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Modelling of extreme wind gusts

Nomenclature

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.

Box 1 Equations 1 to 7

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 2 Equations 8 to 13

Model comparison

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.

Box 3 Model Summary

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.

Figure 1 Model Comparison

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.

Concluding remarks

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.  

References

Baker C J, 2001, Unsteady wind loading on a wall, Wind and Structures 4, 5, 413-440. http://dx.doi.org/10.12989/was.2001.4.5.413

Bierbooms, W., Cheng, P.-W., 2002. Stochastic gust model for design calculations of wind turbines. Journal of Wind Engineering and Industrial Aerodynamics 90 (11), 1237e1251. https://doi.org/10.1016/S0167-6105(02)00255-6.

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

A study of the ancient prebends of Lichfield Cathedral

The Cathedral Prebends

In this post we will use the information provided on the Lichfield Tithe maps to investigate the nature of the Cathedral prebends. Until quite recently (in historical terms) members of cathedral staff (prebendaries)were supported by the income from various estates (prebends). In the case of Lichfield, there were basically two types of prebend – the first consisting of estates of various sizes that were leased for farming, industrial or residential purposes; and the second consisting of the income from specific ecclesiastical foundations. The system is well described in the Lichfield Cathedral section of the Victoria County History. At the peak of the prebendal system, Lichfield had 32 prebends, most of which were held by clergy who were only required to be in Lichfield for a few months a year. Twenty four  these were of the second type, based on the income from various churches in the diocese and eight of the first type based around specific land allocations. It is thought that five of these – the prebends of Freeford, Handsacre, Longdon, Statfold and Weeford were actually the estates that supported the five canons of Lichfield mentioned in the Domedasy book. Since the prebends are named after areas around Lichfield, it seems reasonable to assume that they consisted of specific areas around the city. Now for many of the properties that are listed, the tithe maps give an indication of which prebend they were in in the middle of the nineteenth century, and thus offer the possibility of mapping these prebends in more detail than has been previously possible. In what follows, we will thus attempt to do this, and it will be seen that it offers a description of the Anglo-Saxon geography of the area that is quite distinct from the later geography. It must however be stressed that what the Tithe maps show is the outcome of many hundred years of land sales, exchanges and re-organisations and thus absolute clarity on the original extent of the prebends is not to be expected.

Lichfield from Domesday to the Reformation

Figure 1. Lichfield and the surrounding area

(blue indicates rivers; solid brown lines indicate early, possibly Iron Age roads and trackways that survived to the present time, and dotted brown lines indicate Roman roads)

Figure 1 above shows the area around Lichfield, with the Rivers Tame and Trent and the early road system identified in the topographical studies of Stephen Bassett, that I have briefly described in an earlier post.  The names shown in regular type are the members of the Manor of Lichfield given in Domesday that lie in the vicinity of the city itself, and those in italic type are places that occur in other Domesday entries. It can be seen that the extent of the Manor was large stretching west to Hammerwich and east to the Tame at Tamhorn. There are some obvious gaps on the map – for example around Longdon to the west and Whittington to the east. There are also names not included on the map as their location cannot be identified – Horton, Burweston and Littlebeech. The important thing to observe from the perspective of the current investigation is that the three ancient prebends that are named on the map – Freeford, Hansacre and Weeford have no special importance over the rest. This suggest that if they are basic building blocks of a geography of the area, then this geography significantly predates Domesday and is very old indeed.

The town of Lichfield was set out by Bishop Roger de Clinton around 1140 and became styled as the Manor of Lichfield in its own right, with the rest of the area taking the title of the Manor of Longdon. Over the following centuries many of the members of the Manor became parishes in their own right (as we shall see below) and Lichfield itself shrank to the region of the what were to become the parishes of St Michael’s, St Mary’s and St Chad’s. Within this area there was no parochial system as such, with pastoral care being on the basis of the prebend. The three churches were staffed by the vicars of the five ancient prebends of Freeford, Handsacre, Longdon, Statfold and Weeford. A vicarage was created for St Mary’s with jurisdiction over the city centre in 1491 with the stipend paid from a number of prebends, with the five ancient prebends contributing the majority of the resource. The parishes of St Michael’s and St Chads came into existence in the seventeenth century, although they remained as perpetual curacies until the nineteenth.

Lichfield Parishes

The parishes in the wider area around Lichfield around 1840 are shown in figure 2, drawn with information from The Parish Atlas of England, by Tim Cockin.   The three Lichfield parishes can be seen to be of very different sizes, with St Michael’s parish extending a long way to the west at Burntwood, with a detached portion to the east at Fisherwick. St Chads, occupies the northern area of Lichfield, whilst the parish of St Mary and the extra-parochial areas of the Close and the Friary, are very small in comparison. Whilst much of the rest of the area shown in figure 2 is divided into parishes in the normal way, there are a number of extra-parochial areas, often representing areas of former or existing common land such as the Hays at Ogley, Alrewas and Kings Bromley.

Figure 2. Parishes in the Lichfield area around 1840

(1 – Kings Bromly Hay EP; 2- Croxall; 3- Ingale; 4- Thorpe Constantine; 5 – Statfold, 6- Hopwas Hay EP; 7- Freeford EP; 8 – St Mary’s, Lichfield; The Close EP; The Friary EP; 9 – Detached parts of Farewell)

The immediate area around Lichfield is shown at a somewhat larger scale in figure 3. The individual townships in St Michael’s and St Chad’s parishes are shown. It can be seen that the parish of Farewell and Chorley, to the west of St Chad’s parish has detached portions to the east.

Figure 3. Lichfield parishes and townships

The prebends mapped

Figure 4. Prebends in the Lichfield parishes

(Letters referred to in text; diagonal stripes indicate prebend to which tithe allocated; vertical stripes indicate region with name of prebend; red – Freeford; green – Weeford; blue – Statfold; yellow – Gaia Major)

The tithe maps give details of the tithes payable for each individual property that they list. Where appropriate they also give an indication of which prebend the tithe is allocated to. The information given varies somewhat in form from parish to parish, and thus we will consider each parish in the area around Lichfield below. We begin by considering the Lichfield parishes themselves in figure 4.

