# Beech 99 -- Linear Model

Graduate Research done by Jeff Scott
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):

Flight Conditions
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:

Geometry
Variable | Variable in Code | Description | Units | Value(s) | Source | Notes
--- | --- | --- | --- | --- | --- | ---
b | bw | wingspan | ft | 46 | Roskam pg 508 |
| cbar | wing mean aerodynamic chord | ft | 6.5 | Roskam pg 508 |
S | Sw | wing surface area | ft2 | 280 | Roskam pg 508 |

Control Surface Geometry
Variable | Variable in Code | Description | Units | Value(s) | Source | Notes
--- | --- | --- | --- | --- | --- | ---
emax | demax | maximum elevator deflection | deg | +20 | - | guess
emin | demin | minimum elevator deflection | deg | -20 | - | guess
amax | damax | maximum aileron deflection | deg | +20 | - | guess
amin | damin | minimum aileron deflection | deg | -20 | - | guess
rmax | drmax | maximum rudder deflection | deg | +20 | - | guess
rmin | drmin | minimum rudder deflection | deg | -20 | - | guess

Mass Data
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 |

Propulsion Data
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

Aerodynamic Data
Variable | Variable in Code | Description | Units | Value(s) | Source | Notes
--- | --- | --- | --- | --- | --- | ---
CD0 | CDo | drag coefficient at =0 | - | 0.027 | Roskam pg 509 |
CD | CD_a | drag curve slope | 1/rad | 0.131 | Roskam pg 509 |
CDe | CD_de | drag due to elevator | 1/rad | 0 | Roskam pg 509 | e positive down
CL0 | CLo | lift coefficient at =0 | - | 0.201 | Roskam pg 509 |
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 |
CLe | CL_de | lift due to elevator | 1/rad | 0.60 | Roskam pg 509 | e positive down
Cm0 | Cmo | pitch moment coefficient at =0 | - | 0.05 | Roskam pg 509 |
Cm | Cm_a | pitch moment due to angle of attack | 1/rad | -1.89 | Roskam pg 509 |
Cm | 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 |
Cme | Cm_de | pitching moment due to elevator | 1/rad | -2.0 | Roskam pg 509 | e positive down
CY | 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 |
CYa | CY_da | side force due to aileron | 1/rad | 0 | Roskam pg 510 | a positive right aileron up
CYr | CY_dr | side force due to rudder | 1/rad | 0.148 | Roskam pg 510 | r positive left
Cl | 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 |
Cla | Cl_da | roll moment due to aileron | 1/rad | -0.156 | Roskam pg 510 | a positive right aileron up
Clr | Cl_dr | roll moment due to rudder | 1/rad | 0.0109 | Roskam pg 510 | r positive left
Cn | 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 |
Cna | Cn_da | yaw moment due to aileron | 1/rad | 0.0012 | Roskam pg 510 | a positive right aileron up
Cnr | Cn_dr | yaw moment due to rudder | 1/rad | -0.0772 | Roskam pg 510 | r positive left

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