Gearing and speed for a drivetrain

The first lesson in this track gave you the formula for drivetrain speed and a target range. This lesson puts it to work: real motors, real wheels, worked both forwards and backwards, and the catches the formula hides.

The formula

Three numbers decide a drivetrain's speed: the motor's output RPM, any extra reduction between motor and wheel, and the wheel's diameter.

wheel RPM   = motor output RPM / external ratio
speed (m/s) = wheel RPM × π × diameter (m) / 60
speed (ft/s) = speed (m/s) / 0.3048

Each revolution moves the robot one wheel circumference (π × diameter), so a bigger wheel is exactly like less reduction: faster, and less force at the floor.

Free speed

The speed the robot would reach with nothing slowing it down — motors at their no-load RPM on a full 12 V. It is the number every calculator (including ours) gives you, and real robots never quite reach it.

Worked example: a goBILDA Strafer

goBILDA's Strafer chassis kit uses four 312 RPM Yellow Jacket motors, driving 104 mm mecanum wheels through 1:1 gears.

wheel RPM = 312 / 1           = 312
speed     = 312 × π × 0.104 / 60
          ≈ 1.70 m/s
          ≈ 5.57 ft/s

That matches the 5.57 ft/s that goBILDA lists for the kit — a good sign the formula and the numbers are right.

Swap in 435 RPM motors on the same wheels:

speed = 435 × π × 0.104 / 60 ≈ 2.37 m/s ≈ 7.77 ft/s

Worked example: REV with smaller wheels

REV's mecanum wheels are 75 mm across — smaller, so they need a faster wheel RPM for the same robot speed.

REV's UltraPlanetary gearbox stacks cartridges labelled 3:1, 4:1 and 5:1. The labels are nominal: REV's documentation gives the actual ratios as about 2.89:1, 3.61:1 and 5.23:1. The HD Hex motor itself spins at about 6000 RPM free.

A "20:1" stack (4:1 and 5:1 cartridges):

actual ratio = 3.61 × 5.23 ≈ 18.9 : 1
motor RPM    = 6000 / 18.9 ≈ 317      (REV lists 317 RPM)
speed        = 317 × π × 0.075 / 60 ≈ 1.25 m/s ≈ 4.1 ft/s

A "15:1" stack (3:1 and 5:1 cartridges) instead:

actual ratio = 2.89 × 5.23 ≈ 15.1 : 1
motor RPM    = 6000 / 15.1 ≈ 397
speed        = 397 × π × 0.075 / 60 ≈ 1.56 m/s ≈ 5.1 ft/s

Working backwards from a target speed

Usually you know roughly how fast you want to go and need to choose the parts. Rearrange the formula:

wheel RPM needed = speed (m/s) × 60 / (π × diameter (m))

Target 5.5 ft/s (1.68 m/s) on 104 mm wheels:

wheel RPM = 1.68 × 60 / (π × 0.104) ≈ 308 RPM

The 312 RPM motor, direct to the wheel, is almost exactly right. Game Manual 0 gives the same rule of thumb from the other direction: reductions between about 16:1 and 20:1 suit 4-inch wheels, and about 12:1 to 15:1 suit 3-inch wheels. The 19.2:1 and 13.7:1 Yellow Jacket gearboxes are popular because they land in those ranges with no extra gearing.

Try different combinations in the drivetrain calculator.

What speed to aim for

Game Manual 0 suggests a free speed of about 4.5–6 ft/s for a solid drivetrain, and says most new teams' drivetrains are too slow, not too fast. It also flags 40:1 and 60:1 gearmotors as almost always too slow for a drivetrain.

There is a top end too. A very fast robot is hard to control precisely, and your drivers will spend the match overshooting. You can always scale power down in code for fine control; you cannot make a slow drivetrain faster in software.

Speed versus pushing force

Gearing for speed costs force at the floor. The force a wheel can push with is its torque divided by its radius:

force at floor = wheel torque / wheel radius

Using goBILDA's listed stall torques, four motors direct-driving 104 mm wheels (radius 0.052 m):

Going from 312 to 435 RPM buys about 40% more top speed and costs about 23% of the force. That force is what accelerates the robot and pushes back when another robot leans on you. These are upper limits at stall, before friction and gearbox losses — real numbers are lower, and the wheels may slip on the tiles before the motors ever stall.

Why the robot never reaches free speed

Free speed is a ceiling, not a prediction. Real robots are slower because:

• Friction in bearings, gearboxes, chains and belts uses up some of the motor's output.
• Battery voltage drops under load and through the match, and motor speed drops with it.
• The robot has to accelerate. In a lot of short FTC moves, it spends much of its time speeding up and slowing down, never at top speed at all.
• Mecanum rollers slip, especially when strafing.

That is another reason not to gear right at the edge: a robot that is "a bit fast" on paper is usually just right on the field.

Next

The numbers on paper only hold if the drivetrain is built well. Next: why robots curve, and how to build one that drives straight.

Sources and further reading

• Game Manual 0 — Drivetrains (speed range and gear-ratio guidance)
• Game Manual 0 — Choosing a Motor (planetary versus spur gearboxes)
• goBILDA — Strafer Chassis Kit
• goBILDA — Yellow Jacket planetary gear motors (RPM and stall torque for every ratio)
• REV — HD Hex Motor and UltraPlanetary cartridge details (actual ratios)