# How Does Wheel Size Affect My Robot?

Are you looking to make a wheeled robot and not sure what size wheel you need? Here we provide an insight into some of the equations which affect your robot's speed and distance traveled.

## Angular Velocity

The velocity (feet per second) of a robot is directly related to the angular velocity, w (in radians per second - NOT RPM) of the motor and the radius of the wheel, R (ideally in meters or feet, so when calculating v it is in meters per second or feet per second).

w = v / R

Re-arranging this equation, we find the velocity of the robot:

v = w*R

Most motor manufacturers provide the no load RPM, so to convert RPM to radians per second, you need the following equation:

Often, a "Voltage constant", Kv is provided by the manufacturer; for example, a motor may be rated at Kv= 2.4 Volts / 1000 RPM which correlates the RPM to the voltage.

This is the theory, now the reality: It's not always possible to operate a motor at its nominal voltage, and we often need to operate it at a few volts higher or lower. Keep in mind that the "nominal" voltage runs the motor at near peak efficiency, which is still never 100%; and as you move away from the nominal voltage, the efficiency drops, so the motor needs more current to provide the same torque, consuming the battery even faster. Next, keep in mind that not all motors can be operated at all voltages and all motors have a maximum rated voltage. The Voltage constant usually applies over a small range around the nominal voltage, and outside this range, the curve is not linear and not only will the motor not be operating efficiently, the output will not be anything like what you predict with the equations.

## Distance Traveled

To get an idea of how far your robot has traveled, you need to know the circumference of the drive wheel:

Circumference (C) = 2*pi*R

Distance traveled = w*C*t (where 'w' is in rad/sec and 't' is in seconds)

So what to do? Here are some useful tips:

• Choose smaller sized wheel for flat terrain, larger wheel for more "off-road" (or large obstacles)
• Proportional to the size of the robot (choosing a wheel proportional to the size of the robot will usually mean the motor you will need is also proportional, and the robot has a better chance of moving at a decent speed)
• See what wheels are out there - not all wheels have mounting hubs designed for all motors
• Keep in mind that a larger wheel may require a more powerful motor; we'll go into more detail about this in a future article.
• Use the same wheel for all drive motors: as you can see, changing the radius affects both the speed and the distance traveled: you don't want one wheel "fighting" against the other.

This is a companion discussion topic for the original entry at https://community.robotshop.com/tutorials/show/how-does-wheel-size-affect-my-robot

Here’s how I calculate wheel size.

Any extra money + money I shouldn’t spend - shipping = cost of motor * how cool it is -/+ wheels / number of wheels and divide by 0.

i understand exactly what your talking about. same size parts contributes to the cost size and programming of an object. the “purpose” of the robot transforms into a hole nother lanuguage.

cost, size, and programming simplifies the process

These calculations are incorrect.
First of all, velocity is a vector, meaning it has a rate and direction, so it’s not really applicable here. The angular velocity is also not applicable and should not be used in these calculations at all. What we want is simply the speed, or rate, of the robot. Which IS directly related to motor RMP.

Speed
rate = Circumference * RPM

Usually, wheels are specified by diameter, d. Pi is of course roughly 3.14159
Wheel Circumference = pid
therefore
rate = pi
d*RPM

You may want to convert circumference to feet or meters and RPM to RPS (revolutions per second) first.
RPS = RMP/60s
m = mm/1000

ex: 60mm wheel, 600RMP Geared Motor. Theoretical top speed disregarding weight and torque
robot speed = 3.14159 * .06m * 10rps = 1.8m/s

Distance Traveled
Yikes! Don’t use angular velocity. Angular velocity has units of radians per second (rad/s) and the radians does not cancel out of this equation. We don’t want distance measured in radians, which is a measure of angle.

Distance is simple.
D = rate * time.

We already found our rate above, so multiply it by the time. Continuing the example used above.
rate = 1.8m/s (meters per second)
How far would the robot go in 10 seconds?
D = 1.8m/s * 10s = 18m
Notice that seconds cancels out and we are left meters.

Choosing a wheel diameter
Clearly the larger diameter wheel may make the robot go faster, but it will take more torque from the motor. There is a lot to motors ratings and torques, but the torque will drop linearly with increase wheel radius.