Mariner9
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If all the geese flew to the front of the aircraft, would the pilot have to re-trim due to change in CG?
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The answers is yes. The reason for it is this, if you had no geese in say the first 5 meters of the hold, then move the 3000 kg into the space while flying the density of the fluid being supported by the fuselage in that volume increases, hence an increase in mass, and in increase in weight, therefore a change in CG.
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The geese are flying, and are supported in the air due to pressure differentials generated in by their wings. They are not displacing their own weight in air, as would be the case if they were floating.
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Your idea is correct where the geese would be in contact with the free stream air (fluid), such as in the bird cage.
In this case the geese are not in direct contact with the free stream air, and therefore cannot exert a force on it. The mass of air is fixed inside a controlled volume. The load of the aircraft and all its contents is transferred to the free stream air (fluid) via the wings and the small amount of lift produced by the fuselage.
If you are wondering where the energy is going that the geese are delivering to the air if its not significantly changing the aircraft weight…. It is converted to heat, noise, and friction between the air molecules inside the aircraft.
For all practical purposes the weight of the aircraft does not change, as I have indicted above the weight will reduce but only by the smallest amount.
Cheers