Second-rate Squirts

Jet propulsion is a popular but problematic way to get around, for humans and animals both. It's simple. It's effective. And it's costly.

By Steven Vogel|Monday, August 01, 1994
What could be simpler than a jet? All you have to do is squirt a fluid--either gas or liquid--in one direction and you get propelled in the other. The process can drive an airplane, a ship, or a submarine. It even works in a vacuum, so a squirt will spur a spacecraft.

And what could be more natural for an animal? Wrap a muscle around a bag of liquid and give the bag a squeeze--out will come liquid through any hole, deliberate or fortuitous. Someplace or other, almost every animal above microscopic size does just this. Squeezing our hearts sends blood outbound; contracting our leg muscles helps send that blood inbound again. Likewise, a traveling squeeze of the esophagus pushes food stomachward, while a similar squeeze of the intestine propels the processed slurry farther aft. Voilà--jet propulsion.

And squeezing a bag isn't the only route to a locomotory jet, as shown by animals that harvest oxygen or food by pumping water across internal gills.

The most effective of these systems have separate inlets and outlets--just look at the two siphon tubes sticking up from a buried clam, or the mouth and gill covers of a fish. Minimal modification of this equipment makes an engine that works by forcefully expelling water; and water, since it is nicely dense and flows easily, is a fine thing to squirt, as evidenced by that splendid toy and example, the plastic water rocket. Just half-fill the rocket with water and pump air into the remaining space. When the rocket is launched, reexpansion of the air expels the water downward. Recoil sends the rocket up a hundred feet, with the experienced operator getting only minimally dampened.

Nature has repeatedly contrived such engines. Perhaps no other locomotory scheme, in fact, has independently evolved in so many different lineages. Jellyfish do it. Cephalopods--squid, octopuses, and cuttlefish-- do it. Bivalves and bugs do it: a scallop, for instance, swims in short bursts using a pair of jets on either side of the hinge of its shell; a young dragonfly swims in a pond by squirting water out its anus. The list goes on and on: an obscure group of invertebrates called the salps, which are actually closer to us than any of the previous animals, swim through the sea as colonies of chain-linked, jetting jelly bags. Frogfish maneuver by squirting the water that has passed over their gills out through nozzles placed more or less amidships.

ll these jets work very much like toy water rockets, except that they make muscle contract around a chamber instead of making air expand inside it. A squid, certainly nature's champion jetter, has a water-filled cavity between an outer, muscular sheath and its various internal organs. When the squid tightens that sheath, the water is forced out through a nozzle, and the animal can go elsewhere in a great hurry--at 15 to 20 miles an hour, no slight speed for an aquatic animal less than a foot long. A squid, avoiding an approaching mouth, can at least briefly outdistance all but whales, dolphins, and the fastest fish. As part of its defensive repertoire, a squid can routinely reach heights of 16 feet above the ocean's surface or take an arcing aerial trajectory as much as 50 feet long.

Curiously, though, while no locomotory system may be simpler or more common than jet propulsion, no jet-driven animal ever goes both fast and far. Squid can't maintain their top speed for more than a few pulses. Other jet-setters can go some distance, but only at more stately speeds: jellyfish typically swim at around a quarter of a mile an hour, frogfish about twice that, and dragonfly larvae a little more than one mile an hour. A scallop may zoom up to one and a half miles an hour, but only very briefly.

We humans, too, seem to find jets limited in their usefulness. We have certainly learned how to make very effective jet and rocket engines. (The distinction between the two is simply that a jet uses the ambient fluid, usually air, while a rocket is completely self-contained.) Yet even after 50 years of development, we don't use these engines for cars or trains or boats, only for very fast aircraft. Does some single basic flaw underlie this arm's-length attitude by both natural and human technologies?

The crux of the problem is efficiency--or, more to the point, the low efficiency of jets under all too many circumstances. Efficiency, of course, is our measure of what one gets out of a machine relative to what one puts in; the currency of measurement of input and output is usually energy or power. As it turns out, a close look at efficiency reveals a lot about how animals work and about our human technology. Here, as elsewhere, the same basic constraints and opportunities are incumbent on both.

