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Automotive Engineering DISCUSSION
Car discussions keep repeating that torque gives acceleration and power gives top speed, but I cannot make that agree with the physics. Take an engine making 200 N·m at 4000 rpm, a first gear of 3.5, a final drive of 4.0, a tyre radius of 0.30 m and a 1200 kg car.
How do I calculate the force at the wheels and the acceleration, and is it engine torque or engine power that I should look at when comparing two cars?
Follow the torque through the drivetrain. Wheel torque = engine torque × gear ratio × final drive × efficiency = 200 × 3.5 × 4.0 × 0.9 = 2520 N·m, taking 90 percent driveline efficiency. Force at the tyre contact = 2520 / 0.30 = 8400 N. Acceleration = F / m = 8400 / 1200 = 7.0 m/s², before subtracting drag and rolling resistance, which are small at this speed.
The road speed at that point: wheel speed is 4000 / 14 = 286 rpm, which is 29.9 rad/s, and times 0.30 m that gives 9.0 m/s, about 32 km/h.
Now do the same sum with power. P = torque × angular speed = 200 × 4000 / 9549 = 83.8 kW. At the wheels, 90 percent of that is 75.4 kW. Force = power / speed = 75,400 / 8.98 = 8400 N. Same answer, as it must be, because the gearbox trades torque for speed but cannot create power.
This is the useful form: at any given road speed, the force available at the wheels is wheel power divided by speed. Engine torque alone tells you nothing until you know the gearing; engine power at that moment tells you everything.
So the saying is half right. Acceleration at a given road speed is set by the power the engine is making at that instant, and the best gear for acceleration is the one that puts the engine closest to its power peak. Shifting at the torque peak is a mistake; you shift when the next gear would give more wheel force than the current one, which is normally near the rev limit.
What a high torque figure at low rpm really tells you is that the engine makes good power low in its rev range, so the car pulls without needing a downshift. That is a statement about the shape of the power curve, and it matters more for driveability than for a standing-start time.
The calculated 8400 N is only available if the tyres can transmit it. Maximum traction is friction coefficient × load on the driven wheels. With 60 percent of the 1200 kg on the driven axle and a coefficient of 1.0, that is 0.6 × 1200 × 9.81 = 7060 N, less than the engine can deliver in first gear, so the wheels spin. Under acceleration, load also transfers rearward, which helps rear-wheel drive and hurts front-wheel drive.
This is why launch performance is traction-limited and depends on driven wheels and tyres, while acceleration at higher speeds is power-limited.
For top speed the power statement is direct. Top speed is where wheel power equals the power absorbed by drag and rolling resistance. Aerodynamic drag power goes with the cube of speed, so doubling the power raises top speed by only about 26 percent, the cube root of 2, if drag dominates.
The gearing still has to let the engine reach its power peak at that road speed; a car geared too tall or too short in top gear will not reach the speed its power could sustain.
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