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Grades 6–8 · Machines

Why do a car’s front wheels turn through different angles?

When a car turns slowly, the wheels on the inside of the bend follow smaller circles than the wheels on the outside. Each front wheel must point along its own path. The inside front wheel therefore turns farther away from the straight-ahead direction than the outside front wheel.

M103 visual explanationIdeal slow Ackermann left turn, wheelbase 2.4 m and track 1.6 m. A rear-axle-center radius 4 m places the inner and outer rear wheel paths at 3.2 and 4.8 m. The front wheel angles are 36.87 and 26.57 degrees. Their transverse axes meet the rear axle line at the common turning center. Tire slip, high-speed dynamics and linkage design are not modeled.The inside front wheel turns through a larger angleIdeal slow left turn • top view • wheelbase 2.4 mInside wheel36.87°Outside wheel26.57°Turning centerRear axle lineRear-axle center follows a 4 m radius.Angles concern wheel direction; a differential concerns speeds.

In the diagramThe inside front wheel turns through a larger angleIdeal slow left turn • top view • wheelbase 2.4 mInside wheel36.87°Outside wheel26.57°Turning centerRear axle lineRear-axle center follows a 4 m radius.Angles concern wheel direction; a differential concerns speeds.

The inside front wheel turns about 37 degrees and the outside wheel about 27 degrees. Their wheel axes point toward one shared turning center.

The geometry is called Ackermann steering. In an ideal turn without sideways tire slip, a line drawn across each wheel’s axle points toward the center of that wheel’s circular path. The two front-wheel lines meet the extended rear axle line at the same turning center. Giving both front wheels exactly the same angle would make these directions disagree.

Wheelbase means the distance between the front and rear axles. Track width is the distance across the vehicle between the left and right wheel positions. Here the wheelbase is 2.4 meters and the track is 1.6 meters. When the rear-axle midpoint follows a 4-meter radius, the inside and outside rear-wheel paths have radii of 3.2 and 4.8 meters. The corresponding front-wheel angles are about 37 and 27 degrees.

Steering arms and connecting rods make the wheel directions differ as the steering moves. Real designs approximate the ideal geometry, and tires deform or slip during actual driving. These steering angles describe where the wheels point. A differential has a separate job: allowing powered wheels to rotate at different speeds on their different paths.

About this explanation

Starting knowledge: Recognize a circle’s radius and distinguish wheel direction from wheel rotation speed.

Sources

  • MathWorks — Steering System: Ackermann steering effects
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