Shaft horsepower?

Question

We can build or buy a propeller that is 5 feet in diameter and that has a maximum efficiency of 93% when it is operating at an Advance Ratio of 1.35. The engine we are using to drive the propeller provides optimum torque and fuel economy when turning at a shaft speed of 3000 RPM.

Optimum aircraft airspeed (in knots) for this propeller/engine combination is 337.5 ft/sec.

Mach Number at the propeller’s tip when operating at optimum RPM and airspeed at sea level standard day conditions is 2.492.

Help Please!!!!!!!!!!!!!!!!!!

Find the shaft horsepower required of the engine if the total aircraft drag at the optimum condition above is 500 pounds.

Answer 1

1 HP = 550 ft-lb/sec.
I'll assume "(in knots)" is erroneous, and that the speed is indeed given in ft/sec. Also assumed is that the gearing between engine and prop is lossless, and the gear ratio matches engine and propellor and aircraft so that at the given airspeed the maximum prop efficiency is obtained, as well as combined propellor/engine efficiency. (In other words, without such matching there will be a point of best engine-and-prop efficiency that is not necessarily the point of maximum prop-only efficiency.) With this assumption you can simply use the prop efficiency to calculate engine HP. At the given speed and drag, you require 337.5 * 500 ft-lb/sec, or 306.82 HP from the propellor. With 93% efficiency, you need engine HP = 306.82/0.93 = 329.91 HP.
Are you sure about that mach number at the tip? That's 2.492 * 1116.4 = 2782 ft/sec which requires the prop to spin at 2782/(5*pi) = 177.1 revs per second or 10626 rpm! Are you ready for that? Then if the engine is running at 3000 rpm you'll have to gear up the engine revs by a factor of 10626/3000 = 3.542 (and be ready for the prop to disintegrate). Otherwise check your figures.

Answer 2

i won't be able to argue with Jayce, she's actual the respond is not one of the above. HP= (Torque)(RPM)/(5252) yet in a distinctive thank you to look at horsepower is HP=Torque x RPS x 2Pi/ 550 the place RPS is rotations in keeping with seconds Torque= (HP)(550)/((2Pi)(RPS)) Torque = (20)(550)/4Pi = 875 foot lbs