Modeling questions - VLM Stability analyisis for a flight simulator

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Luca Bottà

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Nov 4, 2022, 5:55:24 AM11/4/22
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Hello everyone,
first of all I would like to thank you again for your help with my previous thread.

I'll start a new one to kindly ask you some clarifications about new questions I wasn't able to answer by online search. I'll make a list, hoping that some answers will be shorter for you to write:

- Why are both U and M derivatives present in the .stab file? What is the reference model behind those?

- Are tip treatments neglected in VLM analysis? If so, should I model them by simply adding wing tip sections (even guessing their impact to be small)?

- I have "complex" shapes for my tail control surfaces (attachment). Is it acceptable to make analyses with simplified cntrl surf geoms (with equal area)? I think it would be possible to find derivatives wrt "exact" geometries manually, by using hinges, but would it be worth it?

- In view of a flight sim implementation, is it worth it to give input conditions for stab analyses as balanced and close to a trim condition as possible?

-Does the "increase tessellation clustering behind propeller tips" advice also work for actuator disks?

Thank you very much for your help, it's very much appreciated!

Have a nice day,
Luca

P.S.
I'll attach my model, it would be great if you could tell me if it looks ok for you or there is something important to be improved! Thank you!





HT.png
half_wing.png
Switchmaster_complete.vsp3
VT.png

Rob McDonald

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Nov 4, 2022, 1:39:12 PM11/4/22
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On Fri, Nov 4, 2022 at 2:55 AM Luca Bottà <luca1...@gmail.com> wrote:
Hello everyone,
first of all I would like to thank you again for your help with my previous thread.

I'll start a new one to kindly ask you some clarifications about new questions I wasn't able to answer by online search. I'll make a list, hoping that some answers will be shorter for you to write:

- Why are both U and M derivatives present in the .stab file? What is the reference model behind those?

In most (steady, incompressible) potential flow codes, the solution is independent of Vinf and Minf=0.  When Mach is introduced to the problem, it is in the form of a compressibility correction.

So, a Mach derivative is really a derivative on the effects of compressibility -- not really velocity.

Your Mach derivatives should be very small unless you are in near transonic flow.

For an unsteady solution, the Velocity becomes important.  First, the Velocity and the length of the aircraft (or the length between the wing and tail) combine to form a  'characteristic time' for the model -- how long a particle takes to travel the length of the aircraft.  Then, you consider the typical frequency of the unsteady motion -- are your oscillations happening faster or slower than the characteristic time for the model.

So, when you're taking a U derivative, you're really taking a derivative of the unsteady behavior.

As weird as it sounds, for a potential flow method, it makes perfect sense to change M and U independently.  Don't worry, potential flow has no concept of temperature.
 
- Are tip treatments neglected in VLM analysis? If so, should I model them by simply adding wing tip sections (even guessing their impact to be small)?

Yes, tip treatments are neglected in VLM.  No, don't fight it, let them go.  They aren't that important and are not worth fighting to get back into the model. 


- I have "complex" shapes for my tail control surfaces (attachment). Is it acceptable to make analyses with simplified cntrl surf geoms (with equal area)? I think it would be possible to find derivatives wrt "exact" geometries manually, by using hinges, but would it be worth it?

VSPAERO does some approximation of the control surface no matter what.  So don't put a ton of effort into making a super complex shape using subsurfaces.

You can certainly try making an all-moving secondary surface and deflecting it yourself to measure a control derivative.  That will be interesting.

VSPAERO will not know that the 'front' and 'back' of the surface are continued -- it will try to attach a Kutta condition wake to the front surface and also the back surface.  I'm not sure how that will work out.

When VSPAERO 'deflects' a control surface, it actually tilts the boundary condition (it does not deflect the geometry in reality).  Whereas you moving a surface in the geometry will be a 'real' deflection.

There will be differences, but you may be able to make it work.

 
- In view of a flight sim implementation, is it worth it to give input conditions for stab analyses as balanced and close to a trim condition as possible?

If your model is well behaved, then most of its response should be linear -- so it won't matter much how close to the trim point you perform the linearization.  On the other hand, it is pretty cheap and easy to run a second point after you find trim based on the second point, so why not.

When doing what I call 'short time' S&C analysis, you usually start from an equilibrium point -- you introduce a perturbation and integrate for a few seconds to a few minutes to measure the response.

When doing a flight simulation -- a 'long time' simulation, you often move around a lot more in terms of V, h, alpha, CL, etc.  So you end up using lookup tables for S&C derivatives, not just a very simple linear plant model.

If your sim is going to work from a lookup table and do lots of interpolation as you change airspeed, the CG moves, and whatever else happens -- then I wouldn't worry too much about the initial trim point. 

 
-Does the "increase tessellation clustering behind propeller tips" advice also work for actuator disks?

Yes.  You'll see the difference in the load distribution on the wing.  With insufficient resolution, you won't capture anything. 

 
Thank you very much for your help, it's very much appreciated!

Have a nice day,
Luca

P.S.
I'll attach my model, it would be great if you could tell me if it looks ok for you or there is something important to be improved! Thank you!

Things mostly look reasonable.

It seemed like you were fighting things with your fuselage.  You specified more cross sections than I would have -- and you weren't using skinning strategically.  Here is a model with only changes made to the fuselage.

Rob



 
Switchmaster_complete_mod.vsp3

Luca Bottà

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Nov 8, 2022, 3:40:34 AM11/8/22
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Thank you very much, it was all very clear and helpfull!

Luca Bottà

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Nov 9, 2022, 1:07:30 PM11/9/22
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Hello,
I managed to make a first version of my sim work;
however, I'm afraid I was forgetting the correct adimensionalization (I looked up Roskam's 'Airplane Flight Dynamics and Automatic Controls).

Can you please tell me if I understood correctly? In VSP .stab output:

- derivatives wrt angles multiply angles in rad (differences wrt trim values, e.g. Cl_alpha*(alpha-alpha_trim), Cl_delta_rudder * (delta_rudder-delta_rudder_trim) and so on);

- derivatives wrt p, q, r multiply pb/(2U_trim), qc/(2U_trim), rb/(2U_trim), respectively, in rad;

- derivatives wrt u multiply U/U_trim, derivatives wrt Mach multiply Mach/Mach_trim,  (non dimensional),

where the trim conditions are U_trim, alpha_trim and so on.

So, for instance, Cx = Cx0 + Cx/alpha*(alpha-alpha_trim) + Cx/beta(beta-beta_trim) +
                                   + Cx/p*(pb/(2U_trim)) + Cx/q*(qc/(2U_trim)) + Cx/r*(rb/(2U_trim)) +
                                   + Cx/u*(U/U_trim) + Cx/M*(Mach/Mach_trim) +
                                   +  Cx/delta_aileron(delta_aileron-delta_aileron_trim) + Cx/delta_elevator(delta_elevator-delta_elevator_trim) + Cx/delta_rudder(delta_rudder-delta_rudder_trim) 

Thank you in advance,
Luca
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