Question: Explain in detail the various external forces commonly acting on a missile flying in the earths atmosphere.Ans: The external forces commonly acting on missiles flying in the earth's atmosphere are: (1) Propulsive force (i.e., Thrust), (2) Aerodynamic forces (Lift and Drag), (3) Gravitational force (Weight). Other forces, such as wind or solar radiation pressure, are small and generally can be neglected for many simple calculations. These forces can be resolved along the missiles body-axis system and fixed to the missiles center of gravity (cg). The reference axis system standardized in guided weapons is centered on the cg and fixed in the body. Thus, any set of axes fixed in a rigid body is a body-fixed reference frame.

Fig: Aerodynamic forces and thrust acting on a missileThrust:

Thrust is defined as the main forward force produced by the propulsion system to sustain the missile in flight. It is produced by the expulsion of a reaction mass, such as the hot gas products of a chemical reaction. It usually acts in the direction along the propeller shaft axis or the rocket nozzle axis. Thrust T, equals the sum of two terms, the momentum thrust and the pressure thrust.

(1)where is the mass expelled in unit time (the propellant mass flow rate), is the exhaust velocity (the average actual velocity of the exhaust gases), is the exhaust pressure, the ambient pressure, and the area of the exit of the motor nozzle.Even when the propellant flow rate and exhaust velocity are constant, so that the thrust force is constant, a rocket will accelerate at an increasing rate because the missiles overall mass decreases as propellant is used up. The change in velocity depends on the missiles initial total weight, glide weight (its final weight after the propellant is expended), thrust magnitude, and the rate at which the propellant is burning.Lift:

Lift is the component of the resultant aerodynamic force that is perpendicular (i.e., upward) to the relative wind (direction of flight) or to the undisturbed free-stream velocity. The aerodynamic lift is produced primarily by the pressure forces acting on the vehicle surface. Also, the lift force is perpendicular to the missiles velocity vector in the vertical plane. The lift is present only when the angle of attack is non-zero.

Drag:

Drag is the component of the resultant aerodynamic force that is parallel to the relative wind. In other words, it is net aerodynamic force acting in the same direction as the undisturbed free-stream velocity. The aerodynamic drag is produced by the pressure forces and by skin friction forces that act on the surface. The drag force is measured along the velocity vector, but in the opposite direction. It is the aerodynamic force in a direction opposite to the flight path due to the resistance of the body to motion in a fluid. It reduces the missile speed, so reducing its acceleration capability. The drag acts as a retarding force, and exists for any angle of attack, including zero.Side force:

In addition to lift and drag, there is another aerodynamic force called side force and it is the component of force in a direction perpendicular to both the lift and the drag and is measured in the horizontal plane. The side force is positive when acting toward the starboard wing, provided that the bank angle is zero.The lift force (L), drag force (D) and Side force (FY) are given by

(2) (3) (4)where

= Lift Coefficient =,

= Drag Coefficient =,

= Side force Coefficient =,

q = Free-stream dynamic pressure at a point far from the airfoil =,

= mass density of the fluid in which the vehicle moves (atmospheric density),

V = Free-stream velocity,

S = typical surface area or reference area, usually the area of one of the airfoils, = total lift coefficient evaluated at = 0 = ,

= total lift-curve slope,

= angle of attack (in radians),

= total drag coefficient evaluated at = 0 (or close to it)

= ,

= total drag coefficient variation with angle of attack =,

= side force coefficient for zero sideslip and zero control deflection = ,

= change in side force coefficient due to a unit sideslip angle =, = sideslip angle (in radians), = change in side force coefficient due to a unit aileron angle =, = aileron angle (in radians).And the drag polar is written in the form (5)where

= zero lift drag coefficient, K = drag due to lift factor (also called the separation drag due to lift factor) =.

Equation (5) states that the total drag may be written as the sum of

(i) the drag that exists when the configuration generates zero lift (), and (ii) the induced drag associated with lift ().The lift and drag coefficients are primarily functions of the vehicle configuration, flight Mach number, and angle of attack, which is the angle between the vehicle axis (or the wing plane) and the flight direction. For low flight speeds the effect of Mach number may be neglected, and the drag and lift coefficients are functions of the angle of attack.For missiles that roll to turn, drag is the same as in equation (3), but the lift and side force are as follows: Lift = (6) Side force = (7)where

= Total lift coefficient in the maneuver plane =,

= Roll angle.

Weight:

Gravitational attraction is exerted upon a flying space vehicle by all planets, stars, the moon, and the sun. Gravity forces pull the vehicle in the direction of the center of mass of the attracting body. Within the immediate vicinity of the earth, the attraction of other planets and bodies is negligibly small compared to the earth's gravitational force. This force is the weight. The gravitational force acting on the missile is given by W = mg.

If the variation of gravity with the geographical features and the oblate shape of the earth are neglected, the acceleration of gravity varies inversely as the square of the distance from the earth's center. If R0 is the radius of the earth's surface and the acceleration on the earth's surface at the earth's effective radius R0, the gravitational attraction g is (8)where h is the altitude. At the equator the earth's radius is 6378.388 km and the standard value of is 9.80665 m/s2.

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