Need help figuring how much torque I need to move a cart.

[qwerty11]

I'm undertaking a little project. I am wanting to outfit a cart like this (http://www.northerntool.com/shop/tools/product_200411313_200411313) with RC gear. It will most likely use a hub mounted gear and a motor shaft mounted sprocket to turn the rear axle. I need to know what size of motor and gears I need to purchase to move the load I will put on it. Would like to build an excel spreadsheet so I can compare gear/motor combinations.

Here is some relevant information:

Mass of trailer and load: 150 lb
Maximum speed: 5 mph
Maximum needed acceleration: whatever is reasonably close to human acceleraton
Tire diameter: 10"
Maximum grade: 30 degrees
Min/max number of teeth on sprocket: 8-20
Min/max number of teeth on axle gear: 40-114
Maximum motor RPM: don't have an exact number but electric motors (as you probably know) can spin pretty fast

I thank you for your help and look forward to learning how to calculate this.

 

[eljose79]

Hello there,

First of all, it's great to see that you are taking on this project and utilizing RC gear to make a functional cart. I would be happy to assist you in calculating the necessary motor and gear size for your project.

To start off, we need to understand the basic physics behind the movement of the cart. The force required to move an object is directly proportional to its mass and acceleration. In this case, the mass of the trailer and load is 150 lb and the maximum needed acceleration is reasonably close to human acceleration, which is about 3 m/s^2.

Using the formula F=ma, we can calculate the required force to move the cart, which is 450 lb-ft/s^2. This force will be applied to the rear axle through the motor and gears.

Next, we need to consider the speed and grade of the cart. Since the maximum speed is 5 mph and the maximum grade is 30 degrees, we can use the formula v^2=u^2+2as to calculate the required acceleration to move the cart uphill. This comes out to be 1.5 m/s^2.

Now, we can use this acceleration value to calculate the torque required to move the cart uphill. Torque is defined as the force applied at a distance from the pivot point. In this case, the pivot point is the rear axle. Using the formula T=Fd, where T is torque, F is force and d is the distance from the pivot point, we can calculate the torque required to move the cart uphill. Assuming the distance from the pivot point to the center of the wheel is 5 inches, the required torque comes out to be 75 lb-ft.

Now, we can use this torque value to determine the motor and gear size. The motor should be able to provide at least 75 lb-ft of torque to move the cart uphill. As for the gears, we need to make sure that the gear ratio is sufficient to provide the required torque. Using the formula gear ratio = number of teeth on axle gear/number of teeth on sprocket, we can calculate the gear ratio for different combinations of teeth on the sprocket and axle gear.

For example, if we choose 12 teeth on the sprocket and 60 teeth on the axle gear, the gear ratio would be 5:1. This means that for every 5 rotations of the sprocket, the axle