Blade Time Constant

The expression for blade damping derived several paragraphs ago allows the blade time constant to be determined. The time constant is the time required by a system

to achieve 63% of its final amplitude following the application of a step forcing function. For the blade subjected to a step moment, Msn the non-oscillatory part of the displacement, is:

-c/2

where MJk is the final value of p when time is very large. If this is evaluated at the time at which

c/2

then

The time that makes this true is called the time constant of the system:

~ c/2

But from one of the previous equations:

The amount of azimuth required for the blade to achieve 63% of its response is thus:

For the example helicopter, this equation gives an azimuth constant of 130°. This relatively fast response, compared to the response of the entire helicopter, will later be used to justify a simplifying assumption when writing the helicopter equations of motion.