The output of a jet engine is a rearward push--a force, or thrust. It's obtained by making fluid move rearward faster than the craft is moving forward. There are two ways to achieve that result: you can take a lot of fluid and give it a small increase in its rearward speed, or you can take a small amount of fluid and make it move back very rapidly. Since thrust is measured by multiplying the amount of fluid being moved by how fast the fluid is moving, the particular mix of those two variables is inconsequential--only their product matters.

Efficiency, however, depends very much on the relationship between the amount of expelled fluid and its speed. Although the rearward push increases with the speed of the fluid, the cost in energy of producing that push increases not directly with the speed of the fluid, but with the square of that speed. (Kinetic energy is what comes into play here, and as you may remember from physics class, it's always equal to one-half mass times velocity squared.) So cost can best be minimized by using lots of fluid while giving the fluid only a little backward push. And there's the rub: that's just the opposite of what a jet or rocket does--it squirts a relatively small but very rapid stream.

The most useful measure of the relationship between output and input is something called the Froude propulsion efficiency, named after the great nineteenth-century British naval engineer William Froude. It's quite a simple thing to compute: you just take twice the speed at which the craft is moving forward and divide it by the sum of the craft's forward speed and the rearward speed of the fluid propelling it--or, if you prefer, 2Vc/(Vc + Vj), where V refers to velocity, c to craft, and j to jet. Thus if you want to achieve 100 percent efficiency, just have fluid go backward at the same speed your craft is going forward. Unfortunately, that wouldn't give you any thrust. Indeed, you'll find that as the jet's speed drops toward that of the craft, the amount of fluid that has to be moved must rise toward infinity in order to produce any forward force--and force, not efficiency, is the bottom line. Perfection, it seems, is not to be obtained either with the machines of mere mortals or, in nature, with mere mortal machines. Realistically, though, Froude's formula does show the benefit of keeping the amount of fluid up and the speed of the fluid down.

How can an engine--or an animal--deal with lots of fluid? Certainly not the way a squid does, by making all the fluid pass through its middle and out a nozzle: too little fluid can get through, and so what goes through will have to go too fast. One can do better by attaching long appendages to the engine to make it work on more air or water--fins, beating wings, paddles, propeller blades, and so forth. All manage to increase the amount of fluid moved relative to the speed imparted to it, and thus to increase propulsion efficiency. All, though, are also more complicated than the simple squirting machine of a squid or a jellyfish. Nonetheless, the complication pays off. A salmon, which moves by waving its body and tail, takes half the power to go twice as far as a squid of the same size using a jet. And the reason for the salmon's superiority is clear--it processes about ten times as much water per unit of time as does the squid.

Should jets, then, be dismissed as primitive because of their simplicity and inefficiency? That's for the most part both unfair and incorrect. After all, if what ultimately matters is not efficiency but the ability to go especially fast, then jet engines look a lot more attractive. And speed, of course, is what we use jet and rocket aircraft for--we make both small and large ones, but we rarely make slow ones. What a squid does is much the same. With small fins on its rear, it has a choice of systems. For slow swimming, as when feeding, it ordinarily uses its fins. But when pursued by a fish, it turns on the jet and achieves its remarkably high speed. Its biological fitness obviously doesn't depend on energetic efficiency in a brief life-or-death maneuver.

For that matter, the jet engines of commercial aircraft have evolved considerably over the past decades, processing larger amounts of air and reducing their average output speeds. Early jets had relatively small intake openings, and all the air coming in entered a fanlike compressor before receiving its charge of fuel. Modern fan-jets have dramatically larger inlets with very large and conspicuous entrance fans. But those fans no longer blow air exclusively back into the combustion area--most of the air goes around the engine proper, then reenters through vents to mix with the exhaust gases just before leaving the engine housing. Engine designers have worked hard to increase the amount of air going around the combustion chamber relative to that going through it--by doing so, they have improved efficiency and thus lowered fuel consumption and increased range and payload.

