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...