Does pumping fuel to each wingtip affect roll trim in a stabilized turn?

Question

If an aircraft is stabilized in a constant-bank, constant rate turn with no sideslip, and then we pump 200 gallons of fuel from a fuselage tank to a tank on the tip of each wing, without changing the position of the ailerons or rudder, and without changing the aircraft CG, will we find that the aircraft tends to roll into the turn, roll out of the turn, or neither?

The intent of this question is that we get the aircraft fully stabilized in a coordinated turn at the original bank angle after pumping the fuel to the tips, and then we put the controls back in their original positions and see if the aircraft tends to roll. This isn't meant to be a question about the effects of suddenly redistributing the mass and the way that this might possibly create a temporary yawing tendency due to yaw rotational inertia, like we see when a skater throws out their arms horizontally while spinning around.

Answer 1

Not if the fuel pumped to the wing tips in equal amounts so that the lateral CG is unchanged. But... there are effects related to the inertia of the fuel mass (the wings become spokes in a flywheel, you could say).

I have some flying time a plane that has all of its fuel in the wing tips, in tuna fish shaped tanks, 25 usg per side.

The difference in handling qualities with the tips nearly full and the tips nearly empty is all related to inertial effects of the fuel mass; roll rate, roll inertia, yaw inertia, and roll response to yaw. The roll rate you can generate by skidding the plane is much lower with the tips full. The influence of dihedral in damping and restoring roll deviations is reduced. Disturbances are amplified because of the flywheel effect of the tip mass and this is especially noticeable in yaw; there is more of a tendency for the tail to wag in bumps.

But in a stabilized bank in smooth air, the amount of fuel in the tips made no difference in increasing or decreasing overbanking/underbanking, except to the extent that the interia of the fuel dampens or inhibits the usual restorative forces. So if you had an airplane that can be banked and holds the bank angle with no input, there is no major effect of fuel in the tips in changing that characteristic, until you hit a bump and the inertial effects start to work. However, where the airplane has an overbanking or underbanking tendency, the flywheel effect will inhibit it starting and tend to keep it going once started.

So to answer the basic question, if you had a plane that naturally wants to roll out of a turn when inputs are removed, the effect of fuel in the tips will be to reduce that effect somewhat, so it will still roll level but take longer, and once level it will tend to overshoot more. It it wants to overbank into a spiral dive, same thing that way.

Answer 2

Here is how I see the problem at this time--

There's no doubt that in a turn, there's a rolling-in torque (toward a steeper bank angle) created by the difference in airspeed, and lift, between the inboard and outboard wingtips.

Does concentrating the mass at the wingtips reduce this roll torque? Obviously roll inertia is increased, but is the roll torque actually reduced?

Let's say we attach a string to the CG and sling the airplane around and around in a circle, somewhat in the matter of a "control-line" model airplane, but with the wings at the zero-lift angle-of-attack, so the aerodynamic roll torque noted in the first paragraph disappears. Is there any intrinsic, inertial tendency for the aircraft to roll to a wings-level attitude, rather than adopting a steeply-banked attitude? A tendency that, if it existed, might be more pronounced if the wingtips were heavily weighted? It intuitively appears to me that the answer is "no".

Therefore the answer to the original question intuitively appears to be "no".

One could argue that the outboard wingtip, travelling at a larger velocity and experiencing more apparent "centrifugal force" than the inboard wingtip, will tend to dominate the situation and therefore there WILL be some very small self-leveling effect, and more so if the weight is concentrated near the tips. This effect appears to have some similarity to a "tidal" effect in orbital dynamics-- it would be based upon the different radii experienced by different parts of the body in the orbit or turn. This effect is surely a very minor player in roll stability dynamics in a normal turn-- unlike in a flat spin, where the center of rotation may be near the center of the aircraft, and any weight added to the wingtips will strongly tend to make the spin go even flatter.

This may be a situation where it is actually most helpful to adopt a reference frame based on the moving aircraft itself. This will not be a valid inertial reference frame, so we'll have to take "centrifugal force" into account. In a fully coordinated turn, the direction of the apparent weight of each tip tank will be straight down in the aircraft's reference frame, but the outboard tip tank will seem to "weigh" more than the inboard one, and this create a rolling-out tendency, or to put it another way, will cancel out the rolling-in tendency created by the difference in airspeed between the two wingtips. A perfectly span-loaded aircraft will experience no rolling-in or rolling-out tendency due either to the difference in apparent weight, or the difference in lift, at different points along the wingspan. If all the weight is concentrated at the wingtips, this would appear to create some self-leveling effect.

Answer 3

Effects of moving fuel would be transitory, eventually restabilized by trim, provided CG did not change significantly.

Pumping fuel out to the tips would naturally slow the roll rate momentarily, but since roll acceleration is governed by roll drag, over time roll rate would resume unchanged (In a stabilized turn, roll is constant, the roll out of the turn would be slower with the same control input).

More interesting is the effect on yaw. Fuel in the fuselage moves at speed x around a circle. Inside wing speed is x-y and outside wing is x+y. So effect of moving fuel to the slower inside will speed it up a bit, and the faster inside wing will slow it down a bit. The result is a yaw to the outside, that again, aerodynamic force will overcome.

As ultimately all aerodynamic motion is governed by drag, effects of moving weight laterally on an equal basis are only temporary, if control inputs are not changed.