# How does wing sweep increase aircraft stability?

I was told at one point that the sweep of a wing can help with the straight line stability of the craft, in fact I think it's one of the main systems that keeps flying wings flying straight (like the B-2 or N9-M, which comes from the 40s, way before the use of flight computers for stability...).

Why is that? Are there trade offs between that stability and say, speed? Is there a such thing as too much sweep?

## Directional stability

When a swept wing is flying in a sideslip, the windward side behaves like a wing with less effective sweep $\varphi_{eff}$ and the leeward side like one with more effective sweep. Wing sweep causes a flattening of the lift curve slope for two reasons:

1. The effective angle of attack is reduced by the cosine of the sweep angle.
2. Only the component of speed normal to the quarter-chord line of the wing is creating lift, so a swept wing creates less lift per area than a straight wing.

The increased lift rolls the aircraft, but also produces increased lift-induced drag which pulls it back to straight flight. The sketch above shows this for the flying wing glider SB-13. This effect is so strong that swept, high-wing configurations need anhedral to keep the sideslip-induced rolling moment down.

For completeness, also the side force $Y$ of fuselage and winglets is added and shows that the winglets help a lot to create directional stability. This is needed in case of the SB-13 because it has a nearly elliptical lift distribution. Using a triangular distribution (N9-M) or even a bell-shaped distribution (Horten flying wings) avoids the need for winglets, but causes higher induced drag in straight flight. Another downside is a low directional stability at high speed, because this sweep effect increases with the lift coefficient on the outer wing.

## Longitudinal stability

Wing sweep also helps in longitudinal stability by stretching out the wing lengthwise. This is important for flying wings which lack a separate tail surface. By changing flap angles at the center or the wing tips, the lift at the most forward or most backward sections can be changed for pitch control, and more sweep increases the lever arm of these changes. Also, in swept flying wings natural static stability can be achieved without the use of reflex airfoils, but by applying washout. Again, the higher the sweep angle, the less washout is required.

## Too much sweep?

Easily! Sweeping a wing creates lots of problems:

1. Sweep reduces the lift curve slope and the maximum lift of a wing. The maximum landing attitude with a highly swept, slender wing is severely limited by wing tip clearance, so swept wings need powerful high-lift devices.
2. Sweep causes the boundary layer to be washed outboard, which will cause nasty stall behavior once a specific ratio of wing aspect ratio and sweep has been exceeded. This can be somewhat limited by wing fences, but should better be avoided altogether.
3. Sweep changes mean that bending moments will partially get converted to torsion moments, requiring a torsional stiffening of the wing.
4. For flying wings, sweep will let the aircraft center pitch up and down when the wing flexes. This creates a powerful interaction between the fast period mode (which is only moderately damped in flying wings) with the wing bending mode, resulting in flutter.

## Why sweep a wing at all?

Generally, an aircraft designer will allow only as much sweep as necessary. Wing sweep reduces drag when the aircraft flies with transonic or supersonic speed. Now the Mach effects depend only on the normal speed component, so they are proportional to the cosine of the sweep angle. For the N9-M this was not a factor, however, the B-2 benefits from it with a higher drag divergence Mach number.

• Can you explain the problem 4 of sweeping the wings? I did not really understand it. I did not understand the words fast period mode and wing bending mode(what do they mean?). I am sorry if I should know what they mean. – Crafterguy Jun 20 '17 at 1:13
• @Crafterguy: Yes, but not in the comments. This is an interaction between two eigenmodes, one the short period mode and the other the elastic bending mode of the wing. – Peter Kämpf Jun 20 '17 at 9:53
• @ Peter Kampf: So what downwash angle did you use for the wing tips and what % semi-span does that start at, eg 25% from tips? – Fred May 10 '20 at 12:46
• @Fred: I gutes you ask about the washout angle. Complicated. We combined washout with flap twist, so there is a 0.8 degree incidence decrease when the airfoil transitions from the HQ34 to the HQ36 at about 50% of span and then a linear -2° washout to the tip, IIRC. This is complemented by 10° of flap twist (I write this from memory, so could be wrong). Since there are two elevons per wing, the outer ones with 3 times the throw of the inner ones, details depend on the flap position which has to match the cg location. – Peter Kämpf May 10 '20 at 14:56
• @ Peter: Thank you. For all the non-aerospace engineers, IIRC stands for centre of pressure, HQ34 was the airfoil used? – Fred May 10 '20 at 16:15

As for flying wings, longitudinal control (let alone stability) depends on being able to being able to move the center of lift backwards and forwards. That would be hard to do with a straight flying wing which doesn't have a separate tailplane or carnard -- all the lift is generated at the same (longitudinal) position.

On the other hand, if your flying wing has sweep, you can get longitudinal control by putting control surfaces at different distances from the center of the aircraft. Increasing lift at the outer parts of the wing will produce a nose-down moment, and vice versa.

• A straight flying wing can be longitudinally controlled with training edge flaps. They re-distribute the lift distribution chordwise. See the Fauvel flying wings for example. – Peter Kämpf Oct 23 '14 at 19:18

A big benefit of swept wings is lower drag at high speed. When an aircraft with swept wings yaws, it is effectively increasing the sweep of the wing in the direction of the yaw, and decreasing the sweep of the other wing. So the wing opposite the direction of yaw will have less sweep, therefore more drag, counteracting the yaw. Likewise, the other wing will have higher sweep and less drag.

Of course you can have too much sweep, otherwise all planes would just sweep their wings completely away and look like the X-24. Your previous question addresses other properties of swept wings well:

Why do some military aircraft use variable-sweep wings?

There are certainly tradeoffs, but vertical surface area is still a more effective means of providing stability. The effect on swept wings of 1 degree of yaw will be less than the force created from the rear fuselage (and vertical stabilizer) being at effectively 1 degree angle of attack. Of course flying wings will primarily rely on this differential drag for stability, but they use things like clamshell brakes to create the necessary drag for extra stability and control.

More sweep is better for speed, but not so good if you want to go slower. So sweep is going to limit low speed performance, and the stability improvement will also be less as airspeed decreases.