If a human falls out of a sixth story window, he/she dies. When a bug falls from a proportional height, six inches or so, it should not. Your post stated that this happens because a bug has a smaller mass to surface area ratio. This may not be true for all bugs, so your logic does not entirely answer the question.
Rather, there is a scientific principle stating that all objects will fall at the same rate regardless of mass. Air resistance, of course, factors in to this. To complicate matters further, air resistance becomes a greater factor when falling from greater distances (for example, six stories instead of six inches) because eventually a falling object will reach terminal velocity, meaning that air resistance totally cancels out acceleration due to gravity. At that point, a falling object will continue falling at its current speed and not fall any faster.
Anyway, as I was saying, there is a more suitable way to explain the original oddity (that a bug will not die if it falls six inches, whereas a human will when falling from a comparable height). Since all objects fall at the same rate, theoretically a bug and a human would both hit the ground at the exact same rate if they were dropped from an identical height. So, a bug and a human would both probably die if they were dropped six stories, because they’d hit the ground at the same rate. And a bug and a human would both probably survive a six inch drop, for the exact same reason.
A bug may be a bad example, because of considerations of terminal velocity.
But I remember an example I read long ago. Given the same mineshaft:
A mouse walks away.
A rat is stunned.
A dog is crippled.
A man is killed.
A horse splashes.
A link to the staff report is appreciated. Why can bugs fall great distances and survive, but humans won’t?
I think there’s a lot more to it than just air resistance. If you correct for that by arranging for the ant and the human to hit the ground at the same speed, I very stongly suspect the ant will still fare better. Again, it’s because of the mass/area ratio. The ant has proportionately more surface area over which to absorb the impact.
Surface area is important here. If God wanted to punish you for not linking to the Staff Report (:D), he might drop you from a great height onto a church below. You would be better off landing on the flat roof (large surface area) than on the steeple (small surface area).
The terminal velocity of a falling ant is negligible, and reached very quickly. As you get smaller, air becomes effectively thicker and thicker, and offers exponentially more resistance (does the term “Reynolds Number” mean anything to you?). The smallest insects (0.015mm) have extreme difficulties reaching the ground again once they become airborne, because the slightest air movements will hold them aloft. Essentially, an ant falling six inches is like you jumping into a six-meter pool wearing a few lead weights - you’ll sink, all right, but you won’t hit the bottom very hard.
here’s my take on it, and I will keep it simple because those damn symbols and equations in physics confuse the hell out of most people, including me.
Assuming that everything falls at the same rate (this is strictly true ONLY IN VACUUM, which is why the staff report correctly discussed air resistance), we’ll assume for the sake of argument that the velocities of a falling ant and a falling human are the same. Even then, take a look at the difference in momenta:
momentum = mass x velocity
p = m x v
(let’s assume the velocity is a constant 20 metres per second in both cases)
so
ANT momentum: 0.00002 Kg x 20 m/s = 0.0004 Kg m/s
HUMAN momentum: 90 Kg x 20 m/s = 1800 Kg m/s
The human has a MUCH higher linear momentum even though both are moving at the same (even terminal) velocity.
Now remember that for every action there is an equal and opposite reaction. Slam your fist in a wall and it will hurt like hell because the wall effectively hit your fist back in the same instant you hit it. A car crashing into a solid wall is wrecked because the wall hit the car back.
When the ant and human crash into the pavement, they come to a full stop in a very short time without significantly budging the pavement; I think this is called a completely inelastic collision. The change in momentum, or impulse, is therefore very simple to calculate (just add a negative sign to our previous figures):
change in momentum for ANT = -0.0004 kg m/s
change in momentum for HUMAN = -1800 kg m/s
The reaction force from the pavement acting on the decelerating human is thus much larger than the reaction force on the ant in the same elapsed time.
Velocity is a factor insofar as it is used to calculate momentum, so even if both ant and human reach the same terminal velocity (impossible in an atmosphere) what will really make the difference is mass, because the human is orders of magnitude heavier than the ant. In this example, the human is splattered from the deceleration/loss of momentum, and the ant will probably walk happily away, because the ant’s mass is much closer to zero than the human’s (if an object has zero mass, it has zero momentum and can collide happily with whatever it wants).
Er, I think that should be more or less right. Feel free to correct any errors or explain items that I have skipped in this process.
While it’s true that a bug would have far less momentum (and hence a far lower force on impact) than a human, acceleration is more relevant than force, for figuring the damage done. Here, humans would actually have a slight advantage over bugs, since we can compress some (a good deal, if we land on our legs), and thus increase the duration of the collision and decrease the peak acceleration. In other words, if a human and a bug both fell the same distance through vacuum (picture a termite in a little miniature spacesuit), the human would have a better chance of survival than the bug.
