3

Find the Depth of a Well or a Deep Hole

Everyone likes a good deep mysterious hole in the ground. It could be an old mineshaft, a cave, a well, or even a lift shaft (though you have to be careful dropping stones down lift shafts). Yes, stones—that is the secret of finding just how deep that hole is.

1. The trick is knowing the formula—a very simple one that dates back to Galileo. It relies on the fact that all objects, whatever their size, accelerate toward the earth at the same rate—9.8 meters per second per second. (Speed is measured in meters per second, acceleration in the increase in speed—hence meters per second per second.) Gravity is the cause of the acceleration, and as long as you don’t choose a feather or a very light stone you’ll get a good result. (A feather does drop at the same rate as a stone if there is no air—but air resistance is minimal on a small heavy stone.) Now 9.8 is a bit clumsy so let’s round it up to 10. Next you’ll need a watch or a way of counting off seconds. I say “one barra barra, two barra barra, three barra barra” and it’s pretty accurate—accurate enough to get a well’s depth to the nearest few meters. So you release the stone and start counting and only stop when you hear the plop. The depth is half of the acceleration (which is half of 10, which is 5) multiplied by the time squared. So if you time a three-second drop it’s 5×3×3=45 meters deep.
2. Is there a barrier to doing this? Not really. Getting the timing accurate is the main thing. You can use a stopwatch if you like.
3. A good stone is hard to find. Well, maybe not that hard, but it’s worth getting one. Sometimes holes and caves have updrafts and a tiny stone will catch in the wind. A massive great boulder is a tad over the top and might hit the walls of the well, which would mess with the time. A stone a little bit smaller than a golf ball will work fine.
4. The payoff for stone dropping is the intense satisfaction gained from knowing the exact depth of a deep crevice, hole, or puncture in the earth’s surface. It is in our nature to want to explore and know things we perhaps should not, and there is something a little miraculous in the idle and even careless gesture of dropping a stone down a well resulting in a precise measure of its depth. Something only otherwise to be discovered by the painstaking and tedious process of lowering a weight on a measuring line.
5. To gamify stone dropping make it competitive. You’ll need a length of string that you premeasure and lower with a weight attached into the well or hole. In other cases you may find that the depth of the well is already known—the person who gets the closest to the official figure is the winner. Obviously you have to exercise a bit of caution and common sense. A stone dropped on the head of a caver or someone down a hole can kill or maim, so make sure the hole is clear before you do it.
6. This is one of the most basic experiments in physics but it leads into the whole realm of measuring things that perplex us on country walks and other excursions, when someone might ask “How wide is that river?” or “How high is that tree?” followed sometimes by the offer of a wager. Well, heights and widths are just as easy to compute from rudimentary tools and simple geometry, something that the practical amateur physicist might like to pursue, having tasted success in well-depth measuring.