Phase 2: Airframe Design A crash-course in aerodynamics. 1. Drag Drag is one of the four key forces that act on any aircraft in flight (the others are gravity, lift and thrust). Whenever a body moves through the air (or any gas/fluid), a certain amount of that body's kinetic energy is imparted to the medium through which it moves. This transfer of energy manifests itself as drag and, in an aircraft flying straight and level at a steady speed, the drag is exactly equal to the amount of thrust being provided by the engine. If we want our LCCM to travel at 600Km/h (400mph) then we'll need to design a craft that produces an amount of drag at that speed which is equal to the amount of thrust being generated by the engine. Rather than delve into some pretty heavy math at this point, let's take a more general look at the main causes of drag and how we can minimize them through careful design. The two main types of drag are form (or pressure) drag and induced drag. Form Drag. If you imagine a simple streamlined shape such as the one illustrated here, you'll see that as it moves along, a certain volume of air is moved aside by a distance equal to half the maximum width of the shape. We could calculate the amount of energy (drag) required to push this form through the air at any given speed by working out the volume of air that would be displaced - hence its mass, the distance of that displacement, and the rate (speed) at which the displacement occurred. So the three critical factors are: air density, the magnitude of the displacement and the speed of the displacement. Reducing Form Drag It's pretty easy to see that the amount of drag generated by this form's movement through the air could be reduced by any of the following: a) reduce the rate of displacement (fly more slowly) b) reduce the density of the air (fly higher) c) reduce the magnitude of the displacement (make the shape thinner) Given that we're trying to obtain the highest possible speed, that leaves only (b) and (c). Unfortunately, to be effective and avoid detection, a cruise missile needs to fly as low as possible, so that rules out (b). Therefore, the only option we have in dealing with pure form drag is to make our form as thin as possible, so as to displace the air by the absolute minimum amount. That means a thin airfoil for the wing and a long, slender body (fuselage). Obviously, as far as the body of the LCCM is concerned, we still have to leave enough space for the payload, guidance system and fuel. The thickness of the wing is limited mainly by the need to ensure that it is strong and rigid enough to withstand the stresses imposed by high-speed flight. But form drag isn't the only type of drag that will be trying to slow our cruise missile down. Induced Drag The only reason an aircraft is able to suspend itself in the air is because it is able to generate an area of low-pressure on the top surface of the wing and an area of higher pressure on the bottom surface. It is this difference in pressures that creates the upward force we call lift. When an aircraft is flying straight and level, the amount of lift being generated is equal to (and opposes) the force of gravity. The low-pressure area on the top of the wing can be thought of as a bubble that runs the full length of the wing but, under normal circumstances, doesn't reach either the front or rear edges. This means that even though the air in the high-pressure area would just love to rush around the wing and fill in the void created by the low pressure bubble, it can't do so. However, since the low-pressure bubble does extend to the wingtip, some of the air from below will move along the bottom of the wing and spill over onto the top, creating what is called a tip vortex. This tip vortex involves the movement of what can sometimes be a significant mass of air, and the energy used to generate that movement has to come from somewhere. This energy drain manifests itself as a type of drag referred to as induced drag. Reducing Induced Drag If you've ever wondered why some aircraft (such as the long-range versions of the 747 jumbo-jet) have vertical fins on the tips of their wings -- it's to make it harder for air from beneath the wing to travel around the tip and into the bubble of low pressure on top. These tip-fins act as a fence to help keep the air from spilling over and creating a tip vortex. The result is less induced drag meaning less thrust is required to sustain a given speed - and that means less fuel needs to be burnt, thus increasing the range of the aircraft. Fortunately, induced drag is more of a problem at low speeds, when there's more time for the air beneath the wing to escape around the tip to the top surface, than it is at high speeds, when air flows past the wing far more quickly. In fact, while form drag tends to increase at a rate roughly equal to the square of the airspeed, there are portions of the operating envelope where induced drag usually declines as the speed of a craft increases. That doesn't mean we can ignore the effect of induced drag though - because immediately after launch, our LCCM will be flying very slowly - at less than a quarter of its top speed. If too much induced drag is present, it may well be that the thrust of the engine will be insufficient to overcome it and the craft will never reach sufficient speed to fly properly. If that happens, our LCCM will simply fall on the ground a few yards from the launcher. There are two basic ways of reducing tip vortexes and the induced drag they generate: get rid of the wing tips, thereby eliminating the chance for a tip vortex to form reduce the pressure differential between the top and bottom of the wing Obviously it's rather difficult to build any kind of wing that doesn't have a tip (although it's not impossible) so the next best thing is to make the tip as narrow as possible so as to reduce the area across which the high and low pressure areas can mix and to install tip-fins, just like a 747-400.. This mandates the use of either a long thin (high aspect ratio) wing, or one that is strongly tapered from root to tip. The second option involves reducing the wing loading - or the amount of work that the wing has to do to keep the craft in the air. This is done by reducing the craft's weight. Since it's the pressure differential between the top and bottom of the wing that creates the lifting force, and since the lifting force in straight/level flight is equal to the weight of the craft, reducing that weight will reduce the pressure differential required. Less differential equals less tip vortex. Less tip vortex means less induced drag. So, the solution to drag might be to simply use a very narrow or highly tapered wing and make the LCCM as light as possible - unfortunately there are limits to how far we can go in these areas. The limiting factors will be: the strength of the craft the stability of the craft It is obvious that, in order it doesn't simply fly apart through the stresses of high-speed flight, our LCCM must be sufficiently strong. If we attempt to build too light a structure, it will not have the strength needed to retain its integrity at high speed, so we need to draw a sensible compromise between strength and weight. Another problem with making highly tapered wings is that they tend to make an aircraft far less stable due to a phenomenon known as "tip stall". An airfoil is said to have stalled when, rather than flowing smoothly over the top surface, the air actually stops following the contour of the wing and instead, forms large swirling vortexes. If this happens, the high pressure air beneath the wing is drawn around the back edge and into the low-pressure area - effectively destroying the differential between the top and bottom and thus significantly reducing the amount of lift being produced. So, when a wing stalls, it stops producing lift and starts producing a lot of induced drag in the form of those large vortexes instead. Now it's a strange quirk of aerodynamics that small (narrow width) airfoils stall more easily than larger (wider) ones. This means that in the case of a sharply tapered wing with very narrow tips, those tips tend to stall very easily. It's easy to see that if one of a craft's wingtips stops producing lift, while the other continues to do so, it will immediately start to roll about its axis due to the sudden loss of lift on that one side. The results are not pretty and often fatal to the craft and its payload. Fortunately, this type of "tip stall" usually only occurs when the wing is trying to produce a lot of lift and not in straight and level flight. Unfortunately, the wing on our LCCM will be required to produce a lot of lift at take-off because it will be flying very slowly and will be heavily loaded due to the full-fuel tanks. This makes the use of a highly tapered (low drag) wing a very risky business.

| Missile Home | About Me | Objectives | Project Diary