resorts. In retrospect this involved a very inefficient use of rolling stock, with the carriages that were used for these excursions often having no other use other than at summer weekends. It also required extensive siding space at the resorts themselves, as the trains often waited there for a significant time before returning. After the demise of such traffic, the strategy (if one can use that word) seems to have been to provide an essentially local service on the routes to resorts, with connections to the main line, and to simply accept overcrowding oh high days and holidays. By its very nature such a strategy was self-limiting in terms of passenger numbers – the experience of trying to crowd onto a two-coach multiple unit with a family and luggage is not one that is willingly repeated if there is another way to travel.

So is there a way in which such traffic can be catered for in a more passenger friendly way? I would suggest there is, but it requires significant changes to the structure of the industry to make it effective. Firstly, it seems to me that there are a number of basic passenger requirements.

  • Passengers wish to go from their point of departure to their destination without changing trains – particularly those travelling with family and luggage.
  • There should be significant space for luggage, so that aisles and vestibules are not blocked.
  • There should be no overcrowding.

On a basic level these points suggest that excursion traffic and local traffic should be kept separate, with the former running directly from departure to destination. With regard to the first bullet point, considering the Birmingham / Bournmouth route as an example, trains should pick up at a small number of points in the West Midlands conurbation (say Wolverhampton, Sandwell and Dudley, Birmingham New Street and Coventry) and run non-stop to Poole and Bournemouth. The normal intermediate stops of Banbury, Oxford and Reading (amongst others), delightful as these places are, are simply of no interest to leisure travellers. The second point suggest that luggage facilities should be provided, perhaps in a separate coach with luggage tagged, loaded and unloaded by station staff. And the third point suggest that such trains should have compulsory reservations and those without reservations not allowed to board.

How could such an operation be achieved, making efficient use of rolling stock? I would suggest that there is already sufficient rolling stock available, particularly with the increasing use of relatively high speed, hybrid multiple units that are not restricted by the extent of electrification. However, a national approach needs to be taken, such that some rolling stock of this type is used for local, regional and  commuter services for much of the year, is transferred to excursion traffic during the summer when the local and regional demand is lowest. This requires a national approach to stock utilisation that cuts across TOC / Operating Unit boundaries, and also a similar integrated approach to timetabling and service provision. One could thus envisage for such services route 9 or 10 coach  hybrid multiple units, that would normally work on local and regional services, operating as excursion stock in the summer, both on weekdays and at weekends. Luggage facilities could be provided in one coach that has fold down seating, which is a perfectly viable concept. Passengers would deposit and collect their luggage at stations, which would require a suitable luggage tracking system and appropriate staffing. Reservations would need to be made before hand and systems put in place at stations for allowing only those with such reservations to access the platform as the train arrives.

The above is a suggestion for only one type of leisure traffic – the medium to long distance excursion market. There are many other types of leisure traffic that need to be catered for and a variety of methods need to be developed. The important point is that such traffic cuts across the neat geographic and organisational boundaries of the current system and require a national approach to stock utilisation, timetabling, station organisation etc. The current organisation of the network, with the multiple internal boundaries and barriers between regions and operating units, would simply not allow such services to be developed. Perhaps a nationwide “Leisure Travel” operating unit needs to be considered? Something for the still slumbering “Guiding mind” to think about?

Journeys by rail and coach

Stagecoach 500 at Dumfries Station

I recently travelled from my home in Lichfield to Gatehouse of Fleet in Galloway. The journey involved three trains (Lichfield to Crewe, Crewe to Carlisle, and Carlisle to Dumfries) and one bus journey (Stagecoach 500 from Dumfries to Gatehouse). The journey in both directions was, apart from some minor late running, pretty much without incident, and all the connections were made comfortably. The trains were comfortable and, as required for the moment, suitably socially distanced. The bus legs were similarly comfortable, with rather plush coaches and helpful drivers. That being said, the journey reinforced thoughts I often have when making journeys of this sort, that the weak links are the interchange between train and bus, and also the physical infrastructure of the bus pick up and set down points. I will consider each of these in turn with regard to my recent journey, but the same or similar points could be made for other journeys of this type.

The problem of train / bus interchange begins well before the journey itself, when journeys are being planned and fares considered. Finding the bus timetable is easy enough, even with current Covid related restrictions, but nonetheless required searching different web sites for the information, and making some sort of assessment of suitable connection times. No information at all was available on the fares, and I had to enquire of the bus driver on the outward leg as to whether returns were available or not. They were, at a very reasonable price, but it would have been good to know beforehand. On the journey itself, having alighted at the quite delightful Dumfries station, we found the rather flimsy bus shelters outside the station, effectively in the middle of a pedestrian thoroughfare. The weather, for both the outward and return journeys, was fine so this mattered little. No information at all was provided on how the bus was running, when it was due etc. But it came on time and all was well.

All the above could so easily be improved – by integrating train and bus timetables and fares; by extending a canopy from the station to serve as a bus waiting area and incorporating the bus area more completely into the station complex, so that toilets, the café etc. are more easily accessible to bus passengers; and developing the passenger information system so that details of both trains and buses were included.

At Gatehouse the facilities are rudimentary – simple bus shelters on the pavement with little by way of information, either on timetables or real time. The latter was not helped by recent Covid related service changes however. Once again this could so easily have been remedied – there is space available for a dedicated bus pick up / drop off point, ideally with more substantial passenger facilities that could act as a transport focus for the town; and the technology is available for real time bus running information to be made available.

Obviously the situation with regard to train / bus interchange and to local bus waiting facilities will be unique to any situation, but it does seem to me that there are two basic areas of improvement as follows.

  • Information – the integration of time, price and ticket information and purchase for at least a selection of important bus / coach routes with the train boking systems; and real time passenger information at interchanges and bus stops.
  • Infrastructure – at interchange points, the full physical integration of bus waiting facilities into the train station facilities; and the provision of more substantial local bus facilities that are ideally not part of a pedestrian throughfare.

But the question that then arises is who should be responsible for such facilities – it is clear that at the moment these fall into gaps between the train infrastructure and service operators; the bus operators; local authorities and community groups. Much has been said recently of the need for a “guiding mind” to oversee the rail network. I would suggest that this guiding mind, should it ever achieve consciousness, should have a wider role in the overall transport network, and particular in the field of modal interchange. The post-Covid recovery of the public transport network would benefit greatly from this.