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Effect of change in speed stability
In a similar manner the effect of a change in the speed stability can be demonstrated by a change to the value of the pitching moment due to speed (Mu). In order to isolate this effect it is necessary to eliminate the influence that the pitching moment due to vertical speed (Mw) may have on the ensuing long-term dynamics. This is achieved by setting Mw to zero. Consider the following three cases:
(1) Standard speed stability (Mw = 0)
£ = — 0.0769, mn = 0.324 rad/s, T1 = 1.06 s, T2 = 0.38 s
(2) Half standard speed stability
|
" — 0.0460 |
0.0385 |
2.7192 |
— 9.8052 |
|
|
A120 = |
0.0221 |
— 0.9008 |
61.5403 |
0.3205 |
|
0.0150 |
0 |
— 2.6060 |
0 |
|
|
0 |
0 |
0.9989 |
0 |
£ = — 0.0115, mn = 0.233 rad/s, T1 = 1.08 s, T2 = 0.37 s
(3) Twice standard speed stability
|
" — 0.0460 |
0.0385 |
2.7192 |
— 9.8052 |
|
|
A120 = |
0.0221 |
— 0.9008 |
61.5403 |
0.3205 |
|
0.0600 |
0 |
— 2.6060 |
0 |
|
|
0 |
0 |
0.9989 |
0 |
£ = — 0.1440, mn = 0.449 rad/s, T1 = 1.04 s, T2 = 0.37 s
The effect of Mu can now be seen clearly. Only the long-term mode is affected significantly and it is evident that stronger speed stability causes a more divergent, and higher frequency, long-term response. The moment arising from flying at an off-trim speed is greater if the speed stability is stronger. This larger moment causes the helicopter to return towards trim more aggressively thereby producing a more divergent response.
