1218

Item 1218

DESIGN: UniCopter ~ Rotor - Disk - Lateral Dissymmetry of Lift (Drag?) - 4-blade Rotors

Overview:

Evaluation of the oscillating rolling moments with two 4-blade rotors caused by any dissymmetry of lift.

There is insufficient clearance between the blades for sufficient pitch to be put in them, particularly at the location where the chord is greatest. See the rotor in the lower left-hand corner of the actual drawing 0854.dc. This may not be a problem if the lower blades are advancing and the blades have Active Blade Twist. This will allow for high root pitch when the blade is advancing and zero or negative root pitch when it is retreating over top of the advancing blades.

For 3-blade rotors see; DESIGN: UniCopter ~ Rotor - Disk - Lateral Dissymmetry of Lift and Drag? - (3-blades)

For longitudinal see; DESIGN: UniCopter ~ Rotor - Disk - Longitudinal Dissymmetry of Lift (& Drag?) - (4-blades)

Drawing of Lateral Moment Arms of a Single Rotor:

Helicopter is flying up the page

Criteria:

Direction of rotation is outside forward.

Stagger is 30".

Calculated values are; Moment Arm x Nbr. of Blades x Square of Tangential Velocity.

No consideration given for secondary factors affecting lift distribution such as angle-of-attack etc. Note that in forward flight the greatest blade pitch will be at (or very close to) azimuth 0º

FORM: Lateral Dissymmetry ~ UniCopter

Rotational speed is 480 rpm

75% of radius is 7'-0"

Rotational velocity at 75% R is 352 ft/sec

Air speeds are 0, 50 mph (73 ft/sec), 100 mph (147 ft/sec), and 150 mph (220 ft/sec).

The above values may change during development but the equality of symmetry should hold.

Calculations ~ Azimuths 45+n*90 & n*90:

Hover:

	Port Side of Craft:		Starboard Side of Craft:
Retreating blades:	60 x 1 x 352²	7,434	38 x 2 x 352²	9,416
Advancing blades:	68 x 2 x 352²	16,850	90 x 1 x 352²	11,515
For & Aft blades:			15 x 2 x 352²	3,717
Totals:		24,284		24,646

Equal

Airspeed = 50 mph:

	Port Side of Craft:		Starboard Side of Craft:
Retreating blades:	60 x 1 x 279²	4,670	38 x 2 x 300²	6,840
Advancing blades:	68 x 2 x 404²	22,197	90 x 1 x 425²	16,256
For & Aft blades:			15 x 2 x 352²	3,717
Totals:		26,867		26,813

Equal

Airspeed = 100 mph:

	Port Side of Craft:		Starboard Side of Craft:
Retreating blades:	60 x 1 x 205²	2,521	38 x 2 x 248²	4,674
Advancing blades:	68 x 2 x 456²	28,279	90 x 1 x 499²	22,410
For & Aft blades:			15 x 2 x 352²	3,717
Totals:		30,800		30,801

Equal

Airspeed = 150 mph:

	Port Side of Craft:		Starboard Side of Craft:
Retreating blades:	60 x 1 x 132²	1,045	38 x 2 x 196²	2,919
Advancing blades:	68 x 2 x 507²	34,958	90 x 1 x 571²	29,343
For & Aft blades:			15 x 2 x 352²	3,717
Totals:		36,003		35,975

Equal

Calculations ~ Azimuths 67.5+n*90 & 22.5+n*90:

Hover:

	Port Side of Craft:		Starboard Side of Craft:
Retreating blades:	13.7 x 1 x 352²	1,697	54.3 x 1 x 352²	6,728
	54.3 x 1 x 352²	6,728	13.7 x 1 x 352²	1,697
Advancing blades:	43.7 x 1 x 352²	5,415	84.3 x 1 x 352²	10,445
	84.3 x 1 x 352²	10,445	43.7 x 1 x 352²	5,415
Totals:		24,285		24,285

Equal

Airspeed = 50 mph:

	Port Side of Craft:	Starboard Side of Craft:
Retreating blades:

Advancing blades:

Totals:

Equal

Airspeed = 100 mph:

	Port Side of Craft:		Starboard Side of Craft:
Retreating blades:	13.7 x 1 x 296²	1,200	54.3 x 1 x 216²	2,533
	54.3 x 1 x 216²	2,533	13.7 x 1 x 296²	1,200
Advancing blades:	43.7 x 1 x 408²	7,274	84.3 x 1 x 487²	19,993
	84.3 x 1 x 487²	19,993	43.7 x 1 x 408²	7,274
Totals:		31,000		31,000

Equal

Airspeed = 150 mph:

	Port Side of Craft:	Starboard Side of Craft:
Retreating blades:

Advancing blades:

Totals:

Equal

The following consists of using the same method as used in 0871

Calculations ~ Azimuths 45+n*90 & n*90: as shown in above drawing

Objective:

To calculated the maximum lateral dissymmetry of lift with 4-blade rotors

Conclusion:

There is no lateral dissymitry of lift.

Supporting Calculations:

The FORM: Lateral Dissymmetry ~ UniCopter was used for these calculations.

The values used are close to what the final ones should be. They are the same for every blade azimuth.

The forward velocity of 100 mph was selected.

A fixed collective value was used and no cyclic values were used. The assumption is that the prop is providing all forward thrust.

The following table is similar to those on 0871 for 3-blade rotors.

The craft's rolling moment is positive (+) when it is CW when viewed from the rear.

______________________________________

Rotors Turning Outside-Forward.

Rotor:	Azimuth:	Lift: (pounds)	Moment; (ft-lb)	Direction of Roll: (viewed from aft)
Port	45º	93	568	CW
Port	135º	93	568	CW
Port	225º	31	-121	CCW
Port	315º	31	-121	CCW
Sum of Port Moments:			894	CW
Starboard	90º	110	-898	CCW
Starboard	180º	58	-65	CCW
Starboard	270º	23	135	CW
Starboard	0º	58	-65	CCW
Sum of Starboard Moments:			-893	CCW
Resultant Moment:			0

Calculations ~ Azimuths 67.5+n*90 & 22.5+n*90: as shown in above drawing

Objective:

To calculated the maximum lateral dissymmetry of lift with 4-blade rotors

Conclusion:

There is no lateral dissymitry of lift.

Supporting Calculations:

The FORM: Lateral Dissymmetry ~ UniCopter was used for these calculations.

The values used are close to what the final ones should be. They are the same for every blade azimuth.

The forward velocity of 100 mph was selected.

A fixed collective value was used and no cyclic values were used. The assumption is that the prop is providing all forward thrust.

The following table is similar to those on 0871 for 3-blade rotors.

The craft's rolling moment is positive (+) when it is CW when viewed from the rear.

______________________________________

Rotors Turning Outside-Forward.

Rotor:	Azimuth:	Lift: (pounds)	Moment; (ft-lb)	Direction of Roll: (viewed from aft)
Port	67.5º	105	805	CW
Port	157.5º	76	290	CW
Port	247.5º	25	-134	CCW
Port	337.5º	43	-67	CCW
Sum of Port Moments:			894	CW
Starboard	22.5º	76	-291	CCW
Starboard	112.5º	105	-805	CCW
Starboard	202.5º	43	67	CW
Starboard	292.5º	25	134	CW
Sum of Starboard Moments:			-895	CCW
Resultant Moment:			0

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Last Revised: July 29, 2005