Transcript AE315 Lsn31
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
2n 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)…
Prior to class
Read text 5.13
Complete problems through #39
In class
Discuss specific excess power, energy
height