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General Tabletop Discussion
*Dungeons & Dragons
Calculating fall damage in special situations
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<blockquote data-quote="jaelis" data-source="post: 6988919" data-attributes="member: 60210"><p>Well I can happily fill in the role of a physics friend <img src="https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f642.png" class="smilie smilie--emoji" loading="lazy" width="64" height="64" alt=":)" title="Smile :)" data-smilie="1"data-shortname=":)" /> But to start, it's clear that the dnd falling rules are based on game play and simplicity, not any attempt to model reality. I think that is a good thing.</p><p></p><p>But just to think about reality a bit: Probably the most accurate simple way to think about falling damage is in terms of stress, which is basically like pressure, equal to force per area. A given material can typically withstand a certain maximum stress before breaking. </p><p></p><p>The force need to bring a body to rest is indeed the mass M times the acceleration. The acceleration however is a little complicated, and depends on how much the material compresses as it strikes the ground. If the body compresses by an amount D, then the acceleration will be about V^2/(2*D) where V is the velocity just before hitting the ground. That velocity is given by the height H of the fall as V^2 = 2*g*H where g is the gravitational acceleration. So that says the acceleration experienced as you hit the ground is g*H/D. The the force is M*g*H/D. </p><p></p><p>Anyway, the stress is the force per area. Since the bodies of different creatures have about the same density, the area hitting the ground is proportional to the mass to the 2/3 power. So the stress should scale like M^(1/3)*H/D.</p><p></p><p>Finally, if you assume the bodies act sort of like springs, then the amount they compress D will be be proportional to the speed they hit the ground at, V. Since V goes like the square root of H, that leaves the stress S proportional to the cube root of M and the square root of H. </p><p></p><p>So up to the validity of those sketchy assumptions, this says a creature that weighs 8 times less could fall four times as far and take the same amount of damage. A creature that weighs 27 times less could fall 9 times as far.</p><p></p><p>Whee!</p></blockquote><p></p>
[QUOTE="jaelis, post: 6988919, member: 60210"] Well I can happily fill in the role of a physics friend :) But to start, it's clear that the dnd falling rules are based on game play and simplicity, not any attempt to model reality. I think that is a good thing. But just to think about reality a bit: Probably the most accurate simple way to think about falling damage is in terms of stress, which is basically like pressure, equal to force per area. A given material can typically withstand a certain maximum stress before breaking. The force need to bring a body to rest is indeed the mass M times the acceleration. The acceleration however is a little complicated, and depends on how much the material compresses as it strikes the ground. If the body compresses by an amount D, then the acceleration will be about V^2/(2*D) where V is the velocity just before hitting the ground. That velocity is given by the height H of the fall as V^2 = 2*g*H where g is the gravitational acceleration. So that says the acceleration experienced as you hit the ground is g*H/D. The the force is M*g*H/D. Anyway, the stress is the force per area. Since the bodies of different creatures have about the same density, the area hitting the ground is proportional to the mass to the 2/3 power. So the stress should scale like M^(1/3)*H/D. Finally, if you assume the bodies act sort of like springs, then the amount they compress D will be be proportional to the speed they hit the ground at, V. Since V goes like the square root of H, that leaves the stress S proportional to the cube root of M and the square root of H. So up to the validity of those sketchy assumptions, this says a creature that weighs 8 times less could fall four times as far and take the same amount of damage. A creature that weighs 27 times less could fall 9 times as far. Whee! [/QUOTE]
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