<< Page 7 Page 8: Page 9 >>   Induced Drag & Wingtip Vortices This is perhaps the least intuitive of all the components. It causes about half the air resistance in an airliner, a little less in a glider, and quite a bit more in a fighter or aerobatic plane (when they’re subsonic). Remember, a wing generates lift by inducing a lower pressure on top than on the bottom. This means that, at the wingtip, air from the bottom will “spill over” onto the top of the wing. At the wingtip, the low pressure at the top of the wing will suck the air at the bottom of the wing around the wingtip, upwards. This generates a vortex: air spinning around a point, at and behind the wingtip. Lift generation will always cause this swirling motion of air, one vortex at each wingtip. In a given airplane, the more lift is generated, the stronger these vortices are. This is why a lighter airplane generates less drag, all other things being equal. Vortices spin very fast, so the air in the middle is at a very low pressure, due to the centrifugal force of the vortex. This causes that air to cool. On a humid day, this will cause the air in the center of a vortex to condense, and the vortex will be visible. At slow speeds (and at the accompanying higher angles of attack), more air spills over the wingtip. This means induced drag is more severe at low speeds than at high speeds for any given airplane. An airplane during takeoff and landing has its engines going stronger than at any other point during flight. This is especially true for fighter planes, which always have especially high induced drag anyways. And it’s not just wings that create vortices – propellers and helicopter rotors – and almost any other air-moving surface like, say, windmills – do too. How can induced drag in wings be minimized? Four main ways: a) Tapering the wing b) Twisting the wing c) Increasing wingspan d) Using winglets e) Reducing weight The first three ways simply ensure that most of the lift is generated away from the wingtips, so that the pressure difference from the bottom of the wingtip to the top is not any higher than it has to be (so less air is pushed to spill over). The fourth method is a “trick” learned only recently by aerodynamicists. The fifth has already been discussed in part in the “Weight” section – it is the induced drag which increases when weight increases. a) Tapering the wing means a smaller cord at the wingtip than at the root (inboard part, base) of the wing. Because the wing has more cord inboard, more lift is generated inboard, and the wingtip is very thin so little air spills over to the top. b) Twisting the wing means setting the inside of the wing at a higher angle of attack than the outside. Again, this means more lift is generated by the wing near the middle. Because the wingtip is at a very small angle of attack, it generates almost no lift, so the pressure under the wingtip is very close to the pressure over the wingtip and less air spill over to the top. Above, an F-106 and a 767 show twisted wings Below, notice how the wingtip of this experimental F-18 points downwards relative to the rest of the plane: c) Increasing wingspan: If a wing is very long (wingtip-to-wingtip-wise), most of the lift is generated far from the wingtips and has less of an effect on pushing the air around the wingtip. If a wing is stubby, then the pressure difference is right there near the wingtip and pushes much more air around. So, in fact it is not the wingspan that tells you how much of a problem an airplane will have with induced drag. It is the wingspan-to-cord ratio, called the aspect ratio. You may have heard that widescreen TVs or widescreen DVD movies have a high aspect ratio. This means the image is much wider than it is tall. It’s the same idea for wings. Gliders and airliners have high-aspect-ratio wings for reduced wingtip-vortex drag, fighters have low-aspect-ratio wings because it helps them be more agile and because there is less supersonic drag that way, as we will see. Above; Two U-2s and a glider (high-aspect-ratio wings), an F-104 Starfighter and an Eurofighter Typhoon (low-aspect-ratio wings, severe induced drag at low speeds). Low-aspect-ratio-winged fighters have such powerful vortices, they condense the water in the air in the vortex during most turns. This is because the air in the vortices spins very fast near the center, which causes the air there to be at very low pressures (Euler-N, page 34). The drop in pressure causes a drop in temperature, raising the relative humidity of the air (i.e. often making the water vapor in the air condense into droplets that look like smoke) d) Winglets: You may have seen these and wondered what the heck they’re for (other than for looking cool). A winglet is a vertical or steeply diagonal plate at the wingtip: Airbus’s modern airliners all sport this distinctive double-winglet, including the A380 (previously the “A3XX”) above and the A320 wingtip below: The idea is very simple: the winglet is in the way of the air spilling over from the bottom to the top. But the winglet hardly stops all the spilling. A very good winglet can stop about 20% of the spilling, thus reducing induced drag by a fifth and reducing total drag by about 10% (which is a LOT – if you need only 90% of the thrust you needed before, your fuel supply will last 11% longer, which can mean almost a thousand extra miles in a long-range jet). Why does the winglet not stop all the air? Two reasons: One, the air still spills over in a vortex after the wing has passed. The air behind a wing is moving downwards, but the air next to it (just outside of the wing) is not, so that forms an eddie right behind the wing, as long as it is deflecting air downwards (i.e. producing lift). This is made worse by the fact that the low-pressure air that was on top of the wing is sucking in air from outside where the wing was, and high-pressure air from under the wing still flows outwards. So the vortex is inevitably formed if lift was generated, even after the wing passes. The second is that, if the winglet is pushing on air to make it stay in place and not spill, then it too is generating some lift (except it’s pushing air outwards, thus generating inwards lift, i.e. the air blowing by it tries to bend it towards the wing), and because it is generating some lift, it has a little vortex of its own at its tip. e) Reducing Weight. This is intuitive: The more lift a wing must generate, the more drastic the pressure differences between the top and the bottom must be. Therefore, a higher load often means higher induced drag. This is why, as discussed in the Weight section, a lighter airplane will (all other things being equal) fly faster, farther, and more efficiently, than a heavier plane (or the same plane carrying more stuff). This is also why a plane is draggier during a turn (they require higher wing loadings – enough to keep the plane in the air AND pull it into the turn), and why wingtip vortices can be seen to condense during turns.