  • St Michael’s parish, St Michael’s township (A on figure). Here the prebendial split was at its most complex. Figure 4 shows only the regions that can be identified as part of Freeford prebend, which occur across the township, and probably indicates the major underlying land unit. The rest of the area was in the main occupied by land that was allocated to Freeford, Handsacre, Statfold and Weeford jointly, either as part of what is referred to as the Part Pound Tithing, or simply a two or more prebends being allocated tithes jointly. In addition each of these prebends were allocated the tithes from cluster of residential properties close to the city in the Greenhill and St John’s area. There was also a small area where tithes were allocated to the prebends of Bishopshull, Bishops Itchington, Prees and Pipa Minor, but in general the underlying prebend, seems to have been Freeford.
  • St Michael’s parish, Burntwood, Edial and Woodhouses, Wall and Pipe Hill townships (B, C, D). Almost uniformly the tithes in this area were allocated to Weeford prebend, again with allocations for small residential areas to the other prebends near the city. The large tract of land to the west is indicated on the tithe map as Burntwood Common and no prebend is indicated.
  • St Michael’s parish, Hammerwich township (E) Tithes in this are allocated to the “Appropriator” – the one to whom the rights to the tithes were sold at some point in the past. No prebends are given.
  • St Michael’s parish, Streethay township (F). Here the major allocation of tithes is to Statfold prebend (shown on the map), with some small allocations to Bishops Itchington, Curborough and Gaia Minor prebends.
  • St Michael’s parish, Fulfen township (G). As with Hammerwich, tithes are allocated to an Appropriator in this region.
  • St Chad’s parish, St Chad’s township (H). Here the situation is again complex. There are large allocations to Freeford and Weeford, together with a large allocation to the prebend of Gaia Major in the central area. There are also smaller allocations to the major prebends in the residential areas, and also small allocations to Bishopshull, Curborough,  Gaia Minor and Pipa Minor.
  • St Chad’s parish, Elmhurst township (I). The tithes of most of the land in this township are allocated to the Mark Part Tithing – jointly between Freeford, Weeford, Handacre, Statfold and Gaia Minor. There are some allocations to Bishopshull, Curborough, Gaia Minor, Handsacre and Pipa Minor prebends in the north.
  • Freeford extra parochial area (J). There is no tithe map available for this area, but it has been assumed on figure 4 that the entire area here was allocated to Freeford prebend, which does not seem unreasonable.

Figure 5. Prebends in the wider area around Lichfield

(Letters referred to in text; diagonal stripes indicate prebend to which tithe allocated; vertical stripes indicate region with name of prebend; red – Freeford; green – Weeford; blue – Statfold; yellow – Gaia Major; purple – Longdon; brown – Handsacre and Armitage)

Figure 5 shows a rather wider area around Lichfield indicating the situation in the surrounding parishes. The parishes of Longdon (A), Weeford (B) and Statfold (C) have tithes allocated to the vicar of the parish, or to an Appropriator, but are here marked as belonging to Longdon, Weeford or Statfold prebend. The outlying pat of St Michael’s parish at Fisherwick (D) has tithes with discrete areas allocated to Statfold and Freeford prebends. The parish of Aldridge and Hansacre (E) has tithes allocated exclusively to the prebend of Handsacre and Armitage, the successor of the ancient prebend of Handsacre. The tithes of the parish of Whittington (F) are allocated to the prebend of Whittington and Berkswell (the latter being in Stafford), which is a relatively modern prebend.  All the other parishes shown have tithes that are allocated to the vicar of the parish, or to an Appropriator. At this point it should be noted that there is a minor discrepancy between the tithe maps and material in the Parish Atlas for Farewell parish. On the tithe maps, the lower arm to the east of the parish is shown to be a detached part of Elmhurst township in St Chad’s parish, with its tithes allocated to Pipa Minor prebend, whilst in the latter it is shown as integrated into Farewell, as shown here.

Discussion

So what of the original premise of this post – can the ancient prebends be said to have well defined territories. I would suggest, on the basis of the maps of figures 4 and 5, the answer is a tentative yes. Let us consider each of the ancient prebends in turn.

  • The area where the tithes are allocated to Freeford, together with the eponymous hamlet, suggest that the original Freeford estate included most of St Michael’s township and part of St Chad’s and probably the city centre parish of St Mary as well. To the east it included Freeford, part of Whittington, the southern part of Fisherwick and perhaps extended to the river Tame through Tamhorn.
  • The territorial extent of Weeford prebend was very large, assuming that the later parish of Weeford was included within it. As well as the parish, it included the eastern part of Brownhills, Edial and Woodhouses township, Pipe Hill township and Wall township, as well as a small part of St Chad’s parish. It also possibly contained the Hammerwich area and the parish of Hints. Figures 4 and 5 suggest that part of Shenstone parish would probably have been included as well in order to make the eastern and western portions more of a coherent whole. If that were the case it would have been centred on Wall, the oldest settlement in the area at the junction of the Roman roads. In total it formed a wide arc around the southern and western edges of the city.
  • Statfold prebend extended from Streethay township in the west, through Whittington and the northern part of Fisherwick, and presumably to the parish of Statfold itself in the east. If it formed a coherent connected estate, it would have to have included parts of Elford and Clifton Campville parishes, for which there is no evidence.
  • The situation with respect to the two western prebends of Longdon and Handsacre is complex, probably because of the early formation of Longdon parish, and its role as the centre of the manor after the setting out of the town by Bishop Clinton. From figures 4 and 5 it can tentatively be suggested that it included Longdon parish itself, Farewell and Chorley parish, Elmhurst township and perhaps the area in St Chad’s parish allocated to Gaia Major. The latter could as easily be part of Weeford or Freeford prebends.
  • Handsacre prebend obviously included the later parish of Armitage and Handsacre in its entirety. If it ever extended closer to the city, it would have needed to include at least part of Kings Bromley parish and perhaps Elmhurst township too. There is no indication that this was ever the case. Geographically the parish boundaries suggest it may once have been associated with Longdon and perhaps represents and early division of the prebends in the Anglo Saxon era.

So what then might be the implications of this study? It points to an early Anglo-Saxon subdivision of the area around Lichfield into a small number of large divisions.  One of these, that later bore the name Weeford, was probably centred on Wall and was thus a territory associated with the Roman settlement of Letocetum.  Another, Freeford, seems to have embraced the location of the current city centre and extended eastwards a considerable direction. The -ford in Freeford has been taken to refer to the rather inconsequential ford over a brook close to the current Freeford House. If one accepts that Freeford originally encompassed the city centre, then the ford referred to might be the more substantial one that would have crossed the Leomansley Brook in the region of the current Minster pool.

