Re: Force instead of lift

"Bill Galbraith" <[email protected]> Sat, 1 Oct 2011 08:27:49 -0400
Newsgroups gmane.games.flightgear.flightmodel
Message-ID <D47BAAD90C154A94B1F7CA1757517CFE@Dell755>
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In this case, the Cl is roll moment coefficient, not CL, the lift
coefficient

The attached file shows a new format for JSBSim files that I came up with.
It works just as well as the older format, but the formulation of the
coefficients more closely matches classical aerodynamic textbook equation
buildup. Feel free to use this, or the older format. They are both equally
valid.

Bill



> -----Original Message-----
> From: Oleksiy Frolov [mailto:[email protected]] 
> Sent: Saturday, October 01, 2011 12:03 AM
> To: Flight dynamics model discussions
> Subject: Re: [Flightgear-flightmodel] Force instead of lift
> 
> Hello Bill
> 
>  This is a good suggestion, thank you.
> 
>  I understand about calculating 2(4) different CL-s.
> 
>  Do I also understand correctly we will than have use 
> something you guys did to the flaps once:
> 
>      <axis name="ROLL">
>       .................
>          <function name="aero/coefficient/CldF3">
>             <description>
>                Roll Moment Coefficient due to Asymetrical 
> Fowler Flaps Deflection
>                calculated as difference between left and 
> right flap lift coef,
>                times distance from centerline to MAC of surface.
>             </description>
>             <product>
>                <value>     21.28</value>
>                <difference>
>                   <property>aero/coefficient/CLdF3R</property>
>                   <property>aero/coefficient/CLdF3L</property>
>                </difference>
>             </product>
>          </function>
> 
> 
> in order to calculate the moments due to difference in 
> individual CLs ?
> 
> With best regards,
> Oleksiy Frolov
> 
> >
> >
> >> -----Original Message-----
> >> From: Oleksiy Frolov [mailto:[email protected]]
> >> Sent: Friday, September 30, 2011 3:43 PM
> >> To: [email protected]
> >> Subject: [Flightgear-flightmodel] Force instead of lift
> >>
> >> Hello
> >>
> >>  I am trying to simulate the effects of the differential 
> wing lift. 
> >> Such as single wing stall due to the propwash loss at a low speed, 
> >> and the effect of the icing on a single wing (which can 
> happen during 
> >> a deicing failure on that wing). All of these are important 
> >> aerodynamic effects.
> >>
> >>  Now, we know we only have one wing in jsbsim currently, not 2. My 
> >> idea is therefor to try using 2 <force> records to 
> simulate the wings 
> >> separately, instead of the usual CL record.
> >> This however would require some kind of algorithm to 
> define how the 
> >> force origin moves to overlay with center of lift for each wing, 
> >> which is probably not an easy task
> >>
> >>  I was wondering if anyone have tried a similar approach 
> before, and 
> >> if this problem pechaps has an easier solution ?
> >>
> >> Thank you
> >>
> >> regards,
> >> Oleksiy Frolov
> >>
> >
> >
> > No reason that you couldn't build this inside of the 
> existing JSBSim 
> > format without using the external forces. Divide your wing into 
> > panels, maybe (on each side) one that is influenced by the 
> propeller 
> > slipstream, one not.
> > Sum
> > all of your lifts to apply them at the aero reference 
> point. So with a 
> > two engine aircraft, you might have a total of four panels, two per 
> > wing half, one inboard in the slipstream, one outboard in 
> clean air. A 
> > mismatch of forces left/right would normally shift the aero 
> reference 
> > point left or right, but that can be resolved with a moment.
> >
> > You have a couple advantages doing this. A force at a distance is a 
> > moment, so if the outer panels are experiencing different 
> lift forces, 
> > that lift times its arm creates a moment. If the aircraft 
> is rolling, 
> > each wing sees a different angle of attack, and therefore different 
> > lift. This is usually handled other ways, but your method has the 
> > advantage of spinning properly.
> > There are disadvantages, though.
> >
> > If you are going to that trouble, you might consider 
> keeping the flaps 
> > and ailerons seperate as well, unless the actuator mechanism is 
> > guaranteed to never give you different flap or aileron angles.
> >
> > Bill
> >
> >
> > 
> ----------------------------------------------------------------------
> > -------- All of the data generated in your IT infrastructure is 
> > seriously valuable.
> > Why? It contains a definitive record of application performance, 
> > security threats, fraudulent activity, and more. Splunk takes this 
> > data and makes sense of it. IT sense. And common sense.
> > http://p.sf.net/sfu/splunk-d2dcopy2
> > _______________________________________________
> > Flightgear-flightmodel mailing list
> > [email protected]
> > https://lists.sourceforge.net/lists/listinfo/flightgear-flightmodel
> >
> 
> 
> 
> --------------------------------------------------------------
> ----------------
> All of the data generated in your IT infrastructure is 
> seriously valuable.
> Why? It contains a definitive record of application 
> performance, security threats, fraudulent activity, and more. 
> Splunk takes this data and makes sense of it. IT sense. And 
> common sense.
> http://p.sf.net/sfu/splunk-d2dcopy2
> _______________________________________________
> Flightgear-flightmodel mailing list
> [email protected]
> https://lists.sourceforge.net/lists/listinfo/flightgear-flightmodel

