Engines · Drivetrain6 min read

The differential: one axle, two speeds

Every time a car turns, its outer wheels travel further than its inner ones — so a solidly-connected driven axle would have to scrub and skip through every corner. The differential is the 250-year-old gear puzzle that lets one propshaft drive two wheels at two different speeds.

One axle, two speeds

Watch a car turn hard in a car park. Its inside rear wheel might trace a circle eight metres around; the outside one, eleven. Same time, different distances — the outer wheel simply must spin faster. Undriven wheels do this for free, each rolling at whatever speed the road asks. But driven wheels share one engine, one gearbox, one propshaft. Bolt both wheels rigidly to that shaft and every corner becomes a fight: one tyre or the other must skid to make up the difference, chirping, scrubbing and trying to straighten the car. Early motorists knew the symptom well; karts and some drag cars still live with it on purpose.

corner centreouter wheellonger arc — fasterinner wheelshorter arc — slower
Geometry, not preference: in any corner the outer tyre's arc is longer, so it must turn faster than the inner one — while both are driven by the same shaft.

The spider-gear trick

The differential solves it with a mechanism that feels like a magic trick the first time it makes sense. The propshaft doesn't drive the wheels — it drives a carrier, a cage that spins around both half-shafts. Inside the cage, small bevel gears (the spiders) mesh with a gear on the end of each half-shaft. Going straight, the spiders don't rotate on their own pins at all; they simply push both side gears around together, and both wheels turn at carrier speed. In a corner, the road slows one wheel — and the spiders begin to roll between the two side gears, subtracting speed from one exactly as they add it to the other. The average of the two wheel speeds always equals the carrier's; how that average is split is left entirely to the road.

from the gearboxring gear + carrierspidersleft wheelright wheelthe spiders roll between the half-shafts, splitting torque equally while letting speeds differ
An open differential, flattened: torque flows from the propshaft into the spinning carrier, through the spiders, out both half-shafts. The spiders only rotate when the wheels need to disagree.

The open diff's weakness

The same freedom is the flaw. Because the spiders roll between the side gears like an honest balance beam, an open differential always pushes both wheels with equal torque. Put one driven wheel on ice and that equality becomes a disaster: the icy wheel can only take a whisper of torque before spinning, so — split equally — the gripping wheel receives the same whisper. The car sits still, one wheel blurring, one doing nothing. Every stuck-in-the-snow scene with a single spinning tyre is an open diff faithfully splitting torque 50:50 with a surface that has none to give.

Limited slip & friends

A limited-slip differential keeps the open diff's cornering manners but adds a clutch pack or worm-gear stack that stiffens as the speed difference grows, dragging torque toward the slower — usually gripping — wheel. Racing cars tune this bias like a suspension setting. Modern performance cars go further with torque vectoring: electronically overdriving the outer wheel in a corner to help steer the car. And most EVs sidestep half the problem — with a motor per axle (or per wheel) there is no propshaft to share, and the "differential" becomes a line of software.

Go deeper: the diff in two equationsfor engineers

The carrier constrains only the average of the two output speeds:

ωleft+ωright=2 ωcarrier\omega_{left} + \omega_{right} = 2\,\omega_{carrier}

Straight ahead, both sides run at carrier speed. In the car-park corner above (8 m and 11 m arcs), the split becomes roughly 0.84 ωc0.84\,\omega_c and 1.16 ωc1.16\,\omega_c — a ±16% disagreement absorbed silently by the spiders. Torque, meanwhile, splits equally regardless of speed:

Tleft=Tright=12 TcarrierT_{left} = T_{right} = \tfrac{1}{2}\,T_{carrier}

so total tractive effort is capped at twice whatever the weaker tyre can transmit — the ice-scenario arithmetic. A limited-slip diff breaks the second equation on purpose, allowing a torque bias ratio of typically 1.5–3:1 toward the slower wheel at the cost of a little cornering freedom; fully locked, the axle reverts to the scrubbing kart.