A comparison of the prebend areas with the road system shown in figure 1 is of interest. Basically each of the prebends is connected with the centre of Lichfield via an ancient road – Freeford via the road that is now the Tamworth Rd, Weeford by the London Road and the Roman road network, Longdon by the Stafford Road and Hansacre by the road to Rugely. Statfold is connected by the road that enters the city via Darnford Lane and Boley Cottagee lane. If this extended all the way to Statfold, its route east of Whittington is however not clear. The prebends thus form a well-connected network with easy access to the central area.

I have argued elsewhere, based in the main on place name studies, that the Lichfield area was a centre of pre-Christian pagan worship, and that the ancient prebends played a significant role in this. The current work does nothing to counter such a proposal, and perhaps, by showing the extent of the prebends tends to confirm it.

The Staffordshire Tithe Maps

Screen shot from Staffordshire Past Track web site

Although it might sound rather odd to many, when I learnt that Staffordshire Records Office had put digitized versions of the county tithe maps on line, together with all the records to which they refer, I was immensely excited. No doubt this says something about my rather odd personality, but having this material easily available opens up a whole range of possibilities for research. In the blogs that may follow over the coming months I will thus present the results of my investigations of the tithe maps of Lichfield – considering land ownership and occupation, urban land use, the tithe recipients and the extent of the prebends (the old cathedral estates) in the city and the surrounding area.

But first in this post some words of introduction. The tithe maps are available at the Staffordshire Past Track web site and cover the whole of the county. The site briefly describes the maps as follows.

The tithe apportionment awards and maps held by the Archive Service stem from the Tithe Commutation Act of 1836, which replaced the payment of tithes as one tenth of agricultural produce (grain, hay, calves, lambs, etc.) with a rent charge apportioned between the landowners in the parish or township. Initially, owners of land and tithes could voluntarily agree a sum, but after October 1838, compulsory commutation began. Maps were drawn up and detailed schedules called ‘awards’, listing owners, occupiers and property details for each individual plot were created. Most processes were completed by 1845.About 70% of the land area of the county was subject to tithe at this time. Exceptions were where tithes had already been commuted or extinguished, for example as part of  an enclosure award. In some cases, tithe had never been paid – on former monastic land, or on land which was too poor in the medieval period to have been titheable, such as parts of the Staffordshire Moorlands.

In addition to the maps, the database contains the following information. – document reference; owner surname and forename(s); occupier surname and forename(s; )township and parish; plot name and plot number; land use; area (in acres, rods and perches); tithers payable; value(s) and notes.

I have concentrated particularly on the Lichfield area in my investigations so far. On the tithe maps Lichfield consisted of three parishes – St Mary’s in the city centre; St Chad’s to the north and east, and St Michael’s in the south and west. St Chad’s was further divided into two townships – St Chad’s itself closest to the city centre, and Elmhurst and Curborough to the north. St Michael’s parish was huge and consisted of the townships of St Michael’s itself, to the east and south of the city centre; the township of Burntwood, Edial, Woodhouses, Pipe Hill and Wall to the south west; the township of Hammerwich west of Burntwood; the township of Streethay to the north east and the detached township of Fisherwick to the east beyond Whittington. In addition there were a number of extra parochial areas – the Close, the Friary, Freeford and Fulfen. Tithe information is only available for the last of these.  The dates of the individual maps are given in the table below.

These dates are actually quite significant, as they cover the period when new parishes were being formed from the old.  Burntwood and Wall became separate parishes in 1845. Christchurch parish was formed from parts of St Michael’s and St Chad’s parish in 1848. The nature of Hammerwich parish at the time is not totally clear, as there was some dispute between its residents and St Michael’s, but it was functioning as a separate parish by the early 1840s. Thus the tithe maps largely represent the situation in the early 1840s in terms of designation of townships, and the classification used on the maps will be adopted in what follows.

My method of working has been to copy and paste all the individual records for the Lichfield area into several spreadsheets (an unbelievably tedious task) and then through some fairly simple programming to get all the records onto one line in the spreadsheet, with the items listed above in individual columns.  This then gives the possibility of ordering the records by different columns, searching for multiple entries and so on.

Whilst the information on the tithe maps can be used to paint a detailed picture of life in the Lichfield area in the 1840s, and I may well do so in later posts, in the next post I will use this information to see what the tither maps can tell us about a much deeper past – the nature of the early, pre-conquest prebendial estates of Lichfield Cathedral It will be seen that this throws a whole new light on the early geography of the area.

The Church of England and Covid19

I have been much exercised in recent days over the latest Church of England guidelines for living with Covid19, and in particular the wearing of masks by congregation and ministers, even during services of Holy Communion. My basic irritation lies in the fact that this goes beyond government guidelines for a range of venues that are comparable to churches – restaurants, bars, museum etc.. On the positive side it has been the source of some amusement in our household when considering how the new mask wearing advice matches with the requirements to sanitize or wash hands before and after removing masks, and the prescriptive way of removing masks without touching them or the face. In the context of receiving Holy Communion this probably required 3 or 4 hands per person. As far as I am aware most Anglicans have two at the most. Personally I am disappointed that no reference is made to removing with dignity a face mask elastic from an ear already occupied by glasses and a hearing aid.

But there are other, deeper issues. The first of these concerns the appreciation of risk. In my current context, in Lichfield in Staffordshire, the number of Covid19 positive cases in the last week given by Middle Super Output Area (MSOA) in England  is less than 3, and as 2 by Coronavirus (Covid-19) in the UK. If we take a figure of 5 to allow for asymptomatic cases, and given a population of 100,000 for Lichfield district, this gives a probability of any one person having the virus of 5 x 10-5. Now let us suppose that the chance of meeting any one person in Lichfield on any one day during normal activities is (say) 1 in a 100 (which is probably a bit on the high side), this gives the probability of meeting someone with the virus of 5 x 10-7. Now suppose that one of those 5 infected folk attend a church service, if any one congregation member spends at least 15 minutes in the presence of each of the others, even without social distancing the risk of being infected is thus around 5 x 10-5. With 2m social distancing and recommended sanitization / washing hands etc. this figure falls by a factor of 100 to 5 x 10-7 again. To give this some context, around 100 people are killed or seriously injured in the UK on any one day. Given a population of 70 million, this gives a daily probability of being killed or seriously injured in a road accident of 1.4 x 10-6. Now whilst these approximations are very crude, it seems that, in the current context in Lichfield, including church services, the probability of catching Covid19 on any one day is probably no worse than the probability of being killed or seriously injured in a road accident.

