Transmission

Transmissions match engine or motor speed to wheel speed. Learn gear ratios and final drive, tractive force, road speed per gear, manual, automatic, DCT and CVT designs, differentials and gradeability.

An engine makes useful torque only over a limited speed range, while a car must crawl up hills and cruise at 130 km/h. The transmission provides several ratios so the engine stays in its useful range.

The final drive and differential then deliver torque to the wheels while letting them turn at different speeds in corners.

An analogy

A bicycle's gears: low gear to climb (lots of force, slow), high gear to cruise (less force, fast). Your legs are the engine with a limited comfortable cadence.

Why gears

First gear multiplies torque for starting and climbing; top gear lowers engine rpm at cruise for efficiency and quietness. Overall ratio = gear ratio × final drive.

Transmission types

Manual (driver shifts, synchronisers), torque-converter automatic (planetary sets, 6–10 speeds), dual-clutch (DCT — two clutches pre-select gears for fast shifts), CVT (belt/chain on variable pulleys — engine held at efficient speed), AMT (automated manual), and single-speed reducers in most EVs.

Differentials and drivelines

In a turn the outer wheel travels farther; the differential lets it spin faster while splitting torque. Limited-slip and locking differentials and torque-vectoring units improve traction. AWD systems use centre differentials or clutches.

Ratio selection and shift strategy

Lowest gear is set by gradeability/launch; top gear by top speed or economy (overdrive). Intermediate ratios roughly follow a geometric progression, tightened in upper gears. Shift maps in automatic/DCT controllers balance economy, performance and drivability using engine BSFC maps.

Formulas

• Tractive force: F_t = T_e · i_g · i_f · η_d / r
• Road speed: v = 2π r N / (60 · i_g · i_f)
• Gradeability (traction permitting): sin θ = (F_t − F_roll) / (m g)
• Geometric gear spacing: i_k/i_{k+1} ≈ constant

Worked example: Tractive force in first gear

Given: T_e = 191 N·m; i_g = 3.5, i_f = 4.0, η = 0.9, r = 0.3 m

Find: Force at the wheels and acceleration potential (1500 kg).

• F_t = 191 × 3.5 × 4.0 × 0.9/0.3 = 8022 N
• a ≈ 8022/1500 = 5.3 m/s² (traction-limited in practice)

Answer: ≈ 8.0 kN

Worked example: Top-gear speed

Given: i_g = 0.8, i_f = 4.0, r = 0.3 m; 5000 rpm

Find: Road speed.

• v = 2π × 0.3 × 5000/(60 × 3.2) = 49.1 m/s
• = 177 km/h

Answer: ≈ 177 km/h

Common mistakes

• Wrong: Forgetting the final drive ratio. — Right: Overall ratio = i_g × i_f.
• Wrong: Assuming tractive force can always be used. — Right: Tyre grip (μ × axle load) limits usable force, especially in first gear.

Applications

• Passenger cars: 8–10-speed automatics, DCTs and CVTs for efficiency and smoothness.
• Trucks: 12–16-speed AMTs to keep large diesels at peak efficiency.
• EVs: Single- or two-speed reducers (~8–10:1) thanks to motors' wide speed range.

Key takeaways

• F_t = T i_g i_f η / r; v = 2πrN/(60 i_g i_f).
• First gear for grade/launch, top gear for speed/economy.
• Many types: MT, AT, DCT, CVT, single-speed EV.
• Traction limits usable force.

Going further

• Planetary automatics: Clutch-to-clutch shifts among Ravigneaux/Lepelletier planetary sets create 8–10 ratios.
• CVT efficiency: Belt clamping losses offset the benefit of optimal engine speed; e-CVTs in hybrids use planetary power split instead.
• Torque vectoring: Active differentials send torque to the outer wheel to improve turn-in and stability.