0919

Item 0919

DESIGN: UniCopter ~ Trim, Stability & Control - Control - Rotor Coordinate Conversion

Overview:

The conversion of locations in a rotor's cylindrical coordinate system to the helicopter's Cartesian coordinate system.

Conversion of Coordinates, for Moment Arms for UniCopter:

Initial Notes re below:

Azimuth is the radian on the swashplate that gives the greatest pitch at the blade.

The Radius (length of arm) increases with the difference between maximum and minimum pitch at the related swashplate (perhaps the difference in the activity between the two swashplates is so little that the position of the cyclic stick can be used for both rotors). This radius is also proportional to this pitch difference and the thrust (the greater the thrust, the less significant the cyclic).

Thrust increases with the amount of collective input at the swashplate.

Cylindrical Parameters:	Port:	Starboard:
Azimuth:	ψ_P	ψ_S
Radius:	r_P	r_S
Thrust:	T_P = 0	T_S = 0

Conversion from Cylindrical to Cartesian, in Plane of Rotor:

	Port:	Starboard:
	x_P' = r_P cos(ψ_P)	x_S' = _Sr cos(ψ_S)
	y_P' = r_P sin(ψ_P)	y_S' = r_S sin(ψ_S)
	z_P' = T_P	z_S' =T_S

Rotation between Rotor Cartesian and Body Cartesian Coordinates (in the Y-Z plane):
Some of the signs + & - in the 4 equations below may be wrong. Check them.

For example coding see; calculate_copter_to_drive() in FORM PT - Frame

	Port:	Starboard:
	x_P'' = x_P'	x_S'' = x_S'
	y_P'' = sin(Yα) z_P' + cos(Yα) * y_P'*	y_S'' = sin(Yα) z_S' + cos(Yα) * y_S'*
	z_P''= cos(Yα) z_P' - sin(Yα) * y_P'*	z_S'' = cos(Yα) z_S' - sin(Yα) * y_S'*

Translation between Rotor Cartesian and Body Cartesian Coordinates (in the Y-Z plane):
For example coding see; calculate_copter_to_drive() in FORM PT - Frame

	Port:	Starboard:
	x_CP = x_P'' - x_CG	x_CS = x_S'' - x_CG
	y_CP = y_P'' - ds/2	y_CS = y_S'' + ds/2
	z_CP = z_P'' - ((ds/2) / tan(Yα)) + z_CG	z_CS = z_S'' + ((ds/2) / tan(Yα)) + z_CG

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Last Revised: June 23, 2001