Rotor Blade Centrifugal Force Calculations
In an effort to prove the relationship between rotor rpm and centrifugal force, instructors often have trouble convincing their students of the increase in forces seen as RPM increases.
The relationship between force and rpm is well known and documented as
F = M * (V
2 / r)
where
| F = M * a | [Force = Mass * Acceleration] |
| V = ((RPM / 60) * 2 * π) * r | [Linear velocity of a point at radius r at required rpm] |
| a = (V 2) /r | [Acceleration seen at a point of radius r, with linear velocity v) |
If we know the mass distribution along the blade we can calculate the centrifugal force experienced by each element of the blade and integrate it along the whole blade.
A doubling of the RPM results in a quadrupling of the centrifugal force. To double the force the RPM must be increased by 1.414 times its original value (1.414 is the square root of 2 and always features in calculations involving squared relationships).
The magnitude of the force will change if the center of mass is moved along the blade, a mass concentration near the tip will increase the centrifugal force and vice versa.
The force is calculated as though the blade is attached at the center of the rotor (where the teetering hinge would usually be).
From
% to
% RRPM
| RPM | RPM % | 1 Blade
Centrifugal Force [N] | CF Metric Tons | δ |
|---|
| 10.2 |
2 |
35.93 |
0.00 |
|
|
| 20.4 |
4 |
143.72 |
0.01 |
0.011 |
|
| 30.6 |
6 |
323.36 |
0.03 |
0.018 |
|
| 40.8 |
8 |
574.87 |
0.06 |
0.026 |
|
| 51.0 |
10 |
898.23 |
0.09 |
0.033 |
|
| 61.2 |
12 |
1,293.45 |
0.13 |
0.040 |
|
| 71.3 |
14 |
1,760.53 |
0.18 |
0.048 |
|
| 81.5 |
16 |
2,299.47 |
0.23 |
0.055 |
|
| 91.7 |
18 |
2,910.27 |
0.30 |
0.062 |
|
| 101.9 |
20 |
3,592.92 |
0.37 |
0.069 |
|
| 112.1 |
22 |
4,347.44 |
0.44 |
0.077 |
|
| 122.3 |
24 |
5,173.81 |
0.53 |
0.084 |
|
| 132.5 |
26 |
6,072.04 |
0.62 |
0.091 |
|
| 142.7 |
28 |
7,042.13 |
0.72 |
0.099 |
|
| 152.9 |
30 |
8,084.07 |
0.82 |
0.106 |
|
| 163.1 |
32 |
9,197.88 |
0.94 |
0.113 |
|
| 173.3 |
34 |
10,383.54 |
1.06 |
0.120 |
|
| 183.5 |
36 |
11,641.07 |
1.19 |
0.128 |
|
| 193.7 |
38 |
12,970.45 |
1.32 |
0.135 |
|
| 203.8 |
40 |
14,371.69 |
1.47 |
0.142 |
|
| 214.0 |
42 |
15,844.79 |
1.62 |
0.149 |
|
| 224.2 |
44 |
17,389.74 |
1.77 |
0.156 |
|
| 234.4 |
46 |
19,006.56 |
1.94 |
0.164 |
|
| 244.6 |
48 |
20,695.23 |
2.11 |
0.171 |
|
| 254.8 |
50 |
22,455.76 |
2.29 |
0.178 |
|
| 265.0 |
52 |
24,288.15 |
2.48 |
0.185 |
|
| 275.2 |
54 |
26,192.40 |
2.67 |
0.192 |
|
| 285.4 |
56 |
28,168.51 |
2.87 |
0.200 |
|
| 295.6 |
58 |
30,216.47 |
3.08 |
0.207 |
|
| 305.8 |
60 |
32,336.30 |
3.30 |
0.214 |
|
| 316.0 |
62 |
34,527.98 |
3.52 |
0.221 |
|
| 326.2 |
64 |
36,791.52 |
3.75 |
0.228 |
|
| 336.3 |
66 |
39,126.92 |
3.99 |
0.236 |
|
| 346.5 |
68 |
41,534.18 |
4.24 |
0.243 |
|
| 356.7 |
70 |
44,013.29 |
4.49 |
0.250 |
|
| 366.9 |
72 |
46,564.27 |
4.75 |
0.257 |
|
| 377.1 |
74 |
49,187.10 |
5.02 |
0.264 |
|
| 387.3 |
76 |
51,881.79 |
5.29 |
0.271 |
|
| 397.5 |
78 |
54,648.34 |
5.57 |
0.279 |
|
| 407.7 |
80 |
57,486.75 |
5.86 |
0.286 |
|
| 417.9 |
82 |
60,397.02 |
6.16 |
0.293 |
|
| 428.1 |
84 |
63,379.14 |
6.46 |
0.300 |
|
| 438.3 |
86 |
66,433.13 |
6.77 |
0.307 |
|
| 448.5 |
88 |
69,558.97 |
7.09 |
0.314 |
|
| 458.7 |
90 |
72,756.67 |
7.42 |
0.321 |
|
| 468.8 |
92 |
76,026.23 |
7.75 |
0.328 |
|
| 479.0 |
94 |
79,367.65 |
8.09 |
0.335 |
|
| 489.2 |
96 |
82,780.92 |
8.44 |
0.343 |
|
| 499.4 |
98 |
86,266.06 |
8.80 |
0.350 |
|
| 509.6 |
100 |
89,823.05 |
9.16 |
0.357 |
|
| 519.8 |
102 |
93,451.90 |
9.53 |
0.364 |
|
| 530.0 |
104 |
97,152.61 |
9.91 |
0.371 |
|
| 540.2 |
106 |
100,925.18 |
10.29 |
0.378 |
|
| 550.4 |
108 |
104,769.60 |
10.68 |
0.385 |
|
| 560.6 |
110 |
108,685.89 |
11.08 |
0.392 |
|
| 570.8 |
112 |
112,674.03 |
11.49 |
0.399 |
|
| 581.0 |
114 |
116,734.03 |
11.90 |
0.406 |
|
| 591.2 |
116 |
120,865.89 |
12.32 |
0.413 |
|
| 601.3 |
118 |
125,069.61 |
12.75 |
0.420 |
|
| 611.5 |
120 |
129,345.19 |
13.19 |
0.427 |
|
Graph of RPM vs Centrifugal Force
From this it can be seen that a doubling of the RPM results in a quadrupling of the centrifugal force.