By the way, a “perfectly inelastic” collision means that the two bodies end up at rest relative to each other, without rebounding. An inelastic collision (not necessarily perfectly inelastic) is any collision in which some of the initial kinetic energy is converted to other forms (usually heat). The deformation of either object isn’t an issue.
Chronos is correct that mass and momentum are irrelevant for this consideration. The impulsive force halting the fall of the object is equal to the integral of the force over the time of impact. Because this has to be equal to the momentum: mv=ma(t2-t1) and mass cancels. Thus objects traveling at the same speed with impacts of the same duration will experience the same net deceleration. The question is then which species can withstand the greatest deceleration?
I’m trying to find a more accurate reference, but I remember a study where the deceleration of a click-beetle at the end of its ‘click’ was in the neighborhood of 2,300g- something I’m sure would turn most people into street pizza. Will return with the cite and more accurate info.
There’s several things here that I wish I could crunch numbers on.
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Chitten (the exoskeleton on bugs) is pretty tough stuff. It also comes to mind that it is easier to break a large thing than a small, I guess 'cuz of leverage. (Breaking a long stick is easier than breaking a short one.) Given the small amount of kinetic energy in a falling bug, the exoskeleton will be safe. It might distort a bit, but should spring back.
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I’m trying to figure out why using your legs to absorb the impact will lead to less damage than, say, a belly flop. Eventually the kinetic energy all gets disappated as heat, but not before it deforms. My first thought was that maybe the heat is evenly distributed over a large amount of muscle, which is designed to deform with minimal damage. Whereas in a belly flop the energy deforms internal organs and bones before the energy is disappated. As for spreading the energy across a period of time, that affects the degree of distortion that the internal organs would suffer. Does that make sense? I think health effects of a fall have a lot more to do with organ damage due to shape deformation than simply the amount of energy that eventually ends up as heat.
As for bugs, do they even HAVE internal organs??? I vaguely remember disecting an earth worm in middle school, and I remember thinking that nothing I saw in there looked particularly necessary for life.
sford wrote: “As for bugs, do they even HAVE internal organs??”
This is so disheartening. It shouldn’t be necessary for anyone in the year 2001 to have to ask such a question, but since it was asked…
ALL members of the Animal Kingdom have internal organs, they just vary in what they are and how they’re arranged. The minimum is in parasitic forms like tapeworms, where the only organs are reproductive. Arthropods are internally quite complex, as invertebrates go, really only surpassed by mollusks.
As for chitin, it is a white, amorphous compound, and virtually the purest form you’ll see in nature is those little white Agaricus mushrooms. Chitin is soft and flexible. The exoskeleton on bugs is made of sclerotin, which is a hard substance based on chitin that has been biochemically altered to various degrees (compare a caterpillar and a beetle).
<< As for bugs, do they even HAVE internal organs??? >>
Don’t fret, Doug. He was probably talking about lawyers (bugs with no hearts) or possibly politicians (vermin with no brains.)
(note to self - use smilies when making a joke)
Reminds me of a Far Side where the boy bug was trying to figure out which doo-hickies are the girl bug’s lips. 
As for chitin/sclerotin, I didn’t know that. Thanks for the info!
That’s incorrect. In fact four Phyla are commonly considered to lack organs. The Porifera (sponges) and the extremely simple Placozoa are usually considered to even lack tissues. In the case of the coelenterate phyla, the Cnidaria (jellyfish, anemones, hydras) and Ctenophora (comb-jellies), because “discrete cells of different types do not carry out the internal functions of the animals,” they “are considered to be organized at only a tissue level.” True organs arise at the “flatworm” level (Platyhelminthes, Nemertea, and Mesozoa).
Actually, come to think of it, the phylum Mesozoa (or Rhombozoa, or Dicyemida) also includes animals that lack tissues and organs, since they consist of as few as 20 cells. The dicyemid Mesozoans are parasitic (or commensal) wormlike organisms found only in the kidneys of cephalopods. (How’s that for a restricted niche!) It is uncertain whether their simplicity is primitive, or whether they are just extremely reduced forms descended from more complex organisms.
(Other animals sometimes included in the Mesozoa, the Orthonectidea, lack all organs except gonads.)
sford said:
It has to do with impulse, or the speed of energy dissipation. Consider the difference between a soft object that gives, like a big fluffy mattress or a trampoline, vs. a hard rigid item like a concrete floor. As the object impacts the soft surface, the soft surface starts to resist a little, but then gives and slowly increases the resistance. Thus energy is dissipated along the whole curve of the stretch of the padding. Whereas impacting the rigid surface means all the resistance happens instantaneously. Your legs act like the trampoline (to a point) while the torso acts like the cement. Those are exaggerations, but there the difference is in how much give there is.
