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A sapper of the 128th Mountain Assault Brigade wearing Ukrainian-made mine-resistant boots.
(files.catbox.moe)
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In short: It's the ~~cube root~~ inverse square law. The ~~damage~~ force from an explosion goes down with distance by an exponential factor (1/x^2).
So the blast force (per unit area) at 2" should be about 1/4^th the damage at 1". At 6", the force would be 1/36^th the force per unit area at 1" distance.
Think of a surface of a balloon. If the skin of the balloon (and it's thickness) represents concussive force, as the balloon gets bigger, the skin (and the force) gets smaller.
The boots work by ensuring that if you set off a mine, the mine is under one of the four prongs and away from your foot (distance = ~6") vs just under your foot (distance <1" or the thickness of your soles).
Edit: corrected damage to force. Shrapnel complicates things a bit, but in general, the further you are from the blast, the less concussive (read bone pulverizing) force you receive and the fewer and more spread out shrapnel fragments you get.
If your bones aren't pulverized and the shrapnel is less concentrated, then there's a better chance the medics can save your leg and foot.
Copying a comment on the study these boots came from:
From the study on the boots, they were way better at lowering the odds of needing an amputation after stepping on a mine than the alternatives. Even when tested against the larger mines (249g of explosive)
Check out figure 4 in the study. The competing alternatives were tested against 25g of explosive (first data point) and the measured acceleration on the test leg was 4000 -11,000 g's. The spider boots tests registered about 700 g's or less.
An alternate source to read the whole study on the spider boots:
https://www.researchgate.net/figure/Spider-Boot-tested-with-a-mechanical-surrogate-leg-at-DRDC-Suffield-Actual-and-simulated_fig3_265925569
I prefer my bones not pulverised, so this seems like a good thing.
Umm... those two things are not equivalent. b^(-x) would be exponential, x^(-k) is inverse-power for whatever k