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):

Variable	Variable in Code	Description	Units	Value(s)	Source	Notes
Flight Conditions
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
C_L	CL	lift coefficient	-	?		not available
C_D	CD	drag coefficient	-	?		not available
C_m	Cm	pitching moment coefficient	-	?		not available

The data input into the simulator is listed in the following tables:

Variable	Variable in Code	Description	Units	Value(s)	Source
Geometry
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

e_max demax maximum elevator deflection deg +20 - guess

e_min demin minimum elevator deflection deg -20 - guess

a_max damax maximum aileron deflection deg +20 - guess

a_min damin minimum aileron deflection deg -20 - guess

r_max drmax maximum rudder deflection deg +20 - guess

r_min drmin minimum rudder deflection deg -20 - guess

Control Surface Geometry
Variable	Variable in Code	Description	Units	Value(s)	Source	Notes
e_max	demax	maximum elevator deflection	deg	+20	-	guess
e_min	demin	minimum elevator deflection	deg	-20	-	guess
a_max	damax	maximum aileron deflection	deg	+20	-	guess
a_min	damin	minimum aileron deflection	deg	-20	-	guess
r_max	drmax	maximum rudder deflection	deg	+20	-	guess
r_min	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

I_xx I_xx roll inertia slug ft² 10085 Roskam pg 508

I_yy I_yy pitch inertia slug ft² 15148 Roskam pg 508

I_zz I_zz yaw inertia slug ft² 23046 Roskam pg 508

I_xz I_xz lateral cross inertia slug ft² 1600 Roskam pg 508

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
I_xx	I_xx	roll inertia	slug ft²	10085	Roskam pg 508
I_yy	I_yy	pitch inertia	slug ft²	15148	Roskam pg 508
I_zz	I_zz	yaw inertia	slug ft²	23046	Roskam pg 508
I_xz	I_xz	lateral cross inertia	slug ft²	1600	Roskam pg 508

Propulsion Data

Variable Variable
in Code Description Units Value(s) Source Notes

T_max simpleSingleMaxThrust maximum thrust lb 1550 Roskam pg 509 estimated from C_{T_x}
at sea level

P_max - maximum power kW 1106 David pg 103 max engine rating
not used in code

Propulsion Data
Variable	Variable in Code	Description	Units	Value(s)	Source	Notes
T_max	simpleSingleMaxThrust	maximum thrust	lb	1550	Roskam pg 509	estimated from C_{T_x} at sea level
P_max	-	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

C_D₀ CDo drag coefficient at =0 - 0.027 Roskam pg 509

C_D CD_a drag curve slope 1/rad 0.131 Roskam pg 509

C_{D_e} CD_de drag due to elevator 1/rad 0 Roskam pg 509 e positive down

C_L₀ CLo lift coefficient at =0 - 0.201 Roskam pg 509

C_L CL_a lift curve slope 1/rad 5.48 Roskam pg 509

C_L CL_adot lift due to angle of attack rate 1/rad 2.5 Roskam pg 509

C_{L_q} CL_q lift due to pitch rate 1/rad 8.1 Roskam pg 509

C_{L_e} CL_de lift due to elevator 1/rad 0.60 Roskam pg 509 e positive down

C_m₀ Cmo pitch moment coefficient at =0 - 0.05 Roskam pg 509

C_m Cm_a pitch moment due to angle of attack 1/rad -1.89 Roskam pg 509

C_m Cm_adot pitch moment due to angle of attack rate 1/rad -9.1 Roskam pg 509

C_{m_q} Cm_q pitch moment due to pitch rate 1/rad -34.0 Roskam pg 509

C_{m_e} Cm_de pitching moment due to elevator 1/rad -2.0 Roskam pg 509 e positive down

C_Y CY_beta side force fue to sideslip angle 1/rad -0.59 Roskam pg 510

C_{Y_p} CY_p side force due to roll rate 1/rad -0.19 Roskam pg 510

C_{Y_r} CY_r side force due to yaw rate 1/rad 0.39 Roskam pg 510

C_{Y_a} CY_da side force due to aileron 1/rad 0 Roskam pg 510 a positive
right aileron up

C_{Y_r} CY_dr side force due to rudder 1/rad 0.148 Roskam pg 510 r positive left

C_l Cl_beta dihedral effect 1/rad -0.13 Roskam pg 510

C_{l_p} Cl_p roll damping 1/rad -0.50 Roskam pg 510

C_{l_r} Cl_r roll moment due to yaw rate 1/rad 0.14 Roskam pg 510

C_{l_a} Cl_da roll moment due to aileron 1/rad -0.156 Roskam pg 510 a positive
right aileron up

C_{l_r} Cl_dr roll moment due to rudder 1/rad 0.0109 Roskam pg 510 r positive left

C_n Cn_beta weathercock stability 1/rad 0.080 Roskam pg 510

C_{n_p} Cn_p adverse yaw 1/rad 0.019 Roskam pg 510

C_{n_r} Cn_r yaw damping 1/rad -0.197 Roskam pg 510

C_{n_a} Cn_da yaw moment due to aileron 1/rad 0.0012 Roskam pg 510 a positive
right aileron up

C_{n_r} Cn_dr yaw moment due to rudder 1/rad -0.0772 Roskam pg 510 r positive left

Variable	Variable in Code	Description	Units	Value(s)	Source	Notes
Aerodynamic Data
C_D₀	CDo	drag coefficient at =0	-	0.027	Roskam pg 509
C_D	CD_a	drag curve slope	1/rad	0.131	Roskam pg 509
C_{D_e}	CD_de	drag due to elevator	1/rad	0	Roskam pg 509	e positive down
C_L₀	CLo	lift coefficient at =0	-	0.201	Roskam pg 509
C_L	CL_a	lift curve slope	1/rad	5.48	Roskam pg 509
C_L	CL_adot	lift due to angle of attack rate	1/rad	2.5	Roskam pg 509
C_{L_q}	CL_q	lift due to pitch rate	1/rad	8.1	Roskam pg 509
C_{L_e}	CL_de	lift due to elevator	1/rad	0.60	Roskam pg 509	e positive down
C_m₀	Cmo	pitch moment coefficient at =0	-	0.05	Roskam pg 509
C_m	Cm_a	pitch moment due to angle of attack	1/rad	-1.89	Roskam pg 509
C_m	Cm_adot	pitch moment due to angle of attack rate	1/rad	-9.1	Roskam pg 509
C_{m_q}	Cm_q	pitch moment due to pitch rate	1/rad	-34.0	Roskam pg 509
C_{m_e}	Cm_de	pitching moment due to elevator	1/rad	-2.0	Roskam pg 509	e positive down
C_Y	CY_beta	side force fue to sideslip angle	1/rad	-0.59	Roskam pg 510
C_{Y_p}	CY_p	side force due to roll rate	1/rad	-0.19	Roskam pg 510
C_{Y_r}	CY_r	side force due to yaw rate	1/rad	0.39	Roskam pg 510
C_{Y_a}	CY_da	side force due to aileron	1/rad	0	Roskam pg 510	a positive right aileron up
C_{Y_r}	CY_dr	side force due to rudder	1/rad	0.148	Roskam pg 510	r positive left
C_l	Cl_beta	dihedral effect	1/rad	-0.13	Roskam pg 510
C_{l_p}	Cl_p	roll damping	1/rad	-0.50	Roskam pg 510
C_{l_r}	Cl_r	roll moment due to yaw rate	1/rad	0.14	Roskam pg 510
C_{l_a}	Cl_da	roll moment due to aileron	1/rad	-0.156	Roskam pg 510	a positive right aileron up
C_{l_r}	Cl_dr	roll moment due to rudder	1/rad	0.0109	Roskam pg 510	r positive left
C_n	Cn_beta	weathercock stability	1/rad	0.080	Roskam pg 510
C_{n_p}	Cn_p	adverse yaw	1/rad	0.019	Roskam pg 510
C_{n_r}	Cn_r	yaw damping	1/rad	-0.197	Roskam pg 510
C_{n_a}	Cn_da	yaw moment due to aileron	1/rad	0.0012	Roskam pg 510	a positive right aileron up
C_{n_r}	Cn_dr	yaw moment due to rudder	1/rad	-0.0772	Roskam pg 510	r positive left

Beech 99 -- Linear Model

Flight Sim Home * Aircraft Models * Beech 99 Model * Beech 99 References

**Flight Sim Home * Aircraft Models * Beech 99 Model * Beech 99 References**