As for what causes the damage, your legs are designed to bend a certain amount, and muscles absorb energy up to a point, whereas your torso is not designed to deform in that manner. So you are correct that the deformation causes the damage that kills. Deformation in this case includes cracked bones (like ribs and skull), smooshed organs (like liver and kidneys and brain), not to mention collapsed lungs, and a strong jolt to the heart that could upset the rhythym of beating. But the brain damage is what does you in.
Think of it this way - when paratroopers are being trained to land from parachute drops, they are taught to land on their feet, but bend their legs and fall to the ground in a roll rather than land it standing up (straight legged) or on their belly. The reason - bending the legs and turning into a roll absorbes the same impact energy spread out over a longer period of time using the bodies natural shock absorber, plus converting some of that energy into kinetic motion in a different direction.
Obviously you reach a point where landing on your legs doesn’t help enough - the leg bones shatter, the spine takes too much of a jar and can break and sever nerves, and the brain gets too shaken.
gonz007, what makes bugs able to take more deceleration?
I knew I was forgetting something in my obsession on momentum.
I don’t understand how momentum and mass are not issues here though. The rate of deceleration clearly affects what happens in a collision, but mass and momentum have a lot to do with it too. In my example, I did not take into account the amortization that our limbs can provide. I don’t think it’s too much of an issue when you are falling from a great height, as whatever you do to save yourself will be pretty much negligible in terms of the concrete pavement (unless you took the precaution to fall out of a window wearing big springs on your soles).
KE = (1/2)m x v squared
Kinetic Energy therefore depends on mass (the higher the mass, the more energy) and on velocity (double the speed and you quadruple the kinetic energy).
So assuming that neither insects nor humans falling from the sixth floor of a building will hit and roll to dissipate energy over a period of time (there is abrupt deceleration for both hitting the concrete), and also assuming that both insects and humans are falling at the same rate, how exactly does one calculate damage?
From what I can figure out, mass is still an issue, and momentum too, along with energy–I say that because all three are closely connected by the formulae. If mass were irrelevant, momentum would be irrelevant too, yet mass determines energy–with low mass there is low energy, and with high mass there is much higher energy. And momentum too, which determines the force of impact.
Abe
Colibri wrote:
"That’s incorrect. In fact four Phyla are commonly considered to lack organs. The Porifera (sponges) and the extremely simple Placozoa are usually considered to even lack tissues. In the case of the coelenterate phyla, the Cnidaria (jellyfish, anemones, hydras) and Ctenophora (comb-jellies), because “discrete cells of different types do not carry out the internal functions of the animals,” they “are considered to be organized at only a tissue level.”
I guess I was subconsciously considering only the Eumetazoa, and thus excluding sponges and placozoans, which definitely do lack internal organs. Cnidarians have a stomach, and, simple as it may be, I think that if zoologists call it a stomach, then it could be called an internal organ; they also do have gonads. It may not satisfy the technical definition of an organ, but it’s close enough. As for “Mesozoa”, I’d never heard of them, and the latest review of all life forms on earth (“The Variety of Life” by Colin Tudge, 2000) does not contain the words Mesozoa, Rhombozoa, Dicyemida, or Orthonectidea, not even as alternative names for known phyla. I have no idea who coined those names.
Okay, I did some web searching, and Mesozoa all appear to be parasites, and are therefore likely to be degenerate members of other phyla that have lost so many features as to be unrecognizable. That’s a common theme in parasitic groups, like Pentastomids and Linguatulids, which were floating around in taxonomic limbo for centuries before someone figured out where they belonged. I’d bet the Mesozoa are a similarly artificial group of things that belong somewhere else, rather than genuine intermediate forms between Parazoa and Eumetazoa.
OK, if you want to think of it this way, a massive organism will take more damage from a fall, but it can also survive more damage. If an elephant has a half-inch deep cut, it’s in fine health, albeit perhaps a bit angry. If an insect has a half-inch deep cut, there isn’t even anything left of the insect. If you’d prefer, instead of humans, think of several million beetles falling, all holding hands to form a human-sized body. Should all the bugs die, now, just because they’re holding hands?
How you land is very important. If a human lands on his torso, you’re talking about the impact being spread over about 5 centimeters (rough estimate of how much the chest could compress). If he lands on his legs and bends his knees, that’s over 50 centimeters, and if he lands on his legs and then rolls, it’s a meter and a half or so. This means that the time of the collision will be extended by a factor of 30 or so, which means that the maximum acceleration will be decreased by the same factor. This means that a person who tucks and rolls will be able to survive a fall from about a thousand times the height of a person who belly-flops.