Now I am not arguing for any relaxation of current procedures imposed by the government. These have necessarily to be rather broad brush and simple to understand. Also, whilst many areas of the country are in a similar position to Lichfield, there are places with much higher rates of infection, so the current procedures are in my view sensible and should be followed. But for the church to go beyond these procedures seems wholly unnecessary. To be consistent in terms of an appreciation of the risk, the church should be advising all its members to give up driving completely. I don’t see that happening any time soon.

Within the risk analysis community there is a basic assumption in the UK that we should aim at risks that are ALARP – as low as reasonably possible, where “reasonably” is understood to be such that the basic function of the procedure that is being analysed can be achieved. In some large organisations (and I am thinking here specifically of Network Rail with whom I have had numerous arguments) the approach by individuals within the organization to setting risk levels is better described as CMOA (Covering my own ___). I will let the reader complete the phrase. I fear I see the same approach in those involved in setting the Church of England guidelines, with no indication that the true nature of the risk in many parts of the country is appreciated. In the recent communications, the recommendations have gone beyond “reasonable” and threaten to undermine the purpose and integrity of the activity – in this case the giving and receiving of Holy Communion.

This brings me to some further considerations on the nature of the Communion service itself. Before making these arguments, it must be emphasized that I am no theologian, as I guess is only too apparent from what I have written already. So when I enter into discussions of eucharistic theology, it is very much as a non-expert.

As things stand, only the presiding minister takes both bread and wine, with the laity restricted to the bread. The rationale for this is that sharing a cup of wine might be a source of infection risk, which I can appreciate, although I do not find at all satisfactory that laity should be denied the cup. A way around this would be to put the wine into individual cups, as do many other churches. The Church of England has set its face against this, on the basis that sharing should be of “one bread and one cup”. This has been severely criticized by, for example, Andrew Goddard. The only comment I would make, based on some perceptive observations by my wife, is that, in Anglican circles we most certainly do not have “one bread” in a physical sense – with the people’s wafers coming from one production batch and the priest’s wafers from another (and any gluten free wafers from a third). I would contend that the oneness of the bread and cup comes from their consecration within a eucharistic community, rather than in any physical sense. Communion in both kinds could be offered, with no additional risk, by the simple use of individual cups, if such an approach were to be taken.

The same reasoning can be applied to what might be termed ”virtual communion”, the practice of allowing the consecration of bread and wine in people’s homes via a priest’s consecration over an internet platform. Again, the Church or England has set its face against this, based on a rather narrow concept of what is required for consecration – the physical proximity of a priest. There is a danger here of at least underestimating the role of an omnipresent God rather than the priest in the consecration. Whilst I would be reluctant to engage in such practices for a completely random audience, it seems for me that if a congregation who have formed the bonds of fellowship between them over the years, come together virtually around their tablets and laptops, then the consecration of the bread and wine would take place within the body of Christ, the gathered Eucharistic community. I can see no objection to this. But then, I am not a theologian. All I can say is that it would certainly eliminate the risk of Covid19 infection.

Kingswinford parish – associations with slavery

In a recent post, I contributed to the debate on to what extent the early railways in Great Britain and Ireland were capitalized by slave-compensation funds to former slave owners. In doing so I used data from the UCL website Legacies of British Slavery. As I write, that debate rumbles on, but in this post I move away from it somewhat, to use the UCL to determine the impact of slavery on the industries in the area and period in which I am most interested – the western Black Country parish of Kingswinford in the 19thcentury.  The discussion will thus be somewhat wider than the railway industry and will also embrace the iron and mining sectors. It will be seen that the evidence for the impact of slavery finance in this area is more than a little ambiguous, but the UCL does nonetheless add to the general body of knowledge of industrial developments in the region, and the relationships between individuals.

There are three potential links with slavery within the parish of Kingswinford in the 18thand  19thcentury – through the Corbyn family, formerly of Corbyn’s Hall; through the Lords of the Manor – the Barons Dudley and Ward; and through the Gibbons family. The former can be quickly dealt with. The last Corbyn in the parish was Thomas, who died in 1688. His heir, Margaret, married William Lygon, and moved to Madresfield in Worcestershire, and Corbyn’s Hall was sold to John Hodgetts – see Kingswinford Manor and Parish (KMAP), Chapter 3. The last generation of the Corbyn’s, other than Thomas, all seemed to have worked in various trades in London. His brother Henry (1629-1675) eventually moved to Virginia. Correspondence between Thomas and Henry reveals that the latter had become at least a part owner of one or more slave plantations – presumably either cotton or tobacco. The Corbyn’s seem to have prospered in North America and the story of their involvement with slave worked plantations could no doubt be told given sufficient research. But that is an American story of no direct relevance to Kingswinford in the Black Country in Britain, and will not be taken further here.

Figure 1 The Dudley Tree

Now let us consider the Lords of the Manor – the Baron’s Dudley and Ward. Their descent is quite complicated, but the relevant parts are shown in figure 1 (from KMAP Chapter 3). The involvement of this family with slavery came through the marriage of John Ward, 6thBaron Ward, 1stViscount Dudley and Ward (1704-1774) to Mary Carver (-1782), who had inherited three plantations in Jamaica from her father John.  She left these to her son William Ward (1750-1823) and then in trust for her grandson John Ward (1781-1833), 4thViscount Dudley and Ward, and from 1823, the 1st Earl of Dudley and Viscount Ednam. He was an MP for various constituencies from 1802 to 1823, before being made and Earl, and as a member of the House of Lords was Foreign Secretary from 1827 to 1828. He spoke against slavery, although advocating reformation rather than abolition of the system.  Nonetheless at his death he was still in possession of the three Jamaican estates. He was succeeded as Baron Ward by his cousin, Rev. William Ward (1781-1835), although his estates were held in trust for William’s son, another William. The trustees were John Benbow, a solicitor who sat as MP for Dudley from 1844 to 1855; Francis Downing, Lord Dudley’s Agent and mayor of Dudley from 1818 to 1819, Edward Littleton, Baron Hatherton and Lord Lieutenant of Staffordshire; and Henry Phillpotts, the Bishop of Exeter, one of the more flamboyant 19thcentury bishops. It was these trustees who made a claim for compensation for the three estates of Whitney (284 slaves); Rymesbury (320 slaves) and New Yarmouth (70 slaves), and whose names thus appear in the records, although they were never slave owners themselves.  They were allocated £12,728 in total. To put this in context, the income of the Dudley Estates in Staffordshire and Worcestershire was around £120,000 per year at the time, and John Ward left £350,000 in his will. The slavery-compensation was thus only a rather small part of the latter William’s overall inheritance. 

