1489

Item 1489

DESIGN: Single-Bladed All Electric Rotor - Disk - Forces & Moments

Objective:

To determine the forces and moments at work on the rotor.

Reference: DESIGN: SynchroLite ~ Rotor - Disk - Centers, Radii & Moments

Symbols:

Symbol:	Name:	Definition:	Units:
T	Thrust	Thrust	pounds
L	Lift	Vertical component of Thrust	pounds
P	Pull	Horizontal component of Thrust	pounds
CF	Centrifugal Force
C	Centroid	Center of mass
M	Moment
D	Drag		pounds
CM	Moment of centrifugal force	Restoring moment of centrifugal force
WA	Weight Arm	Moment arm from teetering hinge to centroid	feet
TA	Thrust Arm	Moment arm from teetering hinge to ctr. of lift	feet
W	Weight		pounds
GW	Gross Weight	Gross weight of craft	pounds
RRPM	Rotor speed		rpm
Ω	Rotor speed		radians
B	Teeter angle		degrees
R	Restoring force	The restoring force of the centrifugal force	lb-ft

Subscripts:		Designated on drawing by preceding dash
_b	Blade
_cw	Counter Weight
_hov	Hover
_max	Maximum teeter
_min	Minimum teeter
_f	Fuselage	Gross weight less weight of rotors
_t	Total
_h	Hub	Hub excluding blades
_ind	Induced - (drag & thrust)
_pro	Profile (drag)

Reference Point: Center of teetering hinge or center of virtual teetering hinge.

Thrust and Centrifugal Force: The 2-blade rotor is only for temporary reference and CF forces in the second and third drawings must be changed.

Algorithms and Calculations: The following is just approximations, at present, to get a feel for the requirements.

W_b	10 lbs.	Value from ~ SynchroLite 3-rotor is 21# for 550 GW
W_cw	20 lbs.	Arbitrarily set at half that of the blade's arm.
WA_b	4.5 ft.	Tapered blade with 10 foot radius
WA_cw	2.25 ft.	(10 lbs / 20 lbs ) * 4.5 ft.

Centripetal Force;

Slug: A unit of mass, which is equal to 1 pound second² per foot. M = W / g in which M = mass in slugs, W = weight in pounds, and g = acceleration due to gravity commonly taken as 32.16 feet per second.

Centripetal Force; For a uniform mass per unit length of blade; F = (M * Ω² * R) / 2. Where [F is in pounds], [M is in slugs], [Ω is in rad per sec.], [R is blade radius, in feet], [2 is to provide the midpoint of R].

Blade: f = (10 / 32.16) * 64² * (10 * 0.45) = 5,731 pounds This equation assumes that the blade is taperd and that the centroid is a 0.45 of Radius.

Counterweight: f = (20 / 32.16) * 64² * (2.5) = 5,731 pounds

Values:

Item:	Value:	Notes:
GW	550 lbs.	254# craft + 296# load
CF_b	5,731 pounds	Centrifugal force of blade
CF_cw	5,731 pounds	Centrifugal force of counterweight
β_hov	2.5º	Tan(A) = a/b = 550/(6368 + 6368) Angle = 2.5º
T_hov	551 lbs.	c = b/ cos(A) = 550/cos(2.5) = 551 lbs
P_hov	24 lbs.	a = tan(A) * b = 0.0437 * 550 = 24 lbs
β_max	14.5º	Maximum Teetering angle = 2.5º + 12º = 14.5º
T_max	568 lbs.	c = b/ cos(A) = 550/cos1(4.5) = 568 lbs
P_max	24 lbs.	a = tan(A) * b = 0.2586 * 550 = 142 lbs
β_min	-9.5º	Minimum Teetering angle = 2.5º - 12º = -9.5º
T_min	568 lbs.	c = b/ cos(A) = 550/cos(-10.5) = 559 lbs
P_min	24 lbs.	a = tan(A) * b = -0.1853 * 550 = -102 lbs

Required Horizontal Shift of Blade + CW Mass to Balance Pull Force of Blade During Flapping:

Shift in the Direction of the Blade to Compensate for Maximum Teeter Angle.

CF of blade must be increased by 0.5 * (142 - 24) = 59lbs

F = (M * Ω² * R) / 2

5731 = (10 / 32.16) * 64² * (10 * 0.45)

(5731 + 59) = (10 / 32.16) * 64² * r

r = (5731 + 59) / (10 / 32.16) * 64²

r = 4.5467

Δr = 4.5467 - 4.5 = 0.0467 ft = 0.56 inches

Shift in the Direction of the CW to Compensate for Minimum Teeter Angle.

CF of blade must be decreased by 0.5 * (102 + 24) = 63lbs

F = (M * Ω² * R) / 2

5731 = (10 / 32.16) * 64² * (10 * 0.45)

(5731 - 63) = (10 / 32.16) * 64² * r

r = (5731 - 63) / (10 / 32.16) * 64²

r = 4.450

Δr = 4.450 - 4.5 = -0.05 ft = -0.60 inches

Drag and Centrifugal Force:

Initially displayed: January 9, 2006 ~ Posted on PPRuNe; January 11, 2006; on Rotary Wing Forum; January 9, 2006~ Last Revised: Friday, February 3, 2006

The above utility invention is openly and publicly disclosed on the Internet to negate an entity from patenting it, to the exclusion of all others whom may wish to use it. ~ Reference patent law 35 U.S.C. 102 A person shall be entitled to a patent unless - (a) the invention was known ... by others in this country, ..., before the invention thereof by the applicant for patent.