Also true?
There’s also the factoid that the energy in the collision is proportional to
1/2 * m * v^2
where m=mass and v=velocity
slow speed (in particular) and small mass => small damage forces?
Welcome to the Message Boards, mvsmith, glad you’re here. It’s helpful to others if you post a link to the Column or Staff Report that you’re commenting on – helps avoid duplication and keeps us all on the same page.
In this case, Why can bugs fall great distances and survive, but humans won’t?
I was just reasing that thread and I think cecil is overlooking the obvious in that particular question.
The 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?
The reason even more than air resistance is the fact that falling from six feet the amount of “g’s” is the same for the bug as for a man dropping 6 feet not the same as a man dropping 6 STORIES.
The sam bug dropped from 6 stories may well NOT survive.
The air resistance WOULD be a factor in a fall of 6 stories and many bugs simply have enough surface area to counteract the pull of gravity, but many particularly most beetles would splat just as effectively as a human body would.
If you consider that gravity is 32ft/sec/sec at 6 feet there is not even time to reach 32 ft per sec. they arent harmed simply because they are not going fast enough.
the above would also explain how a small animal like say a chihuahua can jump from a bed of a 4x4 (which might be equivalent to a person jumping 3 stories) yet is unharmed.
While the Physics in this article is not bad, I think we can probably do better. For one thing, the test human is a 6’7¾" block weighing 200 lbs? I think they have more accurate numbers for this kind of thing. I believe it would be useful to compute, for both the ant and the human, the terminal speed, and also the speed at impact.
It really doesnt matter the acceleration of gravity remains the same regardless of the size of the “test dummy”. 32 ft per sec/ per sec.
It remains the same whether an object is mineral, vegetable or animal. the only thing on earth that needs to be computed along with it is air resistance.
The difference in results with the larger dummy would be tiny compared to say even a 5’ dummy. there would be very very little difference in your results.
Thanks for replying! My first time at this site…cool idea. yuhno, I clicked a button at the bottom of the “bugs” entry that said something like Comment on Staff report, and jumped to what seemed to be a generic Staff Comments board.
Are you saying that I should copy the entire title of the entry
and paste it in my msg? Absolutely no criticism intended (again,
great site), but I sort of assumed that your system would keep track of which report was being commented on, so I was a little confused upon arrival at the board. Of course, I’m often a little confused for no apparent reason…right now, for example…it’s 3:45am, and I’m limping along on barely half a lobe.
(yawn) nightynight…
–Chris
p.s. Stay tuned for my attempted corrections to the “pixels and film” entry, which really needs straightening out. (I can say this because once I wrote entries for a technical dictionary published by a Major Software Company, so nyah!)
The title, mvsmith, is not as important as the URL, the web location. For this Staff Report, it’s:
Echoing Achernar, and you can provide the link by just typing the URL as Achernar did… or you can get fancy, like I did, by typing {url=“http://blahblahblah”}title{/url} … where blahblahblah is the url (keep the quotation marks) and where title is whatever you want for a title.
Except use square brackets [ and ] instead of curly brackets { and }. Hope that’s clear, mvsmith, and we’re glad to have you with us. Sorry if it was a li’l confusing, you’ll catch on.
Mv, that is a bit confusing. The link at the bottom of the columns is a generic link to the board, as opposed to a link to a specific thread for that column. Many a person is thrown by that little detail. So when you come to the board, you first must find the correct forum (Staff Reports vs. Cecil’s columns, etc), then decide if a current thread is already addressing your question, or start a new thread. (It also helps to search for old threads.) If you start a new thread, you should put a link to the column in question in the thread. As described, copy the URL from the column page and then paste it into your text window and it will automatically become a link. For fancy stuff, you can use vB formatting codes that are similar to html, but it isn’t necessary. Also, making your thread title something specific to the question is very useful to help keep redundant threads from forming.
The two important features would be air resistance and impact energy. The column discusses air resistance. The above posters mention imact energy. Both are relevant.
from the stated height of 6 feet the “air resistance” would have a negligible effect on all but the least aerodynamic. 4It isn’t even about impact energy. It is about falling time and speed at impact.
Air resistance is not negligible for small objects like insects. Terminal velocity for a human being is roughly 50m/s (150 ft/s) Terminal velocity occurs when drag on a body equals the force due to gravitational acceleration:
C[sub]D[/sub][symbol]r[/symbol]AV[sup]2[/sup]/2 = mg
where C[sub]D[/sub] is the drag coefficient, [symbol]r[/symbol] is the air density, V is velocity, m is mass, and g is gravitaional acceleration. Rearranging,
V = SQRT(2mg/C[sub]D[/sub][symbol]r[/symbol]A)
Comparing an insect to a human, we know that [symbol]r[/symbol] is the same, we can assume that C[sub]D[/sub] is about the same (I’d guess it’s larger for an insect, actually, what with those legs and all), and, from the analysis in the staff report, (m/A)[sub]human[/sub] = 20.3 and m/A)[sub]insect[/sub] = 0.36. Substituting and dividing,
V[sub]human[/sub]/V[sub]insect[/sub] = SQRT(20.3/.36) = 7.5,
so the terminal velocity of an insect ought to be about 150/7.5 = 20 ft per sec. A six foot fall ignoring air resistance gives a velocity of 19 ft/sec, so you can see that air resistance is indeed an important effect at this scale.
you fail to take into account that with a fall of 6 feet with acceleration of 32ft/sec/sec, the length of time spent falling brings you nowhere near that “terminal speed”. Air resistance would be negligible except as 4I stated above in cases where a particular insect has a very large surface area compared to weight like for instance a butterfly. Something like say a potato bug would have LESS overall air resistance than a human body would. It stills come back to the fact that gravity pulls on all things equally and at 6 feet you simply do not have enough TIME to develop sufficient speed.
consider that a human falling from 60 ft would fall for about a second and a half before impact which would give a speed of about 48 ft/sec at impact. The bug would fall for significantly less time and would have an impact that is also significantly less.
