---
title: "Resistance to vehicular motion"
subject: "Transportation Engineering I"
chapter: 3
key: "semester_6/transportation_engineering_i:resistance-vehicular-motion"
source: https://www.bctengineer.com/q/semester_6/transportation_engineering_i/resistance-vehicular-motion
site: BCT Engineering
---

# Resistance to vehicular motion

Transportation Engineering I · Chapter 3: Geometric Design of Highway

- Asked in: 2066 Magh (old course), 4 marks
- Video: [Vehicle Resistances & Power Required to Propel the Vehicle](https://www.youtube.com/watch?v=iM4SuU22KhI) — Machindra Gaikwad
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/transportation_engineering_i/resistance-vehicular-motion
- Whole chapter: https://www.bctengineer.com/md/semester_6/transportation_engineering_i/chapter-3

## Question

Write a short note on resistance to vehicular motion.

## Short answer

Tractive resistance includes air resistance (proportional to v²), rolling resistance (proportional to weight), gradient resistance (weight × grade), curve resistance on curves, and inertia resistance during acceleration. The total determines the required engine power and influences design of ruling gradients, grade compensation, and climbing lanes.

## Answer

A moving vehicle experiences several resistances that the engine must overcome. Their sum is the **tractive resistance**, and the driving force (tractive effort) must be at least equal to it.

#### Types of resistance
1. **Air (wind) resistance** $R_a$: from the drag of the air on the front, sides and rear of the vehicle. It is proportional to the square of the relative speed:
   $$
   R_a = \tfrac12\rho\,C_d\,A\,v^2
   $$
2. **Rolling resistance** $R_r$: caused by tyre deformation and road surface roughness; $R_r = f_r W$ with $f_r \approx 0.01$-$0.02$ for good paved surfaces, higher for gravel and earth.
3. **Gradient resistance** $R_g$: the component of weight along the slope, $R_g = W\sin\theta \approx W\,G$ ($G$ is the gradient).
4. **Curve resistance** $R_c$: extra resistance on horizontal curves from lateral slip and steering; allowed for in design by grade compensation.
5. **Inertia (acceleration) resistance** $R_i$: the force needed to accelerate the vehicle mass, $= \gamma\,\dfrac{W}{g}a$.
6. **Internal (transmission) resistance:** friction in the engine and the transmission; usually allowed for by an efficiency factor.

$$
R_{total} = R_a + R_r + R_g + R_c + R_i
$$

The total determines the engine power required, the speed on a grade and the gradients adopted in design.

## Check yourself

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

1. What must be true of the tractive effort for a vehicle to keep moving?
   A. It must be less than the total resistance
   B. It must be at least equal to the total tractive resistance
   C. It must be independent of resistance
   D. It must equal only the air resistance
   Answer: B. The driving force must at least match the sum of all resistances to move or hold speed. (Key point: Tractive resistance requirement)

2. How does air resistance vary with the relative speed of the vehicle?
   A. Proportional to speed
   B. Independent of speed
   C. Proportional to the square of speed
   D. Inversely proportional to speed
   Answer: C. R_a = 0.5 rho Cd A v^2, so it rises with v squared. (Key point: Air resistance dependence)

3. What is the gradient resistance of a vehicle of weight W on a slope G?
   A. Approximately W/G
   B. Approximately W x G
   C. Approximately W x G^2
   D. Equal to f x W
   Answer: B. It is the component of weight along the slope, W sin(theta), approximately W x G. (Key point: Gradient resistance)

4. What causes rolling resistance and how is it expressed?
   A. Air drag; R = 0.5 rho Cd A v^2
   B. Slope of the road; R = W G
   C. Tyre deformation and road roughness; R = f_r W
   D. Acceleration; R = gamma (W/g) a
   Answer: C. Rolling resistance comes from tyre deformation and surface roughness, R_r = f_r W, with f_r about 0.01-0.02 on good pavement. (Key point: Rolling resistance)

## Related in other subjects

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