When I learned about this involvement of the Dudley’s with slavery I was in the first instance somewhat surprised. Whilst not being an expert on the Dudley’s by any means, I have read quite widely about them, and not seen any reference to this involvement. This may be that historians did not think this remarkable enough to discuss, or perhaps because of a slight embarrassment.  Certainly the Bishop of Exeter must have so felt when he realized he was responsible for slave owning plantations as a trustee. Alternatively it may be that the Dudley Estate itself thought little of it, other than as a profitable line item in their accounts. Either way it is perhaps somewhat shocking.

Figure 2. The Gibbons Tree

The other possible route of money earned through slavery into the Kingswinford area was through the Gibbons family. The family tree is complicated and is summarized in figure 2, again from KMAP. The Gibbons family were from the Ettingshall / Sedgley area and can be traced back to the 16th century. From Grace’s Guide

After the death of John Gibbons (1703-1778), responsibilities for the business he had built up in iron and coal were divided between his three sons – one son, William (1732-1807), ran the family’s merchant house at Bristol, buying pig iron for the midland forges and overseeing the export of metalwares to the American market. Another of John’s sons, Benjamin (1735-1832) , was entrusted with management of the iron business around Kingswinford. The eldest son, Thomas (1730-1813), took charge of the merchant house at Wolverhampton which was subsequently developed as a bank. 

They continued to work together however and in 1784 took out a lease of land, mines and furnaces  at the Level in Brierley Hill.  The partnership between the brothers was split up in the late eighteenth century. The Bristol house was signed over to William’s only son, William (1782–1848).  It was this latter William who appears in the UCL data as a Bristol merchant and ironmonger, the partner of Benjamin Bickley.  The partners in this firm were William Gibbons, Benjamin Bickley, John Latty Bickley (Benjamin’s son) and Michael Willcox. Bickley counterclaimed on an award in Trinidad for Paradise & Cane Farm plantations in the name of the firm and was awarded £8304. ‘Wm Gibbons’ appears under a second award as an unsuccessful counterclaimant for the Lodge estate on Trinidas, but it is possible that this is the firm not the man.  In both cases Bickley was acting as an Executor on behalf of a deceased person’s estate.

In 1814 Benjamin  (1735-1832) made over the Level furnaces and other industrial plant to his nephews – John (1777-1851), Benjamin (1783-1873) and Thomas (1787-1829) in return for an annuity and ownership of the Corbyn’s Hall  Estate. The three younger Gibbons brothers were declared bankrupt as bankers in 1816, in the slump following the Napoleonic Wars, pulling the iron business down with them. Fortunately the elder Benjamin, as a preferential creditor, was able to take control of some of the iron and coal interests and save the family firm from total ruin. The younger Gibbons brothers continued to develop the Corbyn’s Hall Collieries and Blast Furnaces, which were built by them about 1824. The activities around Corbyn’s Hall went through a number of different iterations over the next 100 years, being leased to a variety of industrialists, but with the Gibbons retaining some sort of interest. Benjamin Gibbons (1815-1863) and Benjamin  Gibbons(1852-) also developed fire clay works and coal mines close by at Dibdale. These works and their successors lasted into recent times. 

The relationship between the Gibbons and the Bickley families continued to the next generation.  In 1838 John Latty Bickley was living at Ettingshall Lodge in Sedgley (the old home of the Gibbons) and was engaged in land transfer deals with the Gibbons brothers John (1777-1851) and Benjamin (1783-1873) and mortgages of land around the Corbyn’s Hall estate.

The question then arises as to the nature of the Gibbons involvement with slave-owning individuals and businesses and whether or not there was significant flow of resource into their activities as a result. The only certainty is that William Gibbons and his partner acted as an Executor for some slave-owners in winning compensation for their estates, perhaps acting as a business rather than individuals. One might speculate that as a merchant trading in Bristol, even in the iron trading sector that wasn’t directly involved with slave-owning, some association would have been inevitable, but again that is supposition. And if there had been any profits from such associations that fed back into the Midlands iron and coal business, it is doubtful whether any traces of these would have survived the 1825 bankruptcy.

To conclude, it would seem to me that the extent of the involvement of industry in Kingswinford parish with slave-owning individuals and organisations was small, and probably had no lasting legacy in industrial terms. The Dudley estate certainly owned plantations in Trinidad together with their slave population, but one senses that this was almost by an accident of marriage rather than by design. Nonetheless this ownership was accepted and the estate no doubt profited from in a manner that was acceptable at the time, but would not be so regarded now. The Gibbons family also had minor associations with slave-owners through their Bristol firm, which illustrates just how difficult it would have been for any organization with activities there to avoid such associations. Thus the interactions of industries around Kingswinford with slavery were small. They are nonetheless worth recording and remembering as part of the history of the area. 

The legacy of slavery on the railways

Birmingham Curzon St 1840

In recent weeks an extraordinary Twitter argument has broken out concerning how much the railway system in the UK and Ireland owes to the capital provided by the slave trade. On the one hand we have Gareth Dennis (@GarethDennis), the author of what will be referred to in what follows as the “Thread”, who argued “that a significant proportion of slave-owner compensation was reinvested into the railways; that Britain’s railways are a direct legacy of slavery and colonialism; and that this legacy is hopelessly under-explored”. On the other hand there was a strong argument from Christian Wolmar (@christianwolmar) that the Thread’s arguments were overstated and not properly evidenced. He has repeated this in a recent edition of RAILmagazine. This post is concerned with trying to establish how much slave owner compensation might have been used for capital investment in the early railway network in the Great Britain and Ireland.

