Lesson 31 Velocity vs. Load Factor (V-n) Diagrams 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 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”

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

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

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 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?   Corner Velocity

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 speed @ 4g ~165 KCAS Stall speed @ 1g ~80 KCAS

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

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

Q: What happens when weight is increased?  

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)

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 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 In class Read text 5.13 Complete problems through #39 In class Discuss specific excess power, energy height