Aero Engineering 315 Lesson 30 Turn Performance

“Turning” the tables…

Turn Performance Overview  Define bank angle and load factor  Calculate load factor needed to sustain a level turn at a given bank angle  Calculate initial turn rate and radius for level turns, pull-ups and pull downs

Turn Performance Definitions  Load factor – Lift/Weight (measured in g’s) n = L/W  Bank angle () – angle created by rotating the aircraft about the aircraft reference line  Turn rate () – radians/second or degrees/second  Turn radius ( r ) – feet L W 

Level Turns  Level flight means constant altitude (no vertical acceleration)  In level flight, bank angle creates a specific load Example: level turn at  = 60° n = 1/cos 60° = 2 L cos  L sin 

Level Turn Load Factor If bank angle is known, you can find load factor and vice versa for a level turn In a level turn: Bank Angle Level Turn Load Factor

Level Turns  Constant velocity turn  Stall speed in a turn:  Stall speed increases as n ½  Extra pilot care when performing high bank angle turns near the ground L cos  W L sin  r L = nW = C LMAX  V STALL S/2 2 V STALL = 2nW C LMAX  S L = nW 

Level Turn Performance Concepts For good turn performance we want: Small turn radius High turn rate To achieve this we should turn with Low velocity High load factor Note: Turn radius and rate are functions only of velocity and load factor. A B-52 and an F-16 at the same airspeed and “g” have identical turn radii and rates.

To get small turn radius ( r ) and large turn rate ()  Maximize “g” loading Structural considerations (max g for the structure) Physiological considerations (human g limits) Aerodynamic considerations (stall limitations)  Minimize wing loading, W/S ( n = C L q S / W )  Maximize lift coefficient High lift devices Pitch vectored thrust  Maximize thrust-to-weight ratio (T/W) High “g” creates very high induced drag Level Turn Design Considerations

F-16 Turn Performance Limits* *F-16 COMBAT AIRCRAFT FUNDAMENTALS, page 46 Stall limits Human/aircraft structural limits Aeroelastic limits

Homework #36 An SR-71 is in a 20° banked level turn at Mach 3.0 and an altitude of 80,000 ft. Assume the ambient temperature is 390°R. a. What is the aircraft’s turn radius in NM? b. What is the aircraft’s turn rate in deg/s? c. If the pilot increases the bank angle to 45° while maintaining a level turn at Mach 3.0, what would the new turn radius be in NM? What would happen to the aircraft load factor?

SR-71 Mach 3 80,000 ft 20 o bank r = 118 nm 10 o bank r = 244 nm 45 o bank r = 43 nm

Vertical turns (loops) WV 2 g r  F R = = L -W  = V/r = g(n-1) V WV 2 g r  F R  = = L  = V/r = g n V WV 2 g r  F R = = L +W  = V/r = g(n+1) V Pull-down Pull-up Vertical Portion

4.0 GR 3.0 GR 5.0 GR 3.3 GR 4.7 GR r = V 2 g(n+1) r = V 2 g(n-1) r = V 2 gn r = V 2 gn GR = denominator term in g’s

Next Lesson (31)…  Prior to class Read text 5.12 Complete homework #36-37 All sections of Fighter Design Project  In class Discuss V-n diagrams