I've always been curious about how much tension is on a djembe skin. It's difficult to estimate. If I stand on the lever of my drum press and apply tension, I might be pushing down on the lever with a force of, say 50 kg. But the lever nearly doubles the amount of force I apply to a vertical and, because the vertical slides around the top lop, effectively making a pulley, that doubles the amount of force yet again. In other words, standing on the lever and applying 50 kg of weight to the pedal applies around 200 kg of pull to the vertical.
If I do the naive thing and just multiply the pull by the number of loops, I'd get around 5 or 6 tons of tension, which is clearly not the case. No goat skin could withstand the weight of four family cars… What happens is that, as I apply tension to one vertical, that actually removes some tension from the previous vertical, so the tension gets distributed around the drum, and it's not correct to simply add up the pull on the individual verticals.
There is calculator for the resonant frequency of tympani membranes
, which I used to work out the tension.
To get the density of the skin, I weighed a skin I recently pulled off a drum. The skin round had 50 cm diameter and weighed 115 g. This will vary a little with the thickness of the skin. (The one I used was a medium-thickness skin.) For this particular skin, density works out to 0.568 kg/m².
The diameter of the playing surface was 0.31 m.
If we assume tones at 400 Hz (solo pitch), the calculator reports 14900 N/m tension. That's 1518 kg/m. Because the skin is only 0.3 m in diameter, that makes it a total amount of pull of 455 kg, which is around 1000 lb.
Almost half a ton of pull. That's a bit higher than I would have guessed. (I estimated around 300 kg before doing the calculation.)
What's amazing here is that a goat skin is actually strong enough to handle that much tension. And it helps to explain why they tend not to last all that long