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Content-Type: text/xml;
	name="Citation_aero.xml"
Content-Transfer-Encoding: quoted-printable
Content-Disposition: attachment;
	filename="Citation_aero.xml"

<?xml version=3D"1.0"?>
<!--


  ****************** IMPORTANT NOTICES **********************

   This file was generated by Datcom+ Pro, a superset of=20
   the USAF Digital DATCOM program.
   This file is considered an intermediary file in the=20
   DATCOM/JSBSim process. This file may be overwritten without
   warning, so any changes that you make in here may be lost.

   If you intend to use this file as it is and modify it, make
   sure that you take the necessary precautions to prevent it=20
   from being overwritten, like renaming it.


   ***********************************************************

   DISCLAIMER REQUIRED BY HQ USAF FOR PUBLIC RELEASE APPROVAL

   THIS SOFTWARE AND ANY ACCOMPANYING DOCUMENTATION
   IS RELEASED "AS IS".  THE U.S. GOVERNMENT MAKES NO
   WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, CONCERNING
   THIS SOFTWARE AND ANY ACCOMPANYING DOCUMENTATION,
   INCLUDING, WITHOUT LIMITATION, ANY WARRANTIES OF
   MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.
   IN NO EVENT WILL THE U.S. GOVERNMENT BE LIABLE FOR ANY
   DAMAGES, INCLUDING LOST PROFITS, LOST SAVINGS OR OTHER
   INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE=20
   USE, OR INABILITY TO USE, THIS SOFTWARE OR ANY
   ACCOMPANYING DOCUMENTATION, EVEN IF INFORMED IN ADVANCE
   OF THE POSSIBILITY OF SUCH DAMAGES.

   ***********************************************************
-->


<!-- =
**********************************************************************
        AERODYNAMICS
     =
*******************************************************************-->
<aerodynamics>

   <!-- *************************=20
             Sign Conventions   =20
        *************************=20

        Control displacements
             Stick    FWD  + / Aft -
             Stick    Left + / Right -
             Wheel    CCW  + / CW -
             Pedal    Left + / Right -
             Elevator trim Nose Up + / Nose down -

        Surfaces
             Elevator  TED + / TEU -
             R Ail     TED + / TEU -
             L Ail     TED + / TEU -
             Rudder    TEL + / TER -

        F&M, Accel, Rates, Displacements
             Pitch     Up  + / Down -
             Roll      Rgt + / Left -
             Yaw       Rgt + / Left -

        Other
             Alpha     Up  + / Down -
             Beta Wind in right ear + / Wind in left ear -
             Slip Ball right of center + / left of center -
   -->


   <!-- **************************************=20
             ASSUMPTIONS AND LIMITATIONS

        There is no interaction between deflected surfaces modeled
        so there is no change in elevator effects with the flaps
        deflected, for example.

        Terms known to be missing from DATCOM:
           Ground effects
           Cyr, dCY_Rud, dCY_Ail, dCl_Rud, dCN_Rud

        **************************************
   -->

   <!-- The following functions provide properties in different units =
than are native to JSBSim -->

   <function name=3D"attitude/pitch-deg">
      <description>Pitch angle in degrees</description>
      <product>
         <property>attitude/pitch-rad</property>
         <value>57.29577951</value>
      </product>
   </function>

   <function name=3D"attitude/roll-deg">
      <description>Roll angle in degrees</description>
         <product>
         <property>attitude/roll-rad</property>
         <value>57.29577951</value>
      </product>
   </function>

   <function name=3D"attitude/heading-true-deg">
      <description>Roll angle in degrees</description>
      <product>
         <property>attitude/heading-true-rad</property>
         <value>57.29577951</value>
      </product>
   </function>

   <function name=3D"velocities/q-deg_sec">
      <description>Pitch rate in degrees per sec</description>
      <product>
         <property>velocities/q-aero-rad_sec</property>
         <value>57.29577951</value>
      </product>
   </function>

   <function name=3D"velocities/p-deg_sec">
      <description>Pitch rate in degrees per sec</description>
      <product>
         <property>velocities/p-aero-rad_sec</property>
         <value>57.29577951</value>
      </product>
   </function>

   <function name=3D"velocities/r-deg_sec">
      <description>Pitch rate in degrees per sec</description>
      <product>
         <property>velocities/r-aero-rad_sec</property>
         <value>57.29577951</value>
      </product>
   </function>


<!-- =
**********************************************************************=20
                LIFT FORCE
     =
********************************************************************** =
-->

