All simulations Simulation 14 · Mechanics

Car Differential

When a car turns, why don't its tyres skid? Steer round corners and watch the differential let the outer wheel spin faster, then lock the axle or hit a patch of ice to see what goes wrong.

Automobile Engineering
Turning: radius 8.8 mInside the differentialLeft wheel192 rpmCarrier177 rpmRight wheel162 rpmSpider gear15 rpm(192 + 162) ÷ 2 = 177 rpm
40% right
20 km/h
Turn radius8.8 mto the middle of the rear axle
Inner wheel18.3 km/hshorter path
Outer wheel21.7 km/h1.19× the inner wheel
Spider gearsSpinningthey let the wheels differ

Try this

0 of 5 done

Drive straight and see what the small spider gears do.Hint: centre the steering

Take a tight turn: radius 6 m or less.Hint: steer hard left or right

Make the outer wheel turn 1.5 times faster than the inner one.Hint: almost full lock

Lock the axle and turn. Hear the tyres complain?Hint: switch on Lock the axle, then steer

Get unstuck when one wheel is on ice.Hint: put a wheel on ice, then lock the differential

What's happening

Wheels travel different distances

When a car turns, the outer wheel follows a bigger circle than the inner wheel, so it has to go farther in the same time. If both wheels were fixed to one solid axle, one tyre would have to skid. That wastes fuel, wears tyres and makes the car hard to steer.

outer ÷ inner = (R + track/2) ÷ (R − track/2)

The differential shares the turning

The engine turns a big ring gear and its carrier. Inside, small spider gears connect the two side gears that drive the wheels. Going straight, the spider gears don't spin and both wheels turn together. In a turn, the spider gears roll round, letting one wheel speed up exactly as much as the other slows down.

carrier speed = (left wheel + right wheel) ÷ 2

The weakness: one slippery wheel

An open differential gives both wheels the same push. If one wheel sits on ice or mud, it can't push back, so it just spins at double speed while the car goes nowhere. Locking or limited-slip differentials fix this by tying the wheels together when needed.

open diff on ice: slipping wheel = 2 × carrier, gripping wheel = 0

Who figured this out?

South-pointing chariot

About 3rd century CE, China

A two-wheeled cart with a figure that kept pointing the same way however the cart turned. It is thought to have used differential gearing to compare the two wheels.

Onésiphore Pecqueur

1827, France

Patented a differential gear for steam-powered vehicles, the ancestor of the one in every car today.

Carl Benz

1886, Germany

His Patent-Motorwagen, often called the first practical car, used a differential to drive its two rear wheels.

Check yourself

1. Why does a car need a differential?

2. Driving straight ahead, the spider gears inside the differential…

3. The carrier turns at 200 rpm and the left wheel at 180 rpm. The right wheel turns at…

4. One rear wheel is on ice and the car has an open differential. What happens?

Common questions

What is a differential in a car?

A differential is a gearbox in the axle that sends the engine's power to two wheels while letting them turn at different speeds. It is needed because in a turn the outer wheel travels farther than the inner wheel.

How does a differential work?

The driveshaft turns a pinion gear that drives a large ring gear fixed to the differential carrier. Inside the carrier, small spider (planet) gears mesh with two side gears connected to the wheels. When both wheels turn equally, everything rotates together. In a turn, the spider gears rotate on their shafts, letting one side gear turn faster and the other slower.

What happens with an open differential when one wheel is on ice?

An open differential always gives both wheels equal torque. If one wheel has almost no grip, it can only take a tiny torque, so the other wheel gets the same tiny torque. The slipping wheel spins fast and the car doesn't move.

What is a limited-slip or locking differential?

A limited-slip differential uses clutches or special gears to send more torque to the wheel with grip when one starts to slip. A locking differential can lock both wheels together so they turn at the same speed. Off-road vehicles and tractors often have them.

What is the relation between the wheel speeds in a differential?

The carrier (ring gear) speed is always the average of the two wheel speeds: carrier = (left + right) ÷ 2. If one wheel slows down by some amount, the other speeds up by exactly the same amount.

Do front-wheel-drive and four-wheel-drive cars have differentials?

Yes. A front-wheel-drive car has its differential built into the transaxle at the front. A four-wheel-drive car can have three: one on each axle, and a centre differential to let the front and rear axles turn at different speeds.

Simplified rear-wheel-drive car at low speed, with no tyre slip except where shown. Real cars also use Ackermann steering for the front wheels.