Calculating Governor Sensitiveness

A governor is a device used to control the speed of an engine. Its primary function is to maintain the engine speed within certain limits despite variations in load. Sensitiveness is a measure of how quickly and accurately a governor responds to changes in speed.

Understanding Governor Sensitiveness

The sensitiveness of a governor is defined as the ratio of the range of speed to the mean speed. A more sensitive governor will show a smaller change in speed for a given change in load.

The formula for sensitiveness is:

Sensitiveness \( = \frac{\text{Speed Range}}{\text{Mean Speed}} \)

Often, sensitiveness is expressed as a percentage:

Sensitiveness \( (\%) = \frac{N_2 - N_1}{\frac{N_1 + N_2}{2}} \times 100 \)

Where:

• \( N_1 \) = Minimum speed of the engine (at full load condition)
• \( N_2 \) = Maximum speed of the engine (at no load condition)

Applying the Formula to the Given Data

We are given the following values:

• Minimum speed at full load, \( N_1 = 245 \) rpm
• Maximum speed at no load, \( N_2 = 255 \) rpm

First, calculate the Speed Range:

Speed Range \( = N_2 - N_1 = 255 - 245 = 10 \) rpm

Next, calculate the Mean Speed:

Mean Speed \( = \frac{N_1 + N_2}{2} = \frac{245 + 255}{2} = \frac{500}{2} = 250 \) rpm

Now, calculate the Sensitiveness:

Sensitiveness \( = \frac{\text{Speed Range}}{\text{Mean Speed}} = \frac{10}{250} \)

To express this as a percentage, multiply by 100:

Sensitiveness \( (\%) = \frac{10}{250} \times 100 \)

Sensitiveness \( (\%) = \frac{1}{25} \times 100 \)

Sensitiveness \( (\%) = 4 \% \)

Therefore, the sensitiveness of the governor is 4%.

Conclusion

Using the given minimum and maximum engine speeds, the calculated sensitiveness of the governor is 4%.