   <function name=3D"aero/coefficient/CL_wbh">
      <description>
         Lift coefficient due to wing, body, and horizontal tail
      </description>
      <table>
         <independentVar lookup=3D"row"> aero/alpha-deg =
</independentVar>
         <tableData>
                 -2.0000        -.0313
                   .0000         .1609
                  2.0000         .3557
                  4.0000         .5533
                  8.0000         .9495
                  9.0000        1.0380
                 10.0000        1.1171
                 11.0000        1.1898
                 12.0000        1.2555
                 13.0000        1.3124
                 14.0000        1.3632
                 15.0000        1.3922
                 16.0000        1.3403
         </tableData>
      </table>
   </function>

   <function name=3D"aero/derivative/CLq-per_rad">
      <description>
         Lift coefficient derivative due to pitch rate, per rad
      </description>
      <table>
         <independentVar lookup=3D"row"> aero/alpha-deg =
</independentVar>
         <tableData>
             -2.0000    9.2943
             16.0000    9.2943
         </tableData>
      </table>
   </function>

   <function name=3D"aero/derivative/CLadot-per_rad">
      <description>
         Lift coefficient derivative due to AOA rate, per rad
         Important contributor to short period damping
      </description>
      <table>
         <independentVar lookup=3D"row"> aero/alpha-deg =
</independentVar>
         <tableData>
                 -2.0000        2.4726
                   .0000        2.5178
                  2.0000        2.6025
                  4.0000        2.6508
                  8.0000        2.4940
                  9.0000        2.3980
                 10.0000        2.2089
                 11.0000        1.8322
                 12.0000        1.4917
                 13.0000        1.2549
                 14.0000         .7177
                 15.0000        -.2527
                 16.0000        -.8221
         </tableData>
      </table>
   </function>

   <function name=3D"aero/coefficient/dCL_Flap">
      <description>
         Lift coefficient increment due to flap deflection
         Positive surface deflection is trailing edge down.
      </description>
      <table>
         <independentVar lookup=3D"row"> fcs/flap-pos-deg =
</independentVar>
         <tableData>
               .0000     .0000
             15.0000     .2360
             30.0000     .4337
             40.0000     .5045
         </tableData>
      </table>
   </function>

   <function name=3D"aero/coefficient/dCL_Elev">
      <description>
         Lift coefficient increment due to elevator deflection.
         Positive surface deflection is trailing edge down.
      </description>
      <table>
         <independentVar lookup=3D"row"> fcs/elevator-pos-deg =
</independentVar>
         <tableData>
            -20.0000    -.1583
            -15.0000    -.1501
            -10.0000    -.1059
             -5.0000    -.0529
               .0000     .0001
              5.0000     .0529
             10.0000     .1059
             13.0000     .1349
             16.0000     .1562
         </tableData>
      </table>
   </function>

   <function name=3D"aero/coefficient/dCL_Power">
      <description>
         Lift coefficient increment due to thrust effects
      </description>
      <table>
         <independentVar lookup=3D"row"> aero/alpha-deg =
</independentVar>
         <independentVar lookup=3D"column"> =
propulsion/total-thrust-coefficient </independentVar>
         <tableData>
                            .0000     .1000     .2000     .3000
                -2.0000     .0014     .0014     .0014     .0014
                  .0000     .0097     .0167     .0237     .0306
                 2.0000     .0172     .0311     .0451     .0590
                 4.0000     .0230     .0439     .0648     .0857
                 8.0000     .0280     .0627     .0974     .1322
                 9.0000     .0276     .0658     .1039     .1421
                10.0000     .0266     .0682     .1098     .1513
                11.0000     .0250     .0699     .1149     .1599
                12.0000     .0227     .0711     .1195     .1679
                13.0000     .0200     .0718     .1235     .1753
                14.0000     .0168     .0719     .1270     .1822
                15.0000     .0132     .0716     .1301     .1886
                16.0000     .0092     .0711     .1329     .1947
         </tableData>
      </table>
   </function>

   <axis name=3D"LIFT">

      <function name=3D"aero/force/lift-lbs">
         <description>
            Lift force =3D ( CL_wbh + CLq*q*cbar/(2*V) + =
CLadot*adot*cbar/(2*V) + dCL_Flap + dCL_Elev + dCL_Power )
                         * q_bar * wing area
         </description>
         <product>
            <sum>
               <property> aero/coefficient/CL_wbh </property>
               <product>
                  <property> aero/derivative/CLq-per_rad </property>
                  <property> velocities/q-rad_sec </property>
                  <property> aero/ci2vel </property>
               </product>
               <product>
                  <property> aero/derivative/CLadot-per_rad </property>
                  <property> aero/alphadot-rad_sec </property>
                  <property> aero/ci2vel </property>
               </product>
               <property> aero/coefficient/dCL_Flap </property>
               <property> aero/coefficient/dCL_Elev </property>
               <property> aero/coefficient/dCL_Power </property>
            </sum>
            <property> aero/qbar-psf </property>
            <property> metrics/Sw-sqft </property>
         </product>
      </function>

