Stability Analysis of Cessna 182

[Michael Stalls]

Hi im looking for your thoughts and feedback on some analysis i did. maybe you can add this to the wiki as a bit of how to guide. I have also attached a spread sheet of the results including the VSPAERO out put files.

I created a model of the cessna 182 aircraft based on geometrical data found in “riding and handling qualities of light aircraft” by smetana, summey and johnson. This document is freely available on the nasa technical reports server here

Riding and handling qualities of light aircraft pdf .

This document gives a good run down of basic stability and control as it affects  light general aviation type fixed wing aircraft, an explanation of the stability derivatives and methods to calculate each derivative via hand calculation. The stability derivatives calculated by VSPAERO were compared to those calculated using the methods shown in the above document and mostly agreed quite well. I have compiled the the geometric data used to create the VSP model as well as the VSPAERO out files into an excel spreadsheet for comparison.

Table of stability derivatives calculated using reference methods.

The first tab of the spreadsheet shows the reference image i used to create the vsp model. This image was sourced from a google search and the geometric data for the cessna 182 taken from pg 195 and 196 of the above reference.

The next tab includes some screen grabs of the Cessna 182 VSP model and a table of stability derivatives calculated using the methods outlined in the reference above.

The next tab shows some screen grabs of the VSP gui and how to set up a simple analysis run using VSPAERO. The following tabs are the VSPAERO output files compiled together.

The first and subsequent analysis is done in  a power off cruise configuration at an altitude of 5000 ft with an angle of attack of 1.5 degrees and an airspeed of 130 kts (219 fps 0.3 MACH). The model is analysed in VSPAERO without the wing, undercarriage struts and wheels which i included in the VSP model.  From this we can see that the VSP computed values of

CL 0.345 and CD 0.0285 compare well with the values presented in the report but the pitching moment Coefficient of CMy -0.369 is well outside of trim. CMy = 0 for the aircraft to be trimmed.

The next tab shows an attempt to get VSPAERO to converge on a trimmed solution. Page 366 of the reference above gives an elevator trim angle of 7.71 degrees. I ran VSP aero with this elevator angle and several others and I was unable to get VSPAERO to converge on a solution with CMy = 0. With an elevator trim angle of 7.71 i got a CMy value of -0.0571. I ran VSP aero for several different elevator angle settings and plotted the values for pitching moment from this i interpolated an elevator trim angle of 7.79 degrees. When i ran VSPAERO with this value it would not converge on a solution at all.

The next tab shows a basic stability run using the same flight conditions without any control inputs. I first did the stability runs using the basic wing - fuselage - tail surfaces model and found that VSP aero ran very slow and would not converge on a solution. Subsequent stability runs were done without the fuselage and vspAero ran quickly and converged well. The following values were obtained.

CL_U 0.043412

CD_U 0.002354

CMm_U 0.017038

Which are small but not quite zero as calculated above.

CL_Alpha 5.339824

CD_Alpha 0.207355

CMm_Alpha -1.870276

The values for Clalpha Cdalpha correspond well to those calculated above and Cmalpha is a bit out possibly due to a lack of a fuselage in the model.

Pitch_Rate_CL 0.743093

Pitch_Rate_CD 0.024355

Pitch_Rate_CMy -0.275148

The values for the pitch rate derivatives agree pretty well with those calculated above.

CL_q 9.588063

CD_q 0.42776

CMm_q-17.611519

The values for CLq out put by VSPAERO differ quite a bit from from those calculated in the reference above but they are of the same order of magnitude and sign. The values obtained from VSPAERO for the lateral stability derivatives match very well the values calculated in the above reference.

CFy_Beta -0.237723

CMl_Beta -0.049011

CMn_Beta 0.093456

CFy_p -0.005558

CMl_p -0.519576

CMn_p -0.046814

CFy_r 0.245756

CMl_r 0.153041

CMn_r -0.109531

The next tab is a stability run using the wing - tail surfaces model with elevator deflection of 7.71 degrees to obtain the elevator control derviatives.

The following elevator control derivatives were obtained from VSPAERO.

elevator_control1_CD 0.01699

elevator_control1_CL           0.505952

elevator_control1_CMm         0.16346

The values for lift coefficient change with respect to elevator input correspond well with the values in the reference although the values for drag and pitch moment less so.

The next tab is a stability run to calculate the Aileron control derivatives. The example in page 376 in the reference above gives a calculated aileron control derivative values of  

CydeltaA = 0

CldeltaA =0.177045 /rad

CndeltaA =-0.016708055/rad

Each aileron was put into a seperate group with a gain of 1 and deflected +- 5 degrees.

The values calculated by VSP aero are

CFy_Aileron1 -0.014389

CMl_Aileron1 -0.189788

CMn_Aileron1 0.015466

Which are very close although they are of the opposite sign. With XZ symmetric aircraft mainly the magnitude of these values is most important.

