# How does 'standalone' propeller efficiency change with altitude?

I've seen questions regarding propeller aircraft and altitude and their interaction. But I'm wondering what the relationship between just the propeller and altitude (changing air density) is. How does the efficiency and ability of a propeller scale with altitude?

Real-life scenario which inspired this question: a two-bladed two-engine propeller system is being used to propel a payload on a balloon platform (i.e lift is handled by helium buoyancy, no minimum speed required to stay afloat). The propeller is only used to move horizontally slowly (< 5m/s). This occurs at 65,000 feet and the propellers were analyzed at these conditions. Now, the new altitude is going to be 85,000 feet. How does that affect the scaling and re-design of the propulsion system? The Reynolds number will of course be different for the same desired airspeed. Additionally, the system drag will be lower so less thrust will be required at the same airspeed. But if the required thrust needed was the same, how does that and other factors affect the efficiency? And knowing that the required thrust will be lower scaled to air density, what is the expected change in propeller requirements?

Addendum: can the same 65,000 feet propellers be used at 85,000 feet, or is a new design required?

• Being limited to sub Mach#, you are already at a wall in terms of blade velocity, so I think it's just a matter of needing more and more blade surface area the higher you go. Somebody here probably knows how to do the calcs. Commented Jul 26, 2020 at 22:33
• You may wish to consider the electric 2 hp 2 meter "laminar flow" Helios props, good to 95,000+ feet. These propelled a wing to sustained flight at that altitude, and may be a good "off the shelf" solution. Commented Jul 27, 2020 at 13:53

## 1 Answer

Yes, the same propeller can be used.

Propeller thrust is proportional to air density. The same is true for aerodynamic drag, so your propeller will work at all altitudes equally well. Since the speed of sound drops with temperature, you need to pick your propeller tip speed for the coldest layer, which normally is the Tropopause. There, the speed of sound is 295 m/s and if the propeller tips don't exceed 85% of that, efficiency should be roughly constant over altitude. A small loss in efficiency with altitude must be accepted, however, since the propeller's friction drag increases with altitude.

This would not be true for airplane propellers where the drag of the airplane they are propelling is constant (actually, rises a bit) with altitude, but since your thrust demand drops in line with density, no new propeller is needed at 85,000 ft.

• I don't quite understand the second paragraph. Why does the drag for airplane propeller stay constant (or slightly increase) with altitude? Do you mean that the aircraft drag drops by about slightly less of a factor as lift due to the altitude, and thus a slightly higher airspeed is required to counter weight, and that would require a slightly greater thrust? Commented Jul 28, 2020 at 6:04
• @spaceprops What I meant is the drag of the plane the propeller is attached to. Since you don't need to generate lift, your thrust requirement over altitude is very different. I'll try to make the answer more readable. Commented Jul 28, 2020 at 8:36
• wouldn't aircraft drag also decrease in proportion with density though according to the drag equation "0.5 * rho * V^2" Commented Jul 28, 2020 at 17:21
• @spaceprops. No, because speed squared has to grow to compensate for lower density. The ratio of lift to drag is about constant (gets a bit worse with altitude) and lift must stay constant because mass doesn't change. Hence, the product of density and speed squared has to stay constant, too. Commented Jul 28, 2020 at 20:07
• ah, right, thanks! Commented Jul 28, 2020 at 20:58