   </axis>

<!-- =
**********************************************************************=20
                DRAG FORCE
     =
********************************************************************** =
-->

   <function name=3D"aero/coefficient/CD_wbh">
      <description>
         Drag coefficient due to wing, body, and horizontal tail
         Main contributor to Phugoid damping: greater Cd, better damping
      </description>
      <table>
         <independentVar lookup=3D"row"> aero/alpha-deg =
</independentVar>
         <tableData>
                 -2.0000         .0154
                   .0000         .0165
                  2.0000         .0210
                  4.0000         .0295
                  8.0000         .0582
                  9.0000         .0668
                 10.0000         .0759
                 11.0000         .0856
                 12.0000         .0954
                 13.0000         .1052
                 14.0000         .1152
                 15.0000         .1232
                 16.0000         .1233
         </tableData>
      </table>
   </function>

   <function name=3D"aero/coefficient/dCD_Flap">
      <description>
         Drag coefficient increment due to flap deflection
         Positive surface deflection is trailing edge down.
      </description>
      <table>
         <independentVar lookup=3D"row"> aero/alpha-deg =
</independentVar>
         <independentVar lookup=3D"column"> fcs/flap-pos-deg =
</independentVar>
         <tableData>
                            .0000   15.0000   30.0000   40.0000
                -2.0000     .0000     .0006     .0078     .0119
                  .0000     .0000     .0041     .0142     .0193
                 2.0000     .0000     .0076     .0206     .0268
                 4.0000     .0000     .0111     .0271     .0343
                 8.0000     .0000     .0181     .0399     .0492
                 9.0000     .0000     .0198     .0431     .0530
                10.0000     .0000     .0216     .0463     .0567
                11.0000     .0000     .0233     .0495     .0604
                12.0000     .0000     .0251     .0527     .0642
                13.0000     .0000     .0268     .0560     .0679
                14.0000     .0000     .0286     .0592     .0716
                15.0000     .0000     .0303     .0624     .0754
                16.0000     .0000     .0321     .0656     .0791
         </tableData>
      </table>
   </function>

   <function name=3D"aero/coefficient/dCD_Elev">
      <description>
         Drag coefficient increment due to elevator deflection.
         Positive surface deflection is trailing edge down.
      </description>
      <table>
         <independentVar lookup=3D"row"> aero/alpha-deg =
</independentVar>
         <independentVar lookup=3D"column"> fcs/elevator-pos-deg =
</independentVar>
         <tableData>
                         -20.0000  -15.0000  -10.0000   -5.0000     =
.0000    5.0000   10.0000   13.0000   16.0000
                -2.0000     .0110     .0101     .0057     .0020     =
.0000    -.0003     .0011     .0026     .0040
                  .0000     .0094     .0085     .0046     .0014     =
.0000     .0003     .0022     .0040     .0056
                 2.0000     .0078     .0070     .0035     .0009     =
.0000     .0008     .0033     .0053     .0072
                 4.0000     .0062     .0055     .0025     .0004     =
.0000     .0013     .0043     .0066     .0087
                 8.0000     .0032     .0027     .0005    -.0006     =
.0000     .0023     .0063     .0092     .0117
                 9.0000     .0024     .0019    -.0001    -.0009     =
.0000     .0026     .0069     .0099     .0125
                10.0000     .0015     .0011    -.0007    -.0012     =
.0000     .0029     .0074     .0107     .0134
                11.0000     .0006     .0002    -.0013    -.0015     =
.0000     .0032     .0081     .0115     .0143
                12.0000    -.0005    -.0008    -.0020    -.0018     =
.0000     .0035     .0088     .0124     .0153
                13.0000    -.0016    -.0019    -.0027    -.0022     =
.0000     .0039     .0095     .0133     .0164
                14.0000    -.0028    -.0030    -.0035    -.0026     =
.0000     .0043     .0103     .0143     .0176
                15.0000    -.0042    -.0043    -.0045    -.0031     =
.0000     .0048     .0112     .0155     .0190
                16.0000    -.0059    -.0059    -.0056    -.0036     =
.0000     .0053     .0124     .0170     .0206
         </tableData>
      </table>
   </function>

   <axis name=3D"DRAG">

      <function name=3D"aero/force/drag-lbs">
         <description>
            Drag force =3D ( CD_wbh + dCD_Flap + dCD_Elev )
                         * q_bar * wing area
         </description>
         <product>
            <sum>
               <property> aero/coefficient/CD_wbh </property>
               <property> aero/coefficient/dCD_Flap </property>
               <property> aero/coefficient/dCD_Elev </property>
            </sum>
            <property> aero/qbar-psf </property>
            <property> metrics/Sw-sqft </property>
         </product>
      </function>

   </axis>

<!-- =
**********************************************************************=20
                SIDE FORCE
     =
********************************************************************** =
-->

