A daylight conundrum

By Marcus Wilson 29/10/2010

Our organic alarm clock has now taken to jumping on the bed at about 5 in the morning and purring very loudly in an attempt to persuade us it’s breakfast time. It’s not surprising, since sunrise (and therefore cat-rise, if not Marcus-rise) is becoming earlier and earlier.

Daylight hours are now long – in fact the South Pole is now in non-stop daylight. If you’re there with no cloud present you’d see the sun circle the sky, at fairly low elevation. A horizontal surface would get non-stop daylight, but a vertical surface obviously wouldn’t. About half the time it would be lit, and half the time in shadow, with the sun behind it.

So here’s the brain teaser. In the course of a 24 hour day, is it possible for a vertical wall to be lit for more than 12 hours (clouds and other obstacles not getting in the way, of course)?

And, if so, where in the world would the wall be, what day of the year would it be and what is the maximum time it could spend illuminated?

No prizes, other than a chance to feel smug.

0 Responses to “A daylight conundrum”

  • A circular vertical wall enclosing the south pole (or near-by geographic high-point) would be lit 24/7 at the present, but I suspect that’s not the answer you’re looking for.

    A straight vertical glass wall in the same location would also be lit 24/7 at the present because it can be lit from either side (or the ends), but I suspect that’s not the answer you’re looking for either.

    There are also fun and games you can play with the definition of “24 hour day” with leap seconds and the like, but they don’t feel like the answer you are after.

    I think the answer you’re looking for is that any straight vertical east-west wall in non-equatorial regions will have more than 12 hours of direct sunlight on one side on the day when the sun is at it’s highest point directly perpendicular to the line of the wall, i.e. the summer equinox.

    • This teaser I encountered as a student in the context of wall mounted sundials. We had a pesky computer programming assignment in which we had to draw out the hour-markings for a wall mounted sundial, given the wall’s latitude, longitude, time zone and orientation. Fortunately we were given the formula…

      At first glance it was hard to believe that one side of a flat vertical wall (e.g. the wall of a house) can be illuminated for more than 12 hours, but it is true (I think). An extreme example would be found on the planet Uranus, which has its axis pretty well in the plane of its orbit. This means its ‘Arctic’ and ‘Antarctic’ circles are almost at the equator. In the middle of northern hemisphere summer, nearly all the northern hemisphere gets non-stop daylight. The sun appears pretty-well motionless in the sky as the planet rotates – it just does a small circle. So if the wall is pointing towards it, it could be illuminated for a considerable period of time.