Structural Loads
V-n Diagrams
Steady Flight Loads
Wing and Tail Loads
MAE 155A
YF-12 Structure Testing (NASA Image)
2
MAE 155A
Maneuvering Load Limits
CFR Part 23 (normal, utility, acrobatic aircraft)
Positive load factor limit
Utility aircraft, n_plus > 4.4 g
Acrobatic aircraft, n_plus > 6 g
Normal aircraft:
Negative load factor limit
Normal and utility, n_minus < -0.4*n_plus
Acrobatic aircraft, n_minus < -0.5*n_plus
CFR Part 25 (transport)
Positive load factor limit, n_plus > 2.5 g
Negative load factor limit
n_minus < -1.0 g at speeds up to V
C
Vary linearly from V
C
value to zero at V
D
value
n
plus
=2.1+
24,000 lb
W+10,000 lb
2.5n
plus
3.8
3
MAE 155A
V-n Diagram
Load
Factor
Equivalent Airspeed
n=
L
W
=
j
2
V
2
( S/ W)C
L , max
=
j
SL
2
V
E
2
( S /W)C
L, max
n=
j
SL
2
V
E
2
( S/ W) k
L
C
L , max
n
minus
n
plus
n=1
V
A
V
stall
Positive limit load factor
Negative limit load factor
M
a
x
i
m
u
m
d
i
v
e
s
p
e
e
d
0.6k
L
1.0
V
E
=V
.
j
j
SL
V
C
V
D
T
r
a
n
s
p
o
r
t
4
MAE 155A
Gust Load Factors
Gust load factors are defined in CFR Part 23
n=1!
|
K
g
C
Lo
U
e
498(W/ S)
V
e
K
g
=
0.88j
5.3+j
K
g
=
j
1.03
6.95+j
1.03
j=
2(W/ S )
jg
c C
Lo
Gust Alleviation
Factor (subsonic)
Gust Alleviation
Factor (supersonic)
Mass ratio
U
e
=equivalent gust velocity( ft / s)
j=density( slug / ft
3
)
W / S=wing loading (lb/ ft
2
)
V
e
=equivalent airspeed ( nmi / hr)
c=mean chord ( ft)
C
Lo
=lift curve slope(1/ rad )
5
MAE 155A
Equivalent Gust Velocity
Equivalent
Gust Velocity
Altitude
0
20,000 ft
50,000 ft
12.5 15
25 30 50 ft/s
up to VD for
transports
up to VC for
transports
up to VD for
normal, utility,
aerobatic
up to VC for
normal, utility,
aerobatic
6
MAE 155A
Combined V-n Diagram
Load
Factor
Equivalent
Airspeed
n
minus
n
plus
n=1 V
A
V
C
V
D
+V
C
gust line
+V
D
gust line
-V
D
gust line
-V
C
gust line
7
MAE 155A
Level Flight Loads
Wing and tail loads are usually established from steady flight conditions.
The following equations are used to find angle-of-attack and elevator deflection
required to maintain a level flight condition.
L=W=
q S C
L
=
q S (C
L0
+C
Lo
o+C
L6
6)
0=M=
q S
c C
m
=
qS
c(C
m0
+C
mo
o+C
m6
6)
Lift Equation:
Pitch Moment:
|
C
Lo
C
L6
C
mo
C
m6
|
o
6
=
|
(W/ S )/
qC
L0
C
m0
q=
j
2
V
2
=dynamic pressure
o=
|(W/ S)/
qC
L0
C
m6
+C
m0
C
L6
C
Lo
C
m6
C
mo
C
L6
6=
C
Lo
C
m0
C
mo
|(W/ S)/
qC
L0
C
Lo
C
m6
C
mo
C
L6
8
MAE 155A
Symmetric Pull-Up
The angle-of-attack and elevator deflection needed for a steady pull-up or push-over
maneuver include a non-zero pitch rate.
L=n W=
q S C
L
=
q S (C
L0
+C
L o
o+C
L6
6)
0=M=
q S
c C
m
=
q S
c(C
m0
+C
mo
o+C
mq(
q
c
2V
)
+C
m6
6)
Lift Equation:
Pitch Moment:
|
C
Lo
C
L6
C
mo
C
m6
|
o
6
=
|
n(W / S)/
qC
L0
C
m0
C
mq
c g (n1)/(2V
2
)
q=
g
V
(n1) Pitch Rate:
q=
j
2
V
2
=dynamic pressure
q=pitch rate
9
MAE 155A
Turning Flight
The steady turning flight equations also require a non-zero pitch rate.
L=n W=
q S C
L
=
q S (C
L0
+C
L o
o+C
L6
6)
0=M=
q S
c C
m
=
qS
c(C
m0
+C
mo
o+C
mq(
q
c
2V
)
+C
m6
6)
Lift Equation:
Pitch Moment:
|
C
Lo
C
L6
C
mo
C
m6
|
o
6
=
|
n(W/ S )/
qC
L0
C
m0
C
mq
c g (n1/ n)/(2V
2
)
q=
g
V
(
n
1
n
)
Pitch Rate:
q=
j
2
V
2
=dynamic pressure
q=pitch rate
10
MAE 155A
Lift from the Wing and Tail
The total airplane lift includes both wing and tail contributions
C
L0
=C
L0w
+C
Loh
j
h(
S
h
S
)
i
h
C
Lo
=C
Low
+C
Loh
j
h(
S
h
S
)
(
1
d e
d o
)
C
L6
=tC
Loh
j
h(
S
h
S
)
C
L0w
=wing lift coefficient at zeroangle of attack
C
Lo h
=tail lift coefficient slope
j
h
=
q
h
q
=
(
V
h
V
)
2
L=L
w
+L
h
=
q S C
L
=
q S (C
L0
+C
Lo
o+C
L6
6)
V
h
=airspeed at tail
V =aircraft airspeed
S
h
/ S=tail area / wing reference area
i
h
=tail incidence angle
C
Lo w
=wing lift coefficient slope
t=elevator effectiveness
d e/ d o=tail downwash parameter
Total airplane lift
11
MAE 155A
Wing and Tail Balancing Loads
The wing and tail loads are obtained from the angle-of-attack and elevator deflection
needed to maintain level flight.
L
W
=
q S (C
L0w
+C
L ow
o)
L
h
=
q S
h
j
h
C
Loh
|
i
h
+
(
1
d e
d o
)
o+t6
Wing Load
Balancing Tail Load (BTL)
