Racer and Modeler's Math
You hated it in school; you need it as an adult. Worry not, just let an
expert help you. While we are at it, we will
build some neat tools that do the calculations for you so your brain doesn't fill up
and cause you to forget your wife's birthday.
Gear Ratio
Distance Traveled
Inches to Millimeters
Gear Ratio
The gear ratio of your car provides a mechanical advantage to the motor, letting it spin
faster than the axle. This allows the motor to spin up to where it has enough torque to
accelerate the car. Theoretically, when this number is high, the motor is spinning much
faster than the axle and the car accelerates fast, but has a lower top speed. A low
number is the opposite, a car with poor acceleration but a higher top speed.
Just to make sure we are all confused, an gear ratio close to 1:1 is considered high
while an axle ratio higher numerically is considered low. I never said any of this
would make sense.
Inline or Spur Drive
Figuring gear ratio on an inline motor is an easy calculation.
Aurora Step Down
Early Aurora cars are more work. We must figure the first step down from the armature
pinion gear to the driven gear. Notice that the idler gear doesn't affect the gear
ratio. It just reverses the rotation of the gear shaft.
Distance Traveled
Distance Traveled from gear ratio and tire size
The gear ratio will tell you how many times the axle will spin for each motor
revolution, how does that relate to how far the car will actually go? The formula for
distance traveled is tire circumference/gear ratio.
Solving for Gear Ratio
As you change your tire size, you may want to adjust you gear ratio so the car travels
the same distance. You do this by solving the above equation for gear ratio.
Inches to Millimeters
Here is a handy chart. It gives you the metric conversion of a decimal inch measure.
As a handy bonus, the drill size is also included.
| Inches | Millimeters | Drill Size |
|---|
| 0.0059 | .1499 | 97 |
| 0.0063 | .1600 | 96 |
| 0.0067 | .1702 | 95 |
| 0.0071 | .1803 | 94 |
| 0.0075 | .1905 | 93 |
| 0.0079 | .2007 | 92 |
| 0.0083 | .2108 | 91 |
| 0.0087 | .2210 | 90 |
| 0.0091 | .2311 | 89 |
| 0.0095 | .2413 | 88 |
| 0.0100 | .2540 | 87 |
| 0.0105 | .2667 | 86 |
| 0.0111 | .2794 | 85 |
| 0.0115 | .2921 | 84 |
| 0.0120 | .3048 | 83 |
| 0.0125 | .3175 | 82 |
| 0.0130 | .3302 | 81 |
| 0.0135 | .3429 | 80 |
| 0.0145 | .3683 | 79 |
| 0.0156 | .3962 | 1/64" |
| 0.0160 | .4064 | 78 |
| 0.0180 | .4572 | 77 |
| 0.0200 | .5080 | 76 |
| 0.0210 | .5334 | 75 |
| 0.0225 | .5715 | 74 |
| 0.0240 | .6096 | 73 |
| 0.0250 | .6350 | 72 |
| 0.0260 | .6604 | 71 |
| 0.0280 | .7112 | 70 |
| 0.0292 | .7417 | 69 |
| 0.0310 | .7874 | 68 |
| 0.0312 | .7925 | 1/32" |
| 0.0320 | .8128 | 67 |
| 0.0330 | .8382 | 66 |
| 0.0350 | .8890 | 65 |
| 0.0360 | .9144 | 64 |
| 0.0370 | .9398 | 63 |
| 0.0380 | .9652 | 62 |
| 0.0390 | .9906 | 61 |
| 0.0400 | 1.0160 | 60 |
| 0.0410 | 1.0414 | 59 |
| 0.0420 | 1.0668 | 58 |
| 0.0430 | 1.0922 | 57 |
