311 AA Lecture 17: Performance in Turning Flight
Dr. Laszlo Techy
Department of Aeronautics & Astronautics University of Washington
Lecture 17 Outline
Basics of turning flight Turning flight for non-winged vehicles Turning flight for winged vehicles Maximum rate of turn Minimum turning radius Two-minute turns V-n diagrams Wind gusts
Where are we?
Previously, we considered rectilinear motion: Wings level flight Constant velocity along straight paths Takeoff and landing Changing velocity along straight paths Now, we consider turning flight: Radial acceleration and circular flight paths.
Turning: Overview Assumption: Ideal Turn -- Constant radius turn at constant altitude (i.e., in a horizontal plane). Non-winged vehicles (e.g., airships): rudder generates yaw moment body side force generates turning motion Winged vehicles rudder and aileron deflect lift vector deflected lift force generates turning motion
Turning Flight for Non-Winged Vehicles
Non-winged vehicles (missiles, airships, submarines) Centripetal acceleration: ar
Turning Flight for Non-Winged Vehicles
Equations of motion: Recall that Solving for turn rate gives: Turn rate is generated by side force Y
Turning Flight for Winged Vehicles
Coordinated turn: No side force: Y = 0 Lift vector deflected inward by angle
Coordinated Turns
Resultant of weight and "centrifugal force" in aircraft plane of symmetry Inward component of lift generates centripetal acceleration Improper coordination gives: Variation in turn radius (skid or slip) Variation in altitude
Load Factor
For turning flight, L > W.
How to relate "load factor" n to , R, and d/dt? Vertical force balance:
Winged Vehicles: Turn Radius
Horizontal (lateral) force balance:
Small turn radius requires high load factor and/or low speed.
Winged Vehicles: Turn Radius Accounting for load factor ( )
Alternative expression for turn radius:
Small turn radius requires high lift coefficient.
Winged Vehicles: Turn Rate Recall:
High turn rate requires large n and/or small V.
Alternatively:
High turn rate large requires CL.
Aside: Pull-Up Maneuver
An airplane initially in descending, level flight pulls up, bottoming out at the instant depicted. From Newton's second law:
Two-Minute Turn
Turn rate of 3 degrees per second Turn-slip indicator: Measures
direction of weight-plus-inertial-force (slip indicator) and heading rate (using a turn rate gyroscope, for example)
Gyroscope attached to needle indicator Needle indicator
Coordinated turn: Ball stays centered
Curved tube containing a ball in liquid
Two-Minute Turn Continued To complete a two-minute turn:
Needle is at the standard "rate one" indicator (3 degrees per second) Ball is centered (for zero sideslip)
Slip-Indicator and Bank Angle
Note: The slip-indicator does not detect the bank angle . Must also know airspeed for that...
Ex: Ex:
An Example
Given:
Find the maximum turn rate, minimum turn radius, and the speeds at which they occur. Can this turn be sustained at sea level?
Example Continued
Unable to sustain turn!
Load Factor Revisited
Observations: Straight and level flight: n = 1 Turning flight: n > 1 Maximum load factor n defined by structure/passenger/payload constraints or maximum lift coefficient CLmax
Idea: Define performance envelope using a V-n diagram...
Velocity and Load Factor
Aim: Express velocity V as a function of load factor n.
Consider maneuvering flight at stall:
variables
Stall Boundary
>0
V-n Diagram (Aero Limits)
Complete V-n Diagram
Corner Points
Corner points: Where structural and stall limits intersect.
Gust Load and Lift Coefficient
Wind gusts and wind shear can cause catastrophic loads when operating near limits Change in load factor due to disturbance can cause stall or structural failure. Effect scales directly with airspeed.
Effects if Gust
Change in lift due to effect of gust:
Change in load factor:
Gust Loading on V-n Diagram
Consider an aircraft in straight & level flight (n = 1):
For this example, a gust of magnitude wg would cause: Stall, if the airspeed is lower than Va Structural failure, if the airspeed is higher than Vb