Item 1163
DESIGN: Dragonfly ~ Rotor -
Hub - Blade Generated Forces - Intermediate:The intermediate accuracy level in calculating the blade generated forces.
This page is not used yet.
The centripetal force
F [in pounds] acting on a body of mass M [in slugs] is given by the equation F = (Mv2)/r, where v [in feet per second] is its velocity and r [in feet] is the radius of its path. See: Mechanical - Definitions & Algorithms ~ Centripetal Force~ The following material is all the old UniCopter I (
DESIGN: UniCopter ~ Rotor - Disk - Blade Forces) and will be changed to Dragonfly ~ Using preliminary Rough Calculations (above) for now|
Blade Element |
Radius (inch) & [feet] to mid point of elements |
Weight (lbs.) & [slugs] (1) |
Velocity (ft./sec.) |
Force (lbs.) |
|
1 |
9.6" / 2 = 4.8" [0.4'] |
1.54 [0.048] |
30 |
108 |
|
2 |
9.6" + 4.8 = 14.4" [1.2'] |
1.54 [0.048] |
92 |
339 |
|
3 |
9.6" + 14.4 = 24.0" [2.0'] |
1.54 [0.048] |
154 |
569 |
|
4 |
9.6" + 24.0 = 33.6" [2.8'] |
1.54 [0.048] |
215 |
792 |
|
5 |
9.6" + 33.6 = 43.2" [3.6'] |
1.54 [0.048] |
276 |
1016 |
|
6 |
9.6" + 43.2 = 52.8" [4.4'] |
1.54 [0.048] |
338 |
1246 |
|
7 |
9.6" + 52.8 = 62.4" [5.2'] |
1.54 [0.048] |
399 |
1470 |
|
8 |
9.6" + 62.4 = 72.0" [6.0'] |
1.54 [0.048] |
461 |
1700 |
|
9 |
9.6" + 72.0 = 81.6" [6.8'] |
1.54 [0.048] |
522 |
1923 |
|
10 |
9.6" + 81.6 = 91.2" [7.8'] |
1.54 [0.048] |
599 |
2208 |
|
Tip weight |
96" [8.0'] |
0.0 [0.0] |
614 |
0 |
|
Total: Based on 100% RRPM. (2) |
15.4 [] |
|
11,371 |
|
(1) The weight is currently equal for every element. (Root end will have more structure and tip end will have more tip/leading edge weight).
(2) In autorotation it is possible that the rotational speed may increase to 3G or 173% RRPM .
Ultimate centrifugal force = 11,371 x (4.0 [LLF - limit load factor] x 1.5 [SF - safety factor]) = 68,226 lb. (303,496 N)
_________________________________
Note: If the pitch bearings could be located out 1'-6" further from the mast, just inside the other mast, then the axial load will be about 8% less.
Radial Force (Aerodynamic Force) on One Blade:
Thrust Force ~ Out of Plane Radial Load on One Blade:
The following is based on thrust = GW / 6 blades = 125 pounds. Less 15.5 pounds for the blade.
|
|
For Pitch Bearings: |
For Mast Bearing & Frame: |
|||||||
|
Blade Element: |
Radius at outside of element (ft.) |
Lift (pounds) (1) |
Lift (pounds) (2) |
Length of Arm to 75% of element (in.) (3) |
Moment (lb.-in.) (4) |
Length of Arm to 75% of element (in.) |
Moment (lb.-in.) |
||
|
0 |
0 |
0 |
0 |
0 |
0 |
|
0 |
||
|
1 |
0.8 |
0 |
0 |
0.2" |
0 |
|
0 |
||
|
2 |
1.6 |
0 |
0 |
9.8" |
0 |
|
0 |
||
|
3 |
2.4 |
0 |
0 |
19.5" |
0 |
|
x |
||
|
4 |
3.2 |
6.8 |
4.6 |
29.0" |
133 |
|
x |
||
|
5 |
4.0 |
10.7 |
8.5 |
38.6" |
328 |
|
x |
||
|
6 |
4.8 |
15.3 |
13.1 |
48.2" |
631 |
|
x |
||
|
7 |
5.6 |
19.8 |
17.6 |
57.8" |
1017 |
|
x |
||
|
8 |
6.4 |
23.4 |
21.2 |
67.4" |
1429 |
|
x |
||
|
9 |
7.2 |
25.6 |
23.4 |
77.0" |
1802 |
|
x |
||
|
10 |
8.0 |
23.0 |
20.8 |
86.6" |
1801 |
|
x |
||
|
|
Total = |
124.6 |
109.2 |
|
7141 |
|
x |
||
(1) These values come from
(2) These values are the previous column with weight of the blade (15.5 lbs) removed equally from all elements with lift.
(3) Element is 9.6" long. Moment arm is at the 75% point of element (7.2") and blades pivot is located at 7" radius from rotor's centerline.
The 7" dimension should probably be increased by a couple of inches.(4) At; hover, gross weight & out of ground effect. From Access Database calculations.
Ultimate thrust moment: 7,141 x (4 [LLF] x 1.5 [SF] = 42,846 lb.-in. (190588 N)
._________________________________
Note: If the pitch bearings were to be located out 1'-6" further from the mast, just inside the other mast, then the radial moment will be about 22% less.
Torque Moment ~ In Plane Radial Load on One Blade:
Operating torque in axle = ((63,000) x 65 HP) / (733 RRPM x 2 rotors) = 3,008 lb.-in.
Ultimate torque (drag) in axle = 3,008 x 2.0 [LLF] x 2.25 [SF or 150% RRPM] = 13,536 lb.-in.
Ultimate torque (drag) in one blade = 13,537 / 3 blades = 4,512 lb.-in. (510 N-m.)
Combined Radial Moment:
Ultimate radial moment
Torsional Force:
This will be handled by the skin.
Carried Forward:
These loads are carried forward to the mast and its bearing on:
DESIGN: Dragonfly ~ Power Train - Bearing - Load Calculations
Same Page ~ Different Craft:
~ UniCopter ~ SynchroLite (none)
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Last Revised: October 2, 2004