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I'm currently in the process of designing a prototype aircraft and since I don't have very much experience with this I have the following question: I know that the center of gravity of an airplane should be located in front of the neutral point (aerodynamic center) so it is self stabilizing. The problem with my design is that the main wings have to be in front of the center of gravity. To counteract that, can I design the back wings in a way so that the neutral point is moved behind the CoG?

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Yes you can, the tail volume needs to be such that the neutral point shifts aft of the CoG. This answer has some details - positive lift from the tailplane, but it must never stall!

More details about tailplane design in the answers to this question. The absolute safest config at a wide range of CoG is the CoG in front of the Centre of Pressure of the main wing, and a downforce from the horizontal tail.

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There are three approaches to this need. First, you could build what amounts to a tandem wing. If you check the CoG location for a Rutan Quickie or its many derivatives, I'm pretty sure you'll find it's between the front (lower) and rear (upper) wings. Likewise, a Flying Flea (aka Pou de Ciel) has the CoG much further aft, relative to the forward/upper wing, than could be the case with a conventional layout.

The other is to build a "lifting tail" proportioned like some of the contest models of the 1940s to 1960s (and a few, like hand-launch gliders, even to the present day). These have very little decalage, often zero, sometimes even negative -- but by airfoil choice, the designer ensured that the forward surface always flew at a higher coefficient of lift than the rear, so that any increase in speed resulted in a nose-up moment. These designs are characterized by CoG locations near or even slightly behind the trailing edge of the wing.

The final, and most modern approach, is active control. A number of modern high performance aircraft (warplanes, generally) are aerodynamically unstable, to the point where a human pilot cannot maintain control if the computer management fails. They depend on a computer stability system (generally combined with fly-by-wire) to manage the surfaces to simulate static stability, while keeping the ability to respond to control inputs at rates that would be impossible with a conventionally stable aircraft.

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