Beech 99 -- Linear Model
Advisor: Prof. Michael Selig
Applied Aerodynamics Group
Department of Aeronautical and Astronautical Engineering
University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
Last updated April 11, 2000
The linear aerodynamics model uses stability derivatives to approximate actual aircraft behavior. The Beech 99 linear model is based on the following flight conditions (low altitude cruise):
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| Variable |
Variable in Code |
Description | Units | Value(s) | Source | Notes |
|---|---|---|---|---|---|---|
| h | Altitude | altitude above sea level | ft | 5000 | Roskam pg 508 |
|
Alpha | angle of attack | deg | 0 | Roskam pg 508 |
V
|
V_true_kts | velocity (true air speed) | kts | 201 | Roskam pg 508 | Mach 0.31 |
| q | Dynamic_pressure | dynamic pressure | lb/ft2 | 118.3 | Roskam pg 508 | |
| C.G. | - | center of gravity location |
% 
|
16 | Roskam pg 508 | |
| CL | CL | lift coefficient | - | ? | not available | |
| CD | CD | drag coefficient | - | ? | not available | |
| Cm | Cm | pitching moment coefficient | - | ? | not available | |
The data input into the simulator is listed in the following tables:
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| Variable |
Variable in Code |
Description | Units | Value(s) | Source | Notes |
|---|---|---|---|---|---|---|
| b | bw | wingspan | ft | 46 | Roskam pg 508 | |
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cbar | wing mean aerodynamic chord | ft | 6.5 | Roskam pg 508 | |
| S | Sw | wing surface area | ft2 | 280 | Roskam pg 508 | |
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| Variable |
Variable in Code |
Description | Units | Value(s) | Source | Notes |
|---|---|---|---|---|---|---|
 emax
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demax | maximum elevator deflection | deg | +20 | - | guess |
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emin
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demin | minimum elevator deflection | deg | -20 | - | guess |
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amax
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damax | maximum aileron deflection | deg | +20 | - | guess |
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amin
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damin | minimum aileron deflection | deg | -20 | - | guess |
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rmax
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drmax | maximum rudder deflection | deg | +20 | - | guess |
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rmin
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drmin | minimum rudder deflection | deg | -20 | - | guess |
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| Variable |
Variable in Code |
Description | Units | Value(s) | Source | Notes |
|---|---|---|---|---|---|---|
| W | Weight | weight at flight condition | lb | 7000 | Roskam pg 508 |
converted to Mass [slug/ft3] in code |
| Ixx | I_xx | roll inertia | slug ft2 | 10085 | Roskam pg 508 | |
| Iyy | I_yy | pitch inertia | slug ft2 | 15148 | Roskam pg 508 | |
| Izz | I_zz | yaw inertia | slug ft2 | 23046 | Roskam pg 508 | |
| Ixz | I_xz | lateral cross inertia | slug ft2 | 1600 | Roskam pg 508 | |
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| Variable |
Variable in Code |
Description | Units | Value(s) | Source | Notes |
|---|---|---|---|---|---|---|
| Tmax | simpleSingleMaxThrust | maximum thrust | lb | 1550 | Roskam pg 509 |
estimated from CTx at sea level |
| Pmax | - | maximum power | kW | 1106 | David pg 103 |
max engine rating not used in code |
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| Variable |
Variable in Code |
Description | Units | Value(s) | Source | Notes |
|---|---|---|---|---|---|---|
| CD0 | CDo |
drag coefficient at =0
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- | 0.027 | Roskam pg 509 | |
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CD
|
CD_a | drag curve slope | 1/rad | 0.131 | Roskam pg 509 | |
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CDe
|
CD_de | drag due to elevator | 1/rad | 0 | Roskam pg 509 |
e positive down
|
| CL0 | CLo |
lift coefficient at =0
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- | 0.201 | Roskam pg 509 | |
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CL
|
CL_a | lift curve slope | 1/rad | 5.48 | Roskam pg 509 | |
CL
|
CL_adot | lift due to angle of attack rate | 1/rad | 2.5 | Roskam pg 509 | |
| CLq | CL_q | lift due to pitch rate | 1/rad | 8.1 | Roskam pg 509 | |
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CLe
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CL_de | lift due to elevator | 1/rad | 0.60 | Roskam pg 509 |
e positive down
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| Cm0 | Cmo |
pitch moment coefficient at =0
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- | 0.05 | Roskam pg 509 | |
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Cm
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Cm_a | pitch moment due to angle of attack | 1/rad | -1.89 | Roskam pg 509 | |
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Cm
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Cm_adot | pitch moment due to angle of attack rate | 1/rad | -9.1 | Roskam pg 509 | |
| Cmq | Cm_q | pitch moment due to pitch rate | 1/rad | -34.0 | Roskam pg 509 | |
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Cme
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Cm_de | pitching moment due to elevator | 1/rad | -2.0 | Roskam pg 509 |
e positive down
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CY
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CY_beta | side force fue to sideslip angle | 1/rad | -0.59 | Roskam pg 510 | |
| CYp | CY_p | side force due to roll rate | 1/rad | -0.19 | Roskam pg 510 | |
| CYr | CY_r | side force due to yaw rate | 1/rad | 0.39 | Roskam pg 510 | |
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CYa
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CY_da | side force due to aileron | 1/rad | 0 | Roskam pg 510 |
a positive right aileron up |
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CYr
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CY_dr | side force due to rudder | 1/rad | 0.148 | Roskam pg 510 |
r positive left
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Cl
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Cl_beta | dihedral effect | 1/rad | -0.13 | Roskam pg 510 | |
| Clp | Cl_p | roll damping | 1/rad | -0.50 | Roskam pg 510 | |
| Clr | Cl_r | roll moment due to yaw rate | 1/rad | 0.14 | Roskam pg 510 | |
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Cla
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Cl_da | roll moment due to aileron | 1/rad | -0.156 | Roskam pg 510 |
a positive right aileron up |
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Clr
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Cl_dr | roll moment due to rudder | 1/rad | 0.0109 | Roskam pg 510 |
r positive left
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Cn
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Cn_beta | weathercock stability | 1/rad | 0.080 | Roskam pg 510 | |
| Cnp | Cn_p | adverse yaw | 1/rad | 0.019 | Roskam pg 510 | |
| Cnr | Cn_r | yaw damping | 1/rad | -0.197 | Roskam pg 510 | |
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Cna
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Cn_da | yaw moment due to aileron | 1/rad | 0.0012 | Roskam pg 510 |
a positive right aileron up |
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Cnr
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Cn_dr | yaw moment due to rudder | 1/rad | -0.0772 | Roskam pg 510 |
r positive left
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