Chevaline: telling the time (2)

Attempting to match the reported time of the "last family photo" (3.17pm French summer time) on 5/9/12 with the time based on a calculation of solar azimuth and elevation - effectively using the building in the image as a giant sundial.

The 'last family photo'

Solar azimuth prediction for photo location at 3.17pm 5/9/12

The first task is to establish the length of of the shadows cast by the building onto the ground. As luck would have it, the solar elevation for 3.17pm is near enough 45 degrees - so the length of a shadow on the ground is going to be pretty much the same as the height of the object casting it. Thus, we can get an idea of shadow length using a series of squares drawn to match the height of part of the building casting the shadow:

 

Calculate shadow length

In the image above, a series of squares shows the length of shadows which would be cast by the sun at elevation 45 degrees if shining from the stream side of the building, perpendicular to the ridge line of the roof and street frontage. The next thing is to transfer this measurement to an overhead view of the building, then turn it to match the azimuth:

In the image above, the red square is an indication of shadow length, effectively one of the red squares from the previous image dropped on its side. The yellow line is the azimuth, the sun shining from the South-West. The blue squares are copies of the red square rotated parallel to the azimuth. Joining the top corners of the blue squares, the black line gives an indication of where the edge of the building's shadow would fall in the road. On this basis it can be seen that the shadow area seen in the family photo is commensurate with the calculation for 3.17pm - but it's a very close-run thing. The shadow line would fall only just beyond the left-hand edge of the photo, almost intersecting with the bottom left corner.

Also, in the image above, green lines indicate an estimation of where shadows are cast from various angles of the roof: two lines of equal length at the rear of the building and a longer line from the ridge line of the roof due to its greater height. The two rear lines were estimated on the basis of being roughly equivalent to the height of the gutter at the front and the ridge height, as with the original gutter height is calcualted by taking a 45 degree line down to ground level. Note that these are heights to the road level, in reality the shadows would be longer due to the lower level of the stream. Joining the top points of the green lines to the black line in the road provides a rough outline of the shadow area cast by the building at 3.17pm.

Black line marks approximate shadow outline at 3.17pm

Doing this, however, brings us up against a problem: the outline appears nowhere near the visible line of shadow seen on the stream in the family photo. By taking the azimuth round to 4.17pm, we start to get a roof shadow line close to the position seen in the photo. But then we encounter another problem: by that time the two adults seen in the photo had been shot dead.

Time for plan B...

Update 27/2/14

As it turns out, there is no need for plan B - I simply needed to get plan A right. When drawing in the green lines to indicate shadow length from the roof I failed to take the oblique angle of the satellite image into account. Taking an estimate of the offset from the ridge line to the ground at the opposite end of the building (see image above) and shortening the green ridge line at the top by that amount (as well as reducing the other green lines proportionately) brings the shadow line down to pretty much exactly down to the point calculated by Max at:

 http://deadzone61.wordpress.com/tck-forum-public/comment-page-6/#comment-2741

I should also give credit to http://www.iesmith.net/tools/solarcalc.html which is the online azimuth calculator used. Other online calculators are available and probably worth using for verification, but this one appeared to be the most straightforward.