# Pioneer -- 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 10, 2000

The linear aerodynamics model uses stability derivatives to approximate actual aircraft behavior. The Pioneer linear model is based on the following flight conditions:

Flight Conditions
Variable | Variable in Code | Description | Units | Value(s) | Source | Notes
--- | --- | --- | --- | --- | --- | ---
h | Altitude | altitude above sea level | ft | 0 | - | assuming sea level
|  | Alpha | angle of attack | deg | 6 | Bray pg 33 |
V | V_true_kts | velocity (true air speed) | kts | 66 | Bray pg 33 |
q | Dynamic_pressure | dynamic pressure | lb/ft2 | 14.7 | - | assuming sea level
C.G. | - | center of gravity location | % | 33 | Bray pg 33 |
CL | CL | lift coefficient | - | 0.945 | Bray pg 33 |
CD | CD | drag coefficient | - | 0.090 | Bray pg 33 |
Cm | Cm | pitching moment coefficient | - | 0.012 | Bray pg 33 |

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 | 16.9 | Bray pg 33 |
| cbar | wing mean aerodynamic chord | ft | 1.80 | Bray pg 33 |
S | Sw | wing surface area | ft2 | 30.42 | Bray pg 33 |

Control Surface Geometry
Variable | Variable in Code | Description | Units | Value(s) | Source | Notes
--- | --- | --- | --- | --- | --- | ---
emax | demax | maximum elevator deflection | deg | +20 | Bray pg 31 |
emin | demin | minimum elevator deflection | deg | -20 | Bray pg 31 |
amax | damax | maximum aileron deflection | deg | +20 | Bray pg 31 |
amin | damin | minimum aileron deflection | deg | -20 | Bray pg 31 |
rmax | drmax | maximum rudder deflection | deg | +20 | Bray pg 31 |
rmin | drmin | minimum rudder deflection | deg | -20 | Bray pg 31 |

Mass Data
Variable | Variable in Code | Description | Units | Value(s) | Source | Notes
--- | --- | --- | --- | --- | --- | ---
GTOW | Weight | gross takeoff weight | lb | 420 | Bray pg 33 | converted to Mass [slug/ft3] in code
Ixx | I_xx | roll inertia | slug ft2 | 34.832 | IAI (manufacturer) MSS notes |
Iyy | I_yy | pitch inertia | slug ft2 | 67.08 | IAI (manufacturer) MSS notes |
Izz | I_zz | yaw inertia | slug ft2 | 82.22 | IAI (manufacturer) MSS notes |
Ixz | I_xz | lateral cross inertia | slug ft2 | -4.902 | IAI (manufacturer) MSS notes |

Propulsion Data
Variable | Variable in Code | Description | Units | Value(s) | Source | Notes
--- | --- | --- | --- | --- | --- | ---
Tmax | simpleSingleMaxThrust | maximum thrust | lb | 150 | - | approximated from max power of 27 hp

Aerodynamic Data
Variable | Variable in Code | Description | Units | Value(s) | Source | Notes
--- | --- | --- | --- | --- | --- | ---
CD0 | CDo | drag coefficient at =0 | - | 0.060 | Bray pg 33 |
CD | CD_a | drag curve slope | 1/rad | 0.430 | Bray pg 33 |
CDe | CD_de | drag due to elevator | 1/rad | 0.018 | Bray pg 33 | e positive down
CL0 | CLo | lift coefficient at =0 | - | 0.385 | Bray pg 33 |
CL | CL_a | lift curve slope | 1/rad | 4.78 | Bray pg 33 |
CL | CL_adot | lift due to angle of attack rate | 1/rad | 2.42 | Bray pg 33 |
CLq | CL_q | lift due to pitch rate | 1/rad | 8.05 | Bray pg 33 |
CLe | CL_de | lift due to elevator | 1/rad | 0.401 | Bray pg 33 | e positive down
Cm0 | Cmo | pitch moment coefficient at =0 | - | 0.194 | Bray pg 33 |
Cm | Cm_a | pitch moment due to angle of attack | 1/rad | -2.12 | Bray pg 33 |
Cm | Cm_adot | pitch moment due to angle of attack rate | 1/rad | -11.0 | Bray pg 33 |
Cmq | Cm_q | pitch moment due to pitch rate | 1/rad | -36.6 | Bray pg 33 |
Cme | Cm_de | pitching moment due to elevator | 1/rad | -1.76 | Bray pg 33 | e positive down
CY | CY_beta | side force fue to sideslip angle | 1/rad | -0.819 | Bray pg 33 |
CYp | CY_p | side force due to roll rate | 1/rad | none |  | not available
CYr | CY_r | side force due to yaw rate | 1/rad | none |  | not available
CYa | CY_da | side force due to aileron | 1/rad | none |  | not available
CYr | CY_dr | side force due to rudder | 1/rad | 0.191 | Bray pg 33 | r positive left
Cl | Cl_beta | dihedral effect | 1/rad | -0.023 | Bray pg 33 |
Clp | Cl_p | roll damping | 1/rad | -0.450 | Bray pg 33 |
Clr | Cl_r | roll moment due to yaw rate | 1/rad | 0.265 | Bray pg 33 |
Cla | Cl_da | roll moment due to aileron | 1/rad | -0.161 | Bray pg 33 | a positive right aileron up
Clr | Cl_dr | roll moment due to rudder | 1/rad | -0.00229 | Bray pg 33 | r positive left
Cn | Cn_beta | weathercock stability | 1/rad | 0.109 | Bray pg 33 |
Cnp | Cn_p | adverse yaw | 1/rad | -0.110 | Bray pg 33 |
Cnr | Cn_r | yaw damping | 1/rad | -0.200 | Bray pg 33 |
Cna | Cn_da | yaw moment due to aileron | 1/rad | 0.020 | Bray pg 33 | a positive right aileron up
Cnr | Cn_dr | yaw moment due to rudder | 1/rad | -0.0917 | Bray pg 33 | r positive left

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