The Thread uses the quite outstanding UCL web site “Legacies of British Slave-ownership” which attempts to chart where the legacies of slave ownership, and in particular the compensation paid to slave-owners following theSlave Compensation Actof 1837, was used in commercial and social ventures.  The Thread takes the data from this web site for those who had both been compensated, and who also invested in the early railway companies, and a simple addition of the sum invested by these individuals in railway companies in Great Britain and Ireland comes to £5,261,768 (a little less than in the Thread, no doubt due to a minor omission somewhere that I can’t locate, but this is of no consequence to what follows). The implication in the Thread is that this sum comes directly from slave compensation and it is argued that this forms a significant proportion of the railway capital in the early years – for example the cumulative capital by 1840 was £30 million, and thus the total invested by the slave owners was around 1/6thof the total.  

However, all is not as simple as it looks. Firstly, an inspection of the UCL web entries indicates that a few of the identifications of slave owners with railway investors are not totally firm and that there is some doubt about them. Nonetheless these are unlikely to affect the above figure significantly, perhaps reducing it by a few tens of thousands pounds and no correction will be made. Secondly the web site lists a few payments to trustees, usually of minors. It is a moot point as to whether the future railway investment of these trustees in their own right should be included in the sum. Again, this is not a significant issue and no corrections have been made for it. 

A much bigger issue however is that, as I read it, the UCL web site shows the total investment of individuals in the railways, and that is what the figure of £5,261,768 actually refers to. Many of the slave-owners received far less in compensation than they actually invested in the railways – these figures are given on the pages for individuals in the list. So that figure for capital investment, which the Thread uses as the basis for its arguments, is a very significant overestimate of they investments that were made from slave compensation. For example, consider the three individuals who feature in the Thread. The first, John Moss invested £222,470 in railway concerns, but only received £40,353 in slave compensation; Robert Browne invested £577,260 but only received £797 in compensation; and Thomas Dunlop Douglas invested £396,100 having received £15,907 in compensation. One Robert Pulsford is included in the database as investing £291,000 in railways concerns. However his inclusion is as a result of five unsuccessful claims for compensation and he actually received no compensation at all. Similar discrepancies between total investment and compensation sums can be identified for nearly all the major investors, although the amounts invested for the smaller investors were often very similar to the amount of compensation they received. So the figure of £5,261,768 money that found its way into the railways cannot all be from compensation payments. In fact if one limits the amount of investment for each investor to the amount they received in compensation, the figure falls to £1,134,031 i.e. 21.6% of the original figure.  

But even this is without doubt an overestimate, as not all the compensation money would have been invested in the railways. It might be more realistic to say that the proportion of invested compensation should be the same as the proportion of the total investment to the overall wealth of the investor. The UCL site allows an estimate to be made of this for a subset of those named by giving their recorded wealth at death. The median of the ratio of investment to total wealth at death comes to 10% (excluding those individuals who went bankrupt or suffered major financial distress at the end of their lives). I am of course very well aware that this methodology is more than a little suspect! On this basis however the amount of slave-compensation money that was invested in the railways falls to around £110,000.

On the basis of these figures, the actual amount of compensation that became railway capital was between £0.1 million and 1 million. Whether of not this is significant in terms of the overall capital investment (£30 million by 1840) I will let the reader decide.  But it is best to use as accurate a figure as possible in coming to a view.

The Thread has done the community a service by raising the issue of slave-compensation investment on the railways, which should not be ignored, although it needs to be carefully looked at to investigate whether it was significant in comparison to other investment. In future posts, I intend to look at this issue further – both in relation to those who received large compensation sums and made large investments in the railways (not necessarily those mentioned in the Thread); but also in relation to that area of the Black Country about which I have posted regularly – the parish of Kingswinford – where traces of slave-owner investment can indeed be found if one looks carefully. 

Some musings on tornado vortex models

From Wikipedia

Recently I have been considering the fundamental nature of a range of analytical models of tornado like vortices, and have written up my musings as an extended essay that can be downloaded at “Some musings on tornado vortex models”. In the essay I look at the class of tornado models that are solutions of the Navier-Stokes or Euler equations. It is clear that they all share a common analytical basis based on the assumption, either implicit or explicit, that the three velocity components (radial, vertical and circumferential) can each be specified by the multiple of two functions – one a function of radius only, and one a function of height only. Assumptions are made concerning the nature of one particular velocity component, and this assumption then allows the other components to be calculated from the continuity and momentum equations via the method of separating the variables. The recognition of this commonality allows a common analytical formulation to be developed that underlies all the models.

Those models that are solutions of the full Navier-Stokes equations (the Burgers-Rott, Sullivan and Vasistas et al models) derive velocity component formulae that are functions of Reynolds number. In the context of a full-scale tornado, this is a Reynolds number based on turbulence eddy viscosity rather than molecular viscosity. The assumptions required to obtain analytical solutions result in vertical velocities that are unbound with height and in some cases radial velocities that are unbound with distance from the vortex centre.  

Those models that are solutions of the Euler equations (two by Baker and Sterling  and two new models A and B) have, on the whole, rather more realistic formulations of the velocity components and, with one exception, all components for these models are bound in the vertical and radial directions. Instead of the Reynolds number, the velocity components are functions of constants of integration that relate to the Swirl ratio – the ratio of the maximum circumferential to radial velocities. As the circumferential velocity profiles in these models fall to zero at ground level in a reasonably realistic way, the boundary layer at the bottom of the tornado is modeled to some extent. The common analytical framework of these models allows, in principle, the derivation of a large number of different models, provided that they are of a form that allows the solutions to be obtained through simple integrations.  However the drawback of such models is that the pressure is zero at the ground for all distances from the vortex core and thus the dip in pressure at the centre of tornadoes is not modeled. This is broadly a consequence of viscous effects not being properly modeled near the ground. 

Whilst most of the models represent single cell tornado vortices, two of them – those of Sullivan and new model B – give solutions for two cell vortices. The essay shows that the Sullivan model, based on the Navier-Stokes equations, has a more general form than that given in the original paper and can model one-cell and two-cell vortices and the transition between them. New model B, based on the Euler equations is also able to model both sorts of vortex.  

