Definition of Terms and Symbols

Terms and Symbols

Below is a list of the terms and symbols used in Ferram Aerospace Research (FAR), with a general description of each. A more in-depth discussion of flight dynamics can be found on wikipedia.

Coordinate System

FAR uses a standard airplane coordinate system, with an origin at the aircraft center of mass, a X (Roll) axis coming out of the nose of the aircraft, a Y (Pitch) axis coming out of the right wing, and a Z (Yaw) axis coming out of the bottom of the aircraft.

General Flight Condition Terms

• M: Mach Number
  • The vehicle's current velocity divided by the local speed of sound
• α: Angle of Attack
  • The angle between the mean chord of the wing and the free-stream velocity
• β: Sideslip Angle
  • The angle between the center line of the airplane or rocket and the free-stream velocity in the lateral plane
• u: Forward Velocity
• w: Vertical Velocity
• v: Lateral Velocity / Total Velocity
  • 'v' is used to denote the lateral velocity and the total velocity (the magnitude of the vector formed with the u, v, and w components). To determine what 'v' represents at any given time, one must use context. In FAR, however, 'v' usually refers to total velocity, and instances where lateral velocity is required are usually handled with β.
• q: Pitch Rate
• p: Roll Rate
• r: Yaw Rate
• L: Lift / Rolling Moment
  • The symbol 'L' is used to represent both lift and rolling moment. To determine what 'L' represents at any given time, one must use context. For longitudinal performance, 'L' typically represents lift. For lateral performance, 'L' typically represents rolling moment.
• D: Drag
• Y: Sideforce
• M: Pitching Moment
• N: Yawing Moment
• X: Net force in the X-direction
• Y: Net force in the Y-direction
• Z: Net force in the Z-direction

Coefficients

• C_L: Lift Coefficient
• C_D: Drag Coefficient
• C_M: Pitching Moment Coefficient
• C_Y: Side Force Coefficient
• C_l: Rolling Moment Coefficient
• C_N: Yawing Moment Coefficient

Stability Derivatives

Longitudinal Derivatives:

• Z_w: How Z-force changes with vertical speed
• X_w: How X-force changes with vertical speed
• M_w: How pitching moment changes with vertical speed
• Z_u: How Z-force changes with forward speed
• X_u: How X-force changes with forward speed
• M_u: How pitching moment changes with forward speed
• Z_q: How Z-force changes with pitch rate
• X_q: How X-force changes with pitch rate
• M_q: How pitching moment changes with pitch rate
• Z_δe: How Z-force changes with elevator deflection
• X_δe: How X-force changes with elevator deflection
• M_δe: How pitching moment changes with elevator deflection

Lateral Derivatives:

• Y_β: How sideforce changes with sideslip
• L_β: How rolling moment changes with sideslip
• N_β: How yawing moment changes with sideslip
• Y_p: How sideforce changes with roll rate
• L_p: How rolling moment changes with roll rate
• N_p: How yawing moment changes with roll rate
• Y_r: How sideforce changes with yaw rate
• L_r: How rolling moment changes with yaw rate
• N_r: How yawing moment changes with yaw rate