Disclaimer: The above post neglected air resistance entirely, as that issue has already been well-covered.
I dunno, Doug, but if I were you I wouldn’t go around admitting I had never even heard of a whole phylum, at least one like the Mesozoa that is often considered to be of some phylogenetic significance. That’s a bit infra dig. for a professional biologist. OK,
Mesozoa isn’t one of your superstar phyla like Arthropoda or Chordata, but because of their extreme simplicity they invariably come up in discussions of the origin of multicellular animals (citations if you want ‘em). It’s not as if they were one of the truly obscure bizarro phyla like the Loricifera (found in the interstices between grains of sediment) or the recently discovered Cycliophora (found only on the mouthparts of lobsters). They are mentioned even in introductory texts like Biological Science (Keeton and Gould) or Life: The Science of Biology (Purves and Orians), and any good text on invertebrate zoology will invariably devote a chapter or at least a sub-chapter to them. To give you the benefit of the doubt, I’ll bet you have at least heard of them, but have just forgotten them. Perhaps a little refresher course in General Biology might be in order. 
I can’t comment on Tudge directly, since our library doesn’t have it. If it is as woefully inadequate as you say, I would recommend pitching it in the trash. (Perhaps there is a good reason why our librarian chose not to get it). In comparison, Five Kingdoms (Margulis and Schwartz 1988), another such review, devotes a couple of pages to the Mesozoa, and lists the genera. FYI, the genus Dicyema was described by von Köllicker in 1849. The Belgian biologist Éduard Van Beneden coined the term “Mesozoa” for them in 1876, since he considered them to be intermediate between the Protozoa and the Metazoa. The phylum has often been considered to include two groups, the dicyemids and orthonectids, but as they are rather dissimilar it is now perhaps more common for them to be split into two phyla, the Rhombozoa (for the dycemids) and the Orthonectidea. The enigmatic Salinella, collected from salt beds in Argentina, is usually lumped with the Mesozoa, although a separate phylum, Monoblastozoa, has also been proposed for it.
Stunkard (1954, Quarterly Review of Biology 29:230-244), has been one of the main proponents of the view that the dycemids are actually degenerate Platyhelminthes. Others have contended (e.g. Willmer, Invertebrate Relationships, 1990) that the putative resemblances to flatworms are spurious, and the dicyemids are independently derived from protozoans. However, recent work on rDNA (Ruiz-Trillo et al. 1999, Science 283:1919-1923.) groups them with the triploblast phyla and indicates that they probably do represent reduced forms, although I believe their true affiliations remain to be determined.
“Close enough?!” I am shocked - shocked! I thought the watchword of Cecildom was accuracy, not close enough. Close enough, as they say, is only good eough for gummint work.
The typical definitions for “tissue” and “organ” are given by Keeton and Gould (p. 121, third edition) as: “A tissue is composed of many cells, usually similar in both structure and function, that are bound together by intracellular material. An organ, in turn, is composed of various tissues (not necessarily similar) grouped together into a structural and functional unit.” Traditionally, among multicellular animals the Porifera and Placozoa have been considered to have a cellular grade of organization, the Cnidaria and Ctenophora a tissue grade, and the remaining Metazoa an organ grade (ignoring such anomalies as the Mesozoa). Hyman,
for example, in The Invertebrates (1940), uses the heading “Metazoa of the Tissue Grade of Construction” for the Cnidaria and Ctenophora. OK, these two groups may have structures that are, in casual usage, referred to as a “stomach” (actually just a layer of epithelial cells lining the gut) and “gonads” (merely aggregations of reproductive cells), but as they are generally
composed of only a single type of tissue they are not really comparable to the organs of other Metazoa.
However, I will grant you there is a lot of sloppiness in the use of these terms. Since it is easy to find references that mention “organs” of one kind or another being present in the Cnidaria and Ctenophora, I’ll cede the point to you. However, these authors are clearly either using a non-standard definition of “organ” (although this is usually unstated), or more commonly are just being careless.
In any case there are at least three phyla, Porifera, Placozoa, and Mesozoa, that lack organs, and as perhaps many as eight if the Mesozoa are and Porifera are split - there’s a recent proposal to split the glass sponges from Porifera - and if the Cnidaria and Ctenophora are included in the list, as they should be.
Heck, even my high school biology text (Biology, Curtis and Barnes, Fifth Edition, 1989) gives them a paragraph and a picture, mentions Dicyema typoides as an example, and comments on the descent from platyhelminthes hypothesis. Admittedly, it was an AP class, but that’s still got to be pretty introductory.
Where do slime molds fit in, meanwhile? Are they currently considered animals, fungi, or protists?