Draw the flight envelope of an aircraft. Adjust the wing area, weight, maximum lift coefficient and limit load factors to see the stall speed, corner speed and dive speed update in real time, and survey the safe flight region bounded by aerodynamic and structural limits.
Parameters
Wing area S
m²
Aircraft weight W
kg
Operating gross mass
Max lift coefficient C_Lmax
Largest lift coefficient the wing can hold just before stall
Air density ρ
kg/m³
1.225 at sea level, falling with altitude
Positive limit load factor n+
3.8 for normal category, far higher for aerobatic or fighter aircraft
Negative limit load factor n−
The negative-g limit from inverted flight or a downward gust
Results
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Stall speed V_s (m/s)
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Corner (manoeuvring) speed V_a (m/s)
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Positive limit load factor
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Negative limit load factor
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Design dive speed V_d (m/s)
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Wing loading W/S (N/m²)
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Flight envelope — V-n diagram animation
The horizontal axis is airspeed V, the vertical axis load factor n. Curves are the aerodynamic stall parabolas, the horizontal lines are the structural limits and the right vertical line is the dive speed. The pulsing point is the corner speed V_a.
Wing loading W/S and design dive speed V_d. The flight envelope is bounded by the aerodynamic stall parabola and the horizontal structural load-factor limits.
What is the V-n Diagram?
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A "V-n diagram" is that chart I keep seeing in aircraft books. I get that the horizontal axis is speed — but what is "n" on the vertical axis?
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The vertical axis n is the "load factor" — roughly, how many g the aircraft is pulling right now. In normal level flight n = 1; in a tight turn or a pull-up it rises to 2g, 3g and so on. So the V-n diagram is a single map of "at which speed can I safely reach which g". The region inside it is called the flight envelope.
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A map, I see. But why is the left side a curve while the top and bottom are flat straight lines? The shape looks lopsided.
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Good eye. The envelope is bounded by two completely different limits. The left curve is the aerodynamic limit: the wing can only generate so much lift at a given speed, so you physically cannot pull more g than that — try, and the wing stalls. The flat top and bottom lines are the structural limit: the airframe is designed to, say, "3.8 g", and exceeding it bends or breaks the wings or fuselage. Raise C_Lmax with the slider on the left and you will see the curve push outward to the left.
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An aerodynamic limit and a structural limit... So the point where those two meet, the corner at the top-left, must be the important one?
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Exactly there. That corner is the corner speed (manoeuvring speed) V_a. You compute it as V_a = V_s·sqrt(n_limit), and it is the lowest speed at which the aircraft can just reach its full structural g. So it is the speed of tightest turning — the speed of best manoeuvrability. In a dogfight or an aerobatic routine, the pilot aims for exactly this speed. In the envelope animation below, I made that corner point pulse and glow.
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I see. So what is the difference between flying faster than V_a and slower than V_a?
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That is the heart of the V-n diagram. Slower than V_a, even with the stick pulled fully back the wing stalls before the structure is in danger, so the g levels off — the stall becomes a safety valve. Faster than V_a, the same abrupt input produces a g beyond the structural limit and can break the aircraft. That is why you are taught: "if you hit severe turbulence, slow down to V_a." It lets a gust shed its overload through a stall.
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There is also that vertical line at the far right, the "dive speed V_d". What limit is that?
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V_d is the design dive speed, the basis of the never-exceed speed. Above it you risk flutter (a self-excited wing vibration) or aerodynamic divergence, so even with structural g to spare it is off-limits. That is why the envelope is a fully closed safe zone — the left curve, the flat top and bottom lines, and this vertical line on the right wrap all the way around.
Frequently Asked Questions
A V-n diagram plots airspeed V on the horizontal axis and load factor n (the multiple of gravity the aircraft is pulling, the "g") on the vertical axis, showing which combinations of speed and load the aircraft can safely reach. The diagram is bounded by two completely different kinds of limit: the curved aerodynamic boundary (the stall parabola) and the flat structural boundaries (the limit load factors). The region inside is the flight envelope, and the aircraft can only fly safely within it.
The corner or manoeuvring speed Va is the airspeed at which the aerodynamic stall parabola meets the positive structural limit line. It is given by Va = Vs·sqrt(n_limit) and is the lowest speed at which the aircraft can reach its full structural g. It is therefore the speed of tightest turning and best manoeuvrability. Flying faster than Va, an abrupt full control input can overstress the airframe; flying slower, the wing stalls before any structural danger. Pilots slow to Va in severe turbulence for exactly this reason.
The 1-g level-flight stall speed is Vs = sqrt(2W/(rho·S·C_Lmax)), where W is the aircraft weight in newtons, rho is air density, S is wing area and C_Lmax is the maximum lift coefficient. Stall speed scales with the square root of weight and inversely with the square root of wing area, air density and maximum lift coefficient. The speed needed to sustain any load factor n is V = Vs·sqrt(n), which forms the stall parabola.
