Thrust

So from reading my book on helicopters I have found the following formulas.

To compute the power needed to lift my quadcopter I need to know the total weight of the chopper....

With the shortened frame, the motors, the batteries and the controller it weighs about 200 grams. I am hoping to thin the supports or replace them with lighter material although the frame itself only weights 17 grams. Where I will most likely be able to trim weight is the batteries and the motors. But for now lets just say 200 grams

So my 4 rotors have to produce 200 grams of thurst or 50 grams of thrust per rotor. Now all my equations are in imperial units so that is 0.440924 lb per rotor.

T =  0.440924

My rotors are 8cm in diameter or 4cm radius so the disk area is 4^2*pi = 50.2654cm^2 or in imperial

A = 0.05410522626595922 ft^2

There is the constant rho = 0.002378 accounts for the viscosity of air at sea level. For reference that is in slugs/ft^3 whatever that unit is.

Therefore I have the induced velocity vi is

vi = sqrt(T/(2*rho*A)
= sqrt(0.440924/ (2*0.002378*0.05410522626595922 )
= sqrt(0.440924/0.000257324456)
= sqrt(1713.49434)
= 41.3943757 ft/s

The ideal power required for each rotor is then Pi = T*vi
P = 0.440924 * 41.3943757
 = 18.2517737 lb*ft/s

and this value can be converted into horsepower by dividing by 550.
therefore My rotors each need 0.0331850431 hp in order to lift my chopper.

Now this is the ideal power required and as everyone knows, nothing is ideal. so I actually  need more than this but its a start.

oh, to convert this into something useful I need to multiply it by 0.7457 to get kW

~(' ')~
so I need 0.0247460866 kW of power or 24.7460866 watts of power