Tractive Effort & Road Load

The balance that decides top speed and acceleration: the force the powertrain pushes forward versus the forces the world pushes back.

Automotive EngineeringLongitudinal DynamicsFree preview

⏱️ About 14 min

Tractive Effort & Road Load — illustration

Decorative illustration.

A car accelerates only while the force at its driven wheels exceeds the forces trying to slow it down. The moment they balance, it stops speeding up — and that balance point is its top speed.

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The big idea: Longitudinal motion is a force balance: tractive effort at the contact patches must overcome the road load (rolling resistance + aerodynamic drag + grade resistance) plus the inertia needed to accelerate.

🎯 By the end, you'll be able to

Name the three road-load components and the inertia term
Write the longitudinal force-balance equation
Interpret a tractive-force-versus-speed diagram and locate top speed
Explain why available tractive force falls with speed in most gears

📎 Helpful to know first

Mass Breakdown & Weight Distribution

Forward force versus resisting forces

Push a car and four things resist you. Rolling resistance is the drag of the tyres deforming against the road — roughly constant with speed. Aerodynamic drag is the resistance of pushing air out of the way — it grows with the square of speed (the full quantitative treatment lives in Module 11). Grade resistance appears on a hill: climbing adds a component of the car's weight pulling it back down the slope. And to accelerate rather than merely cruise, the powertrain must also supply the inertia force m·a. The tractive effort at the driven wheels is what the powertrain delivers; longitudinal motion is simply whether that tractive effort beats the sum of the resistances.

\[ F_{\text{tractive}} = F_{\text{rolling}} + F_{\text{aero}} + F_{\text{grade}} + m\,a \]

The longitudinal force balance. Excess tractive effort over road load becomes acceleration (m·a); when the balance is zero, the car is at constant speed — and at top speed, the maximum available tractive effort exactly equals road load.

Tractive-force diagram: available tractive force (red, gear-dependent, falling with speed) versus road load (blue, rising with speed). Top speed is where the two curves meet; the gap between them at any speed is the force available for acceleration.

✨ Why tractive effort falls with speed

At low speed a car in first gear can shove the road hard — that's why it launches briskly — but as speed rises two effects erode available tractive force. First, each higher gear trades torque for speed (the gearbox multiplies engine torque less), so wheel force drops at every upshift. Second, engine power is roughly torque × speed, and beyond peak power the engine's torque curve falls. Meanwhile road load keeps climbing. The crossover — where available force just equals road load — is top speed; beyond it, there is no force left to push harder.

📝 Worked example: At a given speed a car's road load totals 480 N (rolling + aero, on the flat). The powertrain can deliver 920 N of tractive effort at the driven wheels. If the car has a mass of 1400 kg, what is its acceleration? (Neglect rotating-mass effects.)

Excess force = tractive effort − road load = 920 − 480 = 440 N
a = excess force / m = 440 / 1400 = 0.314 m/s²

✓ 0.314 m/s²

✏️ Practice: A 1300 kg car is at top speed, so its available tractive effort exactly equals road load. If the road load is 720 N, what is the acceleration?

m/s^2

Solution

At top speed the force balance is zero: F_tractive − F_roadload = m·a = 0
So a = 0 m/s² (constant top speed, by definition of the balance point).

🎮 Road-Load & Acceleration Explorer LIVE

Predict first: Predict first: with mass 1400 kg, rolling coefficient 0.012, Cd·A = 0.78 m², and available tractive effort 900 N, what is the acceleration at 20 m/s on the flat?

Set mass, rolling resistance, drag (Cd·A), and available tractive effort, then sweep speed. The bar split shows rolling, aero, and inertia; acceleration is the leftover force divided by mass. Drag uses the Module 11 formula ½·rho·Cd·A·v².

Check your understanding

1. Top speed occurs when:

At top speed the maximum available tractive effort just balances road load, so m·a = 0 and speed holds constant.

2. As a car shifts up through the gears at a fixed speed, available tractive effort at the wheels generally:

Higher gears trade torque for speed — less torque multiplication — so wheel force drops at each upshift, which is part of why acceleration softens as speed builds.

✅ Key takeaways

Longitudinal motion is a force balance: tractive effort = rolling + aero + grade + m·a
Road load rises with speed (aero dominates at high speed); available tractive effort falls with speed (gears, power curve)
Top speed is where available tractive effort equals road load — zero excess force, zero acceleration
Drag's quantitative form (½·rho·Cd·A·v²) is developed in Module 11

➡️ The balance is set. Now let's open the two road-load terms that don't depend on aero — rolling resistance and grade — and quantify them.

Want to test yourself on this? Try the Automotive Engineering Aptitude test →