If you measure the force as a multiple of gravity, the “G” forces would be much less on the bug at impact.
-
Actually, I specifically did take into account the length of time spent falling from six feet. A six foot fall ignoring air resistance gives a velocity of SQRT(232ft/sec/sec6ft) = 19.6 ft/sec. This speed is basically near what the calculated terminal velocity for an insect is anyhow, which would indicate that air resistance is not negligible.
-
In what way do you argue that a potato bug (for instance) would have LESS overall air resistance than a human body? It’s pretty clear (as covered in the staff report) that the human has a significantly higher surface-to-mass ratio. If you’re arguing that the potato bug has a lower drag coefficient, I would disagree. What I ignored in my previous post is that the drag coefficient tends to increase with decreasing scale, particularly as the airflow changes from turbulent to laminar. So, from the effect of either parameter, any bug has a significantly greater air resistance than a human.
-
However, I agree that a primary difference between impact of a human and a bug is the speed of impact. A human falling from 600 feet would probably be near terminal velocity; an insect falling from 6 feet would probably also be near terminal velocity, but these terminal velocities are greatly different.
In thinking about this, I do believe that there is a section of the Staff Report that, while not being wrong, per se, is at least misleading. The Staff Report says that “the human’s mass:surface area ratio is several times greater than that of the ant [and therefore] there is a significant disproportionality between the two species when they hit the pavement.” I disagree with that conclusion.
Consider two squishy objects, one of which (object A) is ten times larger in length, width, and height than the other (object B). Thus, object A has 100 times the surface area and 1000 times the mass of object B. Suppose, furthermore, that both objects were to hit the pavement at the same speed. As the Staff Report implies, every square inch of object A has ten times the weight stacked on it that any square inch of object B does.
However, what the Report overlooks is that force on each square inch is the mass times the deceleration of the body. Since object A is also ten times as tall as object B, it can flex ten times as much, and will take ten times as long to completely stop, giving only one-tenth the deceleration of object B. So, the force per inch seen by both objects ought to be the same, rather than higher in the larger object, as the Staff Report implies.
Of course, just how an object is damaged is more complex: physiological differences (as mentioned in the report) are important, as well as ability of the materials of the body to absorb energy, and so forth.
Bottom line, though: surface/mass ratio is important in establishing a lower terminal velocity (and subsequent impact velocity), but probably little, if any, importance in ameliorating damage at impact.
But the lower terminal velocity does mean less damage at impact. The bug and the person won’t be going the same speed at impact, so there’s no point comparing what would happen if they were.
And a potato beetle will feel less force from air resistance than would a human, but it will feel a greater force per mass. Depending on what definition you use for “coefficient of drag”, you can get a number that’s larger, smaller, or about the same. In any event, though, air resistance is definitely more significant for a smaller object.
Sure, absolutely, it’s the lower terminal velocity that means less damage on impact. However, the Staff Report suggests that, in addition to the effect of lower terminal velocity, the bug suffers less damage upon impact because of it’s smaller mass:surface area ratio. I suggest that the mass:surface area ratio has no effect on impact (although it does on terminal velocity itself). The comparison between two bodies falling at the same speed is simply a thought experiment to demonstrate my point; if you disagree, I’d be interested in an explanation of how a smaller mass:surface area ratio would decrease injury over and above its effect on decreasing terminal velocity.
The only definition of drag coefficient I’ve ever seen is pretty standard:
C[sub]D[/sub] = (Drag Force)/([sup]1[/sup]/[sub]2[/sub][symbol]r[/symbol]V[sup]2[/sup]A)
where [symbol]r[/symbol] is air density, V is velocity, and A is frontal area. This’d be simply a catch-all coefficient that contains the effects of the fluid dynamics around the body. (I’ve tucked in the mass/area idea into the terminal velocity equation in my first post.) Notably, drag coefficient increases for smaller scales (smaller Reynold’s numbers, really). In any case, as you say, air resistance is definitely more significant for a smaller object.
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. The man would have time to fall longer and experience the acceleration of gravity for a longer period and would gain much greater speed.
If a human were shrunk to the size of a bugs mass and jumped from six feet, it should be no more injurious to him than it would be for him fall the same distance at full size. It isn’t the “relative sizes” that matter it is the time of acceleration that matters.
Rhapsody, you’re assuming the structural integrity of the human would not change even though you’ve shrunk it down to the size of an ant. This is most certainly not going to be true. Consider the strength of bone. Femurs the thickness of hairs will not take the impact that femurs the size of, well, femurs. Okay, the thick end of a pool cue. Given that is the case, I don’t think you can blithely dismiss a 6 ft fall for a human shrunk to insect size. The velocity won’t be any higher than a human falling from that height, and the impact energy will actually be a lot less (just like a bug), but the tissue can’t take the impact.