# Marchetti S-211 -- 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 June 7, 2000

The linear aerodynamics model uses stability derivatives to approximate actual aircraft behavior. The Marchetti S-211 linear model is based on the following flight conditions (cruise 1):

Flight Conditions
Variable | Variable in Code | Description | Units | Value(s) | Source | Notes
--- | --- | --- | --- | --- | --- | ---
h | Altitude | altitude above sea level | ft | 25000 | Roskam pg 494 |
|  | Alpha | angle of attack | deg | 0 | Roskam pg 494 |
V | V_true_kts | velocity (true air speed) | kts | 361.2 | Roskam pg 494 | Mach 0.6
q | Dynamic_pressure | dynamic pressure | lb/ft2 | 198.0 | Roskam pg 494 |
C.G. | - | center of gravity location | % | 25 | Roskam pg 494 |
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 | 26.3 | Roskam pg 494 |
| cbar | wing mean aerodynamic chord | ft | 5.4 | Roskam pg 494 |
S | Sw | wing surface area | ft2 | 136 | Roskam pg 494 |

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 | 4000 | Roskam pg 494 | converted to Mass [slug/ft3] in code
Ixx | I_xx | roll inertia | slug ft2 | 800 | Roskam pg 494 |
Iyy | I_yy | pitch inertia | slug ft2 | 4800 | Roskam pg 494 |
Izz | I_zz | yaw inertia | slug ft2 | 5200 | Roskam pg 494 |
Ixz | I_xz | lateral cross inertia | slug ft2 | 200 | Roskam pg 494 |

Propulsion Data
Variable | Variable in Code | Description | Units | Value(s) | Source | Notes
--- | --- | --- | --- | --- | --- | ---
Tmax | simpleSingleMaxThrust | maximum thrust | lb | 600 | Roskam pg 495 | estimated from CTx at cruise 1
Tmax | simpleSingleMaxThrust | maximum thrust | lb | 2500 | David pg 801 | engine rating

Aerodynamic Data
Variable | Variable in Code | Description | Units | Value(s) | Source | Notes
--- | --- | --- | --- | --- | --- | ---
CD0 | CDo | drag coefficient at =0 | - | 0.0205 | Roskam pg 495 |
CD | CD_a | drag curve slope | 1/rad | 0.12 | Roskam pg 495 |
CDe | CD_de | drag due to elevator | 1/rad | 0 | Roskam pg 495 | e positive down
CL0 | CLo | lift coefficient at =0 | - | 0.149 | Roskam pg 495 |
CL | CL_a | lift curve slope | 1/rad | 5.5 | Roskam pg 495 |
CL | CL_adot | lift due to angle of attack rate | 1/rad | 4.2 | Roskam pg 495 |
CLq | CL_q | lift due to pitch rate | 1/rad | 10.0 | Roskam pg 495 |
CLe | CL_de | lift due to elevator | 1/rad | 0.38 | Roskam pg 495 | e positive down
Cm0 | Cmo | pitch moment coefficient at =0 | - | -0.08 | Roskam pg 495 |
Cm | Cm_a | pitch moment due to angle of attack | 1/rad | -0.24 | Roskam pg 495 |
Cm | Cm_adot | pitch moment due to angle of attack rate | 1/rad | -9.6 | Roskam pg 495 |
Cmq | Cm_q | pitch moment due to pitch rate | 1/rad | -17.7 | Roskam pg 495 |
Cme | Cm_de | pitching moment due to elevator | 1/rad | -0.88 | Roskam pg 495 | e positive down
CY | CY_beta | side force fue to sideslip angle | 1/rad | -1.0 | Roskam pg 496 |
CYp | CY_p | side force due to roll rate | 1/rad | -0.14 | Roskam pg 496 |
CYr | CY_r | side force due to yaw rate | 1/rad | 0.61 | Roskam pg 496 |
CYa | CY_da | side force due to aileron | 1/rad | 0 | Roskam pg 496 | a positive right aileron up
CYr | CY_dr | side force due to rudder | 1/rad | 0.028 | Roskam pg 496 | r positive left
Cl | Cl_beta | dihedral effect | 1/rad | -0.11 | Roskam pg 496 |
Clp | Cl_p | roll damping | 1/rad | -0.39 | Roskam pg 496 |
Clr | Cl_r | roll moment due to yaw rate | 1/rad | 0.28 | Roskam pg 496 |
Cla | Cl_da | roll moment due to aileron | 1/rad | -0.10 | Roskam pg 496 | a positive right aileron up
Clr | Cl_dr | roll moment due to rudder | 1/rad | 0.05 | Roskam pg 496 | r positive left
Cn | Cn_beta | weathercock stability | 1/rad | 0.17 | Roskam pg 496 |
Cnp | Cn_p | adverse yaw | 1/rad | 0.09 | Roskam pg 496 |
Cnr | Cn_r | yaw damping | 1/rad | -0.26 | Roskam pg 496 |
Cna | Cn_da | yaw moment due to aileron | 1/rad | 0.003 | Roskam pg 496 | a positive right aileron up
Cnr | Cn_dr | yaw moment due to rudder | 1/rad | -0.12 | Roskam pg 496 | r positive left

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