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Performance, II: Out of the Matrix

When we think, read, or speak about airplane performance, aside from the more obvious implications regarding a relative ability to accomplish a particular goal such as taking off from a short field or getting somewhere in a hurry, in reality we’re thinking and living in a secondary world. When you compare numbers for these things and others like rate of climb, service ceiling, range, or fuel burn, aeronautically speaking, you’re actually inside the matrix, if you will. In other words, there’s a more elemental reality behind them.When we think, read, or speak about airplane performance, aside from the more obvious implications regarding a relative ability to accomplish a particular goal such as taking off from a short field or getting somewhere in a hurry, in reality we're thinking and living in a secondary world. When you compare numbers for these things and others like rate of climb, service ceiling, range, or fuel burn, aeronautically speaking, you're actually inside the matrix, if you will. In other words, there's a more elemental reality behind them.

As I mentioned in an earlier article, in a perfect world, airplanes aren't. If you want an airplane that can go fast, you're going to burn more fuel (and land long). If you want something that can take you the greatest distance, you had better travel light. Optimized designs are for the most part a mélange of compromises. While the airframe's design dictates how much push and power will be required under varying conditions, the engine inside it defines how much of each can actually be made available. How well the engine meets the capability of whatever aerodynamic design surrounds it, and how the airframe itself is configured, dictate what we most commonly consider as performance, toward whatever end most interests us…whether your name is Bohannon, Rutan, Yeager…or Schmidlapp.

Two other performance metrics that I promised to discuss at the close of that earlier discussion are wetted area and aspect ratio. Let's start off with the significance of this thing called wetted area. No, we're not talking about kayak design here. It has to do with one of the four fundamental forces of flight, and the one that is usually mentioned last. Those would be lift thrust, weight, and...drag.

Drag can be divided up into several different types-or two, depending on whether you're a lumper or a splitter. By the mere act of traveling through any fluid possessing at least some inertia, a body suffers from the force exerted upon its effective cross-sectional area and we call this 'form drag'. Form drag depends primarily on the size and shape of an object, and it is minimized by keeping the separation of air (from its smooth flow around a body) to a minimum. The well-known phenomenon we call a stall is in fact nothing more than a flow separation effect. For a streamlined body, some of the high pressure build-up at the front of the body will actually be cancelled out by a high pressure area at its leeward end; a streamlined body might have one tenth the form drag of a blunt one having the same cross-sectional area. For a not-so-streamlined body, a lower pressure area behind such an object (created by the flow separation when the fluid within the boundary layer cannot negotiate an overly abrupt contour change beneath it) can actually account for more drag than the high pressure area in front of it. That's the idea behind wheel pants (not to mention retracting the gear altogether) and other fairings, as well as the teardrop or at least ovoid cross-section for struts, gear legs, flying wires, etc. There is also another type of drag associated with air pressure that we've all heard of I'm sure, which is the induced drag that is a by-product of lift. Some refer to everything else that isn't related to induced drag as 'parasite' drag. Parasite drag includes the effect of a body having cross-sectional area; that is, the cost of a fluid having to get out of the way of an object traveling through it. But then there's the force exerted by the fluid, even on an object having little cross-sectional area but which has a lateral surface, and that is known as friction drag. That's where the wetted area term comes in.

Wetted area then is simply due to the air 'clinging' along the lateral surfaces of an object as though it were 'trying' to pull the surface along with its direction of movement, and it is due to something known as viscosity. All of this happens in what is known as the boundary layer. Skin friction (aka viscous drag) is a function of an object's velocity, its length, and the viscosity of the fluid through which it moves (or which moves by it). It is a function of the fluid and not the surface over which it flows. Somewhat counterintuitively, the viscosity or the thickness (or 'stickiness') of a gas actually increases with increasing temperature (unlike a liquid). So even though it becomes less dense when warmed, and its molecules move further apart and more quickly, a gas becomes, in a way, thicker at the same time that it gets thinner. (Interesting, eh?) Also almost as interesting perhaps is the fact that while friction drag is a function of viscosity, form drag (and induced drag as well) are not, but instead depend upon the density of the fluid. Friction drag involves the wetted area along the outside of the fuselage, but it also to some extent involves internally transiting air needed to cool the engine, great quantities of which must traverse fairly narrow passages. Such frictional drag is sometimes considered separately as 'cooling drag' and can account for nearly a third of the drag in some cases. (There is also interference drag when two surfaces join, which creates zones of interference between their respective boundary layers, as well as control seal drag when air leaks through gaps between the wing and articulating surfaces, such as ailerons or flaps, between the bottom and top of a wing…as well as still other types of parasite drag.) So designers like to keep fuselages smooth, and wetted area to a minimum. Something called the 'fineness ratio' (length/width) dictates that long, skinny aircraft have more skin friction than the ideal 'egg' shape of an airplane like a Questair Venture, but with shorter fuselages and moment arms for the empennage, tail sizes must be increased and with that, drag goes back up again. Both frictional and pressure drag increase with increasing contact area, as well as with the square of (for aircraft at least) the airspeed. Except for very small objects or ones moving only slowly, pressure drag forces are usually well in excess of friction drag. Flow within the boundary layer can be smooth (laminar) or turbulent. Various means of reducing pressure drag are used, such as vortex generators which 'energize' the boundary layer to forestall its separation from an aircraft surface (at a small price of a small increase in skin friction drag). The dimples on a golf ball have the same purpose, actually. But the laminar flow along the boundary layer over even a smooth wing will remain so for only a certain distance, and because turbulent boundary layers create more friction drag, this is another reason why longer wings with shorter chords slip more efficiently through the air. But there are more significant reasons why longer wings fly better. I'll get to those shortly. To wrap up pressure drag and friction drag though, I'll briefly mention something that actually involves both of them (actually the ratio of the two), which is known as the Reynolds number. This is an important number when considering the effects of size and scaling upon given airframe designs. For the same kind of reason that bugs can walk on water and we can't, the air behaves as though it were thicker, for smaller wings. In order to use a wind tunnel to evaluate a model that is one-tenth the size of a real airplane for example, the air must either be pressurized to 10 atmospheres--many wind tunnels run at twice that or more--or sped up tenfold, or cooled to decrease its viscosity.

That's a nice segue into aspect ratio. Aspect ratio indicates how long and skinny a wing is. It's actually defined as the square of the wingspan divided by the wing area (though more intuitively it approximates the ratio between the span and the average chord width). As you may already know, higher aspect ratio wings have a higher maximum lift-to-drag ratio, having an inversely reduced proportion of induced drag as well as slightly greater lift than a wing of lesser span. They'll glide farther, and they will be more efficient, although that comes at a price; they need greater angles of attack and fly most efficiently at relatively slower airspeeds. The aspect ratio of a Mig-29 is about 3.4; that of the somewhat slower Boeing 737 is about 8.8; while that of an even slower sailplane can be well in excess of 20. (The aspect ratio of the global flying albatross is about 20.) The main reason why a longer wing is more efficient has to do with a wing's basic purpose which is to create lift, which comes from the pressure differences between the air above and below a wing. In all wings, some higher pressure air beneath leaks around the wing tips, creating vortices and thus, drag. A low aspect ratio wing allows more of this (that is, over a relatively greater proportional area of wing), while a skinny wing allows less.

So now I've covered wing loading, power loading, wetted area, and aspect ratio. If there's enough interest, I'd be happy to expound and pontificate further on performance parameters, but I suspect most of you would be happier if I got back down where the air is a little less thin!

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