# Would an Ant die if dropped from the ESB?

1. Mar 20, 2005

Relating to the 'would i die' thread

I noticed that Ants survive dropping through a lot more height than we do, of course in proportion to their body size.

No my question is: would it die if dropped from the Empire state building?

2. Mar 20, 2005

### gerben

No, unless it would fall in water or fire perhaps, but it would not die from impact with the floor.

3. Mar 20, 2005

### Danger

I believe not. Things in the insect size category have relatively low density. Terminal velocity for them is lower.

4. Mar 20, 2005

### Billy T

I bet an ant is denser than you are. It is the fact mass goes as the cube of typical dimension and surface area only as the square that saves him. (Same reason that there are not skin breathing insects the same size as cars. - so in some sense you could argue that all creatures that breath only thru their skin get to fall and not die) Ant design has a lot of fine parts sticking out - this also helps with a lot of terminal velocity drag.

Reason i think he is denser than you is that your dense part (bones) are small fraction of total on the inside. His dense parts probably are not as dense, but are on the outside and represent a much greater fraction of his mass. Fact that he can "walk on water" and you can not is not counter proof. this has to due with surface tension in /on water's "skin." I don't know what the results would be, but would not be surprised if he sinks when a little detergent is added to him, to locally destroy the surface tension - try it an let me know.

Last edited: Mar 20, 2005
5. Mar 20, 2005

### gerben

Indeed the ant will have more surface area per unit of its mass than a man, but I think the most important difference is simply the difference in their mass.

Assuming no air friction the end velocity does not differ for different masses, but the force on the body when hitting the ground is larger for the more massive body:

mv = Ft
(where t is the short time that it takes the body to come to a stand still when contacting the ground)

So although v may be a little different (and t also a little) m is very different. Assuming a mass of 1 gram for the ant and 100 kg for the man it will be a factor of 10^5.

(more a biology topic, but as far as I know there are no skin breathing insects. Insects breath through tracheae, skin breathing occurs in worms and amphibians.)

6. Mar 21, 2005

### Billy T

Under your assumption that there is no air friction, the Vs would be the same, but I think / assume that the original question about ant falling from ESB was assuming it was thru air. If in vacuum tube, my money is still on the ant, but I bet he can no longer walk. A "top" to "ground" fall is only implied in original post but not really possible as cross section up there is smaller than a few floors down. i. e. in view of this fact, "fall from top" may be only 30 or 40 meters. Ant might make it, if get him out of vacuum tube in a few minutes, but man will not.
That is what I meant - thru small holes in their "shells" - that term also wrong - I forget correct terms. I think most "amphibians" get most of their oxygen via lungs, but could be wrong about this.

7. Mar 21, 2005

### Danger

Who said I can't? :uhh:

Okay... I can't. But I can run on alcohol for extended distances.

8. Mar 21, 2005

### Billy T

Many years ago I mentally invented "water shoes" that were somewhat like snow shoes. Each had many small holes covered by rubber flaps on their bottoms that would easily open to break "suction" when I lifted my foot. I never made them, but remain convenced that a strong guy in good shape could run across a small calm pond with them - but perhaps he would need some of your alcohol fuel

Last edited: Mar 21, 2005
9. Mar 21, 2005

### cronxeh

Assuming no air friction? Are you kidding?? Thats one of the biggest factors that saves the ant!

P.S.: OP, you are a monster! Should be banned from all skyscrapers :rofl:

10. Mar 21, 2005

### gerben

Yes of course the friction is important but I guess that the difference in the velocity of the ant and the man when they hit the ground would be less than a factor of 10^5

since the force they feel is mv/t, I was just trying to reason what would be more important here m or v...

11. Mar 21, 2005

### krab

At terminal speed, air resistance balances weight, so
$$C_DAv^2=mg$$
The "killability" of a fall relates to the total kinetic energy per unit mass of the body absorbing the kinetic energy. This is simply proportional to v^2. But from above formula, v^2 is proportional to weight over area. Since weight is proportional to length^3, and area to length^2, v^2 is proportional to length. An ant is one thousandth the linear size of a man, so its fall from a height sufficient to achieve terminal velocity (which BTW is only a few inches; ESB not needed) has only 1/1000 the killing power of a fall of a person from ESB.

