---
title: "Porter governor speed range and lift"
subject: "Theory of Mechanism and Machine II"
chapter: 4
key: "semester_7/theory_of_mechanism_and_machine_ii:porter-governor-speed-range"
source: https://www.bctengineer.com/q/semester_7/theory_of_mechanism_and_machine_ii/porter-governor-speed-range
site: BCT Engineering
---

# Porter governor speed range and lift

Theory of Mechanism and Machine II · Chapter 4: Governors

- Asked in: year not given, 8 marks
- Video: [Problem - 1 Porter Governor | Numerical Problem | Step by Step Solution @pragyaniketan92](https://www.youtube.com/watch?v=NC1Z-zEVSME) — Pragya Niketan
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/theory_of_mechanism_and_machine_ii/porter-governor-speed-range
- Whole chapter: https://www.bctengineer.com/md/semester_7/theory_of_mechanism_and_machine_ii/chapter-4

## Question

A Porter governor has equal arms each 300 mm long, pivoted on the axis of rotation. Each ball has a mass of 5 kg and the central sleeve load has a mass of 25 kg. The radius of rotation of the balls is 150 mm when the governor is at its lowest position and 200 mm at the highest position. Neglecting friction, find the range of speed and the lift of the sleeve. Also find the sensitiveness of the governor.

## Short answer

The minimum speed (r=150 mm) is 143.7 rpm, maximum (r=200 mm) is 154.9 rpm, so the range is 11.2 rpm. Sleeve lift is 2(√(0.3²-0.15²)-√(0.3²-0.2²))=72.4 mm. Sensitiveness=(154.9-143.7)/((143.7+154.9)/2)=0.0750.

## Answer

**Data:** $l = 0.3$ m (arms and links equal, hung from the axis), $m = 5$ kg, $M = 25$ kg, $r_1 = 0.15$ m, $r_2 = 0.2$ m.

#### Equilibrium relation
For a Porter governor with arms and links of equal length meeting the axis ($\alpha = \beta$, so $q = \tan\beta/\tan\alpha = 1$):

$$
\omega^2 = \frac{(m+M)\,g}{m\,h}, \qquad h = \sqrt{l^2 - r^2}
$$

```text
         O (pivot on axis)
        /|\
       / | \   arms l
      /  |h \
     B   |   B   balls m at radius r
      \  |  /   links l
       \ | /
        [M]  sleeve load
```

#### Lowest position ($r_1 = 0.15$ m)
$$
h_1 = \sqrt{0.3^2 - 0.15^2} = 0.2598\ \text{m}
$$

$$
\omega_1^2 = \frac{(5+25)\times 9.81}{5 \times 0.2598} = 226.55 \Rightarrow \omega_1 = 15.05\ \text{rad/s},\quad N_1 = 143.7\ \text{rpm}
$$

#### Highest position ($r_2 = 0.2$ m)
$$
h_2 = \sqrt{0.3^2 - 0.2^2} = 0.2236\ \text{m}
$$

$$
\omega_2^2 = \frac{30 \times 9.81}{5 \times 0.2236} = 263.23 \Rightarrow \omega_2 = 16.22\ \text{rad/s},\quad N_2 = 154.9\ \text{rpm}
$$

#### Range, lift and sensitiveness
$$
\text{Range} = N_2 - N_1 = 154.9 - 143.7 = 11.2\ \text{rpm}
$$

$$
\text{Lift of sleeve} = 2(h_1 - h_2) = 2(0.2598 - 0.2236) = 0.0724\ \text{m} = 72.4\ \text{mm}
$$

$$
\text{Sensitiveness} = \frac{N_2 - N_1}{N_{mean}} = \frac{11.2}{149.3} = 0.0750
$$

**Answer:** Speed range $= 143.7$ to $154.9$ rpm (11.2 rpm); sleeve lift $= 72.4$ mm; sensitiveness $= 0.0750$.

## Check yourself

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

1. For this Porter governor (equal arms and links on the axis), the equilibrium speed relation is:
   A. w^2 = (m+M) g / (m h)
   B. w^2 = m g / ((m+M) h)
   C. w^2 = (m+M) h / (m g)
   D. w^2 = M g / (m r)
   Answer: A. With q = 1, w^2 = (m+M) g / (m h) where h = sqrt(l^2 - r^2). (Key point: Governor equation)

2. How is the height h of the governor found at each position?
   A. h = sqrt(l^2 - r^2)
   B. h = l - r
   C. h = l + r
   D. h = r tan(l)
   Answer: A. Arm length l is the hypotenuse, with ball radius r and height h as sides: h1 = 0.2598 m, h2 = 0.2236 m. (Key point: Height h)

3. The sleeve lift for equal arms and links is:
   A. h1 - h2
   B. 2(h1 - h2)
   C. (h1 - h2)/2
   D. r2 - r1
   Answer: B. Sleeve is attached by links of the same length, so it moves twice the change in h: 2 x 0.0362 = 72.4 mm. (Key point: Sleeve lift)

4. Speeds are 143.7 and 154.9 rpm. Sensitiveness is closest to:
   A. 0.075
   B. 0.75
   C. 0.011
   D. 0.15
   Answer: A. Range 11.2 rpm divided by mean speed 149.3 rpm gives about 0.075. (Key point: Range and sensitiveness)

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