Appendix A - Equations

Drag equation: D = CD * S * ˝ r * V^2 D = drag, or the force which acts parallel to the relative wind opposite to the direction of flight. S = Surface Area, or the equation of length multiplied by width multiplied by depth. r = air density, or the number of air particles per cubic slug unit. A slug unit is equal to the amount of mass which would accelerate at a rate of one foot per second squared under a force of one pound force. V = Velocity, or a vector quantity whose magnitude is a body’s speed and whose direction is the body’s direction of motion. This equation is the general equation for determining the drag against an object in flight. Coefficient of Drag: CD = CDI + CDP CD = Coefficient of drag, or the number used to model all of the complex dependencies of drag on shape inclination and some flow conditions. This equation is used because the result is a variable in the main drag equation. Coefficient of Induced Drag: CDI = CL^2 / p * e * AR CDI = Coefficient of induced drag, or the drag produced by the factor of lift. p = pi, or 3.14. This unit was used to determine the radius of our spherical objects. AR = Aspect Ratio, or how long and slender a shape is from tip to tip. e = Oswald efficiency factor, or the number less than or equal to one. It accounts for profile drag variation and non-elliptical wing shapes. It represents the efficiency of the object. This equation is used because the result provides a value that is used in the equation for the coefficient of drag. Coefficient of Parasite Drag: CDP = CL0^2 / p * e * AR CDP = Coefficient of Parasite drag, or equal to the induced drag at 0 lift. This equation is used because the result provides a value that is used in the equation for the coefficient of drag. Coefficient of Lift: CL = (2 * M) / (S * r * V^2) CL = Coefficient of Lift, or the number use to model all of the complex dependencies of lift on shape inclination and some flow conditions. M = Mass, the weight of the object in slug units. This equation is used because the result provides a value that is used in the equation for the coefficient of induced drag.