Item 1013

OTHER: Flight Dynamics - General - Rotor Inertia

Description:

Rotor's inertia is the rotational kinetic energy that exists in a helicopter's rotor.

It equals 1/2 * rotational inertia * angular velocity squared. EKR = (1/2) * JMO * ω2

 Notes:

Tip Weight:

The further the mass is from the center of rotation the greater its contribution to the rotor's inertia. Therefor a weight at the blade tip gives the greatest amount of inertia for the least amount of weight,

Pros and Cons of having High Inertia:

Pros:
    1. To prevent the rotor from decelerating too quickly following an unexpected loss of power. See; OTHER: Aerodynamics ~ General - Autorotation
    2. To provide a source of energy for making a landing flare at the end of an autorotational descent
    3. To increase the stability of rotor. An increase on small helicopters is good, not so for large helicopters.
    4. To reduce the coning angle and thereby reduce the cross-coupling.

Cons:
    1. It increases the empty weight of the helicopter, because of the tip weight addition and the increase in the strength (weight) of the other rotor components.

Calculations:

Time to dissipate all kinetic energy: (sec): tKE = ( 0.5 * J * Ω2 ) / ( 550 * HP )

 

Helicopter:

SynchroLite:

UniCopter:

Robinson R-22:

Schweizer/Hughes 300C:

 

Polar moment of inertia (slug ft2) J

6.344 * 4 blades = 25.4 (2)

not yet calculated

86.3

161

 

Tip speed (ft / sec) ΩR

555

525

699

662

 

Radius of rotor (ft) R

8.67

8

12.58

13.42

 

Angular velocity of rotor (radians / sec) Ω

64.0

65.7

55.5

49.3

 

Maximum usable power (1) HP

58.2

83.7

131

190

 

Power to hover HP

34

57

98 ??

 

 

Time to dissipate all kinetic energy (sec) (1) tKE

1.62 (2.78 (2) )

 

1.84

1.87

(1) The horsepowers used are the maximum available, not the power being consumed at the time of engine-out.

(2) Based upon a one-pound tip weight. Note that the SynchroLite has a lower hover to maximum power ratio then the R-22 and 300C and therefor at hover power, the SynchroLite will be the better.

Rotor decay equation: Ω / Ω0 = 1 / (1 + (t / 2 * tKE))

For a single engine helicopter, Prouty states; "...that the rotor kinetic energy stored in the rotor at normal rotor speed should be sufficient to provide the equivalent of at least one and one half seconds of hover time to insure a satisfactory flare capability."

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Last Revised: February 4, 2007