How is takeoff performance calculated and what factors affect it?

Takeoff performance determines field length requirement. Calculation: Ground roll - Accelerate from V=0 to rotation speed (VR), integrate acceleration with rolling friction and drag; Rotation - Transition from ground to airborne; Climb - Accelerate to V2, climb to 35 ft (transport) or 50 ft (GA). Key parameters: MTOW, temperature, altitude (density altitude), runway slope and condition, wind component. Regulatory requirements: V1 (decision speed), VR, V2, and balanced field length (accelerate-go = accelerate-stop); OEI second-segment climb gradient (minimum 2.4% for 4-engine, 2.7% for 3-engine, 3.0% for 2-engine); Obstacle clearance with OEI. Performance factors: Higher T/W reduces field length, Lower W/S reduces V2 but increases drag, and High-lift devices increase CLmax for lower speeds. Performance guaranteed to airlines; flight test validates.