The last tab includes the rudder control derivatives. The rudder was deflected by -5 degrees and and the following lateral rudder control derivatives were output.

rudder_CFy 0.007141

rudder_CMl 0.000632

rudder_CMn -0.003321

These seem to be an order of magnitude less than the values calculated above possibly due to a lack of fuselage in the analysis model. When comparing these values of stability derivatives in the reference report  it is worth noting that they are not based on test data but are values obtained by using the methods outlined in the report. They could possibly have inaccuracies and errors too.

regards

Michael

[Michael Stalls]

I Also posted the C182 VSP3 model i created and used in the analysis to the VSP hangar !

[corp...@gmail.com]

Hi Michael,

the model in VSP hangar has horizontal tail with a washin of 3 degrees.. Did you make your calculation with this geometry ?

Corrado

[Michael Stalls]

Hi Corrado ,

Its not washin (washout and washin involve twisting the wing) ......its the tail incidence angle - 3 degrees. It gives this value as the tail incidence on page 195 of the report i referenced. i did all the calculations with this model.  Incidence angle is kinda like   "built in trim" 

regards

Michael 

[corp...@gmail.com]

Hi Michael,

in your model only the horiz. stab root has an incidence of -3 deg , the tip is not twisted accordingly ( Section n°1 - Twist = 0 deg) then you have an aerodynamics surface twisted up from root to tip . It is visible from a left view of the stab component. 

Regards

Corrado

[Michael Stalls]

Hi Corrado

I see. the whole stab is supposed to have an incidence angle of 3 degrees. the control in the Stab tab is just for wing root incidence. My mistake!

i changed it to remove the twist in the horiz stab and ran VSPAERO.....it didnt make much difference to the stability derivatives out put.

regards 

Michael

[Moshe Hollander]

Hi all,

I actually managed to get everything to work after I set all of the python paths to my python 2 installation (anaconda2) instead of my python 3 installation. I have no idea why this worked, but it did!

Thanks so much for all your help!

-Moshe.

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[Rob McDonald]

Sorry I haven't had time to dive into this interesting application -- thanks for sharing your progress and your results.

Changing a twist distribution (or incidence or camber) on a wing should not change its CL_alpha or CM_alpha -- but it should change its CL_0 and CM_0 -- which will influence the trim problem.

To convince yourself of this, look into the somewhat forgotten concepts of the 'basic lift distribution' and 'additional lift distribution'....

Rob

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[Michael Stalls]

Hi thanks for the feedback!...i guess the purpose of this analysis was to try to get a better understanding of VSPAERO and to see if i was interpreting the outputs properly. Of course VSPAERO can output a whole lot more than just the derivatives discussed in the reference above. Before you can consider such things as tandem wing, flying wings, asymmetric or other radical concepts you have to have a good understanding of stability and control as it relates to simple  conventional aircraft. i had done some analysis using the methods in the reference above previously on another project and i  thought i would try and generate the numbers shown in the example in the report using VSPAERO. 

I fixed the horizontal stabilizer to make sure it had a constant incidence of -3 degrees i had to do a few runs and set the total number of wake iterations to 25 but i was able to get it to converge with the following values  

	elev angle	Cmy Pitch moment	CL	Cdtot
	6	0.0171	0.55583	0.01959
	6.5	0.00147	0.56125	0.01966
	7	-0.01412	0.56664	0.01976
trimmed!	6.551	-0.00013	0.5618	0.01967

i guess that is close enough to zero ! i also checked the XZ symmetry box and it seemed to converge quicker and give better results.

Here is another dumb question here is a plot of Cl against wing station for the analysis above.

 

what is the difference between the plot of Cl*c/cref??

which is the best data to use for loads analysis ? what is the reason VSPAERO outputs CL (and the other coefficients) multiplied by c/cref

Thanks 

Michael

On Thursday, May 9, 2019 at 2:13:37 AM UTC+10, Rob McDonald wrote:

Sorry I haven't had time to dive into this interesting application -- thanks for sharing your progress and your results.

Changing a twist distribution (or incidence or camber) on a wing should not change its CL_alpha or CM_alpha -- but it should change its CL_0 and CM_0 -- which will influence the trim problem.

To convince yourself of this, look into the somewhat forgotten concepts of the 'basic lift distribution' and 'additional lift distribution'....

Rob

On Wed, May 8, 2019 at 6:04 AM Michael Stalls <michael...@gmail.com> wrote:

Hi Corrado

I see. the whole stab is supposed to have an incidence angle of 3 degrees. the control in the Stab tab is just for wing root incidence. My mistake!

i changed it to remove the twist in the horiz stab and ran VSPAERO.....it didnt make much difference to the stability derivatives out put.

regards 

Michael

On Wednesday, May 8, 2019 at 3:48:51 AM UTC+10, corp...@gmail.com wrote:

Hi Michael,

in your model only the horiz. stab root has an incidence of -3 deg , the tip is not twisted accordingly ( Section n°1 - Twist = 0 deg) then you have an aerodynamics surface twisted up from root to tip . It is visible from a left view of the stab component. 

