HumanPoweredDesigner
Well-Known Member
This assumes zero head wind, though minor modifications can adjust for that. Also assumes 100% of input power goes to thrust without drag of blades or fuselage. It assumes a fan method of thrust, meaning thrust is gained by pulling air behind the prop. I don't know how a foil prop would differ, except that a foil has less spin drag. I'd like to think a foil can get thrust with kinetic energy to the air.
Thrust Th is in Kg
Power P is in W
Area A is in m2
Thrust is related to MV, or in our case, mass flow per second times velocity of that flow, or (kg/s)*(m/s) = kg m/s2. To fight gravity with 1 kg of force, you need 1kg x 9.8 m/s2. If you put 1 kg of force on 1 kg, and got rid of gravity and air resistance, it would accelerate at 9.8m/s2, same as if you drop a rock.
Power is related to kinetic energy, which is 1/2mv2. Power is energy used per second. Energy is force (thrust) x distance / time and has units kg m2/s3. You can pull one extra v out of there, as predicted from mv2 versus mv.
Area is prop area. Velocity x area x density = mass per second.
Air has an average molecular weight of 29grams per mole. There are 22.4 Liters in a mole at standard temp and pressure. density is mass divided by volume. So 1.3grams per liter is 1.3 kg per m3.
Thrust:
9.8 Th = mv
Power:
P = 0.5 mv2
Area:
A*v*1.3=m
To get A, we need v and m. Solve for m in both, then set equal to solve for v. Then plug back in to get m:
9.8Th/v = 2P/v2
v = 2P/9.8Th
9.8Th = m(2P/9.8Th)
m = ((9.8Th)^2)/2P
A*v*1.3 = m
A = ((9.8Th)^3)/((2P)^2*1.3)
A = 181 Th3/P2
D2 = 57.6 Th3/P2
Thrust Th is in Kg
Power P is in W
Area A is in m2
Thrust is related to MV, or in our case, mass flow per second times velocity of that flow, or (kg/s)*(m/s) = kg m/s2. To fight gravity with 1 kg of force, you need 1kg x 9.8 m/s2. If you put 1 kg of force on 1 kg, and got rid of gravity and air resistance, it would accelerate at 9.8m/s2, same as if you drop a rock.
Power is related to kinetic energy, which is 1/2mv2. Power is energy used per second. Energy is force (thrust) x distance / time and has units kg m2/s3. You can pull one extra v out of there, as predicted from mv2 versus mv.
Area is prop area. Velocity x area x density = mass per second.
Air has an average molecular weight of 29grams per mole. There are 22.4 Liters in a mole at standard temp and pressure. density is mass divided by volume. So 1.3grams per liter is 1.3 kg per m3.
Thrust:
9.8 Th = mv
Power:
P = 0.5 mv2
Area:
A*v*1.3=m
To get A, we need v and m. Solve for m in both, then set equal to solve for v. Then plug back in to get m:
9.8Th/v = 2P/v2
v = 2P/9.8Th
9.8Th = m(2P/9.8Th)
m = ((9.8Th)^2)/2P
A*v*1.3 = m
A = ((9.8Th)^3)/((2P)^2*1.3)
A = 181 Th3/P2
D2 = 57.6 Th3/P2
