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I am trying to calculate different propellers for the simple case like helicopter moving slow up like 1 m/s or staying/hanging in one place.

From generic physics point of view it is more efficient to push back more mass with low speed, then to push back less mass with higher speed.

Efficiency (Kg/Watt) I mean how many thrust in kg I will get from 1 Watt of power.

I did calculation using Prop selector software as shown in screenshot below big propeller 4 meters with only 32 RPM procude 1kg of thrust and power is just 13 Watts. Speed of the end of propeller will be 6.7 m/s.

Small propeller 27 cm with 7000RPM with the same 1 kg thrust needs 176 Watts of power. Speed of the end of propeller will be 99 m/s. 13 times more power!

Red thrust in the screenshot means "propeller is stalled", but maybe this "stalled" does not make sence for static case, when propeller is not moving.

enter image description here

My question is Why this type of propeller (big diameter, but low speed) is not in use? Is it just practical consideration like big field will be needed if I make very big propeller, or my calculation is wrong or something else?

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  • $\begingroup$ Propeller stall should mean the blades—which are airfoils like wings—are stalled. That can happen at any forward speed. Probably you need to adjust the pitch angle at the last line—most airfoils stall below 15°, so the 20° and 17° values in your screenshots are way to high for static case. Reducing the pitch angle below stall should increase the efficiency (in both cases). $\endgroup$ – Jan Hudec Nov 4 at 21:16
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You are not wrong, it is more efficient to accelerate a large mass by a little than a small mass by a lot.

This is due to momentum being linear with speed and mass, while energy is linear with mass but quadratic with speed, so the same momentum can be obtained more efficiently by slowly pushing a large amount of air, e.g. with a large propeller.

The reasons against this are as you imagined, like clearance from the ground and other parked craft. Also, extremely long propeller blades will suffer from high inertia and bending moments, without the benefit of centrifugal stiffness. And then there is the issue of keeping the propeller tips subsonic, to avoid wasting a lot of energy in the form of sound.

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  • $\begingroup$ Also there is the parasite drag. Longer blades have more parasite drag and at some point the parasite power becomes more than induced power. $\endgroup$ – Jan Hudec Nov 4 at 21:18
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That makes sense. A Bell 47 helicopter gets way over 3000 lbs of thrust from its 37 ft 300 rpm horizontal "propeller" on only 280 hp (with a chunk of that going to the tail rotor), well over double what that engine can produce turning an 80 inch propeller at 2700 rpm the normal way (maybe 13-1500 lbs thrust). But to use it like a regular propeller would require 20 ft tall gear legs.

So from the standpoint of "as long as possible", setting aside the issue of tip speeds and gear reductions and all that, the prime issue is ground clearance for your prop on a given airframe. The Osprey gets away with those fabulously long rotor/propellers that are super efficient for cruise because it turns them up to hover for landing and doesn't have to deal with the ground clearance problem.

On a regular plane though, you are stuck with a few of feet of radius to play with, and ideally you use the longest prop that can run with the tips subsonic at your engine's rpm limit, without hitting the ground.

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  • $\begingroup$ "doesn't have to deal with the ground clearance problem" – Until it has to land with not enough power to go vertical … $\endgroup$ – Jörg W Mittag Nov 1 at 22:28

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