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 µ	(tractional force of both front wheels, caused by static friction)
Ftr = Nr µ	(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)
Ø	(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?

• moving the center of gravity farther from the rear wheels
• decreasing the slope angle

Four Wheel Drive:

The necessary static coefficient of friction (µ4WD) for a four wheel drive vehicle:

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

• Decrease the slope of the angle

Front Wheel Drive:

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

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

• decrease the anlge of the incline
• move the center of gravity closer to the front wheels
• shortening the distance between the front and rear wheels
• lowering the height of the center of gravity

Rear Wheel Drive:

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

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

• decrease the angle of the incline
• move the center of gravity closer to the rear wheels
• increasing the height of the center of gravity

A Wheel Driving Up a Step