Let's understand the sensitivity of a governor, specifically an isochronous governor.

A governor is a device used to control the speed of an engine or turbine by regulating the supply of fuel or working fluid. Its main function is to maintain the speed as constant as possible despite variations in load.

Governor Sensitivity Explained

The sensitivity of a governor is a measure of its ability to respond to small changes in speed. It indicates how quickly and accurately the governor can bring the engine speed back to the desired level after a load change.

Mathematically, sensitivity is often defined as the ratio of the mean speed to the speed fluctuation.

Speed fluctuation is the difference between the maximum and minimum speeds of the governor balls (or the engine speed) when the load changes from minimum to maximum. Let $\omega_1$ be the maximum speed and $\omega_2$ be the minimum speed. The speed fluctuation is $\omega_1 - \omega_2$.

The mean speed is $(\omega_1 + \omega_2) / 2$.

The coefficient of speed fluctuation is given by: $$ C_s = \frac{\omega_1 - \omega_2}{\omega_{\text{mean}}} $$ where $\omega_{\text{mean}}$ is the mean speed.

Sensitivity is often related to the reciprocal of the coefficient of speed fluctuation, or more generally, to how small the speed change is for a given movement of the sleeve or change in controlling force.

A more sensitive governor will react to smaller changes in speed.

Isochronous Governor and Speed Variation

An isochronous governor is a type of governor that is designed to maintain a constant speed for all loads within its working range. In an ideal isochronous governor, the speed of the engine does not change at all when the load varies. This means the maximum speed ($\omega_1$) and the minimum speed ($\omega_2$) are equal.

If $\omega_1 = \omega_2$ for an isochronous governor, then the speed fluctuation is: $$ \omega_1 - \omega_2 = 0 $$

Sensitivity of Isochronous Governor

Using the relationship between sensitivity and speed fluctuation, a governor with zero speed fluctuation ($\omega_1 - \omega_2 = 0$) is considered to have infinite sensitivity.

If we consider sensitivity related to the coefficient of speed fluctuation $C_s$, a smaller $C_s$ means higher sensitivity. For an isochronous governor, $C_s = 0$ (since the numerator is zero). If sensitivity is proportional to $1/C_s$, then sensitivity approaches infinity as $C_s$ approaches zero.

A sensitivity of infinity implies that the governor is infinitely responsive to even the slightest change in speed, theoretically requiring no speed change to cause a control action. In practice, true isochronism is difficult to achieve perfectly due to friction and other factors, but an isochronous governor is designed to be highly sensitive with minimal speed droop.

Therefore, the sensitivity of an isochronous governor is considered to be infinity.