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Dihedral, Sweep Back Wing and Effect in Static Stability


Dihedral, Sweep Back Wing and Effect in Static Stability


Who hasn’t ever noticed a pigeon in its flight or a falcon diving to get its prey? If you love enjoying artistic things that nature has to offer, then you might have tried to follow birds flying by flapping their wings at some time, or cruising through the air, at other times, with wings swept forward or backwards.

If you have ever wondered if the positioning of their wings does matter, this article will give you some glimpse of how aerodynamics works with wings. Unsurprisingly, most of the, if not all, modern aircrafts have taken inspiration from the wings of birds that have ruled the sky for centuries.

Dihedral_and_Anhedral_Wings

Falcon_normal_and_swept_back_wing_

The wing configuration is imperative in stability, and other condition like the speed of operation, notice that sweep back wings are used in high-speed aircrafts. Not only the birds, aircrafts also have the same protocol of nature; the effect is same.

Background

Most of the commercial airliners have wings that move upwards from root to tip, which is called dihedral and angle measured with the horizontal is the dihedral angle.

On the contrary, most of the military planes have zero dihedral or even negative dihedral or anhedral.

This goes down to the stability requirement with commercial aircrafts needing a stable performance on the pre-planned route while the military ones need to be neutrally stable or slightly unstable.

Surely, this demands a lot more attentive piloting, but it has the benefit of being able to make drastic maneuvers.
Similar is the case of wing sweep, most of the commercial aviation aircrafts employ leading edge sweep back wing owing to their influence in stability while the military ones prefer forward sweep for having an unstable aircraft.

So, it is common practice for aircrafts to use dihedral sweep back or anhedral forward sweep wing, thus giving the added advantage of both in terms of stability or instability. Here, stability is referred to as Static Directional Stability and Static Lateral Stability.

Effect of Wing Dihedral on Stability

Analysis of stability of aircraft goes down to the changes in an angle of attack or the dynamic pressure over the wings and the corresponding inherence of the aircraft to respond to such changes in such a way which reduces the effect of disturbances which caused changes in the first place.

Consider, an aircraft, with no sweep, but constant dihedral angle of Δ, in a steady level flight condition operating at an angle of attack of α, experiences disturbance in horizontal plane in the form of sideslip with an angle of β, then the resulting AOA and dynamic pressure is mathematically shown as;

formula_

Since, the local dynamic pressure on both wings is the same, stability depends upon the changes in AOA and the resulting effects on lift and drag forces.

Now, if the sideslip is positive, then the angle of attack on the starboard wing increases by an amount βsin (Δ), and that of port wing decreases by the same amount. Thus, the drag and lift forces are higher on the right wing and lower on the left wing.

The imbalance of drag forces means that a moment is induced which tends to yaw the aircraft in the direction of the resultant wind direction thus ensuring direction stability.

Similarly, the imbalance in lift forces ensures a rolling moment is induced in the direction the sideslip is generated due to banking. The induced rolling moment is in the opposite direction to the original banking caused due to any disturbances, which means the aircraft is laterally stable.

Effect of Wing Sweep on Stability

Consider an aircraft, with no dihedral, but constant leading edge sweepback angle of κ, in a steady level flight condition experiencing an angle of attack of α, experiences disturbance in horizontal plane in the form of sideslip with an angle of β, then the resulting AOA and dynamic pressure is mathematically shown as;

effect_of_wing_sweep_on_stability

staight,_swept_and_fprward_swept_wing

 

If the disturbance consists of positive sideslip, the local dynamic pressure on starboard wing would increase and also the local angle of attack would be positive.

The reverse would happen for the port side wing. The difference in lift and drag forces on the wings is pronounced due to the effect on both AOA and dynamic pressure.

Higher drag on the right wing and lower on the left creates a moment which tends to yaw the aircraft in the direction of sideslip, thus making it directionally stable.

Similarly, if the disturbances cause the aircraft to bank in one direction, naturally sideslip in the same direction would occur. This has thus resulted in higher lift on right wing and lower on the left, given that the sideslip is positive, thus inducing a rolling moment in the opposite direction, and helping the aircraft gain lateral stability.

Most certainly, there could be other purposes of having or not having a swept or dihedral wing, which are not discussed here.

However, in terms of stability, if we have a wing with no dihedral or sweep, then its effect in directional and lateral stability is very small and often neglected. As such, we need to look into the fuselage, fuselage-wing interference and tail contributions towards stability.


Credit: Gaurav Bhandari
Mechanical Engineering, Tribhuvan University, I.O.E
Image Credit: MSGT Pat Nugent

 

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