   <function name=3D"aero/derivative/CYbeta-per_rad">
      <description>
         Side force coefficient derivative due to sideslip, per rad
         Contributes to damping of dutch roll mode
      </description>
      <table>
         <independentVar lookup=3D"row"> aero/alpha-deg =
</independentVar>
         <tableData>
             -2.0000    -.7503
             16.0000    -.7503
         </tableData>
      </table>
   </function>

   <function name=3D"aero/derivative/CYp-per_rad">
      <description>
         Side Force coefficient derivative due to roll rate, per rad
      </description>
      <table>
         <independentVar lookup=3D"row"> aero/alpha-deg =
</independentVar>
         <tableData>
                 -2.0000        -.0884
                   .0000        -.0965
                  2.0000        -.1050
                  4.0000        -.1137
                  8.0000        -.1312
                  9.0000        -.1341
                 10.0000        -.1365
                 11.0000        -.1382
                 12.0000        -.1392
                 13.0000        -.1391
                 14.0000        -.1405
                 15.0000        -.1862
                 16.0000        -.0434
         </tableData>
      </table>
   </function>

   <function name=3D"aero/derivative/CYr-per_rad">
      <description>
         Side Force coefficient derivative due to yaw rate
         DATCOM does not calculate this term
         Effect is small
      </description>
      <table>
         <independentVar lookup=3D"row"> velocities/r-rad_sec =
</independentVar>
         <tableData>
             -2.0000     .0000
               .0000     .0000
              2.0000     .0000
         </tableData>
      </table>
   </function>

   <function name=3D"aero/coefficient/dCY_Rud">
      <description>
         Side Force coefficient increment due to rudder
         DATCOM does not calculate this term
      </description>
      <table>
         <independentVar lookup=3D"row"> fcs/rudder-pos-deg =
</independentVar>
         <tableData>
            -30.0000     .0000
               .0000     .0000
             30.0000     .0000
         </tableData>
      </table>

   </function>

   <function name=3D"aero/coefficient/dCY_Ail">
      <description>
         Side Force coefficient increment due to plain flap aileron
         DATCOM does not calculate this term
         Usually neglected as small
      </description>
      <table>
         <independentVar lookup=3D"row"> fcs/total-aileron-pos-deg =
</independentVar>
         <tableData>
            -64.0000     .0000
               .0000     .0000
             64.0000     .0000
         </tableData>
      </table>

   </function>

   <axis name=3D"SIDE">

      <function name=3D"aero/force/side-lbs">
         <description>
            Side force =3D ( CYbeta*beta + CYp*p*b/(2*V) + CYr*r*b/(2*V) =
+ CYdRud + CYdAil )
                         * q_bar * wing area
         </description>
         <product>
            <sum>
               <product>
                  <property> aero/derivative/CYbeta-per_rad </property>
                  <property> aero/beta-rad </property>
               </product>
               <product>
                  <property> aero/derivative/CYp-per_rad </property>
                  <property> velocities/p-rad_sec </property>
                  <property> aero/bi2vel </property>
               </product>
               <product>
                  <property> aero/derivative/CYr-per_rad </property>
                  <property> velocities/r-rad_sec </property>
                  <property> aero/bi2vel </property>
               </product>
               <property> aero/coefficient/dCY_Rud </property>
               <property> aero/coefficient/dCY_Ail </property>
            </sum>
            <property> aero/qbar-psf </property>
            <property> metrics/Sw-sqft </property>
         </product>
      </function>

   </axis>

<!-- =
**********************************************************************=20
                ROLL MOMENT
     =
********************************************************************** =
-->

   <function name=3D"aero/derivative/Clbeta-per_rad">
      <description>
         Roll moment coefficient derivative due to sideslip
         Decrease of Clb to small negative value improves dutch roll =
damping
         High Positive value leads to excessive spiral instability
      </description>
      <table>
         <independentVar lookup=3D"row"> aero/alpha-deg =
</independentVar>
         <tableData>
                 -2.0000        -.1362
                   .0000        -.1301
                  2.0000        -.1240
                  4.0000        -.1177
                  8.0000        -.1052
                  9.0000        -.1023
                 10.0000        -.0993
                 11.0000        -.0964
                 12.0000        -.0936
                 13.0000        -.0909
                 14.0000        -.0882
                 15.0000        -.0857
                 16.0000        -.0842
         </tableData>
      </table>
   </function>

   <function name=3D"aero/derivative/Clp-per_rad">
      <description>
         Roll moment coefficient derivative due to roll rate
         Clp alone determines damping-in-roll characteristics
      </description>
      <table>
         <independentVar lookup=3D"row"> aero/alpha-deg =
</independentVar>
         <tableData>
                 -2.0000        -.4558
                   .0000        -.4649
                  2.0000        -.4725
                  4.0000        -.4696
                  8.0000        -.3796
                  9.0000        -.3396
                 10.0000        -.2962
                 11.0000        -.2478
                 12.0000        -.1947
                 13.0000        -.1484
                 14.0000        -.0469
                 15.0000         .3125
                 16.0000         .8656
         </tableData>
      </table>
   </function>

