THE BOX TUNNEL PUZZLE – SOLVED?

Geoff Kirby

21^st April 2022

Summary

The Box Tunnel in Wiltshire was built under the authority of Isambard Kingdom Brunel for the Great Western Railway and opened in 1841.

A story has been persistent for many decades that Brunel designed the tunnel so that the rising Sun would shine down its entire length on his birthday  April 9^th. The validity of this notion has been tested visually and theoretically several times with ambiguous results.

This article uses modern astronomical and mapping software to show that unimpeded sunlight could only pass all the way down the tunnel on the mornings of 6^th, 7^th or 8^th April in the 1840s and on the mornings of 5^th, 6^th and 7^th April in the 2020s.

Photographic evidence by Roger Morgan shows the centreline of the Box Tunnel intercepting green vegetation presumably growing on top of or in the railway cutting so that no part of the sky is visible through the tunnel from the western portal. The writer independently has also come to the same conclusion by analysing a photograph published in 2017 by Great Western Railway engineers.

Recent photographs, some taken in April 2022, show  convincingly that the blockage to the line of sight down the tunnel is by trees rather than the cutting wall or vegetation in the cutting. Thus, the rising Sun may be visible all the way down the tunnel on April 5th, 6th or 7th - but not on Brunel’s birthday - depending on the state of the vegetation, specifically the density of leaves on the trees.

PART 1

Introduction

The Box Tunnel is located about 11 kms (7 miles) east of Bath on the main line between London and Bristol. It is nearly 3 kms (1.8 miles) long and rises in a dead straight line from west to east on a gradient of 1 in 100.

It took seven years to construct and was an enormous challenge to Brunel and his contractors. As work fell behind schedule the number of workmen rose to over 4,000 of whom about one hundred died. The work was carried out by candlelight. One tonne of candles were used each week, 189,000 cubic metres of spoil was removed through vertical shafts to ground level and 30 million bricks were laid.

There is a fascinating account of the building of the tunnel on Facebook ¹

The tunnel was dug out in sections from each end. When they met, the alignment was within 50 mm (2 inches) - an amazing feat of surveying in those days!

Brunel’s contemporary engineers considered the Box Tunnel scheme to be “reckless” which explains the existence in Victorian times of the pub named “The Reckless Engineer” by Temple Meads station in Bristol.

The Western Portal.

The Eastern Portal.

In the above photograph the western portal is the minute spot of light centrally in the tunnel. The apparent size is that of a pea held 2.5 metres (8 feet) from the eye.

The reason that the western portal is so much more elaborate than the eastern portal is that the former can easily be seen from the main London to Bath Road whereas the eastern portal is hidden in a cutting.

The above picture shows the eastern cutting being dug. The tramway bridge passing over the mainline cutting can be seen in the background.

Isambard Kingdom Brunel opened the Box Tunnel in 1841 and the following report appeared in the Devizes & Wiltshire Gazette dated 14^th April 1842

“On Saturday last (9^th April) the Box Tunnel presented a most splendid though singular appearance, caused by the shining of the Sun directly through it, and giving the walls a brilliancy, to use the expression of an eyewitness, as though the whole tunnel had been gilt.”

Various other accounts of the tunnel being flooded by the light of the rising Sun on or around April 9^th appeared. As examples

“The Box Tunnel on the Great Western Railway was an object of some interest on Tuesday last (9^th April), as on that day, at 25 minutes past five, the sun shone through it.  The only other periods that such an event occurs on are the 3rd and 4th of September”

Illustrated London News 1850

“It is remarkable that annually on the morning of April 9th the sun’s rays penetrate through the great Box Tunnel of the Great Western Railway, and on no other day of the year”

Daily Telegraph 1859

There have been several other published sightings of the tunnel being “filled with a golden light” around April 9th each year but it doesn’t seem to have been noted until the 20th century that this date is Brunel’s birthday.

Physical sightings by people brave enough to clamber down onto the tracks at dawn appear to be in favour that the Sun does indeed shine all the way down the tunnel on or around Brunel’s birthday.

Strangely, D. H. Stuart reported that he had made observations of the Sun shining down the tunnel on April 16^th 1965, April 17^th 1967, April 17^th 1971, and April 15^th 1972. ²

However, these sightings must have been confused by the glinting of sunlight off the walls of the tunnel at very low grazing angles; typically less than one degree. Even if the Sun is about one degree off the tunnel’s axis, the illumination will scatter a considerable way down the tunnel such that observers cannot tell whether they are seeing part of the Sun’s surface or a dazzling reflection off the walls close to the eastern portal.

The apparent size of the eastern portal seen from the western portal is only about one-eighth of a degree which is scarcely resolvable by a dazzled eye in an otherwise pitch-black tunnel.

