The Wiltshire projectSunrise down Brunel's tunnel
Two points from an official list, Pythagoras, a compass bearing, and a year of sunrises.
Historic England lists the two portals separately and gives each a grid reference in metres east and north. The west portal is at 382,927 east and 168,905 north; the east portal at 385,800 east and 169,425 north. The learner first checks the data with Pythagoras: the straight-line distance is the square root of 2,873² plus 520², which is 2,919.7 metres. The list entry says 1.8 miles, or 2,896.8 metres. The two agree to within 23 metres, less than one per cent, which is reassuring, since the listed points mark buildings rather than the exact track.
Next, the direction. The atan2 function turns the same two differences into a bearing of 79.74 degrees from map north, a little north of due east. Map north on the British grid is not quite true north away from its central line, so the program converts both portals to latitude and longitude and recomputes: the true bearing is 79.53 degrees, a difference of 0.21 degrees. The gradient of 1 in 100 also matters: looking east from the west portal, the bore rises at 0.573 degrees above level.
Mornings when the sun crosses the tunnel's bearing near the horizon, 2027, our calculation| Date | UK time | Sun's height at that moment | On the tunnel's line? |
|---|
| 6 April | 06:38 | −0.17° | Just below |
| 7 April | 06:39 | 0.31° | Yes, within the sun's disc |
| 8 April | 06:40 | 0.79° | Yes, within the sun's disc |
| 9 April | 06:41 | 1.27° | Just above |
| 5 September | 06:36 | 0.48° | Yes, within the sun's disc |
Finally the sun. Using standard formulas for the sun's position, the program steps through every morning of 2027, finds the moment the sun's compass direction equals the tunnel's, and records how high it is then. For the sun to shine straight along the bore its height must be close to the 0.573-degree slope. That happens on two mornings in early April, the 7th and 8th, and once in early September, the 5th, a little after half past six in the morning.
Now the honest part. Our calculation ignores the atmosphere, which bends light near the horizon by roughly half a degree and would shift the answer by about a day. It ignores the hills and the deep cutting beyond the east portal, which may hide the low sun entirely. And the listed points are not the exact centre line of the track. Every answer in maths or code rests on assumptions, and saying what they are is part of the answer.
Ages 9 to 12
Plot two points on squared paper, measure the line between them, and check it with Pythagoras on a calculator.
Ages 12 to 15
Compute the tunnel's length and bearing in Python with math.hypot and math.atan2, and compare the length with the list entry.
Ages 15 and up
Add a sun-position function, search a year of mornings for the alignment, and then add refraction and see which dates move.
Official facts and our model
The tunnel's dates, length, straightness, gradient and portal locations come from Historic England's list entries. The distances, bearings, dates and times on this page are our own calculation from those figures and standard sun formulas, without refraction or terrain. We make no claim that sunlight can actually be seen through the tunnel.
