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AlephZero
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I tend to be on DaveC's side of this argument.
You need to be careful what you mean by "lifting work" here. Consider the case of hovering, since it's simple (no drag forces, etc).
To create the lift force, you have to add downwards momentum to the air. That's the whole story - Bernoulli's principle etc are just ways to explain HOW you might do it, not WHAT you have to do.
When you move the air downwards you give it KE, which is why you have to do work. For a mass m and velocity v the KE is (1/2)mv^2. For mass 2m and velocity v/2 the momentum is the same, but the KE is (1/4)mv^2 or half as much. In general, it's more efficient to move large of mass slowly, not a small mass quickly.
Having denser air is a good way to move more mass, so less power is reqired to generate the same lift.
BTW This argument also explains why helicopters have huge diameter rotors compared with aircraft propellors. The size of a propellor is limited by clearance of the ground and/or the airccraft body. A heli rotor can be as big as you like, and bigger means more efficient.
One other thing: russ-watters said "the lift required is the same therefore the torque on your shoulders is the same". That would be true if all the force from the wings was transmitted through your arms. However assuming you are going to fly in a horiziontal position you want the centre of lift over the center of mass which implies (to me) the wings attached to a harness to your torso, but powered somehow by the arms. So your arm muscles would be supplying the power, but not also supporting your full weight. That sounds like a better engineering solution to me.
You need to be careful what you mean by "lifting work" here. Consider the case of hovering, since it's simple (no drag forces, etc).
To create the lift force, you have to add downwards momentum to the air. That's the whole story - Bernoulli's principle etc are just ways to explain HOW you might do it, not WHAT you have to do.
When you move the air downwards you give it KE, which is why you have to do work. For a mass m and velocity v the KE is (1/2)mv^2. For mass 2m and velocity v/2 the momentum is the same, but the KE is (1/4)mv^2 or half as much. In general, it's more efficient to move large of mass slowly, not a small mass quickly.
Having denser air is a good way to move more mass, so less power is reqired to generate the same lift.
BTW This argument also explains why helicopters have huge diameter rotors compared with aircraft propellors. The size of a propellor is limited by clearance of the ground and/or the airccraft body. A heli rotor can be as big as you like, and bigger means more efficient.
One other thing: russ-watters said "the lift required is the same therefore the torque on your shoulders is the same". That would be true if all the force from the wings was transmitted through your arms. However assuming you are going to fly in a horiziontal position you want the centre of lift over the center of mass which implies (to me) the wings attached to a harness to your torso, but powered somehow by the arms. So your arm muscles would be supplying the power, but not also supporting your full weight. That sounds like a better engineering solution to me.
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