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Old 05-19-2020, 06:53 PM
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Do larger things fall faster?


In this video called "Being Big on Land: The bigger they are, the harder they fall" at 1:32, it makes the claim that "larger bodies fall faster because, relative to their weight, air drag slows them down less."

Is that true? I thought that (all else being equal, and weight being constant), larger body = greater volume = greater cross-sectional area = greater drag = lower terminal velocity, and thus they fall slower. Shouldn't drag INCREASE with size (area)?

Is the video just assuming larger = heavier, or am I misunderstanding something?

And to be clear, I want to see if I'm understanding this right...

For a given volume, heavier/denser things should fall faster because they are falling with greater force, and more able to counter air resistance.

For a given mass, larger things should fall slower because they have more drag.

Am I mistaken?

Last edited by Reply; 05-19-2020 at 06:54 PM.
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Old 05-19-2020, 07:00 PM
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(Oops, sorry, wrong forum... reported for move to GQ)
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Old 05-19-2020, 07:02 PM
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Frontal area matters. Picture a brick falling end downward compared to falling side first or front first. Same weight, different frontal area. Of course, this is falling far enough to reach appreciable air resistance.. From a few feet up, no measurable difference.

ETA: Material matters too. A small rock will fall faster than a foam boulder.

Last edited by running coach; 05-19-2020 at 07:03 PM.
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Old 05-19-2020, 07:06 PM
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Originally Posted by Reply View Post
In this video called "Being Big on Land: The bigger they are, the harder they fall" at 1:32, it makes the claim that "larger bodies fall faster because, relative to their weight, air drag slows them down less."

Is that true? I thought that (all else being equal, and weight being constant), larger body = greater volume = greater cross-sectional area = greater drag = lower terminal velocity, and thus they fall slower. Shouldn't drag INCREASE with size (area)?

Is the video just assuming larger = heavier, or am I misunderstanding something?

And to be clear, I want to see if I'm understanding this right...

For a given volume, heavier/denser things should fall faster because they are falling with greater force, and more able to counter air resistance.

For a given mass, larger things should fall slower because they have more drag.

Am I mistaken?
You're right - but I suspect that since the video is talking about animals, they are assuming (correctly) that density is constant - and when density is constant, an increase in size by factor x increases mass by factor x-cubed, while surface area increases by x-squared - so air resistance goes down as size goes up.

As JBS Haldane wrote:
"You can drop a mouse down a thousand-yard mine shaft; and, on arriving at the bottom, it gets a slight shock and walks away, provided that the ground is fairly soft. A rat is killed, a man is broken, a horse splashes."

P.S. Animals are generally about as dense as water.

Last edited by Andy L; 05-19-2020 at 07:07 PM.
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Old 05-19-2020, 07:13 PM
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In a simple free body diagram for this situation, the only two forces acting on the object are gravity and drag. Drag will increase as the velocity and frontal area of the object increases. However, the force due to gravity has a mass component, and that will increase too with greater size. Mass is proportional to volume, drag to area, and volume increases faster than area as a given object increases in size.

Ergo, the force due to gravity grows faster than drag does. So the body accelerates until the new higher velocity creates enough drag force to balance the increased gravity force arising from the increase in mass.
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Old 05-19-2020, 07:30 PM
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(Oops, sorry, wrong forum... reported for move to GQ)
Moving to GQ (from IMHO).
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Old 05-19-2020, 08:50 PM
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Old 05-19-2020, 09:01 PM
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In this video called "Being Big on Land: The bigger they are, the harder they fall" at 1:32, it makes the claim that "larger bodies fall faster because, relative to their weight, air drag slows them down less."

Is that true? I thought that (all else being equal, and weight being constant), larger body = greater volume = greater cross-sectional area = greater drag = lower terminal velocity, and thus they fall slower. Shouldn't drag INCREASE with size (area)?

Is the video just assuming larger = heavier, or am I misunderstanding something?

And to be clear, I want to see if I'm understanding this right...

For a given volume, heavier/denser things should fall faster because they are falling with greater force, and more able to counter air resistance.

For a given mass, larger things should fall slower because they have more drag.

Am I mistaken?
You are mistaken in your assumption that they are talking about "for a given mass." They are not. They are talking about for a given density.

Gray Ghost explains it a couple posts up. Drag grows with size, but it doesn't grow as fast as weight does.
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Old 05-19-2020, 10:40 PM
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Andy and Snarky_Kogg, thanks for pointing out that they were referring to a constant density, not mass. It makes sense given that most animals are mostly water.

