| Grand Prix Racing - | The Science of Fast Pinewood Cars |
These estimates are based on measurements accurate to about + or - 1/256 inches. The wheel model is not strictly concentric as cylinders 1 an 2, 3 and 4 overlap slightly in radius. However, 1 is on top of 2 and 4 on top of 3 so no material overlaps. "Top" is the face of the wheel when it is laid on a table - a line through the wheel bore would point up.
Scout wheels are made of a hard plastic that can be machined well with the "right" tools.
Axle weight: 0.04167 oz (0.5oz/12axles)
Axle diameter: 0.0866 +/- 0.004 inches (2.20 millimeters)
Axle play: 0.0101 +/- 0.0015 inches (0.26 millimeters)
Wheel weight: 0.1111 oz (1oz/9wheels)
Mechanical advantage: Outer radius/inner radius = 12.667
| Cylinder | Radius | (in) | Width | Volume | %Mass | Ii/Mi | Ii/M |
| inner | outer | (in) | (in3) | (in2) | (in2) | ||
| 1 | 0.047 | 0.125 | 0.219 | 0.00923 | 5.232 | 0.008911 | 0.00046625 |
| 2 | 0.070 | 0.125 | 0.063 | 0.00210 | 1.189 | 0.010284 | 0.00012230 |
| 3 | 0.125 | 0.313 | 0.055 | 0.01409 | 7.991 | 0.056641 | 0.00452617 |
| 4 | 0.250 | 0.336 | 0.063 | 0.00989 | 5.606 | 0.087677 | 0.004915131 |
| 5 | 0.336 | 0.500 | 0.094 | 0.04039 | 22.903 | 0.181427 | 0.04155198 |
| 6 | 0.500 | 0.594 | 0.313 | 0.10067 | 57.079 | 0.301270 | 0.171961 |
| Totals | v=0.17637 | %M=100 | I/M=0.22354 |
Weight(0.1111 oz)/386.088 = Total Mass (0.000287787 ozs2/in).
I/m (0.20948329) x Total Mass (0.000287787) = I
Total Wheel Moment of Inertia, I = 0.000064333 ozins2.
Wheel Plastic Density, P = mass/volume = 0.000287787/0.17637 = 0.00163 ozs2/in4.
If 1/16 th inch of tread is removed down to 1/32 inch (about 62% of it), this would be an estimate of the result. A thin rim is left (the 7th cylinder) so the wheel can maintain its mechanical advantage over axle friction. This rim must be positioned so the wheel is ballanced on the axle under a load.
| Cylinder | Radius | (in) | Width | Volume | %Mass | Ii/Mi | Ii/M |
| inner | outer | (in) | (in3) | (in2) | (in2) | ||
| 1 | 0.047 | 0.125 | 0.219 | 0.00923 | 8.078 | 0.008911 | 0.00071981 |
| 2 | 0.070 | 0.125 | 0.063 | 0.00210 | 1.836 | 0.010284 | 0.00018880 |
| 3 | 0.125 | 0.313 | 0.055 | 0.01409 | 12.337 | 0.056641 | 0.00698761 |
| 4 | 0.250 | 0.336 | 0.063 | 0.00989 | 8.655 | 0.087677 | 0.00758810 |
| 5 | 0.336 | 0.500 | 0.094 | 0.04039 | 35.358 | 0.181427 | 0.06414893 |
| 6 | 0.500 | 0.531 | 0.313 | 0.03164 | 27.695 | 0.266113 | 0.07369935 |
| 7 | 0.531 | 0.594 | 0.031 | 0.00690 | 6.042 | 0.317383 | 0.01917781 |
| Totals | v=0.11424 | %M=100 | I/M=0.17251 |
Wheel weight: density * volume * 386.088 in/s2 = 0.00163 * 0.11424 * 386.088 = 0.07197 oz
Weight(_0.07197_ oz)/386.088 = Total Mass (0.000186412 ozs2/in).
I/m (0.17251) x Total Mass (0.000186412) = I
Total Wheel Moment of Inertia, I = 0.000032158 ozins2.
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| Grand Prix Racing - | The Science of Fast Pinewood Cars |
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