re: Bugs Falling from Heights

[Rhapsody]

the IMPACT would be much less as the MASS would be much less.

Think of it this way. If say (and I am not going to actually do the math here…) the g-force of a human on impact is 3 g’s, the impact for the bug falling from the same height in a vacuum would also be 3’g’s or 3 times the mass.

Anyway this applies to things besides insects and humans. A squirrel jumping from a 6 foot tall tree can hit the ground running even though if you compare proportional sizes the jump proportionate to humans might be the equivalent of a human doing the same from a branch 40 feet up. It comes back to the simple fact that a six foot fall does not allow enough TIME to reach faster speeds regardless of the size of the creature doing the falling. a human, squirrel or a bug falling from the same height in a vacuum would hit the ground at the same time and at the same speed. You take all of them up to 20 feet and all will be injured.

[zut]

*Originally posted by Rhapsody *
the air resistance really is not the issue here. For that matter you seem to be trying to assign a set value for all insects which makes no sense at all. Anyway, my argument might be better stated as : Even in a vaccum a bug falling from from six feet would not be analogous to a man falling from 60 feet.

I understand what you’re saying, and that’s a good point: speed of impact is an important difference that is overlooked in the Staff Report.

However, air resistance is at least part of the issue here. If you drop an ant from six feet up, it should be pretty clear that it’s going to be moving at close to terminal velocity when it hits the ground. So if the ant can survive a six foot drop, it ought to be able to survive a 60 foot drop, or a 600 foot drop, or a 6000 foot drop.

[Doug_Yanega]

As the author of the Staff Report in question, I suppose I should chime in.

“If you drop an ant from six feet up, it should be pretty clear that it’s going to be moving at close to terminal velocity when it hits the ground. So if the ant can survive a six foot drop, it ought to be able to survive a 60 foot drop, or a 600 foot drop, or a 6000 foot drop.”

This is empirically true. I’ve dropped plenty of bugs off buildings. Tiny insects blow away, sometimes straight up. Normal insects fall very slowly, and the majority hit just as hard when dropped from 6 feet as when dropped from 60 - which is not very hard at all. The only exceptions start to appear when the insect is exceptionally large, say, 1-2 inches or more, and relatively massive - they have a higher terminal velocity, and hit harder, but most will still not be hurt much by the fall. The only insects that can actually be damaged by a fall are those which are truly massive, such as Goliath Beetles, Wetas, and such, which can reach over 50 grams (and then only if they hit a hard surface like concrete or rock). In other words, the speed of fall and force of impact are both highly correlated with mass. Even a nearly spherical insect (and there are many) will fall slowly and hit weakly if it only weighs a few milligrams. You MUST also bear in mind that insects are pretty much all air space inside the exoskeleton; there is a heck of a lot of surface relative to the mass, so an insect is more like a balloon with a rigid shell than like a person. This is the empirical reality, at any rate - you decide which theories and physical explanations are required to match it.

[Rhapsody]

As I mentioned though the make up of the insect while obviously not irrelevant does not help in anyway to explain why a squirrel, mouse, or other small creature can survive what would proportionatly be huge leaps for a human. Air resistance and low mass to surface area ideas simply don’t apply.
Even the larger insects you mention that may splat on concrete from 60 feet will likely be uninjured by a fall from 6 feet even though proportionate to size it would still be a very long drop.
(I know the original question addresses insects specifically, but the question is much broader)

[Nametag]

As I mentioned though the make up of the insect while obviously not irrelevant does not help in anyway to explain why a squirrel, mouse, or other small creature can survive what would proportionatly be huge leaps for a human. Air resistance and low mass to surface area ideas simply don’t apply.

Proportionately??? What the hell does that mean? What makes anyone think that falling 10 feet for a human being is any more or less traumatic than for a squirrel? 10 feet is 10 feet, and gravity is gravity; if the human actually FALLS 10 feet, he’ll suffer the same damage as any similar creature falling 10 feet, regardless of size unless the critter’s so small that air drag becomes a factor. Insects may experience different levels of damage because of their construction as well as their size, but let’s leve this “proportion” nonsense out of it.