The Guardian newspaper has a photograph of the Sun taken in 2017, during a closure of the tunnel for engineering works, allegedly shining into the tunnel but this photograph was clearly taken close to the end of the tunnel.

The article goes on to state that there is no photographic evidence of the Sun shining all the way down the tunnel to the western portal. ^{3, 4}

Overall, claims to have seen the Sun shining down the whole length tunnel cannot be substantiated. The fact that impossible claims have been made for dates late in April shows that it is not possible to tell whether a portion of the Sun’s surface is being seen from the western portal or whether the eye is being dazzled by sunlight being reflected off the walls of the tunnel.

Mathematical Studies

There have been several mathematical studies published over the decades producing conflicting results. One of the most recent, detailed and reliable was published in 1985 by C. P. Atkins of the National Railway Museum. ⁵  Atkins shows that the Sun’s surface might be seen from the western portal on April 6^th or April 7^th but never on April 9^th, Brunel’s birthday.

A more recent paper by Alan Champneys has interesting reflections on the reasons why the tunnel takes the line that it does. ⁶  Amongst these are the need to follow an oxbow bend on the River Avon to keep gradients small, avoidance of the extensive estates of powerful landowners, especially Corsham Court, and avoiding having to put a cutting through the middle of the town of Corsham! ⁷

Obviously, in the course of a year there may be occasions when the Sun will be aligned so that its surface might be seen by looking down the tunnel. The questions to be addressed here is whether the Sun’s surface can ever be seen through the tunnel and, if so, on which dates do these apparitions occur.

Recent improvements in geodetic and astronomical tools

Modern attacks on this problem have significant advantages over previous studies in the twentieth century and earlier. The shape of the Earth is now defined to an accuracy of a few millimetres. This is essential for the application of global navigation satellite systems such as GPS, GALILEO, GLONASS, BeiDou, etc. ⁸

Although there are several global definitions of the Earth’s shape, the one most frequently used is WGS84 developed in 1984. ^{9, 10} This has a definition of latitude and longitude that is significantly different from previous definitions. For example, the meridian dividing the Earth into eastern and western hemispheres used to run through the eyepiece of the Airy Transit Telescope in the Greenwich Observatory. This meridian passes between my feet in this picture.

Now, however, the meridian has been redefined to be 102.5 metres east of the old meridian seen at right.

It should be obvious that old measurements of the position of the Box Tunnel can be as much as one hundred metres different from modern maps using WGS84.

The Ordnance Survey provides online maps based on WGS84 which can be used to locate a feature to better than one metre accuracy. The Ordnance Survey and other authorities provide online algorithms to convert latitude and longitude to local grid coordinates and vice versa. These are also accurate to better than one metre.

Before the introduction of online astronomical programs it was a tedious process to find the apparent position of the Sun in the sky. Printed publications, such as the Nautical Almanac, would have to be searched for tables of positions that would need to be interpolated. Getting values for the Sun’s position in the 1830s when Brunel was planning the Box Tunnel would have required days of work carried out by professional astronomers and this highly manual and error-prone process applied into the 1960s when the first electronic computers became available for this type of work.

Today we have highly accurate free astronomical programs available online. Amongst the best of these is Stellarium ¹¹ which displays the position of the Sun to a very high level of accuracy – far higher than needed for the present problem – over timescales of centuries. Account is taken of the precession of the equinoxes, nutation variations in the axis of the Earth’s spin and the effect of the gradual slowing of the Earth’s rotation.

The apparent positions of astronomical objects are displaced due to refraction as the light travels through the atmosphere. Light is refracted towards the Earth’s surface making objects seem higher in the sky than they would be in the absence of our atmosphere. ¹²

This is illustrated by these two screen shots produced with the Stellarium software. On the left, the atmosphere has been ‘switched off’ and the Sun is shown in its true position mostly below the horizon. On the right the Sun’s image is distorted and displaced vertically by atmospheric refraction. These images are for the same time of day.

Past studies of the ‘Box Tunnel Problem’ have accounted for the refraction of light making the Sun appear higher in the sky than it really is. However, none of the studies seen by the writer take into account the distortion from circularity in the Sun’s image which is very evident in the above picture of a near-horizon Sun.

The amount of refraction is dependent on the density of the atmosphere over its full vertical extent. In the Stellarium software the refraction is related to the barometric pressure and temperature at the Earth’s surface because these dominate the refraction.

The Calculations

West Entrance

East Entrance

For copyright reasons the above maps are reproduced from the Open Map Project. ¹³ The coordinates were taken from the higher resolution Ordnance Survey (OS) map and the Latitude and Longitude derived using the online OS coordinate converter. ¹⁴

Ordnance Survey coordinates converted to WGS84 global profile. ¹⁵

The grid bearing (azimuth) of the tunnel derived from the grid coordinates is 79.76 degrees.

