Steady flight

Steady flight, unaccelerated flight, or equilibrium flight is a special case in flight dynamics where the aircraft's linear and angular velocity are constant in a body-fixed reference frame. Basic aircraft maneuvers such as level flight, climbs and descents, and coordinated turns can be modeled as steady flight maneuvers. Typical aircraft flight consists of a series of steady flight maneuvers connected by brief, accelerated transitions. Because of this, primary applications of steady flight models include aircraft design, assessment of aircraft performance, flight planning, and using steady flight states as the equilibrium conditions around which flight dynamics equations are expanded.

Steady flight analysis uses three different reference frames to express the forces and moments acting on the aircraft. They are defined as:

The Euler angles linking these reference frames are:

The forces acting on an aircraft in flight are the weight, aerodynamic force, and thrust. The weight is easiest to express in the Earth frame, where it has magnitude W and is in the +z_E direction, towards the center of the Earth. The weight is assumed to be constant over time and constant with altitude.

Expressing the aerodynamic force in the wind frame, it has a drag component with magnitude D opposite the velocity vector in the −x_w direction, a side force component with magnitude C in the +y_w direction, and a lift component with magnitude L in the −z_w direction.

In general, the thrust can have components along each body frame axis. For fixed wing aircraft with engines or propellers fixed relative to the fuselage, thrust is usually closely aligned with the +x_b direction. Other types of aircraft, such as rockets and airplanes that use thrust vectoring, can have significant components of thrust along the other body frame axes. In this article, aircraft are assumed to have thrust with magnitude T and fixed direction +x_b.

Steady flight is defined as flight where the aircraft's linear and angular velocity vectors are constant in a body-fixed reference frame such as the body frame or wind frame. In the Earth frame, the velocity may not be constant since the airplane may be turning, in which case the airplane has a centripetal acceleration ${\displaystyle {\frac {(V\cos {\gamma })^{2}}{R}}}$ in the x_E-y_E plane, where ${\displaystyle V}$ is the magnitude of the true airspeed and ${\displaystyle R}$ is the turn radius.

This equilibrium can be expressed along a variety of axes in a variety of reference frames. The traditional steady flight equations derive from expressing this force balance along three axes: the x_w-axis, the radial direction of the aircraft's turn in the x_E-y_E plane, and the axis perpendicular to x_w in the x_w-z_E plane,