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 (f) – angle created
by rotating the aircraft about
the aircraft reference line
L
f
Turn rate (w) – radians/second
or degrees/second
Turn radius (r) – feet
W
Level Turns

L sin f
L cos f

Level flight means
constant altitude (no
vertical acceleration)
In level flight, bank
angle creates a specific
load
Example: level turn at
f = 60°
n = 1/cos 60° = 2
In a level turn:
n L  1
W cos f
If bank angle is known,
you can find load factor
and vice versa for a level
turn
Level Turn Load Factor
Level Turn Load Factor
6
4
2
0
10 20 30 40 50 60 70 80
Bank Angle
Level Turns
L sin f
f
L cos f  W


L = nW
Constant velocity turn
Stall speed in a turn:
2
L = nW = CLMAX r VSTALL S/2
2nW
VSTALL =
L sin f


r
CLMAX r S
Stall speed increases as n½
Extra pilot care when
performing high bank
angle turns near the
ground
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.
Level Turn Design Considerations
To get small turn radius (r) and large turn rate (w)




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
F-16 Turn Performance Limits*
Stall limits
Human/aircraft
structural limits
Aeroelastic limits
*F-16 COMBAT AIRCRAFT
FUNDAMENTALS, page 46
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.
b.
c.
What is the aircraft’s turn radius in NM?
What is the aircraft’s turn rate in deg/s?
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
20o bank
r = 118 nm
45o bank
r = 43 nm
10o bank
r = 244 nm
Vertical turns (loops)
Pull-down
WV2
S FR = g r = L +W
g(n+1)
w = V/r =
V
Vertical Portion
WV2
S FR = g r = L
gn
w = V/r =
V
Pull-up
WV2
S FR = g r = L -W
g(n-1)
w = V/r =
V
T
D
Pull-Down
W
L
T
L
D
W
r
L
T
D
W
Pull-Up
5.0 GR
4.7 GR
4.7 GR
r=
V2
gn
4.0 GR
4.0 GR
GR = denominator
term in g’s
3.0 GR
r=
V2
g(n+1)
r=
V2
gn
3.3 GR
r=
V2
g(n-1)
3.0 GR
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