The grid lines on OS maps do not point to the geodetic North Pole because the Ordnance Survey maps are a representation of features on a curved irregular surface projected onto a plane. This is known as Grid Convergence.

The true north vector points 0.21 degrees to the east. This result was taken from the OS calculator. ¹⁶ However, it was also confirmed by computing the divergence of the latitude and longitude lines from the lines of Easting and Northing.

This means that the true azimuth of the Box Tunnel derived by the writer is 79.76 – 0.21 = 79.55 degrees. Atkins quotes a precise value provided by the OS which is the same as the writer’s value.

Original engineering drawing of the Box Tunnel showing the inclination. ¹⁷

The inclination inside the tunnel is 1:100 uphill towards the east corresponding to the apparent horizon being 0.57 degrees above the Earth’s horizon.

The width of the eastern portal subtends a mere 0.14 degrees as seen from the western portal compared with the Sun’s diameter of about 0.5 degrees.

This diagram shows the relative sizes of the solar disc and the eastern portal as seen from the western portal. The astronomical horizon is 90 degrees from the zenith and the local horizon is as seen from the western portal up the 1:100 incline.

Clearly the area subtended by the eastern portal is much smaller than the area of the Sun.

The Stellarium software was set up to check if any part of the Sun’s surface could be seen through the eastern portal from the western portal. The results are presented in the following table.

Atmospheric refraction was included in the calculations assuming the pressure to be 1017 mB which is the average over Southern England and a temperature of 5^o C for early April in Wiltshire.

Atmospheric refraction will also make the light passing through the tunnel and the eastern cutting curve downwards. However, using standard surveying methods, this has been computed to be about 0.14 metres and can be ignored.

This table shows the time in seconds that the Sun’s surface can be viewed all the way through Box Tunnel. The rather erratic variations from day to day are because the calculations are based on the first and last glimpse of the Sun’s surface within the unique shape of the eastern portal.

We see that, in theory, the Sun may shine down the length of Box Tunnel on either the 6^th or 7^th April each year and more rarely on the 5^th and 8^th of April if there were no obstruction. ¹⁸

After four days the pattern repeats to within a few seconds. This is because of the addition of a leap-year day on years exactly divisible by four. This brings the calendar almost back into line with the time measured by the motion of the Earth around the Sun.

The length of a year, as measured by the orbit of the Earth around the Sun is 365.2422 days. The leap-year extra days corresponds to a year of 365.25 days. Another rule is used which is that there is a leap year every year divisible by four except for years which are both divisible by 100 and not divisible by 400. Therefore, the year 2000 was a leap year, but the years 1700, 1800, and 1900 were not.

The length of a day currently increases by about 1.8 milliseconds every century. This is corrected by the introduction of ‘leap seconds’ of which there have been 27 since 1972. ¹⁹

This shifts the pattern illustrated above for the 1840s relative to the pattern for the 2020s.

These effects, together with the precession of the equinoxes, nutation, etc., means that the results in the above table for the 2020s are quite different to predictions for the 1840s.

PART 2

Can The Sun Actually Shine Down The Tunnel?

It can if nothing blocks the line of sight from the western portal to the Sun. This part of the mystery has largely been ignored in early calculations because the track east of the tunnel appears on maps to continue in a straight line through a deep cutting. This is not true. The track curves gently towards the left before it goes under a small bridge which used to carry a quarry tramway in Victorian times.

The Guardian newspaper published a photograph of the Sun shining into the eastern portal on 9^th April 2017. This was photographed by a Great Western Railway engineer. ²⁰ The accompanying text claims this to be proof that the Sun does indeed shine down the tunnel on 9^th April – Brunel’s birthday.

I have made a tracing of this photograph shown below.

The photographer has taken the picture from the centreline of the tunnel floor between the two sets of rails. There were three engineers standing in the tunnel portal. These give a scale to the diagram. If the photographer had walked backwards keeping to the tunnel centreline the outline of the portal would have diminished in size towards the black circle indicating the vanishing point of the four rails. This would have marked the projection of the floor of the tunnel onto the background.

The background view of the cutting would also diminish in apparent size. However, the portal will diminish faster than the cutting because the portal is closer to the viewer. Thus, relative to the portal opening, the amount of sky visible will diminish.

The photograph shows the Sun immediately over the centreline of the tunnel. By running the Stellarium software it was found that the centre of the Sun was 1.75 degrees above the true horizon at the time indicated on the above graphic.

The base of the portal was 0.57 degrees above the true horizon. We can calculate from these figures that direct sunlight would scarcely have reached 300 metres into the tunnel on that day – far from the claim accompanying the photograph that the Sun shone “...all the way to the western portal”!

