page_title: Flight dynamics (spacecraft)
section_title: Powered flight
hierarchical_section_title: Flight dynamics (spacecraft) / Powered flight
context_page_description: Spacecraft flight dynamics is the application of mechanical dynamics to model how the external forces acting on a space vehicle or spacecraft determine its flight path. These forces are primarily of three types: propulsive force provided by the vehicle's engines; gravitational force exerted by the Earth and other celestial bodies; and aerodynamic lift and drag.
  The principles of flight dynamics are used to model a spacecraft's orbital flight; maneuvers to change orbit; translunar and interplanetary flight; a vehicle's powered flight during launch from the Earth, or spacecraft launch and landing on a celestial body, with or without an atmosphere; entry through the atmosphere of the Earth or other celestial body; and attitude control. They are generally programmed into a vehicle's inertial navigation systems, and monitered on the ground by a member of the flight controller team known in NASA as the flight dynamics officer, or in the European Space Agency as the spacecraft navigator.
  Flight dynamics depends on the disciplines of propulsion, aerodynamics, and astrodynamics.
context_section_description: The equations of motion used to describe powered flight of a vehicle during launch can be as complex as six degrees of freedom for in-flight calculations, or as simple as two degrees of freedom for preliminary performance estimates. In-flight calculations will take perturbation factors into account such as the Earth's oblateness and non-uniform mass distribution; and gravitational forces of all nearby bodies, including the Moon, Sun, and other planets. Preliminary estimates can make some simplifying assumptions: a spherical, uniform planet; the vehicle can be represented as a point mass; flight path assumes a two-body patched conic approximation; and the  local flight path lies in a single plane) with reasonably small loss of accuracy.
  The general case of a launch from Earth must take engine thrust, aerodynamic forces, and gravity into account. The acceleration equation can be reduced from vector to scalar form by resolving it into its tangential (speed ) and angular (flight path angle  relative to local vertical) time rate-of-change components relative to the launch pad. The two equations thus become:
  where:
  F is the engine thrust;
  α is the angle of attack;
  m is the vehicle's mass;
  D is the vehicle's aerodynamic drag;
  L is its aerodynamic lift;
  r is the radial distance to the planet's center; and
  g is the gravitational acceleration, which varies with the inverse square of the radial distance:
  Mass decreases as propellant is consumed and rocket stages, engines or tanks are shed (if applicable).
  The planet-fixed values of v and θ at any time in the flight are then determined by numerical integration of the two rate equations from time zero (when both v and θ are 0):
  Finite element analysis can be used to integrate the equations, by breaking the flight into small time increments.
  For most launch vehicles, relatively small levels of lift are generated, and a gravity turn is employed, depending mostly on the third term of the angle rate equation. At the moment of liftoff, when angle and velocity are both zero, the theta-dot equation is mathematically indeterminate and cannot be evaluated until velocity becomes non-zero shortly after liftoff. But notice at this condition, the only force which can cause the vehicle to pitch over is the engine thrust acting at a non-zero angle of attack (first term) and perhaps a slight amount of lift (second term), until a non-zero pitch angle is attained. In the gravity turn, pitch-over is initiated by applying an increasing angle of attack (by means of gimbaled engine thrust), followed by a gradual decrease in angle of attack through the remainder of the flight.
  Once velocity and flight path angle are known, altitude  and downrange distance  are computed as:
  The planet-fixed values of v and θ are converted to space-fixed (inertial) values with the following conversions:
  where ω is the planet's rotational rate in radians per second, φ is the launch site latitude, and Az is the launch azimuth angle.
  Final vₛ, θₛ and r must match the requirements of the target orbit as determined by orbital mechanics (see Orbital flight, above), where final vₛ is usually the required periapsis (or circular) velocity, and final θₛ is 90 degrees. A powered descent analysis would use the same procedure, with reverse boundary conditions.
caption: Velocity and force vectors acting on a space vehicle during powered descent and landing