Landing Ground Roll Distance Calculator
Solve the classic landing ground roll approximation sL ≈ 1.69 · W² / ( g · ρ · S · CLmax · Davg ) for any of its seven unknowns — ground roll distance, weight, gravity, air density, wing area, max lift coefficient, or average decelerating drag — with step-by-step math, a clean braking schematic, and companion landing metrics.
Ground roll scales with W²
Weight enters squared because it drives both the touchdown speed (VTD ∝ √W) and the deceleration (a ∝ 1/W). The product of the two gives s ∝ W². Landing at maximum landing weight rather than at an average weight can add 40% or more to the ground roll — which is why every aircraft has a maximum landing weight limit.
Braking force is the strongest lever
Average drag appears linearly in the denominator. Doubling the decelerating force halves the ground roll. This is why reverse thrust, spoilers, and anti-skid braking all matter so much: each adds to the effective Davg and cuts the rollout distance proportionally. On a wet or icy runway, Davg can drop by 50% or more.
Hot and high hurts landing too
Low air density raises touchdown speed for a given weight, which increases the kinetic energy that must be dissipated and lengthens the ground roll. A 30% drop in density increases the ground roll by roughly 30%. This effect is why high-altitude airports publish landing distance charts as a function of density altitude.
More flaps usually help
Unlike takeoff, where flaps trade lift for drag, landing flaps mostly help. Higher CLmax lowers the touchdown speed and steeper flap settings add drag during the rollout. The optimum is normally full landing flap unless crosswind or gust considerations dictate a lower setting.
How to Use This Calculator
The landing ground roll approximation links seven quantities: sL, W, g, ρ, S, CLmax, and Davg. Pick which one you want the tool to solve, then fill in the other six.
1. Choose what to solve for
Pick sL, W, g, ρ, S, CLmax, or Davg from the toggle. The calculator rearranges the formula for your chosen unknown, making the active field read-only while the other six stay editable.
2. Use realistic presets
Presets cover typical aircraft classes from Cessna 172 to A380 for weight, wing area, and average drag, plus density presets for various altitudes and temperatures, and CLmax presets for takeoff and landing flap settings.
3. Set the braking force realistically
Davg combines wheel braking, aerodynamic drag with flaps extended, and reverse thrust where fitted. On a dry runway use higher values; on a wet or contaminated runway, reduce Davg by 30–50%. This is the parameter most affected by runway condition.
4. Read the result and verdict
The result card shows the ground roll in metres, feet, and nautical miles, with a colour-coded verdict classifying it as short, typical, long, or unsuitable for most runways.
5. Check the schematic and charts
The runway schematic shows the aircraft at touchdown, the rollout trajectory, the braking force arrow, and the ground roll dimension line. The chart plots ground roll against average drag for three different weights.
6. Switch to Advanced for depth
Advanced mode adds a chart of ground roll vs. weight, a sensitivity check on a +1% input change, and companion metrics including touchdown speed, deceleration rate, Davg/W ratio, and required runway with a safety factor.
What This Tool Offers
Built around the classic landing ground roll approximation sL ≈ 1.69 · W² / (g · ρ · S · CLmax · Davg), a standard first-cut estimate in aircraft performance preliminary design.
Seven-way solving
Solve for ground roll, weight, gravity, air density, wing area, max lift coefficient, or average drag. The calculator rearranges the formula for whichever variable you choose.
Clean braking schematic
A runway diagram showing the aircraft at touchdown, the rollout trajectory, and the average decelerating force arrow acting opposite the direction of motion.
Ground-roll verdict
Each result is classified as short, typical, long, or unsuitable for most runways, with a coloured badge for immediate interpretation.
Altitude & temperature presets
Density presets for 7 km, 3 km, sea-level ISA, and a hot day at 40 °C — all in one click.
Dual comparison charts
Ground roll vs. average drag for three weights, plus an advanced ground roll vs. weight chart for three drag values.
Reference tables
Typical ground rolls by aircraft class, a lookup grid across weight and drag, and a variable reference table.
Reference Tables & Conversions
A distance unit converter, a landing ground roll lookup grid, and typical values by aircraft class.
Ground roll distance unit converter
Landing Ground Roll Lookup at Sea Level ISA
Computed from sL = 1.69 · W² / (g · ρ · S · CLmax · Davg) with ρ = 1.225 kg/m³, S = 70 m², CLmax = 2.4, g = 9.80665. Values in metres.
| W (N) | D = 5 kN | D = 10 kN | D = 20 kN | D = 40 kN | D = 80 kN |
|---|
Typical Landing Ground Roll by Aircraft Class
Representative values at maximum landing weight, sea level ISA, dry runway. Actual figures depend on flap setting, density altitude, and runway condition.