The essay concludes that further work is required in two areas. Firstly there is a need to develop methods that do not rely on the assumption that the velocity components are multiples of two functions – one of radius and one of height – as recent experimental data suggests that the vortex radius can vary significantly with height. Secondly, the tornado boundary layer needs to be modeled in a more satisfactory way than at present, and the essay suggest that this might be done through matching a viscous solution of the Navier-Stokes equation near the ground, with an inviscid solution from the Euler solution away from the ground.  I may have more to say on this in the future.

The Seisdon anomaly

In coming to a the definition of the Original Mercia outlined in “The first Mercian Lands”, I included Seisdon Hundred in south Staffordshire within its bounds (figure 1). The reason for doing so was primarily because this area became part of the Mercian Diocese of Lichfield. However there is some rather disparate evidence that at least part of Seisdon hundred was Hwiccan territory at some stage before the formation of the diocese. 

  • Topographically, the area is in the catchment of the Smestow and Stour and thus of the Severn itself, as is the case for the other Hwiccan territories. Other parts of Staffordshire are in the Trent catchment.
  • There are Domesday linkages between the manors of Tardebigge and Clent in Worcestershire and Kingswinford in Staffordshire – and indeed Clent was for many centuries post-Domesday an island of Staffordshire within Worcestershire.  
  • The manors of Kingswinford and Amblecote (in Staffordshire) and Oldswinford (in Worcestershire) were almost certainly once part of the same land unit. 
  • The ecclesiastical parish of Oldswinford was split between the manors of Oldswinford in Worcestershire and Amblecote in Staffordshire.
  • The large Worcestershire enclave of Dudley has been surrounded by Staffordshire since the Domesday survey.
  • The name of the Hundred itself is taken from the village name of Seisdon, which can plausibly be translated as the Hill of the Saxons. This ties in with the now rather dated assumption that the Hwicce represent the northward advance of Saxons up the Severn valley.

Thus a case can be made that the area of Seisdon Hundred was originally Hwiccan territory that was absorbed into the Original Mercia. The reason for this is clear from the map of figure 1 – strategically it is a very important area. The Roman road system centred on Greensforge controls access along the Saltway from Droitwich to the north, access to Shropshire, the borders and Wales, and gives a direct link to Quatford on the Severn, allowing control of river traffic. Three potential roads are shown on the map that are not shown on the larger scale map of figure 8 in the main text – those from Greensforge north east to Wall, from Water Eaton to Metchley and from Metchley to Greensforge. The routes of the first two can be traced in places on the ground (Horovitz, 2005; Bassett, 2001), but the lines shown on the map are purely conjectural. It is however likely that the two routes crossed at Wednesbury. The route between Metchley and Greensforge (Baker, 2013) begins with the Metchley to Water Eaton route but branches from it through the village known as the Portway near Oldbury and then passing though, or to the south of Dudely, to Kingswinford and Greensforge.  Taken together this road network clearly adds to the connectivity of the region and emphasises its strategic importance. 

Figure 1 – Seisdon Hundred

(Red shows boundary of the hundred  – a solid line where it coincides with the county boundary, and a dotted line otherwise; grey shows other county and hundred boundaries; brown shows the pre-1974 county boundary, reflecting the early post-Domesday losses to Shropshire; roads are shown (schematically) in green and rivers in blue).

D Horovitz (2005) “Place names of Staffordshire”, published by D Horovitz, Brewood

S Bassett (2001) “Birmingham Before the Bull Ring”, Midland History, 26, 1, 1-33,

C J Baker (2013)  “Pensnett – its name and origins” Staffordshire History Journal

More on the Tribal Hidage

Table 1 The three recensions of the Tribal Hidage

On the page “The first Mercian Lands”, 1 have drawn on information in the document known as the Tribal Hidage, as part of the investigation into the location of the original Mercian lands. In this short note, I consider this document in a little more detail. Table 1 above gives a summary of the three separate recensions of the Tribal Hidage. The description of the polities from Recension A is given, together with the location where there is general scholarly agreement. As noted in the main text, there are two combined lists – Primary (P) and Secondary (S). The Hidages from the three recensions are then also given. It can be seen that these vary somewhat. The sum of the hidages in all three recensions is given for both lists A and B. In Recension A, a false total is given for the total hidage of 242,700. 

Figure 1. Tribal Hidage. “Firm” locations of regions in the primary and secondary lists  (figure 3 in main text)

(P1- Myrcna lands; P2 – Wocensætna; P4- Pecsætna: P5 – Elmedsætna: P6 – Lindesfarona mid Hæþfeldlande: P7 – Suþgyrwa: P8 – Norþgyrwa: P11 – Spalda; P13 – Herefinna : P14 – Sweordora P15 – Gifla : P16- Hicca: P18- Noxgaga: P19 – Ohtgaga; S1 – Hwinca; S2 – Cilternsætna; S6 – Færpinga; S9 – Eastwilla; S10 – Westwilla; S11 – Eastengle; S12 – Eastsexena; S13 – Cantwarena; S14 – Suþsexena; S15 – Westsexena)

It was noted on “The first Mercian Lands” that the clockwise ordering of the primary and secondary lists seems to be a very deliberate tactic on behalf of the original compiler of the list – see figure 1 above. At the risk of pushing this schema too far, it is worth asking the question if the location of the polities whose locations are not known can be inferred by imposing this clockwise presentation scheme. Thus let us consider those polities in table 1 where no location is given.

