Watt Governor Calculator: N = (30 / pi) sqrt(g / h)

The speed at which a simple Watt governor holds its balls at a given height.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose which quantity you want to find.

Enter the other values in the units shown.

The calculator gives the answer with the formula, the substituted numbers, and the answer in other units.

Formulas used

  • N = \frac{30}{\pi}\sqrt{\frac{g}{h}}
  • h = \frac{900\,g}{\pi^2N^2}

Worked example

With the default numbers in the calculator above:

  1. The formula, arranged to find the speed of the governor: speed of the governor = ((30 / pi) x sqrt(g)) / (height of the balls below the pivot^0.5)
  2. Put the values in (every value in its SI unit): speed of the governor = ((30 / pi) x sqrt(g)) / (0.1^0.5)
  3. The answer: speed of the governor: 94.5653 rpm
  4. The same answer in other units: 9.90285 rad/s

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: What do you want to find? Height of the balls below the pivot; Speed of the governor (leave it as it is if this is what you are finding) 94.5653 rpm; Height of the balls below the pivot (leave it as it is if this is what you are finding) 1 m.

  1. The formula, arranged to find the height of the balls below the pivot: height of the balls below the pivot = (((30 / pi) x sqrt(g)) / (speed of the governor))^2
  2. Put the values in (every value in its SI unit): height of the balls below the pivot = (((30 / pi) x sqrt(g)) / (94.5653))^2
  3. The answer: height of the balls below the pivot: 0.1 m
  4. The same answer in other units: 100 mm

Common questions

How does a Watt governor work?

The balls swing out as the spindle speeds up. Their height changes and moves a linkage that reduces the supply of steam or fuel.

Does the mass of the balls matter?

Not for the height. The height depends only on the speed.

Why does a lower speed give a greater height?

The height is inversely proportional to the square of the speed, so slow speeds give a long, low hang.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any theory of machines text (governors).

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