| Class | W (N) | Davg (N) | S (m²) | sL (m) | Notes |
|---|---|---|---|---|---|
| Cessna 172 | 11,000 | 2,500 | 16 | ≈ 340 | Short field, dry grass or hard surface |
| Piper Seneca (light twin) | 22,000 | 5,000 | 18 | ≈ 490 | Short field capable |
| Bombardier Q400 | 280,000 | 25,000 | 63 | ≈ 1,050 | Reverse thrust available |
| Embraer E175 | 380,000 | 35,000 | 82 | ≈ 1,150 | Regional jet, thrust reversers |
| Boeing 737-800 | 650,000 | 80,000 | 125 | ≈ 1,180 | Narrow-body transport |
| Boeing 777-300ER | 2,800,000 | 280,000 | 437 | ≈ 1,700 | Wide-body long-haul |
| Airbus A380 | 4,500,000 | 450,000 | 845 | ≈ 1,800 | Largest transport |
Variable Reference
| Symbol | Meaning | Typical range | Units |
|---|---|---|---|
| sL | Landing ground roll distance | 200 – 2,500 | m |
| W | Landing weight | 10⁴ – 5×10⁶ | N |
| g | Gravitational acceleration | 1.62 – 9.81 | m/s² |
| ρ | Air density | 0.55 – 1.23 | kg/m³ |
| S | Wing reference area | 16 – 850 | m² |
| CLmax | Maximum lift coefficient (landing) | 2.0 – 3.2 | — |
| Davg | Average decelerating drag force | 2.5×10³ – 5×10⁵ | N |
| VTD | Touchdown speed | √(2W/(ρ S CLmax)) | m/s |
| aavg | Average deceleration | Davg/W · g | m/s² |
What Does the Landing Ground Roll Formula Measure?
The landing ground roll is the distance an aircraft travels along the runway from main-gear touchdown to a full stop. It is the most operationally critical landing performance number, because it determines the minimum runway length required at a given landing weight, altitude, temperature, and runway condition. The approximation used here captures the essential physics: heavier aircraft need more distance, more drag and braking force reduce it, and thin air at altitude makes it longer.
Landing Ground Roll Formula
The approximation used in this calculator is:
Rearranged to solve for the other six unknowns:
g = 1.69 · W² / ( sL · ρ · S · CLmax · Davg )
ρ = 1.69 · W² / ( sL · g · S · CLmax · Davg )
S = 1.69 · W² / ( sL · g · ρ · CLmax · Davg )
CLmax = 1.69 · W² / ( sL · g · ρ · S · Davg )
Davg = 1.69 · W² / ( sL · g · ρ · S · CLmax )
The constant 1.69 comes from the derivation of the landing rollout integral, and the formula assumes constant average decelerating force during the roll, average deceleration, and constant CLmax right up to touchdown. It ignores the flare phase, thrust reverse spool-up, and the fact that aerodynamic drag drops as the aircraft slows.
Landing Ground Roll Variables
| Symbol | Meaning | Notes |
|---|---|---|
| sL | Landing ground roll distance | Touchdown to full stop; excludes airborne approach |
| W | Landing weight | Newtons; enters the formula squared |
| g | Gravitational acceleration | 9.80665 m/s² on Earth |
| ρ | Air density | Lower at altitude and on hot days |
| S | Wing reference area | Larger wing means lower touchdown speed |
| CLmax | Maximum lift coefficient | Set by full landing flap setting |
| Davg | Average decelerating force | Braking + drag + reverse thrust, averaged over the roll |
How Each Variable Affects Landing Ground Roll
The sensitivities mirror those of takeoff but with one important difference: the 1.69 coefficient is slightly larger than the takeoff 1.44 because the landing rollout has to dissipate the full touchdown kinetic energy down to zero, whereas the takeoff roll stops at VLO rather than at zero. Beyond that, the structure is the same: weight is twice as sensitive as any other parameter because it drives both VTD and the deceleration rate.
Runway condition is the parameter that varies most in real operations. On a dry runway a transport aircraft can achieve a Davg/W ratio of around 0.35–0.45 thanks to anti-skid braking, spoilers, and reverse thrust. On a wet runway that can drop to 0.20–0.30. On ice, Davg/W may fall below 0.10, roughly quadrupling the ground roll compared with dry conditions. This is why contaminated-runway landing distances are published separately in the aircraft flight manual.
Landing Ground Roll Calculation Examples
Numerator: 1.69 × W² = 1.69 × 1.21 × 10¹⁰ = 2.0449 × 10¹⁰
Denominator: g × ρ × S × CLmax × Davg = 9.80665 × 1.225 × 70 × 2.4 × 10,000 = 2.0182 × 10⁷
sL = 2.0449 × 10¹⁰ / 2.0182 × 10⁷ = 1,013.2 m
W² = sL · g · ρ · S · CLmax · Davg / 1.69
W² = 1,800 × 9.80665 × 1.225 × 125 × 2.8 × 80,000 / 1.69
W² = 2.997 × 10¹² → W = 1,731,200 N
Frequently Asked Questions
The factor comes from integrating the deceleration. The aircraft touches down at VTD and decelerates to zero under an average decelerating force Davg. Working out the equation of motion and evaluating the integral gives s = VTD² / (2 · aavg), and when the aerodynamic and braking terms are gathered into the form of the calculator's formula, the numerical coefficient works out to approximately 1.69. It is slightly larger than the takeoff coefficient (1.44) because the landing rollout must dissipate the entire touchdown kinetic energy.
