This set of Aerodynamics Multiple Choice Questions & Answers (MCQs) focuses on “Blade Element Theory”.

1. What is the blade element theory used for?
a) Predict performance of airscrew airfoil
b) Predict performance of wind turbine
c) Predict performance of supersonic airfoil
d) Predict performance of flat plate

Explanation: The blade element theory is used to predict the performance of an airscrew blade which is a type of lifting airfoil used in helicopters. It can be replaced by a single hypothetical bound vortex which sheds vortex from the tip of the blade.

2. Which shape is traced by the trailing vortex at the tip of the airscrew blade?
a) Helix
b) Solenoid
c) Circle
d) Sine curve

Explanation: On examining the vortex system of the airscrew blade, we see that the trailing vortex which is formed at the tip of the blade traces out helix as the airscrew advances and rotates, the trailing vortex takes a helical form.

3. The bound and trailing vortex cancel out each other in the plane of the airscrew blade.
a) True
b) False

Explanation: There are three planes that can be considered- One immediately ahead of the plane, in plane of the blade and one immediately behind the blade. In case of the plane which is immediately ahead of the blade, the angular velocity is zero resulting in bound and trailing vortices canceling out each other.

4. How many times is the angular velocity of flow behind airscrew compared to that of angular velocity in plane of airscrew?
a) Same
b) Twice
c) Thrice
d) Four times

Explanation: If we consider the angular velocity of flow in plane of the airscrew blade as bΩ, and the angular velocity behind the blade as indicated by the bound vortices as +βΩ, then the angular velocity of the flow behind the airscrew is given by:
ω=(b+β)Ω=2bΩ
This value is twice that of the angular velocity in plane of the airscrew.

5. When is the blade element theory applicable?
a) When solidity is much greater than 1
b) When solidity is much lesser than 1
c) When solidity is equal to 1
d) When solidity is equal to 0

Explanation: In order to make sure that the blade element theory is applicable, there are certain conditions that have to be met. First being that the spacing to the chord ratio should be high.
$$\frac {s}{c}$$ >> !
And solidity should be much lesser than 1. Solidity is defined by:
σ=$$\frac {Bc}{πr}$$
Where, B is number of blades
C is the chord length
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6. How does the blade element theory treat the airfoil as?
a) One-dimensional
b) Two-dimensional
c) Three-dimensional
d) One complete body

Explanation: The essence of blade element theory is to divide the blade into numerous segments known as blade elements. These are considered to be independent and not influencing the flow over other elements. Thus, it is treated as a two-dimensional airfoil whose aerodynamic forces are computed based on local flow conditions at that particular element instead of the entire airfoil.

7. Why is blade element theory preferred over momentum theory for designing a propeller?
a) Assumes flow inside stream tube as constant
b) Neglects span wise flow
c) Model thrust lag
d) Account for varying blade geometry

Explanation: There are several reasons why blade element theory is preferred over momentum theory. It can account for varying blade geometry, allows torque estimation, allows non-linearities for example lift curve to be modelled. The other points are some of the disadvantages.

8. What is the formula for the helix angle?
a) Φ=tan-1$$\frac {V_0}{V_E}$$
b) Φ=sin-1$$\frac {V_0}{V_E}$$
c) Φ=cos-1$$\frac {V_0}{V_E}$$
d) Φ=tan-1$$\frac {V_E}{V_0}$$

Explanation: According to blade element theory, When the propeller rotates and advances, the tip traces out helix. Along with this the trailing vortex also traces helix. This angle is measured between the direction of the flow and plane of rotation and is computed using the formula:
Φ=tan-1$$\frac {V_0}{V_E}$$
Where, V0 is the forward airspeed of the aircraft
VE is the effective resultant velocity.

9. What is the inflow ratio for hovering?
a) 1-1.5
b) 0.05-0.07
c) 0.6-1
d) 0.01-0.05

Explanation: Inflow ratio is a nondimensional quantity that is used to compare the results from different rotor blades. The formula for inflow ratio is given by:
λ=$$\frac {V+v}{ΩR}$$
Where, V is the climb velocity which is zero for hovering
v is the induced velocity
Ω is the rate of rotation of the blade
The value of inflow ratio ranges between 0.05 and 0.07 for hovering.

10. What is rotor polar?
a) Plot of power coefficient as a function of thrust coefficient
b) Plot of thrust coefficient as a function of power coefficient
c) Plot of power coefficient as a function of lift coefficient
d) Plot of power coefficient as a function of drag coefficient

Explanation: Plot of power coefficient $$\frac {C_p}{σ}$$ as a function of thrust coefficient $$\frac {C_T}{σ}$$ is known as rotor polar. There is no loss of profile power for an ideal rotor and there is minimum induced loss. Due to profile power loss, the rotor polar for a real rotor is at an offset compared to the ideal polar, and power increases faster with thrust coefficient due to the larger induced power.

11. For low rotor solidity, profile drag increases.
a) True
b) False

Explanation: When the rotor solidity is too low, high angle of attack is required to achieve the lift. This leads to an increase in profile drag. Therefore the rotor should always have solidity which is as low as possible.

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