🔧 Hardware · Engineer · Beginner → Intermediate

Gear Ratio & Drivetrain Speed

The most important design decision on your robot is how fast your drivetrain moves. This guide explains the math, walks through cartridge choices, and includes a calculator that shows your actual speed before you build.

Why this matters: A drivetrain that's too fast is hard to control. Too slow and you lose field position every match. Getting the ratio right is cheaper than rebuilding after your first tournament.

⚙ The Three Cartridges

Cartridge	Free speed	Best for	Feel
Red	100 RPM	Heavy lifts, high-torque arms	Slow and powerful — rarely used for drive
Green	200 RPM	Standard drivetrains, versatile	Most common drive choice for beginners
Blue	600 RPM	Fast drivetrains, high-speed applications	Requires external gearing down to be controllable

📐 How Speed Is Calculated

Final speed in inches per second:

Speed (in/s) = (Motor RPM × Gear Ratio × Wheel Circumference) ÷ 60

Wheel Circumference = π × Wheel Diameter (inches)

Example: 200 RPM motor, 36:48 gearing (ratio 0.75), 3.25" wheel
  = (200 × 0.75 × π × 3.25) ÷ 60
  = (200 × 0.75 × 10.21) ÷ 60
  = 1531 ÷ 60 = 25.5 in/s  ≈ 2.1 ft/s

Gear ratio = driven teeth ÷ driving teeth. A 36-tooth gear on the motor driving a 48-tooth gear = 36/48 = 0.75. Smaller ratio = slower and more torque. Larger = faster, less torque.

🧮 Speed Calculator

Drivetrain Speed Calculator

Motor cartridge

Wheel diameter (inches)

Driving gear teeth

Driven gear teeth

Speed (max = 60 in/s ≈ fast competition robot)

—

Wheel RPM

—

Inches/sec

—

Feet/sec

EZ Template globals.hpp snippet

🏁 Choosing for Push Back

Speed range	Rating	Notes
Under 25 in/s	Too slow	You'll lose field position on every cycle. Hard to recover from
25–35 in/s	Manageable	Fine for push-heavy games. Safe for new drivers. Predictable
35–48 in/s	Competitive	Standard top-team speed. Requires practiced driver to be consistent
48–60 in/s	Fast — risky	Hard to control for new drivers. Worth it only with strong driver practice
Over 60 in/s	Too fast	Almost certainly a torque problem. Will struggle on carpet, defense, and ramps

🖥 Connecting to EZ Template

The three numbers in the ez::Drive constructor must match your physical robot exactly:

// ez::Drive chassis(left_motors, right_motors, imu_port, wheel_diam, ratio, ticks_per_rev)
ez::Drive chassis ({-1,-2,-3}, {4,5,6}, 7, 3.25, 36.0/48.0, 360);
//                                          ^^^^  ^^^^^^^^^  ^^^
//                              wheel diam  gear ratio       encoder ticks (V5 = 360)

Wheel diameter: Measure with calipers. Don't guess. 3.25" is common but worn wheels shrink
Gear ratio: driving ÷ driven — the same fraction from the calculator above
Ticks per rev: Always 360 for V5 integrated encoders

⚙ STEM Highlight Physics: Mechanical Advantage — Torque, Speed, and Power Trade-offs

Gear ratios are a direct application of the Law of Conservation of Energy and the concept of mechanical advantage. A gear ratio of N:1 multiplies torque by N while dividing speed by N. Power remains constant (ignoring friction): P = τ x ω = constant. This means you cannot increase both torque and speed simultaneously — any mechanism design is a trade-off between force and velocity. Understanding this relationship is what separates teams that tune gear ratios systematically from teams that change them randomly.

🎤 Interview line: “We calculate gear ratios before building. For our intake, we needed 80 RPM with enough torque to pull a game element against a 0.3kg load. Using P = F x v, we back-calculated the required gear reduction from our motor specs. This pre-calculation prevented three rebuilds — we built the right ratio the first time because we designed before cutting metal.”

A motor outputs 1.6 N·m of torque at 100 RPM. You add a 4:1 gear reduction. What is the output torque and RPM?

⬛ 6.4 N·m at 400 RPM — gear ratios multiply both torque and speed

⬛ 0.4 N·m at 400 RPM — the gear ratio divides torque and multiplies speed

⬛ 6.4 N·m at 25 RPM — the gear ratio multiplies torque and divides speed

📝

Notebook entry tip: Select Best Solution — Purple slide — Write a gear ratio decision entry: show your torque and speed requirements, calculate the gear ratio needed from your motor specs using τ = F x r, and document why you chose your final ratio over alternatives. This entry is direct evidence of engineering-based design — your gearbox was calculated, not guessed.