I don't know why, but I was envisioning things like an albatross (whose spingspan is "large" though they are are relatively light, at 19 lbs or so) vs the elephant. But for most animals, I suppose larger is inherently heavier. I'm having trouble thinking of a voluminous land animal who isn't also more massive.

I appreciate the clarifications. Just wanted to make sure I was understanding the physics of this right. So: "larger animals fall faster because they are heavier, and gravity's impact increases faster than air resistance's impact."

Last edited by Reply; 05-19-2020 at 10:42 PM.
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Old 05-19-2020, 10:48 PM
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Mass is proportional to volume, drag to area, and volume increases faster than area as a given object increases in size.

Ergo, the force due to gravity grows faster than drag does. So the body accelerates until the new higher velocity creates enough drag force to balance the increased gravity force arising from the increase in mass.
Thanks for stating it succinctly and clearly!
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Old 05-21-2020, 02:31 PM
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Old 05-21-2020, 02:33 PM
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Old 05-21-2020, 02:43 PM
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one of the moon landings had one of the astronauts drop a feather and a hammer and they dropped at the same rate partly because there is no air on the moon.
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Old 05-21-2020, 02:47 PM
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one of the moon landings had one of the astronauts drop a feather and a hammer and they dropped at the same rate partly because there is no air on the moon.
Video
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Old 05-21-2020, 02:58 PM
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one of the moon landings had one of the astronauts drop a feather and a hammer and they dropped at the same rate partly because there is no air on the moon.
video

Similar experiment at NASAs massive vacuum chamber with a bowling ball and feathers.
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Old 05-21-2020, 03:12 PM
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Mass is proportional to volume, drag to area, and volume increases faster than area as a given object increases in size.
Right, under the (to me) obvious assumptions it's two different size things of identical shape and density, falling in air. That doesn't seem clear necessarily to OP or some other people answering, who imply one might be comparing things of differing densities or shapes (in which case it depends on those specifics) or in a virtual vacuum (as on the moon) where everything accelerates equally in the same gravitational field.

But it's a practical result not just a curiosity that for example small caliber bullets slow down much faster due to air resistance (at whatever angle they are travelling relative to the gravitational field) than big artillery shells of relatively similar shape and density. A 155mm artillery projectile would be ~21,700 times as heavy as a 5.56mm bullet of the same shape and material*, but have only ~777 times the cross sectional area and not greatly different drag coefficient (relating cross sectional area to drag). The net deceleration in g's due to air resistance is much less for the shell than the bullet.

*wouldn't be exactly true practically obviously, an HE shell would be ~15% by weight relatively low density explosive charge and the rest mainly steel, the bullet could be various constructions of metal including more dense lead. But the general point would hold.

Last edited by Corry El; 05-21-2020 at 03:15 PM.
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Old 05-21-2020, 06:15 PM
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But it's a practical result not just a curiosity that for example small caliber bullets slow down much faster due to air resistance (at whatever angle they are travelling relative to the gravitational field) than big artillery shells of relatively similar shape and density. A 155mm artillery projectile would be ~21,700 times as heavy as a 5.56mm bullet of the same shape and material*, but have only ~777 times the cross sectional area and not greatly different drag coefficient (relating cross sectional area to drag). The net deceleration in g's due to air resistance is much less for the shell than the bullet.
My confusion was from the video equating volume with mass. In animals and bullets, it makes sense that the two are proportional, since density remains roughly constant.

But for example, I was thinking of a bowling ball vs a beach ball, both dropped from a plane. The bowling ball should land sooner even though it's smaller, because it's much heavier and less affected by air resistance, right? Or let's say you have two identical beach balls, one filled with air and the other with lead. Same deal.

When something similar is LARGER, it is also usually HEAVIER. But it's the increase in mass, not volume, that causes it to fall faster (in an atmosphere). The increase in volume actually slows it down, but not as much as the increase in mass speeds it up. At least I hope I'm understanding now...

Last edited by Reply; 05-21-2020 at 06:15 PM.
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Old 05-21-2020, 06:18 PM
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Right, under the (to me) obvious assumptions it's two different size things of identical shape and density, falling in air. That doesn't seem clear necessarily to OP or some other people answering, who imply one might be comparing things of differing densities or shapes (in which case it depends on those specifics) or in a virtual vacuum (as on the moon) where everything accelerates equally in the same gravitational field.

But it's a practical result not just a curiosity that for example small caliber bullets slow down much faster due to air resistance (at whatever angle they are travelling relative to the gravitational field) than big artillery shells of relatively similar shape and density. A 155mm artillery projectile would be ~21,700 times as heavy as a 5.56mm bullet of the same shape and material*, but have only ~777 times the cross sectional area and not greatly different drag coefficient (relating cross sectional area to drag). The net deceleration in g's due to air resistance is much less for the shell than the bullet.

