V-n Diagram — Flight Envelope with Gust Envelope

The V-n diagram — flight envelope

The V-n diagram (also flight envelope) is the graphical representation of permitted combinations of speed (V) and load factor (n) in which the aircraft may be operated structurally and aerodynamically.

It is the basis of certification under EASA CS-23 / FAR 23.

V-n diagram layout

Schematic V-n envelope. Green = safe operating area. Red = limit load factor and Vne.

Axes:

• X-axis: speed V (KIAS or KEAS), 0 to the right.
• Y-axis: load factor n (in g), negative below, positive above.

Key points and lines:

n
 +6.0 ────────────────────────────────  (Aerobatic Cat limit)
 +4.4 ─────────╲                         (Utility Cat limit)
 +3.8 ─────────╲───╲                     (Normal Cat limit)
 +1.0 ─────────╳───╲╲╲                   (1g level flight)
              ╱    ╲╲╲
   0 ────────╱──────╲╲╲────────── V
              ╲     ╲╲╲
              ╲   GUST
              ╲   ╲╲
 -1.5 ────╲───╲   ╲╲╲                    (Normal Cat neg limit)
              ╲╲╲ ╲╲
        Vs    Va   Vno  Vne

Speed markers

• Vs (Stall speed): stall in 1g level flight. Left edge of envelope.
• Va (Maneuvering speed): maximum speed at which full control deflection does not exceed limit load factor. Lowest point of upper limit line.
• Vno (Maximum structural cruising speed): top of green arc. Up to Vno: normal operation.
• Vne (Never exceed speed): red line. Must never be exceeded.

Load-factor limits

Limit Load Factor (n_max) by category:

Ultimate Load Factor = 1.5 × limit. At this load the aircraft may be permanently deformed but must not fail.

Manoeuvring envelope

The manoeuvring envelope is the region in which the pilot creates load factors via control deflection:

Left edge — Vs curve (stall line):

• At speeds between 0 and Va the aircraft stalls before reaching limit load.
• Mathematically: n_max(V) = (V/Vs)² → the line is a parabola.
• Practically: at very low speed even full control deflection cannot reach limit load — the wing stalls first.

Va (manoeuvring speed):

• Point where the stall line intersects the limit load factor line.
• Below Va: stall limits the load that can be produced.
• Above Va: structural damage possible with full control deflection.
• Va decreases with decreasing mass (often tabulated in AFM for multiple masses).

Upper edge — Limit Load Factor n+:

• Horizontal line at n = +3.8 (Normal Cat).
• Above Vno up to Vne must not be flown at +3.8 g.

Vne — Never Exceed Speed:

• Vertical line at right edge.
• On exceeding: flutter risk, structural damage.

Gust envelope

In addition to the manoeuvring envelope, the gust envelope accounts for the load factor increase from vertical gusts.

EASA CS-23.341 defines the standard gust velocities:

Computing the gust load factor:

Δn = (Ude × V × CLα × ρ × kg) / (2 × W/S)

Where:

• Ude = gust velocity (EAS),
• V = aircraft speed (EAS),
• CLα = lift slope per AoA,
• ρ = air density,
• kg = gust-alleviation factor (1 for sharp gust, < 1 for realistic),
• W/S = wing loading.

Key insight:

• Higher speed → higher gust load.
• At Vno the cruise gust (50 ft/s) is fully experienced — load factor should not exceed n_max.
• At Vne only dive gust (25 ft/s) — half.

The role of Va in gusts

Rule of thumb: in strong turbulence or gusts → reduce speed to Va.

Why: at speeds below Va a gust or control deflection can never exceed limit load — the wing stalls first and protects the structure.

Above Va: a strong gust could exceed limit load → structural damage.

Arcs, Vno and Vne in the cockpit (ASI markings)

Standard ASI markings:

Operational application

In turbulence or gusts:

1. Reduce speed to Va (flaps as appropriate, reduce throttle).
2. Keep wings level, no sudden control inputs.
3. Drift with the wind, don't fight it.

In normal flight:

• Fly within the green arc.
• For brief stretches up to Vno is OK.
• Never in the yellow arc except in absolutely smooth air.

Manoeuvring:

• In steep turns mind the load factor: 60° bank in level flight = 2 g.
• 45° bank = 1.41 g, 60° bank = 2 g, 75° bank = 3.86 g.