Tension on a djembe skin

[michi]

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

Michi.

[djembeweaver]

Nice work Michi. That's another interesting fact I can pull out in school workshops if kids ask about the tension of a skin

While 400Hz might be solo pitch (mine is playing at 400Hz at the moment) some folas crank their djembes to ridiculous tension. I wonder what the upper limit is...

I might look at some recordings with ridiculously cranked djembes if I can find any without accompaniment, but what would be the increase in tension if the same skin played at, say 450Hz? How much extra tension would the extra 50Hz create?

Jon

[michi]

I might look at some recordings with ridiculously cranked djembes if I can find any without accompaniment, but what would be the increase in tension if the same skin played at, say 450Hz? How much extra tension would the extra 50Hz create?

At 450 Hz (which may well be unachievable), you'd be looking at 614 kg of pull.

Make it a thicker skin, at 0.7 kg/m² and, at 450 Hz, you'd get 733 kg. (A thicker skin needs more tension to get to the same pitch.)

Make the diameter of the drum larger by 1 inch, and you are now looking at 925 kg (with the thicker skin).

Go back to 400 Hz and 31 cm diameter, but with a thicker (0.7 kg/m²) skin, and it's 560 kg instead of 455 kg. Skin thickness makes a huge difference in how much pull you need to get to the same pitch. Now increase the drum to 33.5 cm in diameter, and it's 730 kg. In other words, a drum that's 1 inch larger needs to be pulled 1.45 times harder to get to the same pitch.

I guess that's the explanation why it's so difficult to get large drums up to solo pitch. You need much more pull and, for the skin to survive the pull, you need a heavier skin, which requires yet more pull. I know this first-hand from my Jina djembe, which is very large. It's possible to get it up to solo pitch but, by the time it's there, there is so much tension on the skin that it gets difficult to pull diamonds even on a pulling stand. And, obviously, the skins don't last very long.

Cheers,

Michi.

[shortypalmer]

I have no clue what the tension would be, i put a scale under a djembe once while pulling with my table, the scale only went to 400 lbs, i pegged out. does that help?