Design Cookbook: Climbing an Inclined Plane

Cookbook Index


Four Wheel Drive | Front Wheel Drive | Rear Wheel Drive | Step


Introduction:

This handout will examine the physics behind wheeled vehicles climbing slopes.

Fm = mg (gravitational force of the machine)
Nf (normal force of both front wheels)
Nr (normal force of both rear wheels)
Ftf = Nf (tractional force of both front wheels, caused by static friction)
Ftr = Nr (tractional force of both rear wheels, caused by static friction)
L (distance between the front and rear wheels)
Lc (distance between the rear wheels and the center of mass)
h (height of the center of mass)
(angle of incline plane)

Tipping of the Machine occurs at h=hmax when Nf=0:

What can be done to prevent the machine from tipping?

Four Wheel Drive:

The necessary static coefficient of friction (4WD) for a four wheel drive vehicle:

What can be changed to allow for a lower coefficient of friction?

Front Wheel Drive:

The necessary static coefficient of friction (FWD) for a front wheel drive vehicle:

What can be changed to allow for a lower coefficient of friction?

Rear Wheel Drive:

The necessary static coefficient of friction (RWD) for a rear wheel drive vehicle:

What can be changed to allow for a lower coefficient of friction?

A Wheel Driving Up a Step

0 < h < d/2