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2

The downwash is about as high as wide, and angled only by a few degrees (more at slow speed). So the longitudinal distance needs to be many times longer than the wing span to make the wings independent. And it would still be less efficient than increasing the span: If you double the span, you will decrease induced drag four times. If you half the lift, you ...

3

You seem to be confusing force (thrust or drag) with energy (under which concept work and power comes). Don't. You'll be spared much grief. Work done is force times distance. $$W = Fs$$ Power is work done divided by time $$P = W/t$$ When you double velocity, force quadruples. As does work. $$W_\text{new} = 4Fs = 4W$$ Time halves as well, with the ...

6

Let's imagine 2 theoretical wings, both of which have the same area, but differ in aspect ratio. Then the wing with the higher aspect ratio also has more span. This is what counts. If induced drag depends on the downwash angle, why would a longer wingspan reduce the angle? Because the wider wing will affect more air. Think of the air affected by the wing ...

1

Your understanding of induced drag is correct. It is caused by turning the air flow and the force that does it must be tilted, otherwise conservation of energy would be violated. The stream ‘tube’ affected by the wing is obviously as wide as the wing, and always considered to be roughly as high as wide. That is, wings with higher span affect air to greater ...

0

This is my interpretation. See if it helps. Induced drag can be thought of as the energy consumed in making lift, in other words, the energy consumed in inducing a package of air to move down as a result of the wing's passage. It's the energy consumed in accelerating a mass; wing, propeller, helicopter rotor, it's all the same. Vortices are just a ...

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What we commonly call wingtip vortex is technically not a vortex in the strict sense. The spiraling circulating air around the wing tip that trails behind the wing is actually the product of two processes: 1. Trailing Vortex Sheet From the OP, you may know that a lifting surface sheds trailing vortices, everywhere along the trailing edge. The ensemble of ...

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