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 loadExample: level turn at
= 60°
n = 1/cos 60° = 2
L cos
L sin
Level Turn Load Factor
n LW
1cos
If bank angle is known, you can find load factor and vice versa for a level turn
In a level turn:
Bank AngleL
evel
Tu
rn L
oad
Fac
tor
0
2
4
6
10 20 30 40 50 60 70 80
Level Turns
Constant velocity turn Stall speed in a turn:
Stall speed increases as n½
Extra pilot care when performing high bank angle turns near the ground
L cos WL sin
L sin
r
L = nW = CLMAX VSTALL S/22
VSTALL = 2nW
CLMAX S
L = nW
Level Turn Performance Concepts
For good turn performance we want:Small turn radiusHigh turn rate
To achieve this we should turn withLow velocityHigh load factor
Note: Turn radius and rate are functions only ofvelocity and load factor. A B-52 and an F-16 atthe same airspeed and “g” have identical turn radiiand 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 = CL 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?
Vertical turns (loops)
r
L
L
L
W
W
W
D
D
D T
T
T
Pull-Down
Pull-Up
WV2
g rFR = = L -W
= V/r =g(n-1)
V
WV2
g rFR = = L
= V/r =g nV
WV2
g rFR = = L +W= V/r =
g(n+1)V
Pull-down
Pull-up
Vertical Portion
4.0 GR4.0 GR
3.0 GR 3.0 GR
5.0 GR
3.3 GR
4.7 GR4.7 GR
r =V2
g(n+1)
r =V2
g(n-1)
r =V2
gnr =
V2
gn
GR = denominator term in g’s