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.
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.
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.
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.
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.”
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.
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…
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.
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.