Takeoff Distance Estimate

Take-off distance: d ≈ V_R²/(2·a)

Take-Off Distance Required (TODR) is the ground roll plus the flare needed to clear a 35 ft obstacle. For a quick estimate you can use d = V_R²/(2·a_avg), where V_R is the rotation speed and a_avg is the average acceleration during the run. The real TODR leans on more than that: weight W, density altitude (high temperature and high field elevation each cut engine thrust and lift), runway slope, and the headwind/tailwind component. Some reference numbers help. A Cessna 172 needs about 360 m at sea level in calm wind, a Boeing 737-800 at MTOW around 1800 m, and a paramotor roughly 50 m. Runway 27R/09L at Guarulhos International is 3700 m, plenty for a fully loaded Boeing 747. As a worked example, V_R = 60 m/s with a = 2 m/s² gives d = 60²/(2·2) = 900 m.

Applications

Flight planning and W&B sheets. NOTAM-based go/no-go decisions. The mandatory RBAC 121 take-off performance calculation with its V₁/V_R/V₂ schedule. Hot-and-high operations out of places like La Paz and Quito, short-field bush flying, picking a site for a paramotor or ultralight, and sizing drone and eVTOL vertiports.

FAQ

Why does take-off distance grow at hot airports? A higher density altitude means thinner air. Engines make less thrust and the wings produce less lift at the same true airspeed, so the aircraft has to roll farther before it can fly.

How does headwind help? A headwind lowers the ground speed you need to reach V_R, so the roll shrinks roughly in proportion to the wind component. Tailwind does the reverse, and it hurts a lot more.

What is V₁? It's the decision speed on a multi-engine aircraft. Lose an engine below V₁ and you abort the take-off; lose one above V₁ and you keep going, with the aircraft having to be able to clear obstacles.