| 0.0465 | 1.1811 | 56 |
| 0.0469 | 1.1913 | 3/64" |
| 0.0520 | 1.3208 | 55 |
| 0.0550 | 1.3970 | 54 |
| 0.0595 | 1.5113 | 53 |
| 0.0625 | 1.5875 | 1/16" |
| 0.0635 | 1.6129 | 52 |
| 0.0670 | 1.7018 | 51 |
| 0.0700 | 1.7780 | 50 |
| | Inches | Millimeters | Drill Size |
|---|
| 0.0730 | 1.8771 | 49 |
| 0.0760 | 1.9304 | 48 |
| 0.0781 | 1.9837 | 5/64" |
| 0.0785 | 1.9939 | 47 |
| 0.0810 | 2.0574 | 46 |
| 0.0820 | 2.0828 | 45 |
| 0.0860 | 2.1844 | 44 |
| 0.0890 | 2.2606 | 43 |
| 0.0935 | 2.3749 | 42 |
| 0.0938 | 2.3825 | 3/32" |
| 0.0960 | 2.4384 | 41 |
| 0.0980 | 2.4892 | 40 |
| 0.0995 | 2.5273 | 39 |
| 0.1015 | 2.5781 | 38 |
| 0.1040 | 2.6416 | 37 |
| 0.1065 | 2.7051 | 36 |
| 0.1094 | 2.7788 | 7/64" |
| 0.1100 | 2.7940 | 35 |
| 0.1110 | 2.1894 | 34 |
| 0.1130 | 2.8702 | 33 |
| 0.1160 | 2.9464 | 32 |
| 0.1200 | 3.0480 | 31 |
| 0.1250 | 3.1750 | 1/8" |
| 0.1285 | 3.2639 | 30 |
| 0.1360 | 3.4544 | 29 |
| 0.1405 | 3.5687 | 28 |
| 0.1406 | 3.5712 | 9/64" |
| 0.1440 | 3.6576 | 27 |
| 0.1470 | 3.7338 | 26 |
| 0.11495 | 3.7973 | 25 |
| 0.1520 | 3.8608 | 24 |
| 0.1540 | 3.9116 | 23 |
| 0.1562 | 3.9675 | 5/32" |
| 0.1570 | 3.3978 | 22 |
| 0.1590 | 4.0386 | 21 |
| 0.1610 | 4.0894 | 20 |
| 0.1660 | 4.2164 | 19 |
| 0.1695 | 4.3053 | 18 |
| 0.1719 | 4.3663 | 11/64" |
| 0.1730 | 4.3942 | 17 |
| 0.1770 | 4.4958 | 16 |
| 0.1800 | 4.5720 | 15 |
| 0.1820 | 4.6228 | 14 |
| 0.1850 | 4.6990 | 13 |
| 0.1875 | 4.7625 | 3/16" |
| 0.1890 | 4.8006 | 12 |
| 0.1910 | 4.8514 | 11 |
| 0.1935 | 4.9149 | 10 |
| 0.1960 | 4.9784 | 9 |
| 0.1990 | 5.0546 | 8 |
| 0.2010 | 5.1054 | 7 |
| 0.2031 | 5.1587 | 13/64" |
| | Inches | Millimeters | Drill Size |
|---|
| 0.2040 | 5.1816 | 6 |
| 0.2055 | 5.2197 | 5 |
| 0.2090 | 5.3086 | 4 |
| 0.2130 | 5.4102 | 3 |
| 0.2188 | 5.5575 | 7/32" |
| 0.2210 | 5.6134 | 2 |
| 0.2280 | 5.7912 | 1 |
| 0.2340 | 5.9436 | A |
| 0.2344 | 5.9538 | 15/64" |
| 0.2380 | 6.0452 | B |
| 0.2420 | 6.1468 | C |
| 0.2460 | 6.2484 | D |
| 0.2500 | 6.3500 | E |
| 0.2570 | 6.5278 | F |
| 0.2610 | 6.6294 | G |
| 0.2656 | 6.7462 | 17/64" |
| 0.2660 | 6.7564 | H |
| 0.2720 | 6.9088 | I |
| 0.2770 | 7.0358 | J |
| 0.2810 | 7.1374 | K |
| 0.2812 | 7.1425 | 9/32 |
| 0.2900 | 7.3660 | L |
| 0.2950 | 7.4930 | M |
| 0.2969 | 7.5413 | 19/64" |
| 0.3020 | 7.6708 | N |
| 0.3125 | 7.9375 | 5/16 |
| 0.3160 | 8.0264 | O |
| 0.3230 | 8.2042 | P |
| 0.3281 | 8.3337 | 21/64" |
| 0.3320 | 8.4328 | Q |
| 0.3390 | 8.6106 | R |
| 0.3438 | 8.7325 | 11/32" |
| 0.3480 | 8.8392 | S |
| 0.3580 | 9.0932 | T |
| 0.3594 | 9.1288 | 23/64" |
| 0.3680 | 9.3472 | U |
| 0.3750 | 9.5250 | 3/8" |
| 0.3770 | 9.5758 | V |
| 0.3860 | 9.8044 | W |
| 0.3906 | 9.9212 | 25/64" |
| 0.3970 | 10.0838 | X |
| 0.4040 | 10.2616 | Y |
| 0.4062 | 10.3175 | 13/32" |
| 0.4130 | 10.4902 | Z |
| 0.4219 | 10.7173 | 27/64" |
| 0.4375 | 11.1125 | 7/16" |
| 0.4531 | 11.5087 | 29/64" |
| 0.4688 | 11.9075 | 15/32" |
| 0.4844 | 12.3038 | 31/64" |
| 0.5000 | 12.7000 | 1/2" |
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