Item 0908

DESIGN: UniCopter ~ Rotor - Disk - Location of Center of Thrust

Objective of this page:

The thrust vector is always normal to the plane of the disk. The following is done to get a clearer understanding of the location of this thrust vector.

March 29, 2004 ~ It is now proposed that the rotors have a 3º precone. This will probably reduce the total thrust slightly but improve the control slightly. The following notes have not yet been reviewed in light of this change.

Variables:

 

Azimuth of the center of thrust (0º is over the tail)

ψ

 

Radius of the center of thrust (percentage of rotor radius [R])

r

 

Thrust

T

The above variables are in the cylindrical coordinate system. For additional information on this see: UniCopter Coordinate Conversion

Hover:

Operational Conditions: The maximum blade pitch is at azimuth 0º and the minimum blade pitch is at 180º. (i.e. pitching nose down)

The center of thrust [CT] on a rotating blade, when the helicopter is in hover is at approximately 70% of the blade's radius [R]. (r = 0.7R)

In forward flight, the CT will move toward the root on the advancing blade and toward the tip on the retreating blade. See below.

Assuming that the collective is at (near) the bottom and that the blades do not go into negative pitch. Then assume if;

 

@ ψ =

T =

then

@ ψ =

T =

 

 

0º

100 lbs.

 

45º

50 lbs. + cos(ψ) * 50 =

85 lbs.

 

90º

50 lbs.

 

135º

50 lbs. + cos(ψ) * 50 =

15 lbs.

 

180º

0 lbs.

 

225º

50 lbs. + cos(ψ) * 50 =

15 lbs.

 

270º

50 lbs.

 

315º

50 lbs. + cos(ψ) * 50 =

85 lbs.

 

 

 

 

 

 

 

 

 

 

 

120º

50 lbs. + cos(ψ) * 50 =

25 lbs.

 

 

 

 

240º

50 lbs. + cos(ψ) * 50 =

25 lbs.

Since r = 0.7 R then on the X-axis @ ψ = 0º, x = 0.7; and at @ ψ = 120º and 240º, x = 0.35

This means that the moment about the Y-axis is + (0.35 * 25 lbs * 2) - (0.7 * 100 lbs) = 17.5 - 70 = -52.5

The total thrust of the 3 blades is 100 + 25 + 25 = 150 lbs.

Therefor the CT is located at x = -52.5 / 150 = -0.35 & y = 0.0

Check ( 0.35 + 0.35) * 25 * 2 = ( 0.7 - 0.35) * 100 || O.K.

In other words the center of lift is directly behind the hub and back 35% of the disk's radius.

As the collective is increased and the thrust is increased equally around the disk then the thrust from the cyclic becomes a smaller proportion of the total thrust and the distance x = - .35 will decrease.

Forward Flight:

When applying lateral cyclic in forward flight, the azimuth of the center of thrust [CTψ] will move from 0º. If right lateral cyclic is applied then CTψ on the starboard rotor will increase (move in the direction of 90º) and CTψ on the port rotor will decrease (move in the direction of 270º).

When applying lateral cyclic in forward flight, the radius (arm) of the center of thrust [CTr] will start differing between the starboard and port rotors. This is because the location of CT on the starboard rotor is on the advancing side of the disk whereas on the port rotor it is on the retreating side. In other words, r will be greater on the retreating side. This must be tempered by the fact that with ABC the advancing blade will be providing a greater portion of the total thrust.

Related Pages at This Web Site:

UniCopter ~ Trim, Stability & Control - Musings on Trim

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Last Revised: October 5, 2006