Lesson test: Propellers and momentum theory

1.[2p]
In momentum theory, why does a larger propeller need less power to make the same thrust?

It throws a larger mass of air more gently, and the induced velocity is what costs power

Correct

It spins faster, and speed reduces power

The answer is: It throws a larger mass of air more gently, and the induced velocity is what costs power

It weighs more, which stabilises the craft

The answer is: It throws a larger mass of air more gently, and the induced velocity is what costs power

It has a higher pitch

The answer is: It throws a larger mass of air more gently, and the induced velocity is what costs power

2.[2p]
Ideal hover power goes as $T^{3 / 2}$ . If the thrust a propeller must make increases by a factor of 4, by what factor does the ideal power increase?

CorrectNot quite: 8

3.[2p]
Doubling a propeller's disc area, at constant thrust, cuts the ideal hover power by a factor of the square root of two.

True

Correct

False

The answer is: True

4.[3p]
A propeller must make 1.23 N of thrust with a disc area of 0.0129 m² in air of density 1.225 kg m⁻³. What is the induced velocity $v_{i} = \sqrt{T / (2 ρ A)}$ , in metres per second?

CorrectNot quite: 6.24

5.[2p]
Propeller thrust scales as $n^{2} D^{4}$ and power as $n^{3} D^{5}$ . A practical reading of these is that

raising rotation rate buys thrust cheaply but raising it far becomes expensive in power

Correct

diameter has no effect on power

The answer is: raising rotation rate buys thrust cheaply but raising it far becomes expensive in power

power is always proportional to thrust

The answer is: raising rotation rate buys thrust cheaply but raising it far becomes expensive in power

a smaller propeller is always more efficient

The answer is: raising rotation rate buys thrust cheaply but raising it far becomes expensive in power

6.[1p]
The pitch of a propeller, the second number in a size like 5x4.3, sets

how far it would advance per turn, and so how aggressively it bites and loads the motor

Correct

its diameter in inches

The answer is: how far it would advance per turn, and so how aggressively it bites and loads the motor

the number of blades

The answer is: how far it would advance per turn, and so how aggressively it bites and loads the motor

the direction it spins

The answer is: how far it would advance per turn, and so how aggressively it bites and loads the motor

7.[2p]
A propeller's figure of merit, around 0.7 for a good small propeller, measures

how close its real power is to the loss-free ideal of momentum theory

Correct

its thrust in grams

The answer is: how close its real power is to the loss-free ideal of momentum theory

its maximum rotation rate

The answer is: how close its real power is to the loss-free ideal of momentum theory

its diameter divided by its pitch

The answer is: how close its real power is to the loss-free ideal of momentum theory

1.[2p] In momentum theory, why does a larger propeller need less power to make the same thrust?

2.[2p] Ideal hover power goes as T3/2. If the thrust a propeller must make increases by a factor of 4, by what factor does the ideal power increase?

3.[2p] Doubling a propeller's disc area, at constant thrust, cuts the ideal hover power by a factor of the square root of two.

4.[3p] A propeller must make 1.23 N of thrust with a disc area of 0.0129 m² in air of density 1.225 kg m⁻³. What is the induced velocity vi=T/(2ρA), in metres per second?

5.[2p] Propeller thrust scales as n2D4 and power as n3D5. A practical reading of these is that

6.[1p] The pitch of a propeller, the second number in a size like 5x4.3, sets

7.[2p] A propeller's figure of merit, around 0.7 for a good small propeller, measures

1.[2p]
In momentum theory, why does a larger propeller need less power to make the same thrust?

2.[2p]
Ideal hover power goes as $T^{3 / 2}$ . If the thrust a propeller must make increases by a factor of 4, by what factor does the ideal power increase?

3.[2p]
Doubling a propeller's disc area, at constant thrust, cuts the ideal hover power by a factor of the square root of two.

4.[3p]
A propeller must make 1.23 N of thrust with a disc area of 0.0129 m² in air of density 1.225 kg m⁻³. What is the induced velocity $v_{i} = \sqrt{T / (2 ρ A)}$ , in metres per second?

5.[2p]
Propeller thrust scales as $n^{2} D^{4}$ and power as $n^{3} D^{5}$ . A practical reading of these is that

6.[1p]
The pitch of a propeller, the second number in a size like 5x4.3, sets

7.[2p]
A propeller's figure of merit, around 0.7 for a good small propeller, measures