Take-off Performance

Wing Commander Rajagopal

Calculation of Take-off Performance

Take-off performance is the aircraft’s ability to accelerate, lift off and safely climb after take-off under specific conditions. It depends on factors such as aircraft weight, runway length, weather, altitude and engine performance.

Defined Speeds during Take-off

Take-off Segment

  • The take-off segment extends from the Brake Release Point (BRP) to screen height.
  • Take-off consists of a ground run followed by an airborne section.
  • The ground run extends from the start of the take-off roll until lift-off.
  • The airborne section begins at lift-off and ends at screen height.

Stalling Speed

  • Lift is the aerodynamic force acting vertically upward on the aircraft.
  • This lift enables the aircraft to remain airborne.
  • Lift is produced by a combination of airspeed and angle of attack (AoA).
  • At higher airspeeds, a smaller angle of attack is required to generate sufficient lift.
  • At lower airspeeds, the angle of attack can be increased to maintain lift.
  • Beyond the critical angle of attack, lift decreases rapidly while drag increases sharply.
  • Stalling speed is the minimum speed required to maintain level flight.

Minimum Control Speeds

  • Minimum control speed is the lowest speed at which the aircraft remains controllable after failure of the critical engine.
  • Above this speed, yaw resulting from engine failure can be corrected using rudder.
  • The two minimum control speeds during take-off are VMCG and VMCA.
  • VMCG is the minimum control speed on the ground.
  • VMCA is the minimum control speed in the air.

Rotation Speed (VR)

  • Rotation speed is the speed at which the pilot initiates aircraft rotation.
  • Backward control pressure raises the aircraft nose.
  • At VR, the elevator has sufficient authority to rotate the aircraft.
  • The aircraft is rotated to the required angle of attack for lift-off.

Lift-off Speed (VLOF)

  • Lift-off speed is the speed at which the aircraft leaves the runway.
  • VLOF is the speed at which the main wheels become airborne.
  • It is also known as the unstick speed.
  • Typically, VLOF is between 1.1 and 1.2 times the stall speed.

Take-off Safety Speed (V2)

  • Take-off safety speed must be achieved before reaching screen height.
  • V2 is determined using stall speed and minimum control speed requirements.

Decision Speed (V1)

  • If an engine fails, the pilot has two possible actions.
  • Reject the take-off and stop the aircraft if sufficient runway remains.
  • Continue the take-off with one engine inoperative.
  • The aircraft must still achieve lift-off performance on one engine.
  • Decision speed (V1) is the speed where:
    • Take-off Run Required (TORR) equals Accelerate-Stop Distance Required (ASDR).
  • At V1, both stopping and continuing the take-off require the same distance.

Aerodrome Limitations during Take-off

Take-off Run Required (TORR)

  • TORR is the runway distance required to complete the take-off.
  • It begins at brake release.
  • It ends when the aircraft reaches screen height.

Take-off Distance Required (TODR)

  • Initial climb distance extends from lift-off to screen height.
  • TODR equals the take-off run plus the initial climb distance.
  • It represents the distance from brake release to screen height.
  • TODR must not exceed TODA.

Aerodynamics in Take-off Segment

Effective Mass

  • Aircraft performance is directly influenced by aircraft weight.
  • The weight carried is commonly referred to as payload.
  • Aircraft mass acts vertically downward through the centre of gravity.
  • The gravitational force acting on mass is called weight.
  • Weight is also referred to as the effective mass of the aircraft.

Thrust

  • Thrust accelerates the aircraft to generate lift.
  • Higher airspeed produces greater lift over the wings.
  • Thrust is the forward propulsive force generated by the engines.
  • Sufficient thrust allows the aircraft to reach take-off speed.

Jet Engine Thrust

  • Jet engines ingest large quantities of air through the intake.
  • The engine accelerates this air rearwards, producing forward thrust.
  • According to Newton’s Second Law:
    • Force = Mass × Acceleration
  • Greater airflow mass increases thrust.
  • Greater acceleration of airflow also increases thrust.

Intake Momentum Drag

  • As aircraft speed increases, intake momentum drag also increases.
  • The incoming air already possesses forward velocity.
  • This reduces the change in air velocity across the engine.
  • Reduced acceleration of airflow decreases engine thrust.

Compressibility Effect (Ram Recovery)

  • Above approximately Mach 0.2, compressibility increases air density entering the engine.
  • This reduces intake momentum drag.
  • The reduction is known as thrust recovery or ram recovery.
  • Ram recovery causes thrust to increase at higher speeds.

Take-off Thrust – Jet Aircraft

  • Ram recovery does not significantly occur during take-off.
  • Take-off speeds remain below Mach 0.2.
  • Consequently, thrust gradually decreases during the take-off roll.

Propeller Thrust

  • Propellers accelerate air rearwards to generate thrust.
  • The engine drives the propeller through the air.
  • The accelerated airflow produces lift over the wings.

Propeller Thrust Variation

  • Propeller thrust depends on blade angle of attack.
  • Higher blade angle of attack generates greater thrust.
  • Increasing aircraft speed changes the relative airflow.
  • This reduces blade angle of attack and therefore reduces thrust.

