Bank angle 2026-11-05
The bank angle measures an aircraft's lateral tilt relative to a local horizontal reference. In the ideal fixed-wing aircraft turning model, the lift vector tilts with the vehicle. For more general motion, vehicle attitude, flight-path direction and aerodynamic force direction must be distinguished; a banked vehicle need not follow a level circle.[ref]
Aircraft Rotations by NASA Glenn Research Center. Roll axis, wing-tip motion and attitude-control discussion
For steady horizontal circular motion with negligible vertical thrust and lift tilted by , the force balance developed in fixed-wing aircraft gives the aerodynamic load factorAt , the required lift is twice the gravitational weight. If the maximum usable lift coefficient is held fixed, implies the model's limiting airspeed scales asA stipulated wings-level limit of therefore becomes at this loading. This is a comparison at fixed configuration and air mass density, not a claim that a particular aircraft can sustain the required condition. Aerodynamic stall and structural limits constrain the accessible turn.
A banked glider also needs a different loading balance from the shallow straight-glide model used to define minimum sink speed. Increasing bank angle cannot be analyzed merely by rotating a drawing of its still-air trajectory. Measured performance must specify the turn condition as well as airspeed; the FAA's performance discussion illustrates how bank and loading affect glider operation.[ref]
Earll Murman 2026-11-05
Earll Murman is an aerospace engineer and MIT professor emeritus whose institutional profile identifies aircraft systems engineering among his specializations. His authored lecture on aircraft performance connects aerodynamic forces, propulsion, energy and maneuvering constraints. The lecture title page credits him directly and is dated 18 September 2003; the host course is a separate Fall 2004 offering.[ref][ref]
Introduction to Aircraft Performance and Static Stability by Earll Murman. Title slide and Today's Topics
Earll Murman in the portrait provided by his official MIT AeroAstro faculty profile
. One useful connection in that lecture is aircraft energy height. For constant mass , gravitational acceleration , altitude and true airspeed in a still-air model, divide the sum of gravitational potential energy and kinetic energy by gravitational weight:If thrust acts along the motion, drag opposes it, and other energy exchanges are neglected, the specific excess power isThis expresses the possibility of using the available mechanical power for climbing, accelerating, or both.[ref]
Introduction to Aircraft Performance and Static Stability by Earll Murman. PDF pp. 21–24, Specific Energy and Excess Power and Summary of Power Characteristics
For an original stipulated example, take , , and . Then . At constant true airspeed, that is the model's climb rate. At constant altitude, the same instantaneous power gives . These are alternative allocations at the stipulated condition, not a claim that an actual engine maintains the same excess thrust throughout a maneuver.
The distinction illustrates why satisfying a lift or aerodynamic load factor requirement alone does not establish sustained performance. Measurements of speed change, altitude change, thrust and drag test different terms of the energy account. The lecture's force and energy models make those assumptions explicit; they do not replace configuration-specific experimental data.
