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.

Chevaline: telling the time

Various media sources have reported that the last photos were taken by the al Hilli family between 3.12pm and 3.17pm French time (GMT+2) on the afternoon of 5th September 2012. Nonetheless, a question that frequently comes up on internet forums is "what if the clock on the phone/camera wasn't set to French time?"

Thanks to the release last week by BFMTV of what they reported as being "the last family photo" it is now possible to clarify the issue by using the information provided by the shadows visible in the image in conjunction with a calculation of solar azimuth (bearing) and elevation (height) - in effect using the building shown in the photo as a sundial.

So, simple question first:

Was the photo taken before or after 3pm?

The "last family photo" as published by BFMTV

In the photo, a clear line of shadow cast by the buiding is visible to the right of the frame, so we know there was direct sunlight on the day. Making a calculation of time based on this line is complicated, however, by the irregular shape of the building and the pitch of the roof - the shadow appears to run nearly parallel to the road, but when perspective is taken into account it is clear that this is not the case.

The background building from the front and above

As luck would have it, however, we don't need to worry about the shadow on the right since at 3pm on 5/9/12 the solar azimuth is almost exactly parallel to the roof line of the building:

Solar azimuth 3pm - the sun shining from direction SSW

Thus, at 3pm the gutter running along the street frontage of the building will cast a shadow directly below itself, forming a line of shadow along the grass strip below it (see Google Streetview image, above). Any time before 3pm and the sun will be shining directly onto the street frontage. At any time after this the shadow line will start to move out into the street as the sun moves around the sky towards the west.



Going back to the original photo at the top of this post, it is clear that the street frontage of the building is in the shade and there is no visible dividing line of direct sunlight and shade at the left of the frame, indicating that by the time it was taken the shadow line had already moved into the road.

Thus, it is clear that the photo was taken after 3pm.

Next comes the rather more complicated task of establishing whether the shadows in the photo match the reported time of 3.17pm...