   <function name=3D"aero/derivative/Clr-per_rad">
      <description>
         Roll moment coefficient derivative due to yaw rate, per rad
         Considerable effect on spiral mode.=20
         Large positive values leads to strong sprial instability
      </description>
      <table>
         <independentVar lookup=3D"row"> aero/alpha-deg =
</independentVar>
         <tableData>
                 -2.0000         .0311
                   .0000         .0628
                  2.0000         .0951
                  4.0000         .1276
                  8.0000         .1897
                  9.0000         .2013
                 10.0000         .2114
                 11.0000         .2198
                 12.0000         .2261
                 13.0000         .2304
                 14.0000         .2332
                 15.0000         .2297
                 16.0000         .2051
         </tableData>
      </table>
   </function>

   <function name=3D"aero/coefficient/dCl_Ail">
      <description>
         Roll Moment coefficient increment due to aileron deflection
         Positive surface deflection is trailing edge down.
         Positive rolling moment is right wing down
      </description>
      <table>
         <independentVar lookup=3D"row"> fcs/total-aileron-pos-deg =
</independentVar>
         <tableData>
            -64.0000    -.0687
            -40.0000    -.0576
            -20.0000    -.0369
            -10.0000    -.0184
               .0000     .0000
             10.0000     .0184
             20.0000     .0369
             40.0000     .0576
             64.0000     .0687
         </tableData>
      </table>
   </function>

   <function name=3D"aero/coefficient/dCl_Rud">
      <description>
         Roll moment coefficient increment due to rudder
         DATCOM does not calculate this term
      </description>
      <table>
         <independentVar lookup=3D"row"> fcs/rudder-pos-deg =
</independentVar>
         <tableData>
            -30.0000     .0000
               .0000     .0000
             30.0000     .0000
         </tableData>
      </table>
   </function>

   <axis name=3D"ROLL">

      <function name=3D"aero/moment/roll-lbsft">
         <description>
            Roll Moment =3D ( Clbeta*beta + Clp*p*b/(2*V) + =
Clr*r*b/(2*V) + dCl_Ail + dCl_Rud )
                         * q_bar * wing area * wing span
         </description>
         <product>
            <sum>
               <product>
                  <property> aero/derivative/Clbeta-per_rad </property>
                  <property> aero/beta-rad </property>
               </product>
               <product>
                  <property> aero/derivative/Clp-per_rad </property>
                  <property> velocities/p-rad_sec </property>
                  <property> aero/bi2vel </property>
               </product>
               <product>
                  <property> aero/derivative/Clr-per_rad </property>
                  <property> velocities/r-rad_sec </property>
                  <property> aero/bi2vel </property>
               </product>
               <property> aero/coefficient/dCl_Ail </property>
               <property> aero/coefficient/dCl_Rud </property>
            </sum>
            <property> aero/qbar-psf </property>
            <property> metrics/Sw-sqft </property>
            <property> metrics/bw-ft </property>
         </product>
      </function>

   </axis>

<!-- =
**********************************************************************=20
                PITCH MOMENT
     =
********************************************************************** =
-->

   <function name=3D"aero/coefficient/CM_wbh">
      <description>
         Pitch moment coefficient as a function of alpha
         CM0 is included in this term
      </description>
      <table>
         <independentVar lookup=3D"row"> aero/alpha-deg =
</independentVar>
         <tableData>
                 -2.0000         .1134
                   .0000         .0487
                  2.0000        -.0155
                  4.0000        -.0791
                  8.0000        -.2067
                  9.0000        -.2388
                 10.0000        -.2702
                 11.0000        -.3030
                 12.0000        -.3385
                 13.0000        -.3745
         </tableData>
      </table>
   </function>

   <function name=3D"aero/derivative/CMq-per_rad">
      <description>
         Pitch moment coefficient derivative due to pitch rate, per rad
         Pitch damping derivative - Very important to short period =
damping of oscillations
      </description>
      <table>
         <independentVar lookup=3D"row"> aero/alpha-deg =
</independentVar>
         <tableData>
             -2.0000  -18.4339
             16.0000  -18.4339
         </tableData>
      </table>
   </function>

   <function name=3D"aero/derivative/CMadot-per_rad">
      <description>
         Pitch moment coefficient derivative due to AOA rate, per rad
         Negative CMadot increase short period damping
      </description>
      <table>
         <independentVar lookup=3D"row"> aero/alpha-deg =
</independentVar>
         <tableData>
                 -2.0000       -7.3596
                   .0000       -7.4939
                  2.0000       -7.7462
                  4.0000       -7.8900
                  8.0000       -7.4230
                  9.0000       -7.1375
                 10.0000       -6.5746
                 11.0000       -5.4534
                 12.0000       -4.4398
                 13.0000       -3.7349
                 14.0000       -2.1362
                 15.0000         .7521
                 16.0000        2.4471
         </tableData>
      </table>
   </function>

