Doug, I’m a little puzzled by why arthropods can be larger in water than on land. Your column says that it takes less muscle power to lift a limb underwater - how so? Water is heavier than air. The bouyancy of water may mean some measure of support for a larger creature’s weight, but I’d think that actual motion would require more power, not less.
The water will resist the movement more, so speed becomes an issue, but the bouyancy will keep it from having to exert as much effort to lift so long as it does so slowly.
Imagine the moon with a very heavy atmosphere. You’d have to do less work to lift your leg, but if you tried to do it speedily, you’d run into resistance from the air.
I think.
Interesting that the oxygen is the first limit, but that could be easily remedied with a more advanced respiration/circulation system. I don’t think muscles could be increased in efficiency enough to allow much larger sizes, but what about the structural integrity of the shell? If you took away muscle limits, how big could an exoskeleton be before you would need a stronger material than chitin?
Jonathan
Given that crabs don’t use chitin (that I’m aware of), you begin to have some idea from that branch of the arthropods…
Very interesting and well-written, even if it does set back my plans to create a giant race of mantids to do my nefarious bidding. :mad:
Make them robotic mantids and you’re back in business!
Hmmm. I like the cut of your jib, dropzone!
Personally, I think his Jib is cut too narrow.
But, it’s a matter of taste, I suppose.
From the article
Actually it’s more like two meters long. Or more. These were not insects and they didn’t have much height, but they count as bugs in my book.
The article implies that insects could get larger if there were more oxygen in the air. So would this plan work?
-
Take the largest known dragonfly, breed the species in a hyperoxygenated (is that the right word?) chamber.
-
Once they reach a 75-cm wingspan, outfit them with a tiny oxygen tank to keep them alive and happy and unleash your horde on an unsuspecting populace.
-
Profit!!!
That would be so cool. 
Murdoch, we discussed millipedes (and similar arthropods) in this ancient thread on arthropod size limits. Our take on it was that an elongated body with many legs would be better adapted for growing to great length than the critters we generally think of as “bugs”. Essentially, the distance between the exoskeleton and the innermost tissues could remain small relative to the length, making it possible for the spiracle-and-trachea respiratory system to support those tissues. Even now, centipedes and millipedes grow to much greater lengths than insects. Presumably, there would still be some theoretical limit on length, but I’m not sure what it would be–as long as the diameter remains small and there are enough legs to support each segment, they could probably grow much longer than they currently do.
Also, you gave me an excuse to link to that thread, which I am still perversely fond of. 
A fiber muscle acts as a string. The force it develops is proportional to the variation of its length x.
F = kx
Of course, the constant k is proportional to the cross-section area. So, in the whole, the force developed by a muscle is proportional to the third power of length and not to the second. This is the reason because flies, frogs and humans can all jump to a height of approximately 50 cm. The weight to be lifted and the force to do it both increase with the third power of length.
Where I wrote flies, please read fleas.
The report is generally well-done, but it’s not entirely correct. Not all arthropods employ spiracles. Insects and most other terrestrial arthropods do, but there are a fair number of other models. Aquatic arthropods generally use gills of some description. Spiders have book lungs. Coconut crabs (the largest land arthropods) use gills specialized for breathing air. Now, they do have an open circulatory system, which is rather less efficient, but for the arthropods that don’t use spiracles, the oxygen limit never comes into play. They are instead limited by the mathematics of their muscles. So, some do get around the first barrier to run smack into the second.
A problem with these bugs being too large is molting. While the hardened exo. would support them, what kind of troubles would they have when the rigidity of their shells was removed? Under water this would be less of a problem, try that on land.
Correct conclusion, but incorrect derivation. The stiffness constant k is proportional to the cross-section area but also inversely proportional to the length, so force is still proportional to length squared, as Doug said. The length dependence of the stiffness constant should make intuitive sense: if you have a puck of rubber only an inch high, it takes a large force (F) to squash it, say, 1/4" (x). Make the same rubber into a column three feet high, and it takes much less force to squash it the same 1/4".
Fleas, frogs, and humans can all jump approximately the same height not because the muscle force scales with weight, but because the muscle energy output scales with weight (both to the third power of length). Energy is force * distance, and again this should make intuitive sense: a deep knee bend by a flea covers a much shorter distance than a deep knee bend by a human; when jumping, a human has more distance (and more time) to puch against the ground.
Doug: In what technical sense are strength and power the same? Is this a specialized physiological use of the word “power” (as in “power lifting”)? Even if so, I’d suggest you rephrase or delete this, because in physics/engineering “technical lingo” the two words are most certainly not equivalent. It’s apt to be confusing if people come away with the impression that strength and power are equivalent in all technical usages, particularly when abstract discussions of the scale effect quickly drop into general physics/engineering territory.
So, how strong are the larger insects? like the japanese spider crab-are its 7’ legas as strong as a man’s? Or those alaskan King Crabs-are they strong enough to take off a man’s finger?