# How do I calculate the total cruise power from the propellers accounting for the losses?

Let's say I have an aircraft with four propellers (see diagram below) and I am supposed to calculate the cruise power required to drive the aircraft forward. The wing creates the lift and propellers provide the forward thrust.

If I don't account for the wake of the front propellers affecting the rear propellers it's easy. I just have to calculate the thrust required and get the power. But how do I account for the losses and the actual power required?

• Are the four rotors only providing forward thrust and the wing provides the lift? Commented May 22, 2019 at 10:07
• Yes ,Wing provides the lift and the rotors provide the forward thrust Commented May 22, 2019 at 10:24
• Why is there downwash? What angle are the rotors? Commented May 22, 2019 at 10:29
• 90 deg. its not the downwash I meant to say the flow leaving the front rotors Commented May 22, 2019 at 10:33
• If you counter rotate them the losses might be gains. Commented May 22, 2019 at 11:56

The flow leaving the propeller:

• Contracts, as a function of distance behind the propeller. The impulse theory gives a contraction factor - for an idealised homogeneous outflow field. The contracted wake has a higher velocity than free stream.
• Has a whirl component due to the drag of the blades.
• Has propeller tip vortices in a contracting corkscrew field.

So if the aft propellers are far enough behind the forward ones, the aft propeller tips are unaffected by the wake of the forward ones.

If the aft prop counter-rotates, the whirl component from the front props will be removed. Optimal blade angle of the aft prop is different from that of the fwd prop, but the tips would remain relatively unaffected.

Picture above is from Leishman, which has a whole chapter devoted to rotor wake. There has been quite some research done on co-axial rotors for helicopters. There is some info and a link in this answer as well.

But I reckon you'll be in the right order of magnitude if you just compute required power as you would in an undisturbed flow, especially if you use ducted propellers which reduce the tip vortices.

• I appreciate your answer but can you tell me in terms of percentage how much will be the loss?..Can it be neglected Commented May 23, 2019 at 10:33
• The Ray Prouty book mentions about co-axial rotors: "Separate them 20% of the rotor radius, and you still have a 7% power advantage over a single 4-blade propeller, as computed by Kamov [(reference)][3]." Counter rotating props can actually have a power advantage - a gain, not a loss. That would mean that losses can be neglected. Commented May 23, 2019 at 14:03