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Moment coefficient and airfoil shape:
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The shape of an airfoil can always be thought of being composed of two parts: a camber distribution (camber line) and a thickness distribution, which is distributed along the camber line. The requirements for the three classes of tailless planes can be translated in corresponding airfoil shapes and wing twist distributions. The only way to achieve a positive moment coefficient and the required amount of lift is to use a S-shaped camber line, which is also called a reflexed camber line.
wing without sweep (plank)
A positive moment coefficient results in a reflexed camber line. A twist does not help for stability, but can improve the stall characteristics of the wing.
swept wing
Low moment coefficients and a small amount of twist can be achieved by airfoils with little camber and a neutral or slightly reflexed camber line.
wing with a low position of the center of gravity (parafoil)
The moment coefficient poses no strong restriction on the airfoil shape
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Reflex and moment coefficient:
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We already know, that the moment coefficient Cm and the shape of the camber line are closely connected. If we examine airfoils with a reflexed camber line more closely, we find, that the shape of the rear part of the camber line has a big influence on Cm. In fact, it is possible to adjust the shape near the trailing edge to achieve nearly any desired Cm. The figure below shows how cm can be controlled: starting from a symmetrical airfoil, a flap is deflected smoothly upwards by 5° and 10° - the moment coefficient follows the deflection
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Using this trick, the problem seems to be solved. We simply bend the railing edge upward until we achieve the moment coefficient necessary to stabilize our tailless plane and there we go...
But we probably prefer an airplane, which not only flies safe and stable, but also performs with a low sink speed, a high penetration speed and a good L/D ratio - that's where all the trouble begins.
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Reflex and lift and drag :
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The shape and location of the lift and drag polar of the airfoil is the key to airplane performance. The images below show, how the cd-cl polar changes, when the camber line gets reflexed.
Now we have a problem: while we add reflex to the camber line, in order to shift the moment coefficient towards the positive values, we shift the lift vs. drag polar down. This means, that we actually reduce the lift at a certain angle of attack and, what's even worse, we also reduce the maximum lift coefficient. A reduced maximum lift coefficient leads to higher stall and landing speeds, which is not exactly our aim. Of course the aerodynamicist already knows a remedy against low lift: he increases the amount of the maximum camber. Indeed, this increases the lift, but also reduces the positive moment coefficient
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