Regards

Corrado

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[Rob McDonald]

Michael,

One of the best ways to learn and build confidence with a tool is to run a case where you have appropriate validation data -- no need to explain what you're doing, you're doing it right!

25 wake iterations is likely substantial overkill.  One of the other tabs in the GUI shows the convergence history with wake iteration -- unless you have a lot of crazy interactions, it usually converges in just two or three wake iterations.

The cl and cl*c/cref curves look very similar because the Cessna wing doesn't have substantial taper.  If c varied significantly over the span, then you would see these two charts look more different.

Note that cl is the sectional lift coefficient and CL would be the 3D airplane lift coefficient.

The lift force L=CL*q*Sref.  Similarly, the sectional lift is l=cl*q*c.  Typically, Sref=bref*cref.  Of course, q=0.5*rho*V^2.

When we talk about an elliptical lift distribution being optimal, we are talking about the sectional lift l -- not the lift coefficient cl.  Similarly, if you are going to transfer forces over to a structural analysis, you are interested in the loads, not the coefficients.  That said, we still like to work in non-dimensional terms.

A potential flow calculation (like VSPAERO) should be independent of velocity and density (and therefore q).  One result can apply to many values of q.  By dividing l/q, we remove the dependence on q -- but the load distribution would still be dimensional and would have units of length.  So, we further divide by cref to non-dimensionalize by the scale of the aircraft -- a small model should have the same load distribution as the full-size aircraft.

So, the non-dimensional form of lift distribution that makes sense to use is l/(q*cref) -- which happens to be cl*c/cref.

I can tell by the number of points in your load distribution charts that you don't have adequate spanwise resolution in your model.  I suggest you look at performing some tests to get a good feel for the chordwise and spanwise resolution requirements that you want to meet.

Rob

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[Anna Valcarcel]

Hello,

I'm curious where you can find C_Mn_beta in VSP Aero? I'm trying to find the value in the analysis but it doesn't seem to get outputted directly. Did you have to do a calculation or is there a relationship between another variable? 

Thank you!

Anna 

[Brandon Litherland]

That will be part of the *.STAB file that is output as part of a Stability run in VSPAERO.  For those runs, you'll want to use the Steady Stability Type under the Advanced tab.

If you run an unsteady PQR stability test, the output files will be *.pstab, *.qstab, or *.rstab.  See the example of the default wing below.

#             Base    Derivative:                                                                               

#             Aero         wrt          wrt          wrt          wrt          wrt          wrt          wrt    

Coef          Total        Alpha        Beta          p            q            r           Mach         U      

#              -           per          per          per          per          per          per          per    

#              -           rad          rad          rad          rad          rad          M            u      

#

CFx      -0.0092475   -0.2951327    0.0003431   -0.5471826   -2.3210837    0.0023522   -0.0003073   -0.0000000 

CFy      -0.0000000   -0.0000003    0.0092651   -0.0000075   -0.0000131   -0.0538853    0.0000000    0.0000000 

CFz       0.1417486    1.9895036   -0.0026338   -0.1163761   16.7870588    0.0064173    0.0046708    0.0000000 

CMx       0.0000013   -0.0000056    0.2841644   63.9907837    0.0004339   -8.0202347   -0.0000001   -0.0000000 

CMy      -0.4132847   -5.8011705    0.0077055    0.4768790  -54.0382819   -0.0196622   -0.0145238   -0.0000000 

CMz       0.0000000   -0.0000003    0.0430215    9.5342219    0.0000147   -0.2894765    0.0000000    0.0000000 

CL        0.1420483    2.0057530   -0.0026513   -0.0779231   16.9080770    0.0062376    0.0046808    0.0000000 

CD        0.0018206    0.0585263   -0.0000343    0.1748241    0.5678086   -0.0011206    0.0001196    0.0000000 

CS       -0.0000000   -0.0000003    0.0099292   -0.0000075   -0.0000131   -0.0538853    0.0000000    0.0000000 

CMl      -0.0000013    0.0000056   -0.2841644  -63.9907837   -0.0004339    8.0202347    0.0000001    0.0000000 

CMm      -0.4132847   -5.8011705    0.0077055    0.4768790  -54.0382819   -0.0196622   -0.0145238   -0.0000000 

CMn      -0.0000000    0.0000003   -0.0430215   -9.5342219   -0.0000147    0.2894765   -0.0000000   -0.0000000 

[Grant Hiller]

Hi folks,

Would anyone have a copy of the Cessna 182 vsp3 file that was used for the above work, given that the hangar is down? It would be much appreciated!

I am looking to run this model to help build some tools to do the processing of the stability derivatives, and to correlate it to the abovementioned NASA report.

Cheers,

Grant.