# Is flutter speed always smaller than divergence speed for aircraft?

Ludovic C.
• Is flutter speed always smaller than divergence speed for aircraft? Ludovic C.

In aeroelasticity, there are three main phenomena that one should take care of: divergence, aileron reversal and flutter. Each of them has an associated speed at which the phenomenon might start to occur.

During wind-tunnel tests it is possible to increase the flutter speed to have access to the divergence speed first by using some small masses smartly placed on the wing. This is due to the fact that usually flutter speed is smaller than divergence speed.

Is it always the case for aircraft (without additional masses on the wing)? If not do you have any example? If yes do you have an explanation why or a mathematical proof of it?

• Flutter speed will usually be smaller than divergence speed. Flutter will appear first because as a phenomenon, by definition, describes the state of the deformation of the wing where it deflects for example up and down in a vibrating fashion. Divergence on the other hand is when the moments from the aerodynamic forces acting on the wing are larger than the restoring moments due to structural stiffness thus resulting in failure.

For the sake of simplicity -since the entire calculation is pretty lengthy- let's imagine an airfoil at an angle of incidence `θο` that's been twisted by an angle `θ` due to aerodynamic loading. This additional angle θ is used to measure the twisting strain (dynamic) energy `0.5*K*θ^2` where K is the stiffness of the airfoil - much like a spring's K constant. An increase in speed will increase angle θ and the corresponding strain energy stored in the structure. When the speed reaches the divergence speed the restoring forces are smaller than the aerodynamic forces and the angle θ becomes infinite but since infinite is impossible in reality, the structure fails.

Very early airplanes (Wright, Langley) had major divergence problems and where unable to fly although they had airfoils capable of generating the lift necessary. The same airplanes with stiffer wings in later designs where able to fly. Modern airplanes due to proper design and stiffer materials have divergence speeds higher than flutter speeds. Divergence is a measure of the overall stiffness of the structure and is also used in order for the aircraft to get certified.

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• In aeroelasticity, there are three main phenomena that one should take care of: divergence, aileron reversal and flutter. Each of them has an associated speed at which the phenomenon might start to occur. During wind-tunnel tests it is possible to increase the flutter speed to have access to the divergence speed first by using some small masses smartly placed on the wing. This is due to the fact that usually flutter speed is smaller than divergence speed. Is it always the case for aircraft (without additional masses on the wing)? If not do you have any example? If yes do you have

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