Determining the sign of control derivatives

[eqm]

I'm having quite a deal of trouble trying to figure this out. Say, for example, you wanted to have a statically stable aircraft. How do you determine what the signs (positive or negative) of the control derivates need to be for this condition to be satisfied ( C_Xα, C_Zα, C_mα, C_mq, C_Zδe, etc) ?

 

[Stella.Physics]

what do these signs stand for?

 

[NatSusan]

Hey there! I can understand your struggle with trying to figure out the signs of control derivatives for a statically stable aircraft. It can definitely be a bit confusing and overwhelming.

First of all, let's define what we mean by a statically stable aircraft. This refers to an aircraft that will naturally return to its original position after being disturbed. In other words, it will maintain its desired attitude without any additional control inputs.

To determine the signs of the control derivatives, we need to look at the overall stability of the aircraft. For a statically stable aircraft, we want the pitching moment (Cm) and the pitching moment coefficient (Cmα) to be negative. This means that when the aircraft is disturbed and its nose pitches up, the pitching moment will push it back down to its original position.

As for the other control derivatives, it will depend on the specific design of the aircraft and its control surfaces. For example, the lift coefficient (CX) and lift derivative (CXα) should also be negative to maintain pitch stability. However, the vertical force coefficient (CZ) and its derivative (CZα) can be either positive or negative, as long as they are not too large in either direction.

The control derivative Cmq, which represents the moment due to the pitching rate, should also be negative for a statically stable aircraft. This means that when the aircraft is rotating in pitch, the moment will oppose the rotation and bring the aircraft back to its original attitude.

Finally, the control derivative CZδe, which represents the effect of the elevator on the vertical force, should also be negative. This ensures that when the elevator is deflected, it will produce a downward force and help maintain pitch stability.

In summary, for a statically stable aircraft, the control derivatives Cm, CX, CZ, Cmq, and CZδe should all have negative signs. However, it's important to keep in mind that the specific values of these derivatives will depend on the design and configuration of the aircraft.

I hope this helps clarify things for you. Let me know if you have any other questions or if you need further explanation.