| Grand Prix Racing - | The Science of Fast Pinewood Cars |
In order to use the simple closed race model equations, you will need the following information about each car you want to enter in your "virtual" race. Below, you will find several parameters to measure directly, some to estimate or measure experimentally and some that are computed from the others. Typical values are given for an AWANA Grand Prix car.
To make the measurements, you will need a ruler marked in inches, preferably marked down to 16ths. You will need a weight scale marked in ounces (Imperial ounces, not troy ounces etc.). A caliper marked in inches would be helpful, but not necessary. For the measurements deduced by experiment, see the experiment write-up for materials needed. A scientific calculator may be needed.
| SYMBOL | VALUE (typical) | UNITS | How to measure |
|---|---|---|---|
| N (nose) | ________(1.4) | in | Measure on a straight line from the very front of your car to the center of the front axle |
| B (base) | ________(3.875) | in | Measure from the center of the front axle to the center of the rear axle |
| Bw (body width) | ________(1.75) | in | Measure the widest place on your car |
| A (crosssection area) | ________(2.4) | in2 | Measure or estimate front crosssection |
| CMx (center of mass x-part) | ________(1.9) | in | Find and measure CM |
| CMy (center of mass y-part) | ________(0.45) | in | Find and measure CM |
| Rf (front wheel outer radius) | ________(0.59) | in | Measure front wheel diameter and divide by two |
| Rr (rear wheel outer radius) | ________(0.59) | in | Measure rear wheel diameter and divide by two |
| rf (front wheel inner radius) | ________(0.049) | in | Measure front wheel bore diameter and divide by two - a caliper works best |
| rr (rear wheel inner radius) | ________(0.049) | in | Measure rear wheel bore diameter and divide by two - a caliper works best |
| SYMBOL | VALUE (typical) | UNITS | DESCRIPTION |
|---|---|---|---|
| a (aerodynamic drag factor) | ________(0.5) | scalar | Measure aerodynamic drag coefficient |
| nf (front axle friction) | ________(0.2) | scalar | Measure axle friction coefficient |
| nr (rear axle friction) | ________(0.2) | scalar | Measure axle friction coefficient |
| uf (front tread friction) | ________(0.01) | scalar | Measure tread friction coefficient |
| ur (rear tread friction) | ________(0.01) | scalar | Measure tread friction coefficient |
| m (total car mass) | ________(0.01295) | ozs2/in | Measure weight of car then divide by 386.088 in/s2 |
| mf (front wheel mass) | ________(0.000216) | ozs2/in | Measure weight of two front wheels then divide by 772.176 in/s2 |
| mr (rear wheel mass) | ________(0.000216) | ozs2/in | Measure weight of two rear wheels then divide by 772.176 in/s2 |
| If (front wheel moment of inertia) | ________(0.000048) | ozins2 | Measure the moment of inertia of a wheel |
| Ir (rear wheel moment of inertia) | ________(0.000048) | ozins2 | Measure the moment of inertia of a wheel |
| SYMBOL | VALUE (typical) | UNITS | DESCRIPTION |
|---|---|---|---|
| b (car body mass) | ________(0.01209) | ozs2/in | m - 2mf - 2mr |
| M (inertial mass) | ________(0.01381) | ozs2/in | m + 2If/Rf2 + 2Ir/Rr2 |
| * (base slope) | ________(0) | radians | Use a scientific calculator in radians mode or math tables to
find arctan((Rf-Rr)/B) |
| Ffr (weight supported by a front axle on ramp) | ________(2.333) | oz | bg(CMx-CMytan(O+*))/B The "O" is from your track measurement work sheet, g = 386.088 in/s2, the acceleration due to gravity at sea level |
| Frr (weight supported by a rear axle on ramp) | ________(2.333) | oz | bg(B-CMx+CMytan(O+*))/B The "O" is from your track measurement work sheet, g = 386.088 in/s2, the acceleration due to gravity at sea level |
| Fff (weight supported by a front axle on flat) | ________(2.333) | oz | bg(CMx-CMytan*)/B The "O" is from your track measurement work sheet, g = 386.088 in/s2, the acceleration due to gravity at sea level |
| Frf (weight supported by a rear axle on flat) | ________(2.333) | oz | bg(B-CMx+CMytan*)/B The "O" is from your track measurement work sheet, g = 386.088 in/s2, the acceleration due to gravity at sea level |
| Dr (total drag on ramp) | ________() | oz | (nfFfrrf/Rf + 2uf(Ffr/2+mfg) + nrFrrrr/Rr + 2ur(Frr/2+mrg))cosO |
| Df (total drag on flat) | ________() | oz | nfFffrf/Rf + 2uf(Fff/2+mfg) + nrFrfrr/Rr + 2ur(Frf/2+mrg) |
| k (air mass displacement per inch of track) | ________(0.00000070) | ozs2/in2 | apA/2 p = 0.000001877865 ozs2/in4, density of air, 1 atm, 60 F |
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| Grand Prix Racing - | The Science of Fast Pinewood Cars |
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