Davg is the average total decelerating force acting on the aircraft during the ground roll. It is the sum of three contributions: wheel braking (usually dominant on a dry runway), aerodynamic drag (including the added drag from full flaps and extended landing gear), and reverse thrust where fitted. All three vary during the roll — braking force peaks early, aerodynamic drag falls with V² as the aircraft slows — so Davg is the mass-weighted average over the entire rollout.
Both coefficients come from integrating the equation of motion, but the boundary conditions differ. The takeoff roll ends at liftoff speed VLO, where the aircraft is still moving. The landing roll ends at zero speed, so the full kinetic energy must be dissipated. That difference shows up as a slightly larger numerical coefficient. The ratio 1.69/1.44 ≈ 1.17 reflects the fact that landing rollout has to remove the last bit of energy that the takeoff roll leaves in the aircraft at liftoff.
For transport aircraft on dry runways, the approximation is typically within 10–20% of flight-test data. Accuracy is best when the braking force is roughly constant during the roll, the aircraft is not operating near the limits of its anti-skid system, and the runway is dry. Real flight-test data accounts for anti-skid cycling, spoiler deployment timing, thrust reverse spool-up, and pilot technique — all of which the simple formula ignores.
Touchdown speed is the airspeed at which the main wheels contact the runway. By convention it is 1.15–1.30 times the stall speed in the landing configuration, depending on aircraft class and certification rules. In terms of the formula, VTD ≈ √(2W / (ρ · S · CLmax)), which shows explicitly that touchdown speed rises with the square root of weight and falls with the square root of density, wing area, and CLmax. This is why hot-and-high conditions lengthen the landing ground roll — thinner air means a faster touchdown.
Because wheel braking force is limited by the friction coefficient between the tyres and the runway. On a dry runway, the coefficient can reach 0.5 or more, allowing very high braking forces. On a wet runway it drops to 0.3 or below; on ice it can fall below 0.1. Since braking is usually the dominant contributor to Davg, a 50% loss of braking friction can roughly halve the total Davg, doubling the ground roll. This is why contaminated-runway landing distances are published separately in the flight manual and why runway condition reporting is such a critical part of aviation operations.
No — this formula gives only the ground roll from touchdown to full stop. The full landing distance from a 50 ft (15 m) screen height to a complete stop also includes the airborne segment (approach, flare, and transition to touchdown), which typically adds 30–50% to the total. Certification rules such as FAR Part 25 and CS-25 require demonstration of the total landing distance from 50 ft, and operational rules require an additional safety factor of 1.67 for dry runways or 1.92 for wet runways.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| s_L | Landing ground roll distance | m |
| W | Weight | N |
| g | Gravitational acceleration | m/s2 |
| ρ | Air density | kg/m3 |
| S | Wing area | m2 |
| C_Lmax | Maximum lift coefficient | |
| D_avg | Average deceleration force | N |
What it means
The landing ground roll is the distance required to decelerate from touchdown speed to a stop. The formula assumes a constant deceleration force (braking + drag) and uses a factor of 1.69 (derived from energy considerations). It depends on landing weight, density, wing area, C_Lmax (which determines touchdown speed), and average drag (including braking). This estimate is used for field length certification and for design of braking systems. Understanding this relation is essential for ensuring safe landing performance.
Worked example
Landing Ground Roll – Two Examples
Real‑World| Parameter | Value |
|---|---|
| W | 75,000 N |
| S | 20 m² |
| C_Lmax | 2.0 |
| D_avg | 30,000 N |
| Parameter | Value |
|---|---|
| W | 140,000 |
| S | 30 |
| C_Lmax | 2.2 |
| D_avg | 50,000 |
Common mistakes
- Landing ground roll distance (simplified): s_L ≈ 1.69 · W² / (g·ρ·S·C_Lmax·D_avg).
- D_avg: Average drag during landing (including braking).
- 1.69 factor accounts for deceleration.
- Assumes no reverse thrust.
- Braking effectiveness affects D_avg.
Applications
Landing ground roll distance, s_L ≈ 1.69·W²/(g·ρ·S·C_Lmax·D_avg), estimates the distance needed to stop after touchdown. This is essential for airfield design and for ensuring safe landing performance. The factor 1.69 accounts for the average deceleration during braking. Engineers use this to design braking systems, to evaluate landing gear performance, and to set approach speeds. By reducing landing distance through aerodynamic braking (spoilers) and efficient brakes, aerospace engineers can improve safety and enable operation on shorter runways.
- Landing field length and certification analysis
- Braking system design (wheel brakes, thrust reversers)
- Landing gear and tire wear analysis
- Spoiler and lift‑dump design for deceleration
- Airfield compatibility and operational planning
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