   <function name=3D"aero/coefficient/dCM_Elev">
      <description>
         Pitch moment coefficient increment due to elevator deflection
         Positive surface deflection is trailing edge down
      </description>
      <table>
         <independentVar lookup=3D"row"> fcs/elevator-pos-deg =
</independentVar>
         <tableData>
            -20.0000     .4592
            -15.0000     .4367
            -10.0000     .3081
             -5.0000     .1540
               .0000    -.0003
              5.0000    -.1540
             10.0000    -.3081
             13.0000    -.3923
             16.0000    -.4548
         </tableData>
      </table>
   </function>

   <function name=3D"aero/coefficient/dCM_Flap">
      <description>
         Pitch moment coefficient increment due to flap deflection
         Positive surface deflection is trailing edge down.
      </description>
      <table>
         <independentVar lookup=3D"row"> fcs/flap-pos-deg =
</independentVar>
         <tableData>
               .0000     .0000
             15.0000    -.0988
             30.0000    -.1854
             40.0000    -.2203
         </tableData>
      </table>
   </function>

   <function name=3D"aero/coefficient/dCM_Power">
      <description>
         Pitch moment coefficient increment due to thrust effects
      </description>
      <table>
         <independentVar lookup=3D"row"> aero/alpha-deg =
</independentVar>
         <independentVar lookup=3D"column"> =
propulsion/total-thrust-coefficient </independentVar>
         <tableData>
                            .0000     .1000     .2000     .3000
                -2.0000    -.0010    -.0880    -.1749    -.2619
                  .0000    -.0072    -.0942    -.1811    -.2681
                 2.0000    -.0127    -.0997    -.1867    -.2736
                 4.0000    -.0171    -.1041    -.1910    -.2780
                 8.0000    -.0208    -.1077    -.1947    -.2817
                 9.0000    -.0205    -.1075    -.1944    -.2814
                10.0000    -.0197    -.1067    -.1937    -.2806
                11.0000    -.0185    -.1055    -.1925    -.2794
                12.0000    -.0169    -.1038    -.1908    -.2778
                13.0000    -.0148    -.1018    -.1888    -.2757
                14.0000    -.0125    -.0994    -.1864    -.2733
                15.0000    -.0098    -.0967    -.1837    -.2707
                16.0000    -.0069    -.0938    -.1808    -.2678
         </tableData>
      </table>
   </function>

   <axis name=3D"PITCH">

      <function name=3D"aero/moment/pitch-lbsft">
         <description>
            Pitch Moment =3D ( CM_wbh + CMq*q*MAC/(2*V) + =
CMadot*adot*MAC/(2*V) + dCM_Elev + dCM_Flap + CM_Power )
                           * q_bar * wing area * wing MAC
         </description>
         <product>
            <sum>
               <property> aero/coefficient/CM_wbh </property>
               <product>
                  <property> aero/derivative/CMq-per_rad </property>
                  <property> velocities/q-rad_sec </property>
                  <property> aero/ci2vel </property>
               </product>
               <product>
                  <property> aero/derivative/CMadot-per_rad </property>
                  <property> aero/alphadot-rad_sec </property>
                  <property> aero/ci2vel </property>
               </product>
               <property> aero/coefficient/dCM_Elev </property>
               <property> aero/coefficient/dCM_Flap </property>
               <property> aero/coefficient/dCM_Power </property>
            </sum>
            <property> aero/qbar-psf </property>
            <property> metrics/Sw-sqft </property>
            <property> metrics/cbarw-ft </property>
         </product>
      </function>

   </axis>

<!-- =
**********************************************************************=20
                YAW MOMENT
     =
********************************************************************** =
-->

   <function name=3D"aero/derivative/CNbeta-per_rad">
      <description>
         Yaw moment coefficient derivative due to sideslip, per rad
         Determines dutch roll and spiral characteristics
         Prevents side-slip and counters yawing moments
      </description>
      <table>
         <independentVar lookup=3D"row"> aero/alpha-deg =
</independentVar>
         <tableData>
             -2.0000     .0680
             16.0000     .0680
         </tableData>
      </table>
   </function>

   <function name=3D"aero/derivative/CNp-per_rad">
      <description>
         Yaw moment coefficient derivative due to roll rate, per rad
         Reduces Dutch Roll damping. Positive value desireable
      </description>
      <table>
         <independentVar lookup=3D"row"> aero/alpha-deg =
</independentVar>
         <tableData>
                 -2.0000         .0001
                   .0000        -.0154
                  2.0000        -.0314
                  4.0000        -.0479
                  8.0000        -.0839
                  9.0000        -.0925
                 10.0000        -.1011
                 11.0000        -.1093
                 12.0000        -.1171
                 13.0000        -.1238
                 14.0000        -.1322
                 15.0000        -.1374
                 16.0000        -.2479
         </tableData>
      </table>
   </function>