*wouldn't be exactly true practically obviously, an HE shell would be ~15% by weight relatively low density explosive charge and the rest mainly steel, the bullet could be various constructions of metal including more dense lead. But the general point would hold.
True. I was making an assumption based on what I thought I read, not what was there. I read, what if the thing we're dropping was only bigger---same density, same shape, just more of it---than the first thing we dropped.

On your example, does sectional density enter into something like a G7 ballistic coefficient calculation? Or is that purely based on the form and surface area of the projectile? I'm just used to punching them into a freeware ballistics calculator, not actually calculating the BC.

I always wondered, but never really thought about until this thread, why something like a howitzer shell, muzzle velocity somewhere around 2K FPS, could go for miles and miles. While my deer bullet starting off at 3K FPS, would be lucky to make it 2 or 3 miles.

Last edited by Gray Ghost; 05-21-2020 at 06:21 PM.
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Old 05-21-2020, 06:36 PM
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Doesn't have to do with the kinetic energy of the shell? It takes a lot more to move or stop it.

Think a 9mm has like 500 joules. A battleship shell, maybe 300,000,000?
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Old 05-21-2020, 10:57 PM
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When you are talking animals - most animals above a certain mass are roughly the same density as water - since animals are mostly water. The extra weight of bones is usually oofset by the airspace of lungs; some animals have more body fat, which makes them - slightly - less dense than those that are all muscle. Anyone who has seen a wet cat realizes too part of the perceived volume is simply fluff.

The key number here is terminal velocity - the speed at which the force of gravity on the mass equals the resistive force of air drag. For humans, this is typically about (rumor has it) 100mph. A mass will accelerate until it reaches that velocity. Cross-sectional area obviously increases with size, but as others point out, less than total mass increases with size, so the rule of thumb would be that bigger objects or relative same density have a higher terminal velocity. As others have pointed out, which particular cross-section is presented to the airflow determines the amount of resistance and so can affect the terminal velocity. An active faller can change that, as we see with skydivers; but typically, a motionless body tends to have a preferred stable position (or several) where the center of mass is forward of the most air-resistive parts - which is why bombs and missiles have fins and arrows have fletching.
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Old 05-22-2020, 06:38 AM
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The key number here is terminal velocity ... For humans, this is typically about (rumor has it) 100mph.
More like 120, for the standard belly-to-earth stable position.
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Old 05-22-2020, 09:05 AM
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Doesn't have to do with the kinetic energy of the shell? It takes a lot more to move or stop it.

Think a 9mm has like 500 joules. A battleship shell, maybe 300,000,000?
Assuming they have the same velocity (which is close enough to make a rough point in case of say M4 carbine firing 5.56mm bullet, relatively slightly higher muzzle velocity than a modern long barreled 155m gun-howitzer at full charge; a 9mm round fired from a pistol has much lower muzzle velocity than a 16"/50 AP shell with full propelling charge), the energy is in the ratio of mass, ~m*(v^2)/2, so back to my example the 155mm shell has around 21,700 times as much energy, or momentum (m*v) as the rifle bullet.

However air resistance is acting on a cross section only ~777 times larger in case of the 155mm shell than 5.56mm bullet, and air resistance is approximately proportional to that area. That's assuming same drag coefficient because same shape, which is not quite correct because of scale effect on flow regime (different Reynolds number), but it's practically close. A bigger error is assuming air density is the same. Actually you'd fire the 155mm at greater than theoretical 45deg elevation for max range (in a vacuum) because of the benefit of getting the shell to thinner air sooner in its flight. You'd fire the rifle at <45 deg elevation to get max range because even at 45 deg you waste too much energy overcoming air resistance.

Anyway the *biggest* effect between those two is the bullet's much higher air resistance (in a given density of air at a given velocity) relative to its mass. The air decelerates it according to F=ma. 'F', the force of air resistance, is much bigger relative to 'm' for a rifle bullet than an artillery shell.

Last edited by Corry El; 05-22-2020 at 09:05 AM.
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Old 05-22-2020, 02:58 PM
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video

Similar experiment at NASAs massive vacuum chamber with a bowling ball and feathers.
Loki's arrival on Earth in The Avengers was filmed in that same chamber: https://www.youtube.com/watch?v=pQKYN-yR2oM
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Old 05-23-2020, 08:00 PM
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Rosenkrantz et al already proved it.
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Old 05-24-2020, 09:40 AM
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