Short-period oscillations in different flight conditions

[MattH150197]

Homework Statement

In a lab experiment we ran the simulation of 3 different flight conditions into a program that produced graphs of the oscillations in them conditions and we have to do a comparison of the SPO (short period oscillations) characteristics for the 3 flight conditions which are the following with FlightCondition 1 being the first value ,FC2 the 2nd and of course FC3 the 3rd:
: velocity = 177, 177, 177 Pitch Inertia = 7.6x 10^5, 7.6x10^5, 7.6x10^5 Change in pitching moment due to change in pitch rate = -4.2x10^5, 0, 5x10^5 Change in pitching moment due to change in normal speed = -9.11x10^4, -9.11x10^4, -9.11x10^4 then the last is the velocity * change in pitching moment due to a change in rate of change of normal speed = -3.12x10^5, 0, 3.7x10^5.

The graph produced for FC1 was a damped/stable oscillation, FC2 was undamped/ critically stable and FC3 was unstable /divergent oscillation. But I am struggling to get my head around why change in pitching moment due to change in pitch rate and velocity * change in pitching moment due to a change in rate of change of normal speed (these two in particular because the rest were the same for each condition) had the effect they did on the SPO? Thanks hope what I am asking makes sense.

 

[FactChecker]

Looking at "change in pitching moment due to change in pitch rate" = -4.2x10^5, 0, 5x10^5. The negative sign of the first one means that the pitching moment will decrease as the pitch rate increases. So that will feed back and decrease the pitch rate. It may damp out any disturbance and be stable if the feedback is not too great. The positive sign of the third one means that the pitching moment will increase as the pitch rate increases. If that was the only feedback factor, the plane would pitch up (or down) exponentially at the slightest disturbance and immediately lose control.
The other factors need to be examined the same way and some may interact. The third case must have interacting factors to get an oscillation.

 

[MattH150197]

Thanks!

 

[FactChecker]

Thanks!

I'm afraid that I missed a point that might be important to you. Since the "change in pitching moment due to change in pitch rate" is all in terms of changes, this is a relationship between the derivative of pitching moment and pitch rate. Suppose there is a constant nose up pitch rate. Then the pitching moment will not change so this relationship will not necessarily act to stabilize the plane. Things like that need to be considered in the other relationships also.

 

[MattH150197]

Okay that makes sense but how do I go about analysing how they affect the stability if I don't know how the unknown constant affects the relationship

 

[FactChecker]

Okay that makes sense but how do I go about analysing how they affect the stability if I don't know how the unknown constant affects the relationship

A constant nose-up pitch rate is just one hypothetical situation. If a plane starts to pitch up, it's angle of attack, lift, and normal velocity increases. So look at "Change in pitching moment due to change in normal speed = -9.11x10^4, -9.11x10^4, -9.11x10^4". The first number is negative so there will be a decrease in pitching moment. This is true even if the pitch rate is constant. That would make the pitching moment negative and bring the nose back down to normal.

 

[MattH150197]

Thanks for taking the time to explain