tl;dr: For a hovering aircraft, upward thrust equals weight, but this isn’t what determines engine power.
I’m no expert, but the important distinction is between power and force (thrust). Power is work done (energy transferred) per unit time, and if you were just gliding slowly in a large and light unpowered glider at a fixed altitude (pretending negligible drag), or to be actually realistic, hovering in a blimp, with lift equalling weight, you’re doing no work! (And neither is gravity.) On the other hand when a helicopter hovers at a fixed altitude it’s doing a great deal of work accelerating a volume of air downwards. (See also Gravity loss for a rocket.)
Now the interesting part: although for a hovering airplane, blimp or helicopter the upward force produced is equal to the weight, the power needed is different because the formulas for thrust and power aren’t directly linked. Thrust: F=ddtmv=ma. To compute work done on the air, consider the kinetic energy imparted on the air pushed down in one second. Power: P=ddt12mv2. Let’s say your helicopter is 1000kg, and simplify the gravitational constant as g=10ms−2, so your weight is 1000g=10000N. To create an equal upward thrust you could push 200kg of air per second downwards at 50ms−1… or 400kg of air at 25ms−1. But the former requires a power of P=12200⋅502=250kW=335hp while the latter is only P=12400⋅252=125kW=168hp! (This is a lower bound on, and directly proportional to, the energy in the fuel the engine must burn.)
So, to be fuel efficient a helicopter would have to have long blades that turn slowly, moving a large volume of air down slowly. But they don’t, apparently it’s not feasible. I imagine lighter helicopters can be more efficient though? And I’m not going to do any calculations for fixed wing aircraft. IANAAE.
This is also why turboprob and turbofan engines are more efficient than plain turbojet engines: they can produce the same thrust while expelling air at a lower velocity, hence with less work done, by using the jet engine to drive a propeller or fan.
tl;dr: For a hovering aircraft, upward thrust equals weight, but this isn’t what determines engine power.
I’m no expert, but the important distinction is between power and force (thrust). Power is work done (energy transferred) per unit time, and if you were just gliding slowly in a large and light unpowered glider at a fixed altitude (pretending negligible drag), or to be actually realistic, hovering in a blimp, with lift equalling weight, you’re doing no work! (And neither is gravity.) On the other hand when a helicopter hovers at a fixed altitude it’s doing a great deal of work accelerating a volume of air downwards. (See also Gravity loss for a rocket.)
Now the interesting part: although for a hovering airplane, blimp or helicopter the upward force produced is equal to the weight, the power needed is different because the formulas for thrust and power aren’t directly linked. Thrust: F=ddtmv=ma. To compute work done on the air, consider the kinetic energy imparted on the air pushed down in one second. Power: P=ddt12mv2. Let’s say your helicopter is 1000kg, and simplify the gravitational constant as g=10ms−2, so your weight is 1000g=10000N. To create an equal upward thrust you could push 200kg of air per second downwards at 50ms−1… or 400kg of air at 25ms−1. But the former requires a power of P=12200⋅502=250kW=335hp while the latter is only P=12400⋅252=125kW=168hp! (This is a lower bound on, and directly proportional to, the energy in the fuel the engine must burn.)
So, to be fuel efficient a helicopter would have to have long blades that turn slowly, moving a large volume of air down slowly. But they don’t, apparently it’s not feasible. I imagine lighter helicopters can be more efficient though? And I’m not going to do any calculations for fixed wing aircraft. IANAAE.
This is also why turboprob and turbofan engines are more efficient than plain turbojet engines: they can produce the same thrust while expelling air at a lower velocity, hence with less work done, by using the jet engine to drive a propeller or fan.