  • Westerna (P3). Scholars usually identify this as one of the Magonsaete in south Shropshire / Herefordshire, somewhere in Wales, or the region around Chesire. Higham would see it as representing the tribute payment of the Welsh Overkingship from somewhere in Gwynedd. It does not seem to the author that the Magonsate is a possibility as this kingdom seems to have been established late in the 7thcentury i.e. after the Tribal Hidage was compiled. The clockwise rotation would best place this polity in Wales or the Cheshire region. My preference would be to see it as the Western half of the Civitas of the Cornovii that was ultimately to become the kingdom of Powys, which fits best with both the name and the clockwise rotation.
  • East and West Wixna (P9 and P10). Within the Fenland there seems to be a subsiduary clockwise rotation, at least based on those polities identified by Oosthuizen.  If this is the case then the East and West Wixna would lie somewhere on the Fenland margin between the Gwyre and the Spalda. This is not however consistent Oosthuizen’s analysis.
  • Wigesta (P12). The clockwise rotation within the fens would place this to the south and west of the Spalda.
  • Wiht gara (P17). This is taken by most scholars to be the Isle of Wight. The present author finds this very difficult to believe, as it lies within the primary list, but is separated from all the other polities in that list by those in the secondary list.  In the author’s view this probably represents a typographical error, with the original name being confused for the (more familiar) name for the Isle of Wight. The clockwise rotation would see this region in the Bedfordshire area. 
  • Noxgaga (P18) and Ohtgaga (P19).It has already been argued on “The first Mercain Lnds”, that the clockwise rotation places these two sizeable entities in the Northanptonshire /Leicestershire area.
  • Hendrica (S3).The Ciltern sætna and Hendrica together have an assessment of 7000 or 7500, suggesting they are subdivisions of one unit. If so this would obviously place the Hendrica in the Chilterns area, which is consistent with the clockwise rotation of the secondary list.
  • Unecunga-ga (S4).This name is clearly corrupt and no convincing location seems to have been proposed.  Again, the clockwise rotation would suggest that it be placed somewhere in the Oxfordshire area.
  • Arosætna (S5). Conventionally, this polity is identified as being in the valley of the River Arrow in Worcestershire and Warwickshire. However there is no indication elsewhere that this area was ever anything other than part of the Hwicce, and I find it difficult to accept this identification. The clockwise rotation would again suggest that this be placed somewhere in the Oxfordshire region.
  • Bilmiga (S7) and Widerigga (S8). Various locations have been suggested for these entities, including the area of Lincolnshire to the west of the Wash, and regions in Eastern Northamptonshire. Both these suggestions however cut across the boundary between primary and secondary lists i.e. between the Midlands and Southern Overkingships. The clockwise rotation would see them best placed in the south Midlands area perhaps in Buckinghamshire or Hertfordshire. 

It has been noted above that the hidage values are generally expressed in terms of a duodecimal system for the smaller polities, and in units of 7000 for the middle sized polities. The larger kingdoms seem to have punitive assessments of 30,000 or 100,000. One must approach these numbers with a very great deal of caution and be very wary of giving them too great a significance. In an early study of the Tribal Hidage,Russell (1947)give an interpretation of the significance of the numbers in a tour de force of somewhat dubious arithmetic and remarkable assumptions of copyists errors to show hidden additions and totals throughout the list. What he actually demonstrates is the remarkable flexibility of the duodecimal system to provide all sorts of totals and subtotals from any subset of numbers. However there are perhaps two numbers that do have some significance – the figure of close to 36000 of the primary list of the Tribal Hidage (excluding the original Mercia), and the approximate 144,000 total of the primary and secondary lists excluding Wessex. Both these numbers have rich biblical symbolic meanings, which would have been well appreciated by later copyists, and in particular latter might be thought to emphasize the totality of the tribute being paid by the Midlands and Southern overkingships. These numbers are not of course exact, but there is perhaps some indication that those who later edited the lists attempted to make the additions more precise.  For example Recension C removes a 100 hides from the 900 for the Wigesta, which would reduce the overall total for the primary list (excluding the original Mercia) to 36,000 – although he also removes 600 from the Pecsaete and 598 (!) from the Herefina, which destroys this calculation. A similar change of 100 hides would also bring the overall total for the two lists to 144,000 (excluding Wessex), although this is again obscured by other minor changes (which are possibly copyists errors). It is not argued here that the numbers in the list should be seen as having any particular significance – but rather that later editors and compilers thought that this might be the case and tried to make them fit to what they believed were appropriate numbers. 

Climate and plague

At the page “The first Mercian Lands” I have argued that a plausible historical context for the establishment of Mercia was the northward expansion of Wessex during the third quartile of the sixth century. This followed, if the general thrust of the various annals and chronicles is taken as reliable for this period, a period of relatively calm between the various ethnic groups in southern England – the peace following the Battle of Mons Badonicus as recorded by Gildas (Higham, 1994). The question then arises as to what caused this renewed military activity on behalf of Wessex. It seems clear to the author that the primary reason for this was the climate upheavals of the 530s and 540s and the associated first pandemic of plague that swept across Europe, which resulted in depopulation and political destabilization. This effect is well documented, and probably resulted from multiple volcanic eruptions with or without some sort of impact event around that time (Degroot, 2016; Newfield, 2016). Yet this effect hardly seems to be considered at all by the academic historical community. The author can see no reason for this, other than a perhaps understandable reluctance to become involved in any way with the more speculative theories outlined in a number of popular works. Yet it seems that the objectivity of these events have a number of implications for academic historians.

  • Gildas’s magnum opus De Excidio Britanniaemust have been written before the first climatic catastrophe, which occurred in 535AD according to reliable tree ring evidence. Otherwise he would surely have included it within his polemic against the moral failure of the rulers of his day. 
  • The fact that this polemic was in some way validated by major external events (either through coincidence or divine action depending on your point of view), may well have been a major reason why Gildas and De Excidio Britanniaewas held in such high authority by his contempories and subsequent writers.
  • The plague hit a weakened Roman population in 542 AD, and would have spread throughout Europe over the next two or three years, judging by the speed of progress of the second pandemic (the Black Death) that has a well established chronology. The Historia Brittonum, regarded by most historians as unreliable for this period, gives the death date, by plague of Maglocunus, one of the rulers castigated by Gildas, as 547AD. This is perhaps three or four years too late, but does (perhaps uncomfortably for some) give an external validation to the Historia Brittonum.
  • The Annales Cambriaegives the death date of Gildas as 570AD, which, on the basis of the above, may be a few years too late. Now Gildas writes that he was born in the year of Mons Badonicus and was 44 years old at the time. Thus supposing he wrote De Excidio Britanniaein 534AD, this gives a date for his birth and the battle of 490AD, which is roughly where many historians would locate it, and would give him an age of, something less than 80 at his death, which does not seem impossible.

Thus, at the very least, a consideration of the effects of the global events of the 530s has the potential to cast some light on the chronology of the mid / late seventh century, and to give a little more confidence in the various annals and chronicles from that period.

N Higham (1994) “The English Conquest – Gildas and Britain in the firth century”, Manchester University Press

D Degroot (2016) “Volcanoes, Comet Crashes, and Changes in the Sun: How Sixth-Century Cooling Transformed the World”, 

T Newfield (2016) “The Global Cooling Event of the Sixth Century. Mystery No Longer?”