# Motor sizing for an autonomous mower

I plan (one day) to build an autonomous mower. This page is dedicated to the motor sizing. To size the motors, I need the following data:

## Number of motors

I plan to build a four-wheel drive mower, so I'll need four motors.

## Diameter of the wheel

I don't know yet, but I current have a Worx Landroid and we'll assume the wheels will be the same size, about 21 centimeters:

## Weight of the mower

As for the wheel diameter, I'll assume my mower will have approximatively the same weight than my Landroid mower. Let's say about 12kg:

## Maximum velocity

Not easy to estimate the maximum velocity of my future mower. As for the weight and wheels diameter, I check on my mower. I'll take this opportunity to do the acceleration.

Here is the result. Blue points are the point measured on my mower, the red line is the modelization.

The cruising speed of the mower is close to 0.4 m/s, let's take some margin, our goal will be 0.5m/s or 1.8km/s after conversion.

## Maximum acceleration

We don't need a strong acceleration to avoid wheel slip. On the previous model, the acceleration is 0.0125 m/s². Let's take some margin: 0.015 m/s² will be great.

## Maximum slope angle

Let's be ambitious! 45 degrees seems a great goal.

## Motor sizing

Thank's to this wonderfull online motor sizing calculator, we get the following specifications for our motors:

### Four wheels drive

• Velocity: 45.47 rpm
• Torque on wheel: 2.2 N.m
• Power: 12.9 W

### Two wheels drive

• Velocity: 45.47 rpm
• Torque on wheel: 4.4 N.m
• Power: 25.8 W

## Selected motor

After some research, I chose a ZD Motors 42mm motor (reference Z42BLDPN2440-30S with a planetary gearbox having a ratio of 58.22).

• The motor can reach a speed of 52 rpm.
• Maximum torque is 6 N.m

The motor power is 40W. But considering 52 rpm = 5.45 rad/s, we can deduce that the maximum output power of the gearbox will be 5.45 rad/s x 6 N.m = 32.7 W.

All that's left to do now is to check that the motor is actually suitable!