Item 0850
DESIGN: UniCopter ~
Rotor - Blade - VR-7mod - Planform, Profiles and Lift [old]This page has the calculations on blades weight and strength etc.
It must be transferred to the desired blade and modified at some point in time.
Airfoil modified VR-7. 5.25" chord, 8'-0" radius. Six blades required. Three right-hand and three left-hand.
For related information see:
SynchroLite ~ Rotor - Blade VR-7b - Composite
Drawing:
Proposed Blade Thickness:
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Percent of span: |
Thickness (% of chord) |
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Root |
Round |
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1 foot from root |
Round |
At end of hub spindle. |
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25% |
24% |
Near other mast. |
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50% |
15% |
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70% |
12% |
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Tip |
12% |
Consider VR-8 at tip w/ no core |
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Approximate Blade Spar Loading;
at 70% of Span (at location of mean lift):
The following is based on standard VR-7 blade with 12% thickness
(30% * 8 feet) = 2.4 feet
Mean loading will be at roughly 60% location
(2.4 feet * .6 * (550 pounds * .5 of the load) * 10G) /6 blades = 660 foot-pounds.
Approximate distance between centroids at 70% of span [12% thick] = 0.30 inches = 0.025 feet
660 / 0.025 = 26400 pounds
Carbon is 70,000 to 160,000 psi.
26400 / ((70,000 + 160,000) / 2) = 0.230 square inches on the bottom in tension. Amount of carbon is 0.428 square inches in lower flange OK
at 50% of Span:
The following is based on standard VR-7 blade with 15% thickness
(50% * 8 feet) = 4 feet
Mean loading will be at roughly 65% location
(4 feet * .65 * (550 pounds * .85 of the load) * 10G) / 6 blades = 2,026 foot-pounds.
Approximate distance between centroids at 70% of span [15% thick] = 0.38 inches = 0.032 feet
2026 / 0.038 = 53,311 pounds
Carbon is 70,000 to 160,000 psi.
53,311 / ((70,000 + 160,000) / 2) = 0.463 square inches on the bottom in tension. Amount of carbon is 0.428 square inches in lower flange
at 25% of Span (over other mast):
The following is based on 24% of chord thickness at 25%
(75% * 8 feet) - 2 feet = 4 feet
(4 feet * 550 pounds * 10G) / 6 blades = 3,667 foot-pounds.
Approximate distance between centroids at 25% of span = 0.5 inches = 0.0625 feet
3,667 / 0.0625 = 58,667 pounds
Carbon is 70,000 to 160,000 psi.
58,667 / ((70,000 + 160,000) / 2) = 0.510 square inches on the bottom in tension. Not quite OK blade could be thickend here also if need be or Use more carbon?
at Root:
The following is based on thickness of 3" at the root.
(8 feet * 550 pounds * 10G * .70) / 6 blades = 5,133 foot-pounds.
Approximate distance between centroids at root = 2.5 inches = 0.208
5,133 / 0.208 = 24.680 pounds
Carbon is 70,000 to 160,000 psi.
24,680 / ((70,000 + 160,000) / 2) = 0.215 square inches on the bottom in tension. OK
Blade Loading (rough calculation):
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per blade |
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Gross weight of helicopter |
750. |
125 lbs. |
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Length of moment arm |
73% of 8 ft |
70 in. |
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Bending moment at root |
125 * 70.1 = |
8,760 in.-lb. |
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Maximum loading on a blade |
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10 G |
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Bending moment at centerline of mast @ 10G |
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87,600 in.-lb. |
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This does not take into account that ABC will result in the advancing blade being subjected to a higher loading; but 10 G is fairly high. |
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Blade Loading (detailed calculations)
(at; hover, gross weight & out of ground effect. From Access Database calculations):Values at Blade Elements. Based on center of moment arm at center of mast:
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Element: |
Radius (ft.) |
Coefficient of Thrust |
Lift (pounds) * |
Moment (lb.-in.) ** |
Profile |
Centroids Distance (in.) |
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0 |
0 |
0 |
0 |
0 |
Round |
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1 |
0.8 |
0 |
0 |
0 |
Oval ? |
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2 |
1.6 |
0 |
0 |
0 |
0050 ? |
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3 |
2.4 |
0.0006 |
15.6 |
449 |
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4 |
3.2 |
0.0011 |
28.6 |
1098 |
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5 |
4.0 |
0.0019 |
49.5 |
2376 |
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6 |
4.8 |
0.0029 |
75.5 |
4349 |
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7 |
5.6 |
0.0040 |
104.2 |
7002 |
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8 |
6.4 |
0.0052 |
135.4 |
10399 |
VR-7 |
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9 |
7.2 |
0.0064 |
166.7 |
14403 |
VR-7 |
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10 |
8.0 |
0.0067 |
174.5 |
16752 |
VR-7 |
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Total CT = |
0.0288 |
750 |
56828 *** |
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* This is all six blades and the G.W. is only 750 pounds.
