---
title: "V-belt compared with flat belt"
subject: "Machine Design I"
chapter: 8
key: "semester_6/machine_design_i:vbelt-versus-flat-belt"
source: https://www.bctengineer.com/q/semester_6/machine_design_i/vbelt-versus-flat-belt
site: BCT Engineering
---

# V-belt compared with flat belt

Machine Design I · Chapter 8: Design of belts

- Asked in: year not given, 5 marks
- Video: [Differences between Flat Belt Drive and V Belt Drive@MechanicalEngineering4u](https://www.youtube.com/watch?v=HFd119GOa-0) — Mechanical Engineering Study Material 
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/machine_design_i/vbelt-versus-flat-belt
- Whole chapter: https://www.bctengineer.com/md/semester_6/machine_design_i/chapter-8

## Question

Differentiate between flat belt drives and V-belt drives. Derive the ratio of tensions for a V-belt and explain why a V-belt can transmit more power.

## Short answer

Flat belt uses friction on a flat pulley; V-belt wedges in a groove, giving an effective friction coefficient μ/sinβ. The tension ratio is (T₁−Tc)/(T₂−Tc)=e^(μθ/sinβ). Because sinβ<1, the exponent is larger, allowing a higher T₁/T₂ and more power for the same tight-side tension.

## Answer

#### Differences

| Point | Flat belt | V-belt |
|---|---|---|
| Cross-section | Rectangular, thin, wide | Trapezoidal, wedges in a groove |
| Grip | By friction on the flat face | Wedging action in the groove gives a much higher normal force |
| Power per belt | Lower | Higher |
| Centre distance | Large (up to about 10 m) | Short (compact drives) |
| Speed ratio | Up to about 5 | Up to about 7 to 10 |
| Slip | More; the belt may slip and creep | Little slip |
| Belt joint | Joint needed (laced, cemented), causes noise | Endless belt, no joint |
| Multiple belts | Single belt | Several belts side by side |
| Speed and smoothness | Suits long drives and high speeds (up to about 50 m/s) | Quiet; absorbs shock |
| Cost | Cheaper belt and pulleys | More expensive |
| Pulley | Plain or crowned | Grooved sheaves |

#### Ratio of tensions in a V-belt

The belt sits in a groove whose included angle is $2\beta$ (usually 34 to 40 degrees). If $R$ is the total normal reaction from the two flanks, each flank carries a normal reaction $R_n$ with $R = 2R_n \sin\beta$. The friction on both flanks is $2\mu R_n = \dfrac{\mu R}{\sin\beta}$.

So the V-belt behaves like a flat belt with an **effective coefficient of friction** $\mu/\sin\beta$. Using the flat-belt derivation:

$$
\frac{T_1 - T_c}{T_2 - T_c} = e^{\mu\theta/\sin\beta}
$$

#### Why a V-belt transmits more power

For $\beta = 17^\circ$ to $20^\circ$, $\sin\beta \approx 0.3$, so the exponent is about three times larger. With $\mu = 0.3$ and $\theta = 160^\circ$ (2.79 rad), a flat belt gives $e^{0.84} = 2.3$, while a V-belt with $\beta = 20^\circ$ gives $e^{0.84/0.342} = e^{2.45} = 11.6$. A bigger ratio $T_1/T_2$ means a bigger difference in tension for the same tight-side tension, and thus more power. The belt need not be stretched so tightly, so the bearing loads are smaller.

## Check yourself

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

1. Why does a V-belt grip better than a flat belt?
   A. It is wider and thinner
   B. The wedging action in the groove gives a much higher normal force
   C. It is stretched much tighter
   D. It has a joint that locks into the pulley
   Answer: B. The wedge in the groove multiplies the normal reaction on the flanks, increasing friction for the same belt tension. (Key point: Grip mechanism)

2. What is the V-belt tension ratio with groove half-angle beta?
   A. (T1 - Tc)/(T2 - Tc) = e^(mu theta sin(beta))
   B. (T1 - Tc)/(T2 - Tc) = e^(mu theta / sin(beta))
   C. (T1 - Tc)/(T2 - Tc) = e^(mu theta cos(beta))
   D. T1/T2 = e^(mu theta) as for a flat belt
   Answer: B. Friction on both flanks is mu R / sin(beta), so the effective coefficient is mu / sin(beta) in the flat belt formula. (Key point: V-belt tension ratio)

3. For mu = 0.3, theta = 160 degrees and beta = 20 degrees, how does the tension ratio compare?
   A. Both are about 2.3
   B. V-belt about 11.6, flat belt about 2.3
   C. V-belt about 2.3, flat belt about 11.6
   D. V-belt about 4.6, flat belt about 2.3
   Answer: B. Exponent 0.84 gives 2.3 for the flat belt, while 0.84/0.342 = 2.45 gives 11.6 for the V-belt, so more power can be transmitted. (Key point: Power comparison)

## Related in Machine Design I

- [Open flat belt power and cross belt length](https://www.bctengineer.com/question.md?key=semester_6%2Fmachine_design_i%3Aopen-flat-belt-power-and-length) — Machine Design I, chapter 8
- [Tension ratio of a flat belt drive](https://www.bctengineer.com/question.md?key=semester_6%2Fmachine_design_i%3Abelt-tension-ratio-derivation) — Machine Design I, chapter 8

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