Formula & Calculator
Stall Speed
Minimum airspeed at which a wing can generate enough lift to sustain level flight before stalling.
Interpretation
Stall speed: V_stall = √(2W/(ρ·S·C_Lmax)). It is the minimum airspeed at which the wing can generate enough lift to support weight. Example: W=20,000 N, ρ=1.225, S=20 m², C_Lmax=1.5 → V_stall = √(40000/(1.225×20×1.5)) = √(40000/36.75) ≈ 33.0 m/s.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| V_stall | Stall speed | m/s |
| W | Weight | N |
| ρ | Air density | kg/m3 |
| S | Wing area | m2 |
| C_Lmax | Maximum lift coefficient |
What it means
Stall speed is the minimum steady flight speed at which an aircraft can maintain level flight; below this speed, the wing exceeds its maximum lift coefficient and stalls. It depends on weight, air density, wing area, and maximum lift coefficient (influenced by flaps, slats, etc.). Stall speed is critical for takeoff and landing performance: lower stall speeds allow shorter ground rolls and lower approach speeds, enhancing safety. It is also used to calculate manoeuvring speeds and to set approach speeds (typically 1.3 V_stall). In design, increasing C_Lmax (via high‑lift devices) reduces V_stall, but adds weight and complexity. Understanding stall speed is essential for flight operations and for designing aircraft with adequate low‑speed performance.
Worked example
Stall Speed – Two Examples
Real‑World| Parameter | Value |
|---|---|
| W | 80,000 N |
| ρ | 1.225 kg/m³ |
| S | 20 m² |
| C_Lmax | 1.5 |
| Parameter | Value |
|---|---|
| W | 15,000 N |
| S | 18 m² |
| C_Lmax | 1.6 |
Common mistakes
- Stall speed V_stall: V_stall = √(2W / (ρ·S·C_Lmax)).
- Weight W: In Newtons – varies with fuel burn.
- Maximum lift coefficient C_Lmax: Occurs at stall angle of attack – depends on flaps, slats.
- Density ρ: At altitude – stall speed increases with altitude.
- Units: All SI to get m/s.
Applications
Stall speed, V_stall = √(2W/(ρ·S·C_Lmax)), is the minimum speed at which an aircraft can maintain level flight. It is a critical safety parameter that determines takeoff and landing speeds. Engineers use C_Lmax (maximum lift coefficient) to calculate stall speed, which must be above the minimum control speed to ensure safety margins. Stall speed affects runway length requirements, climb performance, and the design of high‑lift devices. By reducing stall speed through flaps, slats, or larger wings, engineers improve takeoff performance and reduce landing distances. Understanding stall speed is essential for flight envelope definition, pilot training, and airworthiness certification.
- Determination of takeoff and landing speeds (V_S, V_S0, V_S1)
- Design of high‑lift systems to lower stall speed
- Runway length and performance analysis
- Flight envelope definition and stall warning systems
- Compliance with airworthiness regulations (CS‑23, CS‑25)
Frequently Asked Questions
The stall speed is the minimum airspeed at which a wing can generate enough lift to sustain level flight. It is a critical parameter for takeoff, landing, and low‑speed manoeuvring.
W = aircraft weight (N)
ρ = air density (kg/m³)
S = wing area (m²)
CL,max = maximum lift coefficient (at the stall angle)
Stall speed increases with the square root of wing loading. A heavier aircraft or smaller wing area raises the stall speed.
Flaps increase CL,max, which reduces stall speed. Slats also increase the stall angle and CL,max, further lowering stall speed.
At higher altitudes, ρ decreases, so stall speed increases (Vstall ∝ 1/√ρ). Pilots must fly faster at altitude to avoid stall.
In a turn, the load factor n = 1/cos(φ). The stall speed in a turn is Vstall,turn = Vstall,level · √n. The higher the bank angle, the higher the stall speed.
- Using CL,max from the clean configuration when flaps/slats are deployed.
- Forgetting to account for load factor in turns.
- Using gross weight instead of actual weight (fuel burned).
Aircraft weight W = 150,000 N, ρ = 1.225 kg/m³ (sea level), S = 50 m², CL,max = 1.5. Vstall = √(2×150000/(1.225×50×1.5)) = √(300000/91.875) = √(3265) ≈ 57.1 m/s (≈ 111 kt).
From wind tunnel tests or flight testing, measure the lift coefficient at the stall angle of attack. It is the maximum value before the lift curve drops.
Certification regulations specify minimum speeds (e.g., VSO, VS1) that must be met. Stall speed directly affects takeoff and landing distances and is a key safety parameter.