** Moment arm is to the end of each element. It should be changed to the 73% of each element.
*** Moment per blade is 56,828 / 6 = 9,471 in-lb. The center of the moment arm is the center of the mast, It will be less for each of the pitch bearings and the hub bearings.
Values at Blade Elements. Based on center of moment arm at root of blade and distance to 75% of element.
Blade root is 0.5' from center of mast and 975%) 0.2' from end of element.
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Element: |
Radius (ft.) from center of mast |
Radius (ft.) from root to 75% of element |
Coefficient of Thrust |
Lift (pounds) * |
Moment (lb.-in.) ** from center of mast |
Moment (lb.-in.) from root of blade |
Profile |
Centroids Distance (in.) |
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0 |
0 |
0 |
0 |
0 |
0 |
0 |
Round |
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1 |
0.8 |
0.1 |
0 |
0 |
0 |
0 |
Oval ? |
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2 |
1.6 |
0.9 |
0 |
0 |
0 |
0 |
0050 ? |
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3 |
2.4 |
1.7 |
0.0006 |
15.6 |
449 |
318 |
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4 |
3.2 |
2.5 |
0.0011 |
28.6 |
1098 |
858 |
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5 |
4.0 |
3.3 |
0.0019 |
49.5 |
2376 |
1960 |
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6 |
4.8 |
4.1 |
0.0029 |
75.5 |
4349 |
3715 |
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7 |
5.6 |
4.9 |
0.0040 |
104.2 |
7002 |
6127 |
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8 |
6.4 |
5.7 |
0.0052 |
135.4 |
10399 |
9261 |
VR-7 |
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9 |
7.2 |
6.5 |
0.0064 |
166.7 |
14403 |
13003 |
VR-7 |
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10 |
8.0 |
7.3 |
0.0067 |
174.5 |
16752 |
15286 |
VR-7 |
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Total CT = |
0.0288 |
750 |
56828 *** |
50528 **** |
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**** Moment per blade is 50,528 / 6 = 8,421 in-lb. The center of the moment arm is the root of the blade, It will be less for the outer pitch bearing.
Deflection
(at; hover, gross weight & out of ground effect. From Access Database calculations):Properties of Beam:
Reaction force [R] =
Shear force [V] =
Loading Force (at blade element) [F] =
Moment [M] =
Blade length [l] = Feathering bearings to tip?
Support to force (furthest end of blade element) dimension [r] =
Force to blade end dimension [b] =
Location [x] =
Modulus of Elasticity [E] =
Moment of Inertia [I] =
Deflection [y] =
Engineering Power Tools is in agreement with WinBeam for concentrated load at end.
Calculations:
ACCESS DATABASE FORM: Rotor - Blade - Deflection
Ymax = (F * r2) / (6 * E* I) * (r - 3 * 1) at x = 1
Whatever x = 1 means.The output is 8.10 inches.
The above algorithm was take from T302 and put in Access as a reiterative program. It is based on the Coefficient of Thrust at each blade element; and this gives a curved thrust line along the span. This value is probably correct since this program is inline good when compared to the others above.
Deflection Notes:
See:
DESIGN: UniCopter ~ Rotor - Disk - Anhedral
Miscellaneous Notes:
Strain gauges located near the blade root or the static hub; to sense the amount of aerodynamic lifting force imparted by the blade.
Why, the vibration will advise the pilot of an imbalance loading on the disk.Design the blades to pivot horizontally, if possible, so that they can be 'bundled' for ground transportation.
Twist and/or taper will bring the center of lift closer toward the blade root and thereby reduce the length of the moment arm slightly. Too much twist will be detrimental to high forward speed.
Thickness:
Worse than Item 0884|
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% of Radius |
Distance from center of hub |
Airfoil |
Chord |
Thickness |
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30% |
28.8" |
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* ( + ) = " |
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50% |
48" |
VR-7 15% |
5.25" |
* (0.1142 + 0.0362) = 0.7896" |
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70% |
67.2" |
VR-7 12% |
5.25" |
* (0.0914 + 0.0290) = 0.6321" |
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90% |
86.4" |
VR-7 12% |
5.25" |
* (0.0914 + 0.0290) = 0.6321" |
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Last Revised: February 28, 2002