[Duck_Duck_Goose]

DAMN straight. And I think the squirrel should sue, definitely.

psst, Tag? I think he means “proportionately” as in the way a 5-inch long hamster can survive falling off a bookshelf that’s three feet above the ground, which “proportionately” would be the same thing as a 5-foot-tall human surviving a fall from a bookshelf that’s…that’s…that’s…

[Emergency Math Alarm Sounds]

ANNH ANNH ANNH ANNH…

ill let sumbudy els do the math my hed just xploded

[Chronos]

I think that Nametag’s point is that the equivalent of a hamster falling three feet is the equivalent of a human falling three feet. You can’t just say that doubling the height of the creature will double the height of a “proportionate” height, though I can understand the cause for confusion.

For that matter, though, even if we don’t adjust the height, a small critter can survive a fall from a greater height than a large critter. Doug, while you’re at it with the experimental data, could you please drop a hippopotamus from the same 60 feet, and report back to us on the results?

[Irishman]

Rhapsody, why can a deer leap an 8 ft fence while a human can barely jump a 4 ft one? A deer is not a squirrel or mouse or other small animal, much less an insect. Animals are built differently from each other, even if they seem similar.

[zut]

But, Irishman, there’s more at work here than just physiological differences between humans and squirrels, or insects, or deer. There’s also scale effects as you change from one size animal to another.

I think the real answer to Rhapsody’s question is this: as you change scale, not all effects change with the same proportion. To make things simple, let’s imagine a 6’ tall human and a mini-human that is 1/10 scale. We’ll also ignore air resistance. However (and this is obvious, but important!), the two have the same body density, and the acceleration due to gravity, are identical for both. So here’s the comparison:

All sizes: scaled 1/10
Masses: scaled 1/1000 (mass is proportional to densitylength[sup]3[/sup])
Velocities: scaled SQRT(1/10) (velocity is proportional to SQRT(accelerationlength))
Accelerations: are the SAME in both cases (including g-loading)
Forces: scaled 1/1000 (Force = mass*acceleration)
Stresses: scaled 1/10 (Stress = force/length[sup]2[/sup])

What’s important, and what causes damage, are the stresses. And smaller critters survive “proportional” falls because the stresses get smaller when the scale gets smaller. This is the same reason ants can carry proportionately huge leaves. It’s also why elephants have proportionately large legs, and insects have proportionately small ones.

Also, it’s not particularly silly to compare things based on their proportionate size. Airplane and ship designers test scale models all the time. The trick is, though, to remember that not all effects scale the same way, and you have to design the test to match the effects you want. So a scale model airplane may be tested in different density fluid, or at a different “proportional” speed, than the full-scale model. These differences are intended to “cancel” some of the scale effects and accurately reproduce the effect you’re looking for*. Note you might need to design different tests, depending on whether you want to match, say, drag forces around a ship’s bow, or stress due to buoyancy, or speed past the propeller, or whatever.

In this “human-animal falling” comparison, we ought to get similar results from a proportional fall if the 1/10th scale mini-human were to fall from a proportional height under a 10g gravitational acceleration. Of course, this still ignores air resistance. And, one final note: it turns out, in this case, that increasing the falling distance by a factor of 10 (i.e., having the mini-human hall from the same height as the normal human) will also match stresses. However, I see no reason that ought to be intuitively obvious, and simply assuming that to be the case, although correct, is dangerous.
*footnote: I Googled for a good explanation of scaling (possible keywords: similitide, dimensional analysis, Froude number scaling, Reynolds number scaling), and couldn’t find a reference that wasn’t either very technical or very short. Best I could do was this page, which is kinda thick, but does have some “scaling theory”.

**footnote 2: this contradicts, somewhat, a point I was trying to make above about mass/surface area ratio. I hadn’t thought this all the way through yet. Sorry Doug.

[Nametag]

Velocities: scaled SQRT(1/10) (velocity is proportional to SQRT(acceleration*length))
Accelerations: are the SAME in both cases (including g-loading)

And the fallacy begins. Why, pray tell, are you assuming from the beginning that the distances MUST be proportional to the falling object’s size? Isn’t this what you’re “proving”? If you leave out that assumption, height, velocity, and acceleration are ALL the same.

