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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.

Crown: / Pinion: = Ratio:


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.

Cluster: / Armature Pinion: = Armature Ratio
Crown: / Pinion: = Drive Ratio
Armature Ratio: X Drive Ratio: = Final Drive Ratio:

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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.

Tire Diameter: X 3.1416 / Gear Ratio: = Distance Traveled:


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.

Tire Diameter: X 3.1416 / Distance Traveled: = Gear Ratio:


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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.

InchesMillimetersDrill Size
0.0059.149997
0.0063.160096
0.0067.170295
0.0071.180394
0.0075.190593
0.0079.200792
0.0083.210891
0.0087.221090
0.0091.231189
0.0095.241388
0.0100.254087
0.0105.266786
0.0111.279485
0.0115.292184
0.0120.304883
0.0125.317582
0.0130.330281
0.0135.342980
0.0145.368379
0.0156.39621/64"
0.0160.406478
0.0180.457277
0.0200.508076
0.0210.533475
0.0225.571574
0.0240.609673
0.0250.635072
0.0260.660471
0.0280.711270
0.0292.741769
0.0310.787468
0.0312.79251/32"
0.0320.812867
0.0330.838266
0.0350.889065
0.0360.914464
0.0370.939863
0.0380.965262
0.0390.990661
0.04001.016060
0.04101.041459
0.04201.066858
0.04301.092257
0.04651.181156
0.04691.19133/64"
0.05201.320855
0.05501.397054
0.05951.511353
0.06251.58751/16"
0.06351.612952
0.06701.701851
0.07001.778050
InchesMillimetersDrill Size
0.07301.877149
0.07601.930448
0.07811.98375/64"
0.07851.993947
0.08102.057446
0.08202.082845
0.08602.184444
0.08902.260643
0.09352.374942
0.09382.38253/32"
0.09602.438441
0.09802.489240
0.09952.527339
0.10152.578138
0.10402.641637
0.10652.705136
0.10942.77887/64"
0.11002.794035
0.11102.189434
0.11302.870233
0.11602.946432
0.12003.048031
0.12503.17501/8"
0.12853.263930
0.13603.454429
0.14053.568728
0.14063.57129/64"
0.14403.657627
0.14703.733826
0.114953.797325
0.15203.860824
0.15403.911623
0.15623.96755/32"
0.15703.397822
0.15904.038621
0.16104.089420
0.16604.216419
0.16954.305318
0.17194.366311/64"
0.17304.394217
0.17704.495816
0.18004.572015
0.18204.622814
0.18504.699013
0.18754.76253/16"
0.18904.800612
0.19104.851411
0.19354.914910
0.19604.97849
0.19905.05468
0.20105.10547
0.20315.158713/64"
InchesMillimetersDrill Size
0.20405.18166
0.20555.21975
0.20905.30864
0.21305.41023
0.21885.55757/32"
0.22105.61342
0.22805.79121
0.23405.9436A
0.23445.953815/64"
0.23806.0452B
0.24206.1468C
0.24606.2484D
0.25006.3500E
0.25706.5278F
0.26106.6294G
0.26566.746217/64"
0.26606.7564H
0.27206.9088I
0.27707.0358J
0.28107.1374K
0.28127.14259/32
0.29007.3660L
0.29507.4930M
0.29697.541319/64"
0.30207.6708N
0.31257.93755/16
0.31608.0264O
0.32308.2042P
0.32818.333721/64"
0.33208.4328Q
0.33908.6106R
0.34388.732511/32"
0.34808.8392S
0.35809.0932T
0.35949.128823/64"
0.36809.3472U
0.37509.52503/8"
0.37709.5758V
0.38609.8044W
0.39069.921225/64"
0.397010.0838X
0.404010.2616Y
0.406210.317513/32"
0.413010.4902Z
0.421910.717327/64"
0.437511.11257/16"
0.453111.508729/64"
0.468811.907515/32"
0.484412.303831/64"
0.500012.70001/2"
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