---
title: "Tractive resistance explained"
subject: "Transportation Engineering I"
chapter: 3
key: "semester_6/transportation_engineering_i:tractive-resistance"
source: https://www.bctengineer.com/q/semester_6/transportation_engineering_i/tractive-resistance
site: BCT Engineering
---

# Tractive resistance explained

Transportation Engineering I · Chapter 3: Geometric Design of Highway

- Asked in: 2065 Chaitra (old course), 2+6 marks
- Video: [Tractive Resistances](https://www.youtube.com/watch?v=iSYVtejG-4E) — alinda dey
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/transportation_engineering_i/tractive-resistance
- Whole chapter: https://www.bctengineer.com/md/semester_6/transportation_engineering_i/chapter-3

## Question

What do you mean by tractive resistance? Explain it in brief.

## Short answer

Tractive resistance is the sum of air, rolling, gradient, curve, and inertia forces opposing vehicle motion. The tractive effort must overcome it, limited by adhesion (μ × weight on driving wheels), and it governs engine power requirements, maximum gradients, grade compensation on curves, and climbing lane length.

## Answer

**Tractive resistance** is the total resistance that opposes the motion of a vehicle on the road. The tractive effort (the force at the driving wheels) must be at least equal to it for the vehicle to move or maintain its speed.

#### Components
1. **Air resistance:** $R_a = \tfrac12\rho C_d A v^2$, rises with the square of speed; dominant at high speed.
2. **Rolling resistance:** $R_r = f_r W$ due to tyre deformation, road surface, and bearing friction; $f_r$ depends on the surface (0.01-0.02 on good paved road, 0.04-0.1 on gravel/earth) and the tyre pressure.
3. **Gradient resistance:** $R_g = W\sin\theta \approx WG$; positive on upgrades and negative (helps) on downgrades.
4. **Curve resistance:** the extra resistance on a horizontal curve due to lateral slip and off-tracking; large on sharp curves; compensated for in gradient by grade compensation.
5. **Inertia (acceleration) resistance:** $R_i = \gamma\dfrac{W}{g}a$, which is the force required to accelerate the vehicle and its rotating parts.
6. **Transmission losses** in the engine, gear box and axle (about 10-20% of the engine power).

$$
T_{required} = R_a + R_r + R_g + R_c + R_i
$$

#### Limit by adhesion
The tractive effort delivered can not be more than the friction between the driving tyres and the road: $T \le \mu\,W_d$ ($W_d$ = weight on driving wheels). Otherwise the wheels spin.

#### Uses in highway design
Tractive resistance fixes the engine power needed, the maximum gradient (ruling gradient), the grade compensation on curves, the length of the climbing lane and the speed of heavy vehicles on grades.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is tractive resistance?
   A. The friction between driving tyres and road only
   B. The total resistance opposing vehicle motion, which the tractive effort must at least equal
   C. The engine power lost in the gearbox only
   D. The force that accelerates the vehicle
   Answer: B. It is the sum of all resistances to motion; tractive effort at the driving wheels must at least equal it. (Key point: Definition of tractive resistance)

2. Which set lists the components of tractive resistance?
   A. Air, rolling, gradient, curve and inertia resistance (plus transmission losses)
   B. Air, braking, lateral friction and skid resistance
   C. Rolling, centrifugal force and superelevation
   D. Gradient, camber and sight distance
   Answer: A. T_required = Ra + Rr + Rg + Rc + Ri, with transmission losses allowed separately. (Key point: Components of tractive resistance)

3. What limits the tractive effort that can be delivered to the road?
   A. T <= mu x W_d, the friction on the driving wheels; otherwise the wheels spin
   B. T <= W x G
   C. T <= 0.5 rho Cd A v^2
   D. T is not limited
   Answer: A. Tractive effort cannot exceed friction between the driving tyres and road, where W_d is the weight on driving wheels. (Key point: Adhesion limit)

4. How does gradient resistance behave on a downgrade?
   A. It is positive and doubles
   B. It is zero
   C. It is negative, i.e. it helps the motion
   D. It equals rolling resistance
   Answer: C. On downgrades the weight component acts along the motion, so gradient resistance is negative. (Key point: Gradient resistance sign)

5. Which highway design item is fixed using tractive resistance?
   A. Width of shoulders
   B. Radius of sight triangles
   C. Maximum (ruling) gradient and grade compensation on curves
   D. Camber of the pavement
   Answer: C. Tractive resistance fixes the engine power needed, the ruling gradient, grade compensation, climbing lane length and heavy vehicle speed on grades. (Key point: Use in highway design)

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