Thread: When people fall to their death

yeah, I was thinking it would be that too. Trying to land on your feet.

Originally Posted by tommo

Well, not really. We are sort of the same shape. Obviously they are just smaller. But they are also lighter so it evens out. So they would fall at ABOUT the same speed as us. I would guess anyway. As I said I suck at maths, but I think it's pretty obvious they wouldn't survive. Go try it.

Good guess, I thought the same at first, but our intuition is off in this case. I looked up the terminal velocity of a human (the coefficient of drag is difficult to determine, as it is in the drag crisis region for our free-fall conditions), and it is around 53 - 56 m/s depending on whether your arms are outstretched or not (not that big of a difference in speed)

The mass to weight ratio of a mouse, is about 11 kg/m^2, and for a human, it is about 120 kg/m^2, probably due to our longer, heavier limbs, compared to the mouse's small little feet. While the mass to area ratio to a degree determines the terminal velocity an object has, the coefficient of drag also plays an important role, and is completely dependent on the shape, and size of the object, as well as the speed it is falling, and the fluid it is falling through. The coefficient of drag does not depend on the mass of the falling object at all, which throws a wrench into the gears of intuition in some ways.

Assuming a mouse with a mass of 0.035 kg, and a projected area of about 0.0032 meters^2, falling in air, it would reach a terminal velocity of approximately 12.6 m/s. This is much slower than our terminal velocity. The coefficient of drag for a mouse is approximately 1.1, and is about a factor of 10 away from the drag crisis region (the area on the Reynolds number vs Drag Coefficient plot that gets all screwy and isn't a straight line, resulting in pain in the ass iterative calculations)

At the moment of impact, the mouse would have a kinetic energy of 2.78 Joules, whereas a human with a mass of 72 kg (about 160 pounds), would have a kinetic energy of 112,900 Joules.

But the real damage comes from the momentum of the collision over the time in which the collision occurs. Assuming that the collision occurs over a 0.1 second interval, from the moment your feet hit, to the moment you come to a rest, a person would experience 40.3 Kilo-Joules of force (38.1 kJ if you're falling with your arms out). A mouse, being much smaller, could be assumed to take 0.01 seconds for the impact to occur, this would result in only 44 Joules of force, (note 40.3 Kilo-Joules is 40,300 Joules), which is a much smaller impact force, and thus, a lot more survivable.

Having your arms spread out, would decrease the energy of your impact with the ground by 2200 Joules. I say it's worth the effort, as that's only less energy your bones have to absorb. That being said, 38.1 KJ is still a dangerously high amount of physical energy. If you were to belly flop into the ground, instead of landing feet first, your collision time would be reduced dramatically, resulting in much greater forces.

Originally Posted by Schmaven

Good guess, I thought the same at first, but our intuition is off in this case. I looked up the terminal velocity of a human (the coefficient of drag is difficult to determine, as it is in the drag crisis region for our free-fall conditions), and it is around 53 - 56 m/s depending on whether your arms are outstretched or not (not that big of a difference in speed)

The mass to weight ratio of a mouse, is about 11 kg/m^2, and for a human, it is about 120 kg/m^2, probably due to our longer, heavier limbs, compared to the mouse's small little feet. While the mass to area ratio to a degree determines the terminal velocity an object has, the coefficient of drag also plays an important role, and is completely dependent on the shape, and size of the object, as well as the speed it is falling, and the fluid it is falling through. The coefficient of drag does not depend on the mass of the falling object at all, which throws a wrench into the gears of intuition in some ways.

Assuming a mouse with a mass of 0.035 kg, and a projected area of about 0.0032 meters^2, falling in air, it would reach a terminal velocity of approximately 12.6 m/s. This is much slower than our terminal velocity. The coefficient of drag for a mouse is approximately 1.1, and is about a factor of 10 away from the drag crisis region (the area on the Reynolds number vs Drag Coefficient plot that gets all screwy and isn't a straight line, resulting in pain in the ass iterative calculations)

At the moment of impact, the mouse would have a kinetic energy of 2.78 Joules, whereas a human with a mass of 72 kg (about 160 pounds), would have a kinetic energy of 112,900 Joules.

But the real damage comes from the momentum of the collision over the time in which the collision occurs. Assuming that the collision occurs over a 0.1 second interval, from the moment your feet hit, to the moment you come to a rest, a person would experience 40.3 Kilo-Joules of force (38.1 kJ if you're falling with your arms out). A mouse, being much smaller, could be assumed to take 0.01 seconds for the impact to occur, this would result in only 44 Joules of force, (note 40.3 Kilo-Joules is 40,300 Joules), which is a much smaller impact force, and thus, a lot more survivable.

Having your arms spread out, would decrease the energy of your impact with the ground by 2200 Joules. I say it's worth the effort, as that's only less energy your bones have to absorb. That being said, 38.1 KJ is still a dangerously high amount of physical energy. If you were to belly flop into the ground, instead of landing feet first, your collision time would be reduced dramatically, resulting in much greater forces.

You forgot to factor in the elasticity of mouse bones compared to human bones. B+

If you can find the tensile strength and cross sectional area data for both human and mouse bones, just multiply the tensile strength by the cross sectional area to get the force required to break them (assuming random contortion of the skeleton upon impact, resulting in both compressive and tensile stresses). Divide that by the collision force (in Newtons) in my previous post to find what I call "the factor of carnage" (ie. how many times over the breaking point, or perhaps under for the mouse, that the impact energy would be)

anyways, it's way past my now

Originally Posted by Xaqaria

You forgot to factor in the elasticity of mouse bones compared to human bones. B+

Lol, I was going to say that too.

Originally Posted by Schmaven

If you can find the tensile strength and cross sectional area data for both human and mouse bones, just multiply the tensile strength by the cross sectional area to get the force required to break them (assuming random contortion of the skeleton upon impact, resulting in both compressive and tensile stresses). Divide that by the collision force (in Newtons) in my previous post to find what I call "the factor of carnage" (ie. how many times over the breaking point, or perhaps under for the mouse, that the impact energy would be)

anyways, it's way past my now

Uhmmmm.... you can do that for us?

Good post by the way. "How to survive a fall with mathematics". The nerds would eat that up lol.

After more math and physics classes than I can shake a stick at, I am quite amazed at what can be done using math. Going into college, having only seen an introduction to calculus, I had not even the faintest idea about how many things math could be applied to. Now I have a rough idea, and it's staggering.

Last semester we covered terminal velocities briefly, among other things, so it is still fresh in my mind. I have no problems with using what I've learned so far, as the saying goes, use it or lose it

Yep, very true. Wish I was good at math. Although most people wish they were good at anything they aren't lol.

The best way (perhaps the only way) to get good at math, is to practice doing math. I used to avoid homework at all costs, but now, it's the only way to learn the concepts.

Yeah, I know that. I used to be good up until about year 10, maybe 9. Then it just got too much for me lol. Anyway I meant like mathematician level. Thinking of everything mathematically, seems like a nice way to live lol. No hope of me getting to that. Anyway I'm way passed doing maths homework now.

Thinking of everything mathematically seems like a very impersonal way to live. There's definitely many situations where thinking mathematically is helpful, but usually, those do not involve people, and if they do, well that's just not the way I think relationships should be handled.

On a more related note, flailing your arms around changes your moment of inertia, which is directly proportional to your rotational speed. So perhaps unconsciously, we flail our arms in such a way as to land in a better orientation.