The surprise when I produced this graphic was to see that, from the western portal, the view out of the eastern portal is obscured by the background. The quality of the original photograph is too poor to see what is obscuring the line of sight to the rising Sun at the small black circle and the area above it.

After getting this result I found that Roger Morgan had made the same discovery. ²¹ His photographs and video show that looking down the Box Tunnel from the western portal will only show a view of vegetation as does the picture below taken by Great Western Engineers during a maintenance survey of the tunnel. On the original photograph the open end of the eastern portal looks greener than has reproduced in the picture below.

The view towards the eastern portal showing no sky visible – just the green colour typical of vegetation. ²²

There is also a video on Roger Morgan’s website taken from a train passing through the tunnel clearly showing that the sky is not seen once the train has passed about one kilometre from the eastern portal.

This observation would have been obvious to every train driver travelling eastwards through the tunnel – has nobody ever asked a train driver what can be seen travelling through the tunnel?

I have superimposed onto this late Victorian map a straight line along the centre of the tunnel and extrapolated this to show that it intercepts the cutting wall near to the old tramway bridge adjacent to Pockeredge Lodge. However, photographs and information communicated to me privately in April 2022 show that the vegetation are trees in the area of the tramway bridge.

Conclusions

There is no evidence that Brunel aligned the tunnel so that the Sun shone down its entire length on his birthday. He had good reasons, both from his need to restrict curves and gradients on the line together with avoiding landownership disputes, to build the tunnel where it is.

It appears that the view of the rising Sun is now intercepted by vegetation, mostly trees, in the vicinity of the tramway tunnel about 800 metres east of the Box Tunnel eastern portal. Trees may not have been in place in the 1840s in which case the Sun would have passed uninterrupted down the full length of the tunnel on April 6th or April 7th and rarely on April 8th.

Thus, in the 1840s the rising Sun may well have shone down the tunnel but vegetation now interrupts that sight unless the modern trees are sparsely leaved.

The scattering of sunlight on the insides of the eastern portal of the tunnel would have given the appearance of sunlight shining into the tunnel on dates other than those calculated above.

Acknowledgement

My inspiration for this study came from attending an excellent talk about Box Tunnel by Alan Jefferis given to the Wessex Astronomical Society on April 5th 2022 .He kindly provided additional observations which are incorporated above. Diagrams and photographs are copyright free either by virtue of age, are taken from Wikimedia, permission was granted by the owner or were produced by the writer who is happy for them to be reproduced freely.

References

1. An account by Julian Carosi of the building of the tunnel with over forty interesting pictures old and new can be seen here.

2. Stuart, D. H., Journal of the Stephenson Locomotive Society, 50, (591), 302 (1974 October)

3. https://www.theguardian.com/technology/2017/apr/10/isambard-kingdom-brunel-birthday-box-tunnel-bath-sun

4. Atkins, CP, “Box Railway Tunnel and I K Brunel’s Birthday: A Theoretical Investigation” Journal of the British Astronomical Association, 1985, vol 95, part 6 pp 260

5. Atkins, C. P., “Box Railway Tunnel and I K Brunel’s Birthday: A Theoretical Investigation” Journal of the British Astronomical Association, 1985, vol 95, part 6 pp 260

6. Champneys, Alan, “Westward Ho! Musings on Mathematics and Mechanics”, Mathematics TODAY, October 2021, p193

7. Champneys, Alan, “Westward Ho! Musings on Mathematics and Mechanics”, Mathematics TODAY, October 2021, p197

8. https://en.wikipedia.org/wiki/Satellite_navigation

9. https://en.wikipedia.org/wiki/World_Geodetic_System

10. The shape of the Earth is defined by 2,160 spherical harmonics!

11. https://stellarium.org/

12. https://en.wikipedia.org/wiki/Atmospheric_refraction

13. OpenStreetMap Foundation - https://en.wikipedia.org/wiki/OpenStreetMap

14. https://www.ordnancesurvey.co.uk/business-government/tools-support/os-net/coordinates

15. https://en.wikipedia.org/wiki/World_Geodetic_System

16. https://www.ordnancesurvey.co.uk/business-government/tools-support/os-net/coordinates

17. Copyright-free figure - http://www.networkrail.co.uk/VirtualArchive/box-tunnel/

18. It has been suggested that Brunel aligned the tunnel to celebrate one of his sister’s birthdays which was April 6^th This is even less likely than that he was celebrating his own birthday.

19. https://en.wikipedia.org/wiki/Leap_second

20. https://www.theguardian.com/technology/2017/apr/10/isambard-kingdom-brunel-birthday-box-tunnel-bath-sun

21. Morgan, Roger, “The light at the end of Box Tunnel”, 2006, http://www.xenophon.org.uk/box.html

22. Photograph reproduced by kind permission of the BBC.

Keywords: Box Tunnel, Brunel, Geoff Kirby, GJK01305