I'm designing a plane, and I have a question. What is the best place for the center of gravity, relative to the center of lift? I've heard that it's best put just behind the center of lift, but I would like a second opinion.
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$\begingroup$ Where did you hear that? $\endgroup$– Fred LarsonFeb 1, 2017 at 18:37
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3$\begingroup$ It depends on what kind of stability you want the plane to have, see related questions: How does an aircraft tailplane work? and Do any airplane designs exist that don't involve a flight surface that provides downforce? $\endgroup$– foootFeb 1, 2017 at 19:24
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$\begingroup$ I would guess that it really depends on how you want the loading envelope to look like. The CG will change depending on different loading characteristics so you should be designing for a load envelope. $\endgroup$– Ron BeyerFeb 1, 2017 at 19:24
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$\begingroup$ I would want the CG to be on the center of lift in terms of front to back, and left to right. In terms of vertical, would it be better to have the CG near the top of the craft or the bottom? (this is assuming the plane is landed and just sitting there, for orientation purposes). $\endgroup$– NicholasApr 7, 2017 at 21:56
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1 Answer
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The center of gravity (cg) should be right above or below the center of lift. Otherwise the airplane will start to pitch and never stabilize.
But you do not select the position of the cg, instead, you adjust the center of lift such that lift will act along the same axis as weight. This is called trimming the aircraft and is done by adjusting the elevator deflection (or the incidence of the stabilizer). Of course, you should select the cg position such that the available elevator deflection range will not only shift the center of lift to the cg, but leave enough margin for manoeuvring.
The next condition is to ensure proper natural stability. Once the tail surface produces more lift per area than the forward surface, the aircraft will be instable, so that any angle of attack deviation from the desired state will quickly increase. Therefore, the cg should be placed slightly ahead of the neutral point of the airplane. The neutral point is the cg location at which angle of attack changes will not cause a change in pitching moment. The neutral point of a single wing is near its quarter chord point (it moves forward from the quarter chord point with decreasing aspect ratio), and the neutral point of the whole aircraft is the mean of the neutral points of all components, adjusted for their lift curve slope.
A good first position for the cg is at the quarter chord point of the wing. This ensures that the tail surface will be only lightly loaded, but it might be that stability at this position is not satisfactory. To increase stability (and reduce pitch agility), move the cg further forward, and vice versa. If you want to optimize the aircraft's lift-to-drag ratio (and minimize trim drag), select the most backward cg position with still acceptable stability.
GA aircraft are normally very stable, and their cg position might even be close to the leading edge of the wing. Details depend on tail size, aspect ratios of all surfaces and the desired agility.
answered Feb 1, 2017 at 21:44
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$\begingroup$ Your first statement is NOT correct. Centre of lift is usually behind CG for a normal flight even when the airplane pitch increases. Airplane is stable because of a tailplane which counteracts the moment created by lift acting at CP around CG. Trimming does not directly affect CP because it does not change wing parameters. The initial reason is a tailplane moment change, and the wing AoA change is the consequence. Then CP really moves (but not for any aerofoil - it does not for symmetrical one), and sum of moments are changing again. $\endgroup$ Feb 19, 2019 at 21:06
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$\begingroup$ If it would be like you described, the airplane would not require a tailplane at all. All control would be possible with ailerons (symmetric movement for climbing/descending, asymmetric movement for rolling). But that kind of airplane would be dramatically unstable because it is a typical unstable equilibria: any disturbance will cause further increasing change in the same direction. It can be probably good for a fly-by-wire fighter, but not for a civilian airplane, which should be very stable. $\endgroup$ Feb 19, 2019 at 21:20
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$\begingroup$ @avtomaton: Please consider that your understanding of the center of pressure might be incorrect. And stop hectoring others with false knowledge. $\endgroup$ Feb 20, 2019 at 21:19
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$\begingroup$ Actually your answer is the first source where I see CP of the whole aircraft consideration instead of wings and a tailplane. Could you please share some references with that terminology? I refer to conventional training books (ATPL books from Jeppesen, Oxford and Bristol), aircraft aerodynamics books and some internet resources like skybrary, avstop.com, flightlearnings.com. Most of them consider CP and Aerodynamic centre of the aircraft as CP/AC of the wings when we are talking about terminology. $\endgroup$ Feb 21, 2019 at 7:37