This matter of propulsion efficiency implies that jets just aren't practical devices for flying animals--animals are too small and, as we'll see, fly too slowly. Not only do we know of no living jet aircraft, but we're almost certain that nature has never made one, some engaging bits of science fiction (and flatulent humor) notwithstanding. To achieve thrust of any magnitude, an animal would have to move small amounts of air very, very fast. In that case, of course, the Froude propulsion efficiency would be dismally low--so low, in fact, that the cost of producing that thrust would almost certainly be unbearably high for any poor engine of muscle.

Oddly enough, though, jets aren't so disastrous for very slow swimming. At low speeds, drag--the friction that's created when a body moves through a fluid--is disproportionately low. That means very little thrust is needed to counterbalance its effects. Some squid make lengthy migrations using their jets, but they do so at very low speeds of around a body length a second, less than a mile an hour. This evasion of drag by simply being slow probably underlies the persistence of all those slow jetters such as jellyfish, scallops, dragonfly larvae, and frogfish.

The same rules govern movement through air and water--that's why both ships and planes find propellers useful and why the shapes of blimps and nuclear submarines are similar. But it's harder to fly than to swim. The lower density of air may help a craft go forward, but it also means that force has to be exerted to keep the craft aloft. Except for buoyant blimps and balloons, this additional component consumes a lot of power, whether or not the craft goes forward at all. As a result, the constraints on flying turn out to be quite different from those on swimming.

Because of this additional cost to staying aloft, moving slowly to take advantage of the correspondingly very low drag gains you nothing. Slower flight just means longer periods aloft and thus more costly trips. So the drag-evading slow swimming of jellyfish or frogfish provides no model for the flight of any heavier-than-air craft.

To stay aloft, such a craft must push air downward. As before, a quantity of air must be moved faster than the craft is moving, but now that producing a downward force is what's at issue, the relevant speed of the craft is how fast it's going up--and if, as is usual, the aircraft is simply holding altitude, then ascent speed is zero. Also as before, the choice is between giving a large amount of air a small speed increase and giving a small amount of air a large speed increase. Now that we're equipped with the notion of propulsion efficiency, our choice should be clear. The lower the downward speed the better, so we should move a very large amount of air downward very slowly. Clearly, a jet pointing downward is about the worst choice--a small, high-speed stream of air directed downward is about as inefficient a device for staying up as one can possibly arrange. Even using a small downward propeller is a relatively costly way to stay up.

We can now see why helicopters have long rotors and why tilting the engines of an ordinary propeller plane upward creates a very inefficient hovercraft. The ideal would be a helicopter with infinitely long blades--it could hover at no cost at all, using as little power to produce lift as does the chain that maintains the chandelier.

This same argument, based on propulsion efficiency, explains a basic difference between flying animals and most airplanes. Birds, bats, and insects, by beating their wings, get both thrust, to go forward, and lift, to stay aloft. And ordinarily they beat their wings not just up and down but to some extent fore and aft. Slower flight is usually associated with less up-and-down and more fore-and-aft motion--a creature just tilts the plane of beating backward. A hummingbird, for example, when hovering at flower or feeder, has its head up and tail down, and its wing stroke is almost entirely back and forth. What a hovering helicopter does is almost identical, moving its rotor in a horizontal plane.

Successful airplanes, though, preceded successful helicopters by about 35 years. We humans didn't manage to build machines that flew until we gave up the bird arrangement and began using lift-producing wings in two different ways--as wing and propeller--on the same craft. (A cross section of a propeller reveals a teardrop shape--albeit with one side flattened-- just like that of a wing; they really are the same kind of device.)

