# What are the relative contributions of the body and wings to missile lift?

Slender bodies like arrow shafts, airliner fuselages, and submarine hulls are all capable of generating lift, albeit much less efficiently than a high aspect ratio wing. They also generate little drag, which is their main advantage. I would like to know how their lifting properties compare to that of a wing; to this end I would like to refer to a use case where the slender body makes up most of the airframe: guided missiles.

Consider a missile with a long slender body and short lifting surfaces, with a "conventional" air to air missile aspect ratio like that of the R-27 or AIM-120. The exact wing and control surface layout is not relevant, only the form factor. This means we should purposefully exclude munitions equipped with a moderate aspect ratio wing such as the TLAM or JSOW: I am interested in low aspect ratio BVR designs:

To avoid complications due to the engine or absence thereof, consider it flying in the coasting phase. The lift needed to stay aloft or even climb is then provided by a combination of the wings and the slender main body (where the guidance systems, warhead and sometimes engine are housed).

The question is, what is the proportion of lift coming from the wings compared to that of the fuselage?

NOTES:

• A good answer should use a real or realistic design to base their calculations on.
• I have purposefully left the choice of design open, so people can pick one they are familiar with or have data on. All that matters to me is that the general shape must be similar to that of modern AAMs.
• Feel free to elaborate on how the lift proportion changes at different flight conditions (subsonic vs supersonic); it is quite clear that higher speeds lead to smaller wings.
• I am aware that short range WVR missiles like the R-60, R-73 or AIM-9 are designed to reach their target before engine cutoff or shortly after; this has no bearing on the question.
• This answer below presents a good extreme where most of the lift has to come from the body, because the only fins are too far away from the center of mass. In such cases, where the fins act as a stabilizer, their lifting force can still be calculated and compared to the total lift required, if we can assume the location of the CG.
• The missiles you refer to do not typically operate "in the coasting phase" - they are supposed to strike before they "run out of gas". – Mike Brockington Oct 3 '19 at 13:23
• @MikeBrockington if you have a source I would really like to see it. To my knowledge burn time of the AIM-120 is about 6 seconds, which would not account for most of it's range (source). That being said, assuming engine cut off is a simplification that should not impact the calculations by more than $Sin (\theta)$ with $\theta \ll 1$ and can be disregarded for a first approximation. – AEhere supports Monica Oct 3 '19 at 13:31
• @MikeBrockington Only very short-range missiles have the luxury of hitting before the gas runs out. The exact properties of the solid fuel and the fuel-fraction/aerodynamics of the missiles may not be openly published, but are simple enough that reasonably-detailed simulations can show they won't get anywhere near the designed range if they could only make the kill with the engine active. – aerobot Oct 3 '19 at 15:14
• @CamilleGoudeseune at my university we used the term wings to distinguish them from moveable control surfaces and traditional fins (fixed surfaces at the rear whose main purpose is providing stability). But whether they can be rightfully called wings (in this case) is part of my question :) – AEhere supports Monica Oct 3 '19 at 15:37
• @Jimmy neither can a glider... your point? The fact is that missiles can maneuver in the coasting phase, so they must be able to generate lift at the expense of increased drag, and trade kinetic energy for height like any other aircraft. – AEhere supports Monica Oct 3 '19 at 21:58