Here are step-by-step examples and instructions on how to calculate the most common specs, such as Gear ratios, Motor and Wheel RPM’s and the calculated “Top Speed” of a remote control car or similar.
Gearing Ratios (Driver, Internal and Final Gear Ratio)
The ‘Pinion’ gear is usually smaller and attached to the motor. The ‘Spur’ gear is generally bigger (has more teeth).
Driver Ratio (aka Spur/Pinion Ratio) [-Equals-] Spur Gear [-Divided by-] Pinion Gear
Example: Spur Gear 75T / Pinion Gear 32T (T stands for Teeth – if you are not sure how many teeth your gear has, just count them).
75 / 32 = 2.34 | The Driver Ratio is 2.34, which means that the Pinion Gear will turn 2.34 times, while the Spur Gear turns 1 time.
Internal Gear Ratio (aka Transmission Ratio) [-Equals-] Final Drive Ratio (found at the wheels) [-Divided by-] Driver Ratio (aka Spur/Pinion Ratio)
Example: Final Drive Ratio 7.16 : Driver Ratio 2.34
7.16 / 2.34 = 3.06 | The Internal Gear Ratio (often pre-set by the manufacture) is 3.06
Final Drive Ratio (aka Overall Gear Ratio found at the Wheel) [-Equals-] Internal Gear Ratio (aka Transmission Ratio) [-Multiplied by-] Driver Ratio (aka Spur/Pinion Ratio)
Example: Internal Gear Ratio 3.06 x Driver Ratio 2.34
3.06 x 2.34 = 7.16 | The Final Drive Ratio is 7.16, which means that the Motor will turn 7.16 times, while the Wheels will turn 1 time.
Theoretical Maximum Motor RPM in relation to KV Rating
Electric Motors are often rated with a KV number such as 4300 RPM/Volt DC
In a very simplified way this means the motor will turn 4300 times per minute for each Volt applied. Motors are rated for a certain maximum Voltage which consequently limits the maximum RPM (Rounds Per Minute)
Example: The Novak SS 4300 Motor is rated 4300RPM/Volt DC with a maximum Voltage of 7.2 Volt.
4300 RPM x 7.2 Volt = 30960 | The motor has a theoretical maximum RPM of 30960, in other words the motor turns 30960 times in a minute.
Tamiya’s Mabuchi 540 Stock Motor has a maximum RPM of 23400.
Please note that the RPM under load (meaning once the motor is in the car working hard) is lower than the calculated maximum RPM.
Wheel Diameter, Circumference and Travel distance for each turn
Wheel travel distance (meaning how far does the car move forward each time the wheel turns) depends on the size of the wheel.
Wheel size is easily measured with a Ruler. Just measure the overall outside diameter.
Example: The Tamiya Block Rally Tire measures 6.8 cm, which means the outside diameter is 6.8 cm (2.6 inches)
To calculate how far the wheel travels per turn simply multiply the Diameter with Π (Pi 3.141)
Example: 6.8 cm x 3.141 = 21.35 cm | Meaning the wheel travels 21.35 cm (8.4 inches) on each turn.
Theoretical Maximum Top Speed
How fast should (or can) my car go?
Based on all steps above we can now calculate how fast our car should theoretically drive.
Step 1) How fast (often) do the wheels turn based on maximum motor RPM?
For this we will use the Tamiya Stock 540 Motor with the assumption that it will turn at 23400 rpm. We also assume that we are running the out-of-the-box Spur and Pinion which comes with the model, resulting in a final gear ratio of 7.16. We now need to divide the motor rpm by the final gear ratio.
Example: Tamyia Stock 540 Motor at 23400 RPM [-Divided by-] Final Gear Ratio 7.16 (found at the wheels).
23400 RPM / 7.16 = 3268 | Which means the Wheels turn 3268 times per minute
Step 2) How fast and how far does the car travel per minute and hour
We calculated earlier that the car travels 21.35 cm (8.4 inches) per turn. We will now figure out how far the wheel will travels each minute based on our RPM calculated above. To make it easy we will first convert cm into meter 21.23 cm / 100 = 0.213 m
Example: 3268 Wheel RPM’s (-multiplied by-) 0.213 m tire circumference
3268 RPM x 0.213 m = 696 | Which means the car will travel 696 meters every minute
Let’s calculate meters per minute into meters per hour by multiplying with 60; because there are 60 minutes in one hour.
696 m x 60 = 41760 | Which means the car travels 41760 meters in one hour
Lets calculate meters into kilometers, which is done by dividing through 1000; because there are 1000 meters (m) in 1 kilometer (km)
41760 meters per hour / 1000 = 41.75
Which means the car has a theoretical calculated top speed of 41.75 kph or 25.94 mph
The complete formula with all steps above would look something like this:
1) Calculating the true scale weight of an RC Car.
2) Take a look how the top speed changes with different gear ratios here.
Products used or mentioned in the blog post: