Aerodynamic Coefficients of Extended Medium Range Air-to-Air Technology (EMRAAT) Missile

This parameter list belongs to EMRAAT missile used by Smith (1989).

 EMRAAT Missile Airframe

The data listed is for the airframe with no fuel (empty weight). The first variables listed are those that do not change.

d = Missile reference diameter (0.625 ft = 0.1905 m)

S = Missile reference area (0.3067 ft² = 0.0285 m²)

m = Missile mass (empty) (227 lb = 102.9672 kg) 


Moments of Inertia:

Ixx = 1.08 slug.ft² = 1.4643 kg.m²

Iyy = 70.13 slug.ft² = 95.0823 kg.m²

Izz = 70.66 slug.ft² = 95.8008 kg.m²

Unfortunately, Smith (1989) do not list the length of missile. But, using Iyy, m, and d, we can estimate the length using this relation

                Iyy = (1/12)mL² + (1/16)md²

then L = 3.333 m.

Products of Inertia:

Ixy = 0.274 slug.ft² = 0.3715 kg.m²

Ixz = 0.704 slug.ft² = 0.9545 kg.m²

Iyz = -0.017 slug.ft² = 0.0230 kg.m²

The following data is a function of the flight conditions. The data is listed for two conditions:

Condition #1:

                Angle-of-attack 10 degrees

                Sideslip angle    0 degrees

                Roll rate               0 deg/sec

                Pitch rate            0 deg/sec

    Yaw rate              0 deg/sec

    Altitude               40.000 ft

    Mach                     2.5

Condition #2:

                Angle-of-attack 10 degrees

                Sideslip angle    0 degrees

                Roll rate               0 deg/sec

                Pitch rate            0 deg/sec

    Yaw rate              0 deg/sec

    Altitude               65.000 ft

    Mach                     3

Q  Dynamic pressure:

                Condition 1: 1719.93 lb/ft² = 82350.2484 N/m²

                Condition 2: 749.29 lb/ft² = 35876.0052 N/m

Aerodynamic Force Equation:

Fy = QS(C_Yββ + C_Ypp + C_Yrr + C_Yδpδp + C_Yδrδr)

Fz = QS(C_Nαα + C_Nα̇α̇ + C_Nqq + C_Nδqδq)

Aerodynamic Momen Equation:

l = QSd(C_lββ + C_lpp + C_lrr + C_lδpδp + C_lδrδr)

m = QSd(C_mαα + C_mα̇α̇ + C_mqq + C_mδqδq)

n = QSd(C_nββ + C_npp + C_nrr + C_nδpδp + C_nδrδr)

Following are the aerodynamic derivatives (units are per rad). Note that C_Nα was obtained by taking the slope of the aerodynamic derivative C_N (not listed).

	Condition 1	Condition 2
CNα	-50.7067	-47.3550
CNα̇	0.0221	0.0182
CNq	-0.0103	-0.0082
CNδq	-3.1182	-2.4653
CYβ	-16.1902	16.2871
CYp	-0.0004	-0.0003
CYr	0.0082	-0.0051
CYδp	0.2229	0.5171
CYδr	3.5252	3.2733
Clβ	-9.3923	-7.5674
Clp	-0.0069	-0.0027
Clr	0.0011	0.0051
Clδp	-4.0739	-3.2080
Clδr	-5.5816	-4.7366
Cmα	-17.6108	-16.8330
Cmα̇	0.0124	0.0182
Cmq	-0.1329	-0.1043
Cmδq	-25.4394	-20.4340
Cnβ	3.6044	1.9920
Cnp	0.0026	0.0019
Cnr	-0.1231	-0.928
Cnδp	5.8220	5.7507
Cnδr	-28.4375	-25.7876

Reference

Smith, Roger L. (1989). An Autopilot Design Methodology for Bank-to-Turn Missiles. Interim Report for Air Force Systems Command, US Air Force, Florida.