Ordinary airplanes use propellers to go forward and fixed wings to stay aloft. The propeller produces forward thrust by moving air backward at a speed greater than that of the plane's motion. Moving a very large quantity of air with a rotor of large diameter isn't necessary; all that's needed is a little air moving faster than the speed of the plane--which is already quite considerable. But with the plane moving rapidly through the air, long fixed wings can be used to give a very large amount of air a little downward push. Since longer wings intercept more air, the longer the wings the better--or at least the higher--the efficiency with which the necessary downward force is produced.

In essence, then, an airplane produces forward thrust by using small propellers or even smaller jets operating at substantial forward speeds. It diverts some of that thrust to produce lift by using large fixed wings that operate at vertical speeds near zero. This devious arrangement is efficient, which is why we persistently build planes that have high takeoff speeds, even though helicopters have now long been available. Not surprisingly, helicopters are still profligate fuel consumers.

How then do birds, bats, and insects manage so well with only one set of wings? The argument turns on basic geometry and on the different sizes of flying creatures and flying machines. A wing produces lift in proportion to its surface area. But a craft needs lift in proportion to its weight. After all, for steady, level flight, lift and weight must be equal and opposite forces. The crux is the relationship between area and weight. Consider what happens if the size of any object is doubled without change in shape or density: All linear measures--such as wingspan--will double. All areas--total external wing surface area, say--will go up fourfold. Volume and weight, though, will increase eightfold. So the bigger object will have twice the weight, relative to its surface area, of the small one. Thus a larger aircraft will weigh more, relative to its wing area, than a small one. The larger craft will be relatively lift-deprived, something not at all propitious for flight.

One solution to the problem is to use disproportionately large wings for larger craft. That's why the original Wright Flyer, of 1903, had huge wings, as does the ultrasophisticated Gossamer series of human-powered aircraft. Another solution, though, is simply to go faster. Like the cost of producing thrust, lift does not increase directly with the speed of the moving air but with the square of that speed. In this case, though, that's an advantage--double the flying speed, and the lift of a wing goes up fourfold.

Aircraft generally use this faster-flight solution. In practice, larger size demands higher speed. Higher speed, in turn, requires a smaller and faster air pusher. And the latter is less efficient, more power hungry, for slow-speed use--especially for direct production of lift. That, then, underlies the advantage of the separation of wings and propellers in our airplanes.

Only a few large birds, however, can exceed 50 miles an hour. Birds, being smaller than planes, fly more slowly and find larger and slower air pushers quite practical--hence they don't have to use separate fixed wings for lift and flapping ones for thrust.

But even flying animals aren't completely out of the woods. Big animals weigh more, relative to their wing area, than do small ones; and they fly at least a bit faster. As a result, big birds don't have enough wing area to hover effectively--their propulsive system moves too little air too fast for decent efficiency in hovering, and they simply can't generate the necessary power. Many midsize birds can hover for a few seconds, but they can't maintain sufficient power output for long. Only the hummingbirds and flying insects can hover for long periods. What these small creatures have going for them is just a consequence of their small size--a lot of lift-producing wing area relative to lift-requiring body weight. With all that wing area they can move a lot of air downward, so they don't have to move it downward very fast.

This tale of jets and squids and helicopters and birds carries at least two general messages--even a story about science can convey a moral or two. First, while we're understandably dazzled by the diversity of nature's contrivances, we can gain insight by considering just what we don't find. The absence of fast, long-distance, jet-propelled swimmers and of any jet-propelled fliers prompts reexamination of the general utility and promise of jet propulsion. Jet-propelled automobiles, jumping with jet backpacks, commuting by personal jet aircraft--all remain impractical dreams. For us as for other animals, the elegant simplicity of squirt as engine is more than offset by its inescapable inefficiency.

Second, copying nature is a hazardous enterprise. Certainly the evolutionary process has produced enormously effective devices, but that effectiveness is realized in their natural roles and not necessarily in our technological uses. Sure, we might never have had the temerity to attempt flight had birds not provided ample proof of the concept. On the other hand, we succeeded only when we stopped copying and directly faced the technological challenge--when we put propellers on fixed-wing aircraft and left the birds behind.
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