12. Mar 21, 2005

### Danger

I like the idea, but I think that's there's a lot more engineering involved. For one thing, the flaps when open would cause a lot of drag. I don't know what's abovethe flaps, so whether you're dealing more with vacuum suction or surface tension is in question. No doubt you can work something out that works. At least make your flaps hinged at the front so that they act as little ratchets to keep you from sliding back. That will also minimize their drag. The most serious difficulty that I see is in maintaining balance and not just doing a face-plant combined with the splits. Maybe longitudinal strakes? Anyhow, good luck with it.

13. Mar 21, 2005

### Danger

Now, enough theorizing. Will someone in the New York area please just throw a damned ant off of there and see what happens? (You might want a ground-based observer with very good eyesight.)

14. Mar 21, 2005

### Billy T

I am too old to do it now. Idea was many approx 1/2 inch dia. holes in hex pattern about 1.5 inches apart. Each thin flap was much smaller than you are guessing with only a staple at front for ease of construction. (no drag -slight thrust see below)

I had computed the "contact time" of each foot/shoe and as recall the verticle impulse gained from only about two square feet of water being forced down one inch was enough to hold me up. The flaps are to let me extract my foot/shoe from this one inch depression with as little effort as possible (and as secondary consideration, shed some of the water that got on top of shoe thru the shoe (as well as off the sides and ends) I was pleased to note that falling water thru the tilted flaps had some (insignificant) forward thrust as it slid down the open flap.

You are perhaps correct that the flaps might give some traction for placing a forward force on your body. (Unlike running on dirt, water's coefficient of friction is not much help in this regard.) I was not counting on this, and think it a net disadvantage as makes it harder to lift foot, (speed of impact with water is essential) so I also had several thin vertical fins (about 3 inches deep/tall - I thought would be good) that went transversely on the bottom of each shoe to get some "purchase" on the water for generation of forward force - don't need too much once you get going (Newtons first law and all that stuff.). That is, IMO, it is better to divide the "break suction/ lift foot easy" task for the "get some traction" task and optimize each separately. Your welcome to my design ideas - just let me know if I was right. Good luck to you - summer is soon there in your hemisphere. get busy. (You can swim can't you )

Last edited: Mar 21, 2005
15. Mar 21, 2005

### Brinx

I'm not perfectly sure, but I believe the critical 'to die or not to die when falling at terminal velocity' mass for animals is somewhere close to that of the average mouse. Of course, it depends on specific body geometry - but if that isn't too exotic the value should hold.

16. Mar 21, 2005

### Danger

You are too old to do it now? If you're anything like typical of this site, I have socks older than you.

No, actually. Semi-true: I know how, and used to love to when I was a kid (mostly underwater, though). My problem now is that I go into hypothermia if I get wet. I've tried even heated indoor pools, and just can't handle it. I even had to buy a deep-sea wetsuit to play baseball in because they refused to call our tournament games in a hail storm. I couldn't see the catcher through it, and the batter was a blur. That might not have been so bad if I hadn't been the pitcher. (If my bathing habits concern you, I use a very hot bathtub and into a terry robe as fast as possible.)

Last edited: Mar 21, 2005
17. Mar 21, 2005

### Danger

I live in Alberta! What the hell is 'summer'?

18. Mar 22, 2005

### Billy T

Easy question - It is when you need my "water shoes" to walk across the still zero degree C, but now liquid, pond.

19. Mar 22, 2005

### Billy T

I doubt it - I never throw anything away.

I mentioned that I had estimated the "contact time" - let me tell a little more about how as it gives someway for you to judge my age.

When Roger Banister did the "imposible" - ran a mile in under 4 minutes - the local newspaper gave some of his stats - from his stride, 5280 feet/ mile and 4 minutes, I computed the contact time, assuming that in the case of my water shoes, one shoe would always be in contact. His feat, was also partially responsible for me doing the "serious calculations" /design but many years earlier I had thought of the basics idea as I watched ducks run on the water to get up "flight speed" (I assumed that a strong sprinter could keep up his pace for nearly a minute even though it would be much harded to brake contact with the water. That is why the target crossing is only a "small calm pond.")

I probably should also note that I was fishing when watching the ducks - gun powder had not yet been invented. (but socks had, so you still have a case, if yours are really old.)

Last edited: Mar 22, 2005
20. Mar 22, 2005

### Billy T

Also depends on what you hit at end of fall - Concrete not recommended, even for skinny mouse.