Understanding Governor Sensitiveness

The sensitiveness of a governor is a crucial concept in understanding how effectively it responds to changes in engine speed. It essentially measures how much the speed must change to cause the sleeve (or the ball mass) to move from its lowest to its highest position.

Defining Governor Equilibrium Speeds

To calculate the sensitiveness, we need to understand the different equilibrium speeds:

• Minimum Equilibrium Speed ($N_1$): This is the lowest speed at which the governor can operate stably. Below this speed, the governor mechanism tends to move towards its lowest position.
• Maximum Equilibrium Speed ($N_2$): This is the highest speed at which the governor can operate stably. Above this speed, the governor mechanism tends to move towards its highest position.
• Mean Equilibrium Speed ($N$): This is the average of the minimum and maximum equilibrium speeds. It can be calculated as $N = (N_1 + N_2) / 2$.

Calculating Governor Sensitiveness

The sensitiveness (also sometimes called the 'effort' or 'definition') of a governor is defined as the ratio of the change in the mean equilibrium speed to the change in speed required to raise the sleeve from the lowest position to the highest position.

Mathematically, the formula is derived from the difference between the maximum and minimum equilibrium speeds ($N_2 - N_1$) divided by the mean equilibrium speed ($N$):

Sensitiveness = $\frac{N_2 - N_1}{N}$

Comparing this formula with the given options:

• Option 1: $\frac{N_2 - N_1}{N_2 + N_1}$ is incorrect.
• Option 2: $\frac{N_2 - N_1}{N}$ is the correct formula for governor sensitiveness.
• Option 3: $\frac{N_2 + N_1}{N}$ is incorrect.
• Option 4: $\frac{N_2 + N_1}{N_2 - N_1}$ is incorrect.

Conclusion

Therefore, the sensitiveness of the governor is correctly represented by the expression $\frac{N_2 - N_1}{N}$. A lower value indicates a more sensitive governor, meaning it reacts quickly to speed variations.