How can engine positioning affect flutter tendency?

Question

I understand that moving the engines towards the wingtips would increase flutter tendency, but are there any other positioning options which could affect flutter?

How about moving the engine position forward, or backward on the wing. What about the twist of the wings, & the set angle of attack on the ground. Do these have to be considered when positioning an engine on the wings of the airplane?

Also, what about rear mounted engines. What should be considered here to reduce flutter tendencies of the stabilizers?

Answer 1

To better understand what flutter is, see the structure as a mass-spring system like a spring pendulum that has a damper attached to it. The aerodynamic forces both make the spring stiffer and dampen the movement. Crucially, they will act with a delay to the motion of the spring pendulum. Since we are dealing with oscillatory phenomena here, this delay causes a phase shift. The amount of damping increases with dynamic pressure and the phase shift angle decreases with flight speed.

Things start to get interesting when the phase shift angle approaches π. Now the damper will not work against the movement of the spring pendulum but will support it. Instead of reducing the amplitude of the movement, it will increase it - damping will become negative*. Flutter happens.

There are several ways to shift that point outside of the flight envelope:

• Reduce the mass or inertia of the mass-spring system: Now the eigenfrequency of the system will be higher, so the phase shift will approach π at a higher speed. Moving the engines closer to the fuselage will increase the bending eigenfrequency of the wing, so any flutter that involves wing bending will be shifted to higher speeds. A typical case would be the flutter resulting from the coupling of the fast-period mode with the wing bending mode in swept-back flying wings.

• Make the spring stiffer: This again raises the eigenfrequency of the spring, so a stiffer structure will shift the flutter speed up. This is no panacea, however: When the Rockwell Commander 112 was developed, flight test revealed flutter of the horizontal tail. A professor from Kansas recommended stiffening of the tail spar and was so convinced that this would cure the flutter that he joined the next test flight, only to crash with the aircraft. As it turned out, the stiffening shifted the flutter speed up such that the forces involved broke the spar while flutter was non-destructive with the softer spar at a lower speed (like in this video).

• Change the Eigenmode of the spring: If the motion of the bending wing will at the same time add a torsion moment which twists the wing, resulting in a lower local angle of attack and, consequently, lower lift on the up-moving part of the cycle and vice versa, the aerodynamic damping can be increased. By shifting the engines forward, the engine mass will introduce such a torsion moment into the wing. Of course, when placed further outboard, the engine mass will cause a larger torsion angle with the same torsion moment, so shifting the engines out towards the wingtips makes this more effective.

• Shift the resonance speed below minimum flight speed: This might sound silly, but works sometimes: When flying fast enough, the phase shift can be small enough to turn aerodynamic damping back into the positive region, and the plane will not flutter with that particular flutter mode. But it might still flutter at a harmonic …

Generally, to achieve positive damping, the center of gravity of a part should be ahead of its elastic axis. In the case of control surfaces, their center of gravity should be in or ahead of their hinge line. That is the reason for balancing masses!

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* to be precise: As long as damping retards the motion, the damping term is mathematically negative and turns positive when it starts to support it.

Answer 2

This is a very interesting question, with a very complicated answer! The problem of Aero-Elasticity is not easy or simple to solve. The reason is, that the equations (or better the system of equations) which describe it are not simple (in this case the non-linearity of the aerodynamic forces create most of the analytical problems). Flutter can be assessed with an aero-elastic simulation. The following graphic (from EPFL) illustrates the system of equations.

As you can see there are roughly speaking three things (and their interaction) a designer needs to keep in mind: Dynamics, Fluid-Mechanics, and Structural Mechanics. Usually this is done using simplified versions of the airplane like the following (taken from DLR).

Based on this simplified representations of the air-plane trade-studies can be done to collect a better understanding.

The TL;DR answer to your question is: Yes, all the things you mentioned need to be taken into account to design an air-frame.

When designing an airplane the position of the engine does matter. But it is not only the position but also the mass and the elastic properties of the air-frame. On top of this the aerodynamic forces need to be taken into account as well.

There are no simple recipes to reduce flutter because most of them only work for a limited set of boundary conditions. A very (vague) basic one could be: Place engines so that manoeuvre loads will result in a small (as small as possible) elastic deformation (thereby reducing the amount of potential energy which is stored in the airframe).

The other recipe is to look what others have done. Given you are planing to use the aeroplane in a similar way other manufacturers offer aeroplanes and given you are using similar materials and manufacturing techniques: you could use existing designs as starting points for your trade-study.

Answer 3

No, moving the engines towards the wingtips would not increase flutter tendency. Flutter can be pictured as the tendency of the airfoil to twist itself perpendicular to the airflow. The wing structure is elastic, and the elastic torsion box springs the wing back again - flutter is just like any underdamped spring-mass-damper system that can start to oscillate.

In general, the measures that can be taken against flutter are:

• Reduce the twisting force: reduces the amplitude of the oscillation
• Increase the torsion stiffness. Make it stiff enough and there is hardly any oscillation
• Increase damping forces. Reduces the number of overshoots and the amplitude. This one is not easy to do in a wing construction.

Increasing the mass of the mass-spring-damper system increases overshoot amplitude, increases the time period of the oscillation, and increases the number of overshoots.

So the practical measures that can be taken against flutter are:

• Mount an engine near the wing tip, forward of the aeroelastic axis, this reduces the backward twisting force of the airstream. The closer to the wing tip, the better it does its job as flutter force reducer and wing bend reliever. But too close to the tip and the landing jolt will be excessive: there is an optimum.
• Mount the engine at the optimum distance forward of the aeroelastic axis, too far forward and the construction for increasing torque stiffness will become too heavy. Too far back and it does not do its job well.

The design twist of the wing is computed at cruise conditions, set angle of attack on the ground is not really critical if the plane can rotate back far enough.

Mounting the engine at the back of the fuselage in pods is basically not done anymore for larger aircraft, that question has been answered a couple of times on this site.