Aircraft Takeoff Speed

Rotation speed (V_R) formula

V_R (rotation speed) is the airspeed at which the pilot pulls back on the yoke to raise the nose during takeoff. Before V_R comes V₁ (decision speed — continue or abort); after it come V_LOF (lift-off) and V₂ (takeoff safety speed). The simplified physics form is VR = √(2·W·g / (ρ·S·CL,max·k)), where k is a safety coefficient of ~1.1–1.2 above stall. A common operational rule is VR ≈ 1.1 · Vstall. Example: a Cessna 172 with V_stall ~50 kt rotates at ~55 kt (93 km/h); a commercial airliner rotates at 140–160 kt (260–300 km/h). Heavier weight or higher density altitude (heat, altitude, humidity) raises V_R; this is the Density Altitude effect, critical at hot/high airports.

Applications

Flight planning (Weight & Balance, performance charts), ANAC commercial pilot training, general aviation pre-flight, high-altitude takeoff briefings (TBT — Take-off Briefing), and simulator training for rejected takeoffs at V₁.

FAQ

Why does V_R change every flight? Weight, temperature, runway altitude, flap setting, and wind shift the stall speed and required margin — V_R is read from a performance table or FMS, not memorized.

Is V_R the same as V_LOF? No — V_R is when you start rotating; V_LOF is when the wheels actually leave the ground, a few knots later.

What if I rotate too early? Risk of tail strike or extended ground roll because the wing has not yet generated enough lift; on heavy jets it can also trigger the stick shaker.

Why is hot-and-high so dangerous? Lower air density (ρ) drops engine thrust and lift simultaneously, raising V_R and lengthening the takeoff roll — short runways can become unusable.