Below the corner speed Va, even a strong vertical gust makes the wing stall before it reaches the structural limit, so no excessive g is generated; the stall acts as a safety valve that sheds the load. Above Va, the same gust can produce a g that exceeds the structural limit and bend or break the wings or tail. For this reason operating procedures require slowing to the design manoeuvring speed (turbulence-penetration speed) when entering severe turbulence.
Real-World Applications
Aircraft structural design and certification: The V-n diagram is one of the starting points of aircraft design. Airworthiness standards (FAR/CS 23 and 25) set positive and negative limit load factors by category — about +3.8g / −1.5g for the normal category, +4.4g for the utility category, +6.0g for the aerobatic category and roughly +2.5g for transport aircraft. From the corners of this diagram (corner speed, dive speed) the designer derives the design loads on the wing spar, tail and control surfaces and sizes the structure.
Pilot training and operations: Pilots always learn the V-n diagram in their flight training. The reasons for the rules — slow to the design manoeuvring (turbulence-penetration) speed in turbulence, never exceed the never-exceed speed V_ne, avoid abrupt control inputs that strain the structure — all come from this diagram. Aerobatic flying uses the corners of the envelope to the fullest, while transport aircraft fly comfortably inside the envelope for passenger comfort.
Gust loads and weather assessment: In an actual airworthiness review, designers draw a gust V-n diagram that superimposes the loads from vertical gusts on top of the manoeuvre V-n diagram. Because the same gust produces a larger g the faster you fly, the gust load near the dive speed often governs the design. This tool handles the basic manoeuvre envelope; the gust diagram is an extension of it.
UAV, drone and model-aircraft design: The strength-design logic is the same for unmanned and large radio-controlled aircraft. If the limit load factor is set too low while chasing minimum weight, a small amount of turbulence or a sharp turn can break the airframe up in mid-air. Drawing a V-n diagram from wing loading, maximum lift coefficient and the expected operating g, then back-calculating spar strength, is a sound design procedure regardless of aircraft size.
Common Misconceptions and Pitfalls
A common misconception is forgetting that all the speeds on a V-n diagram are airspeeds (IAS/EAS), not groundspeed. Both stall and structural load are governed by the dynamic pressure of the air around the aircraft. The V_s and V_a in this tool are computed as true airspeeds at the given air density. As you climb and air density drops, the true airspeed (speed over the ground) for the same indicated airspeed becomes higher. When reading the diagram, always be aware of which speed your instrument is showing.
Next, the assumption that the stall speed is a single fixed number for an aircraft. The stall speed V_s = sqrt(2W/(rho·S·C_Lmax)) depends on aircraft weight. It differs between take-off with full fuel and landing after burning fuel, and the corner speed V_a changes with it. Extending the flaps raises C_Lmax and lowers V_s. The "stall speed vs aircraft weight" chart below shows exactly this dependence. A V-n diagram is "one chart for one weight and one configuration" — never forget that its shape changes during operation.
Finally, the misconception that any load up to the limit load factor is harmless. The limit load is "the load guaranteed not to cause permanent deformation", and above it there is normally an ultimate load set at 1.5 times higher. Exceeding the limit load does not cause instant failure, but plastic deformation or fatigue damage can accumulate in the structure. Understand the edge of the envelope not as "safe up to here" but as "no design guarantee beyond here", and in everyday operation fly comfortably inside it.
How to Use
Enter wing area (m²), aircraft weight (kg), and maximum lift coefficient (Cl_max) using sliders or numeric inputs.
Set air density (kg/m³), positive and negative limit load factors (typically ±3.75g for general aviation, ±6g for aerobatic).
Define design dive speed (V_d) as a percentage of maximum structural speed; simulator calculates stall speed (V_s), corner speed (V_a), and plots the complete flight envelope boundary.
Read output statistics: wing loading (W/S in N/m²), stall speed, corner speed, and load factor limits defining safe operating region.
Worked Example
Cessna 172-class aircraft: wing area 16.2 m², weight 1100 kg, Cl_max 1.40, air density 1.225 kg/m³, limit load factors +3.75g/-1.5g. Wing loading = (1100×9.81)/16.2 = 665 N/m². Stall speed V_s = √(2×1100×9.81)/(1.225×16.2×1.40) ≈ 14.1 m/s. Corner speed V_a = 14.1×√3.75 ≈ 27.3 m/s. Design dive speed V_d set to 1.9× cruise speed ≈ 68 m/s. Envelope shows safe maneuvering region between V_s and V_a at full positive g.
Practical Notes
Corner speed (V_a) marks the transition where load factor limitation replaces aerodynamic limit; above V_a, structural load factor governs—never exceed posted V_a in turbulence.
Negative load factor envelope is shallower; negative Cl_max typically 0.4–0.6, so negative stall speed is higher than positive stall speed (inverted flight stalls faster).
Wing loading directly scales stall speed: doubling weight increases V_s by √2; optimize for your mission profile (trainer vs. patrol).
Air density reduction at altitude shrinks the envelope vertically; recalculate V_s for 3000 ft cruise (ρ ≈ 1.1 kg/m³).