In this “human-animal falling” comparison, we ought to get similar results from a proportional fall if the 1/10th scale mini-human were to fall from a proportional height under a 10g gravitational acceleration. Of course, this still ignores air resistance. And, one final note: it turns out, in this case, that increasing the falling distance by a factor of 10 (i.e., having the mini-human hall from the same height as the normal human) will also match stresses.

We’re not talking about scaled-up hamsters or scaled-down humans; we’re comparing humans directly to hamsters. Humans are more massive than hamsters, true, but they have thicker bones to compensate (as well as other physiological adjustments). That scaling has already been done. If you drop a human from 6 feet, (center of mass, not allowing him to use his legs), the effects will be the same as on a hamster dropped 6 feet (or at least any difference will be smaller than can be explained by “proportion”).

However, I see no reason that ought to be intuitively obvious, and simply assuming that to be the case, although correct, is dangerous.

I’m not saying that scaling doesn’t matter; it’s as important, and as complicated, as you’ve made it out to be. What I am saying is that the notion that the distance of a fall should somehow be directly proportional to the length of the object falling IS patently absurd, and that should be intuitively obvious to anyone who lives in a gravitational field.

[zut]

Originally posted by Nametag
Why, pray tell, are you assuming from the beginning that the distances MUST be proportional to the falling object’s size? Isn’t this what you’re “proving”?

I’m “assuming” that because that’s what the question was. The original Staff Report question was: “I want to know why a person falling from a 6 story window is killed, but a bug is dropped from a proportional height–say, 6 feet–gets up and walks away. Why isn’t it dead?” Rhapsody’s extension of the question was: “why [does] a squirrel, mouse, or other small creature… survive what would proportionatly be huge leaps for a human[?]” To show why small things can survive proportionately large falls, you’ve gotta examine what happens when they fall a proportional distance.

If you leave out that assumption, height, velocity, and acceleration are ALL the same.

Well, yes and no. Gravitational acceleration would be the same, but g-loading on impact (also an acceleration) would not be the same.

We’re not talking about scaled-up hamsters or scaled-down humans; we’re comparing humans directly to hamsters.

Well, yeah, but it’s easier to explain scale effects, in a thought experiment, when physiological differences are eliminated.

Humans are more massive than hamsters, true, but they have thicker bones to compensate (as well as other physiological adjustments). That scaling has already been done. If you drop a human from 6 feet, (center of mass, not allowing him to use his legs), the effects will be the same as on a hamster dropped 6 feet (or at least any difference will be smaller than can be explained by “proportion”).

Do you realize that you’re contradicting yourself? If you drop a human from 6 feet, the effects (or, rather, the stresses, which I’m assuming are the most important) will be the same as on a mini-human dropped 6 feet. The thinner bones of the hamster would make the effects of its 6-foot fall more severe.

Also, I don’t think your statement that “that scaling has already been done” is strictly accurate. Some scaling is already done (compare an elephant skeleton with that of a mouse [which is your point, I know]). However, if the required physiological “structure” of animals were scaled exactly already, then ants wouldn’t be able to lift many times their own body weight. I suspect that hamsters, even though they have proportionately thinner bones than humans, don’t have bones as thin as perfect stress scaling would entail.

[Rhapsody]

what I am trying to get at is that from six feet you simply do not fall LONG ENOUGH to gather as much speed as you do from a sixty foot fall.
Consider dropping in a vacuum a small bug like a lady bug or something from a height of say 4 feet. Drop a human from a proportionatly taller structure and the impact will be much more severe to the human than the bug. The reason is that the bug has not fallen for a long enough TIME at 32/ft/sec/sec.
If you were to convert the impact to gforce the bug and a human falling from the same height will impact with EQUIVILANT G-FORCES. In other words if the impact/weight load of a human dropping 4 feet is equal to 2 g’s the bug also would experience 2 G’s or 2 times its weight at impact. A 6 inch tall human should be able to fall off a coffee table with no more likelyhood of injury than a full size human falling off the same table.