Blade Element Theory

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Blade Element Theory

• Actuator Disc Theory Rankine (1865, 1820-1872,
  Scotland) and R. E. Froude (1886)
• Blade Element Theory W. Froude (1878) and Taylor
  (1893)

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Velocity Vertical Flight

• f inflow angle
• q pitch angle
• a angle of attack
• a q - f

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Lift, Drag, Thrust, Torque
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Small Angle Assumption
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Dimensionless
l inflow factor
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Thrust
1 blade
N blade
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Thrust
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Torque
1 blade
N blade
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Torque
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Power
Power requirement
Power coefficient
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Thrust Approximation
CL
a
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• Assumptions
• a is measured from the no-lift line.
• Stall and compressibility effects can be
  neglected.

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• Assumptions
• The blade has zero twist, i.e., q is constant.
• The induced velocity is uniform , i.e., l is
  constant.

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Blades with (negative) twist
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Blades with (negative) twist
A blade has linear twist has the same thrust
coefficient as one of constant q equal to that of
the twisted blade at 3/4 radius.
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Momentum Theory
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Non-uniform Inflow
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Momentum Theory
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Example
q0 12º, q1 6º, s 0.08, a 5.7
Uniform inflow CT 0.00453 Non-uniform inflow
CT 0.00461
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Ideal Twist
If qr qt constant, l constant. From
momentum theory, uniform induced velocity
corresponds to minimum induced power.
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Linear Twist
Ideal Twist
At r 2/3, q qt3/2 q0.75.
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Example
Linear Twist, q0 12º, qt 6º, q0.75
7.5º. Ideal Twist, qr qt 7.5º2/3 5º.