   <function name=3D"aero/derivative/CNr-per_rad">
      <description>
         Yaw moment coefficient derivative due to yaw rate, per rad
         Main contributor to damping of Dutch Roll
      </description>
      <table>
         <independentVar lookup=3D"row"> aero/alpha-deg =
</independentVar>
         <tableData>
                 -2.0000        -.1099
                   .0000        -.1111
                  2.0000        -.1118
                  4.0000        -.1121
                  8.0000        -.1115
                  9.0000        -.1113
                 10.0000        -.1110
                 11.0000        -.1107
                 12.0000        -.1104
                 13.0000        -.1102
                 14.0000        -.1100
                 15.0000        -.1101
                 16.0000        -.1111
         </tableData>
      </table>
   </function>

   <function name=3D"aero/coefficient/dCN_Ail">
      <description>
         Yaw Moment coefficient increment due to aileron deflection
         Positive surface deflection is trailing edge down.
         Positive yawing moment is nose right
      </description>
      <table>
         <independentVar lookup=3D"row"> aero/alpha-deg =
</independentVar>
         <independentVar lookup=3D"column"> fcs/total-aileron-pos-deg =
</independentVar>
         <tableData>
                         -64.0000  -40.0000  -20.0000  -10.0000     =
.0000   10.0000   20.0000   40.0000   64.0000
                -2.0000     .0002     .0002     .0001     .0001     =
.0000    -.0001    -.0001    -.0002    -.0002
                  .0000     .0013     .0011     .0007     .0003     =
.0000    -.0003    -.0007    -.0011    -.0013
                 2.0000     .0023     .0020     .0013     .0006     =
.0000    -.0006    -.0013    -.0020    -.0023
                 4.0000     .0034     .0029     .0018     .0009     =
.0000    -.0009    -.0018    -.0029    -.0034
                 8.0000     .0056     .0047     .0030     .0015     =
.0000    -.0015    -.0030    -.0047    -.0056
                 9.0000     .0060     .0050     .0032     .0016     =
.0000    -.0016    -.0032    -.0050    -.0060
                10.0000     .0063     .0053     .0034     .0017     =
.0000    -.0017    -.0034    -.0053    -.0063
                11.0000     .0067     .0056     .0036     .0018     =
.0000    -.0018    -.0036    -.0056    -.0067
                12.0000     .0069     .0058     .0037     .0019     =
.0000    -.0019    -.0037    -.0058    -.0069
                13.0000     .0071     .0060     .0038     .0019     =
.0000    -.0019    -.0038    -.0060    -.0071
                14.0000     .0072     .0061     .0039     .0019     =
.0000    -.0019    -.0039    -.0061    -.0072
                15.0000     .0072     .0060     .0039     .0019     =
.0000    -.0019    -.0039    -.0060    -.0072
                16.0000     .0065     .0054     .0035     .0017     =
.0000    -.0017    -.0035    -.0054    -.0065
         </tableData>
      </table>
   </function>

   <function name=3D"aero/coefficient/dCN_Rud">
      <description>
         Yaw coefficient increment due to rudder
         DATCOM does not calculate this, but a default value is supplied
      </description>
      <table>
         <independentVar lookup=3D"row"> fcs/rudder-pos-deg =
</independentVar>
         <tableData>
            -10.0000    -.0100
               .0000     .0000
             10.0000     .0100
         </tableData>
      </table>
   </function>

   <axis name=3D"YAW">

      <function name=3D"aero/moment/yaw-lbsft">
         <description>
            Yaw Moment =3D ( CNbeta*beta + CNp*p*b/(2*V) + CNr*r*b/(2*V) =
+ dCN_Ail + dCN_Rud )
                         * q_bar * wing area * wing span
         </description>
         <product>
            <sum>
               <product>
                  <property> aero/derivative/CNbeta-per_rad </property>
                  <property> aero/beta-rad </property>
               </product>
               <product>
                  <property> aero/derivative/CNp-per_rad </property>
                  <property> velocities/p-rad_sec </property>
                  <property> aero/bi2vel </property>
               </product>
               <product>
                  <property> aero/derivative/CNr-per_rad </property>
                  <property> velocities/r-rad_sec </property>
                  <property> aero/bi2vel </property>
               </product>
               <property> aero/coefficient/dCN_Ail </property>
               <property> aero/coefficient/dCN_Rud </property>
            </sum>
            <property> aero/qbar-psf </property>
            <property> metrics/Sw-sqft </property>
            <property> metrics/bw-ft </property>
         </product>
      </function>

   </axis>

</aerodynamics>


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All of the data generated in your IT infrastructure is seriously valuable.
Why? It contains a definitive record of application performance, security
threats, fraudulent activity, and more. Splunk takes this data and makes
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