1. Lesson 31 Velocity vs. Load Factor (V-n) Diagrams
Aero Engineering 315
Lesson 31 Velocity vs. Load Factor (V-n) Diagrams

2. 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

3. 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

4. V-n Diagrams: Limits Note: Flight within the “envelope” is possible
without stalling or damaging the aircraft.
(Safe operating region = inside the box)

5. 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”

6. Maximum n available prior to stall
At any point in flight
Solving for n:
For a given weight, altitude and aircraft, max n is
L = nW = CL r SV2/2
CL r S 2W
n = V2
CLMAX r S 2W
nMAX = V2
Defines stall limit load factor line, not structural limit load factor

7. Structural (g) Limit Typical structural limits: Fighter: -3 to +9 g
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

8. 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)

9. V-n Diagrams: Corner Velocity
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

10. 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?

11. Q: What is the corner velocity (V*) for this aircraft?
Corner Velocity

12. Q: Where are the positive and negative stall limits for this aircraft?
Q: What’s the stall speed at 1g?
How about at 4g’s?
Stall 4g ~165 KCAS
Stall 1g ~80 KCAS

13. Q: What happens to stall limit when altitude is increased?
Shift as h increases
(r decreases)

14. Q: Where are the positive and negative structural limits for this aircraft?
Positive g Limit
No shift as h increases
Negative g Limit

15. Q: What happens when weight is increased?

16. May shift as h increases
Q: Where is the ‘max q’ limit for this aircraft?
q limit
May shift as h increases
(M and r changes)

17. 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

18. 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)

19. Example V - n Diagram Vmax = 382 KIAS / 0.7 Mach Page from T-37B
Flight Manual

20. T-38 V-n
diagram for
9,600 lbs
Vmax = 720 KEAS / 1.62 Mach

21. T-38 V-n
diagram for
12,000 lbs
Vmax = 720 KEAS / 1.62 Mach

22. Homework #38
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?

23. Next Lesson (32)… Prior to class In class Read text 5.13
Complete problems through #39
In class
Discuss specific excess power, energy height