Aero Engineering 315
Lesson 31
Velocity vs. Load Factor (V-n) Diagrams
V-n Diagram Objectives
State reason for each limit in a V-N diagram
 State limitations and usefulness of V-n diagram
 Sketch a typical V-n diagram
 Annotate changes with weight and altitude
 Define and calculate corner velocity
 Given a V-n diagram find available and max
load factors, stall speeds, maximum velocity,
and corner velocity (velocity where max turn
rate and min turn radius is achieved)
 Actual min turn radius and max turn rate
may be calculated using corner velocity and
max g

V-n Diagrams: Description



Commonly known as the “flight envelope”
Plot showing various structural and
instantaneous performance limits
 Aerodynamic (stall) limits
 Structural (g) limits
 Dynamic pressure (q) limit
Many aircraft flight manuals have one of these
diagrams
 Each plot good for one weight, one altitude,
one configuration
V-n Diagrams: Limits
+
"q" Limit
Stall limit
Structural Limit
n
V
Note: Flight within the “envelope” is possible
without stalling or damaging the aircraft.
(Safe operating region = inside the box)
Aerodynamic (stall) limit



The aerodynamic limit is a “lift limit”
and occurs where the aircraft stalls
Varies as a function of the square root
of weight and load factor
When stalling while above 1 g, it’s
known as an “accelerated stall”
V s ta ll 
2nW
  S C L m ax
Maximum n available prior to stall

At any point in flight
L = nW = CL  SV2/2

Solving for n:
CL  S 2
n=
V
2W

For a given weight, altitude and aircraft,
max n is
CLMAX  S 2
nMAX =
V
2W
Defines stall limit load
factor line, not structural
limit load factor
Structural (g) Limit



Max design load factor (n)
 Positive and negative g limit
Will vary as a function of weight and
configuration
 Heavier gross weight – lower g limit
 Flaps and gear down – lower g limit
 Carrying stores – lower g limit
Speed or Mach may also effect structural limit
Typical structural limits: Fighter: -3 to +9 g
Transport: -1 to +3 g
Dynamic pressure (q) limit


Maximum design speed (Mach or KCAS or KEAS)
 Type and nature depends on specific aircraft
 Critical mach – controllability, mach tuck etc
 Aeroelastic effects – Aileron reversal, flutter,
etc
 High q – canopy implosion
 High Mach – Engine limit, directional stability
 Sustained High Mach – too high temperature,
heating
May be affected by load factor
Typical q limits: Fighters: Mach 2.5 (heating)
Transports: ~ Mach 0.8 (critical mach)
V-n Diagrams: Corner Velocity
+
V 
*
n
2 n maxW
  SC L max
V *- Corner Velocity
V
-
The corner velocity is the velocity at which the stall limit
and the structural limit make a corner on the graph
Flight at the corner velocity gives the minimum
turn radius and maximum turn rate
Corner Velocity Example
An A-10 with a wing loading (W/S) of
92 lbs/ft2 and CLmax = 1.5 has a
maximum structural load limit of 7g’s.
What is its corner velocity at sea level?
Q: What is the corner velocity (V*) for this aircraft?
8
Altitude: Sea Level
Weight: 5800 lbs
Clean Configuration
6
Positive Structural Limit
Load Factor, n
4
Positive Stall Limit
2
q Limit
Corner
Velocity
Corner Velocity
0
0
-2
-4
50
100
150
200
250
Negative Stall Limit
Negative Structural Limit
Calibrated Airspeed, Vc, knots
300
350
Q: Where are the positive and negative stall limits for this aircraft?
Q: What’s the stall speed at 1g?
8
How about at 4g’s?
Altitude: Sea Level
Weight: 5800 lbs
Clean Configuration
6
Positive Structural Limit
Load Factor, n
4
Positive Stall Limit
2
q Limit
Corner Velocity
Stall speed @ 4g
~165 KCAS
0
0
-2
-4
50
100
Stall
speed
1g
Negative
Stall@Limit
~80 KCAS
150
200
250
Negative Structural Limit
Calibrated Airspeed, Vc, knots
300
350
Q: What happens to stall limit when altitude is increased?
8
Altitude: Sea Level
Weight: 5800 lbs
Clean Configuration
6
Positive Structural Limit
Load Factor, n
4
Positive Stall Limit
2
q Limit
Corner Velocity
Shift as h increases
( decreases)
0
0
-2
-4
50
100
150
200
250
Negative Stall Limit
Negative Structural Limit
Calibrated Airspeed, Vc, knots
300
350
Q: Where are the positive and negative structural limits for this aircraft?
Positive g Limit
8
Altitude: Sea Level
Weight: 5800 lbs
Clean Configuration
6
Positive Structural Limit
Load Factor, n
4
No shift as h increases
Positive Stall Limit
2
q Limit
Corner Velocity
0
0
-2
-4
50
100
150
200
250
Negative Stall Limit
Negative Structural Limit
Negative g Limit
Calibrated Airspeed, Vc, knots
300
350
Q: What happens when weight is increased?
8
Altitude: Sea Level
Weight: 5800 lbs
Clean Configuration
6
Positive Structural Limit
Load Factor, n
4
Positive Stall Limit
2
q Limit
Corner Velocity
0
0
-2
-4
50
100
150
200
250
Negative Stall Limit
Negative Structural Limit
Calibrated Airspeed, Vc, knots
300
350
Q: Where is the ‘max q’ limit for this aircraft?
8
Altitude: Sea Level
Weight: 5800 lbs
Clean Configuration
6
Positive Structural Limit
Load Factor, n
4
Positive Stall Limit
2
q limit
q Limit
Corner Velocity
0
0
-2
-4
50
100
150
200
250
300
350
Negative Stall Limit
Negative Structural Limit
Calibrated Airspeed, Vc, knots May shift as h increases
(M and  changes)
V-n usefulness and limitations


Works well for identifying:
 Instantaneous g capabilities
 g and speed limitations
 Corner velocity (point where max turn rate
and min turn radius occur)
Does not give any indication of:
 Sustained performance
 Actual values for turn rate and radius
 These can be calculated from info on V-n
diagram though
 Performance at other weights, altitudes,
configurations, asymmetric load limits etc
Design Considerations


To get small r and large w:
Minimize wing loading (W/S)
Maximize “g” loading



Structural considerations
Physiological considerations
Maximize lift coefficient

Use high lift devices (maneuvering flaps,
slats)
Example
V-n
Diagram
Vmax = 382 KIAS / 0.7 Mach
Page from T-37B
Flight Manual
T-38 V-n
diagram for
9,600 lbs
Vmax = 720 KEAS / 1.62 Mach
T-38 V-n
diagram for
12,000 lbs
Vmax = 720 KEAS / 1.62 Mach
Homework #38
a.
b.
c.
d.
e.
f.
From the T-38 V-n diagrams…
What is the maximum instantaneous load factor for
a 12,000 lb T-38 at 15,000 ft and Mach 0.6?
What is the maximum instantaneous load factor for
a 9,600 lb T-38 at sea level and Mach 0.8?
What is the maximum Mach number for a 12,000 lb
T-38 at sea level?
What is the maximum Mach number for a 9,600 lb
T-38 at 15,000 ft?
What is the corner velocity for a 12,000 lb T-38 at
25,000 ft?
What is the corner velocity for a 9,600 lb T-38 at
sea level?
Next Lesson (32)…
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Prior to class



Read text 5.13
Complete problems through #39
In class

Discuss specific excess power, energy
height