Stability Derivatives not working?

[doug.hunsaker]

Question from user:

I have seen a new result that has me puzzled. The attached .mu file is for the F-5 TigerII.

When running the stability derivatives at zero alpha and zero beta, we’re getting dihedral effect about 5 times the magnitude of the yaw stiffness.

Cl,beta= -0.4683, Cn, beta= 0.0826

If I set the sideslip to 1 degree, and solve for the moments, I get Cn= 0-.0029, and Cl= 0.0001

So, 1 deg of sideslip creates more yaw moment than roll moment, but the yaw stiffens is one fifth the dihedral effect.

What’s the approach MachUp uses to estimate the static and dynamic derivatives?

[doug.hunsaker]

I dug into the code and couldn’t find any issues. MachUp uses a delta_alpha and delta_beta of 0.5 for the stability derivative calculations. So I backed up and made some plots. I think they tell the story.

The first figure shows Cl and Cn as a function of beta in steps of beta=0.1 degrees from 0.1 to 2.0. This is all with the current airframe. It originally was using 40 nodes per semispan. I reran the numbers using 80 nodes per semispan as well. You can see that at beta = 0.5, Cl and Cn are much different than at beta = 1.0. In fact, Cl and Cn are strong functions of beta. Note the oscillations in Cl. These oscillations double in frequency when you double the nodes. I assumed these were caused by vortex interference from the main wing on the horizontal stabilizer. I see this sometimes when those two surfaces are closely vertically aligned.

The second figure shows the exact same airframe using 80 nodes per semispan, but with the main wing shifted to z=0. This offsets it vertically from the horizontal. You can see from the second figure that Cn,beta and Cl,beta are fairly constant.

In short, make sure your main wing and horizontal are offset slightly to minimize vortex interference from one on the other.

[doug.hunsaker]

Response from user: 

That’s really interesting that the results are so sensitive to beta increments, or to vertical alignment of the tail and wing. The actual TigerII does have the tail set very slightly below the wing.  I’ll know to look for this in the future.