Take-off Thrust – Propeller Aircraft

  • As speed increases during take-off, propeller thrust decreases.
  • This behaviour is similar to that of jet aircraft.

Drag

  • Drag is the resistance opposing aircraft motion.
  • Air resistance is called aerodynamic drag.
  • Wheel friction produces wheel drag.
  • Aerodynamic drag consists of parasite drag and induced drag.

Aerodynamic Drag

  • Parasite drag results from airflow over the aircraft structure.
  • It depends primarily on airframe design.
  • Induced drag is associated with lift generation.
  • Induced drag increases as aircraft speed increases.
  • Overall aerodynamic drag increases with speed.

Wheel Drag

  • Wheel drag is caused by tyre friction with the runway.
  • It depends on wheel loading and surface friction.
  • As lift increases during take-off, wheel loading decreases.
  • Wheel drag reduces to zero at lift-off.

Total Drag

  • Aerodynamic drag increases while wheel drag decreases during take-off.
  • Total drag gradually increases throughout the take-off roll.
  • Initially, excess thrust is high.
  • Excess thrust reduces as take-off progresses.
  • Acceleration therefore decreases throughout the take-off roll.

Excess Thrust

  • Engine thrust decreases while drag increases during take-off.
  • Initial excess thrust is greatest at brake release.
  • Reducing excess thrust results in lower acceleration.

Simple Take-off Equation

  • Acceleration decreases during the take-off roll.
  • Drag increases while excess thrust decreases.
  • Take-off distance is proportional to:
    • Velocity² ÷ (2 × Acceleration)
  • Acceleration equals force divided by mass.
  • Acceleration is directly proportional to excess thrust.
  • Available thrust equals total thrust minus total drag.
  • Acceleration is inversely proportional to effective mass.

Factors affecting Take Off Performance

Effect of Aircraft Mass

  • Increasing aircraft mass increases inertia.
  • Higher mass increases wheel loading and wheel drag.
  • Acceleration decreases.
  • Higher lift-off speed becomes necessary.
  • Ground run increases.
  • Initial climb angle decreases.
  • The aircraft requires more distance to reach screen height.
  • Overall take-off distance increases.

Effect of Air Density

  • Lower air density reduces engine thrust.
  • Lift-off speed increases.
  • Acceleration decreases.
  • Dynamic pressure decreases.
  • True Airspeed (TAS) must increase to maintain the same IAS.
  • Initial climb gradient decreases.
  • High temperature, high altitude and high humidity all reduce air density.
  • Hot, high and humid conditions reduce aircraft performance.

Effect of Wind

  • Headwinds increase dynamic pressure.
  • Ground speed required for take-off decreases.
  • Take-off distance decreases.
  • Tailwinds increase ground speed.
  • Take-off distance increases.
  • Headwinds improve climb angle while tailwinds reduce climb angle.

Wind Calculations

  • Performance calculations use conservative wind assumptions.
  • Only 50% of the reported headwind is credited.
  • 150% of the reported tailwind is assumed.
  • Aircraft are also limited by maximum allowable crosswind components.

Effect of Runway Slope

Upslope

  • On an upslope, a component of aircraft weight acts opposite to thrust.
  • This increases effective drag.
  • Take-off distance increases.

Downslope

  • On a downslope, a component of weight acts in the direction of thrust.
  • This improves acceleration.
  • Take-off distance decreases.

Slope Rule of Thumb

  • A 1% runway slope changes take-off distance by approximately 5%.
  • This corresponds to a correction factor of 1.05.
  • Maximum runway slope at most aerodromes is approximately 2%.

Runway Surface

  • Grass runways increase wheel drag and take-off distance.
  • Standing water, slush and snow also increase drag.
  • Spray impingement creates additional aerodynamic drag.
  • Water, snow and ice reduce braking effectiveness.
  • Accelerate-stop distance increases on contaminated runways.
  • Water ingestion may lead to engine failure.
  • Contaminated runways can also reduce directional control and increase structural damage risk.

Runway Surface Condition

  • Runway surfaces are classified as damp, wet or contaminated.
  • Damp: moist but non-reflective.
  • Wet: moist and reflective.
  • Contaminated: at least 25% of the runway covered with 3 mm or more of water, slush or snow.
  • Contamination details are published in SNOWTAMs or NOTAMs.

Airframe Contamination

  • Ice, snow and water contamination disrupt airflow over the aircraft.
  • They increase drag and reduce lift.
  • Aircraft weight increases.
  • Wheel drag increases.
  • Acceleration decreases.
  • Take-off distance increases significantly.

Weather

  • Heavy rain reduces lift and increases drag.
  • Hazards include wind shear, micro-bursts and airframe icing.

Aircraft Configuration

  • Flaps are trailing-edge devices that increase wing camber.
  • Flaps increase lift but also increase drag.
  • The aircraft can lift off at a lower speed.
  • Initial climb angle becomes shallower with flap extension.
  • Using the recommended flap setting generally reduces take-off distance.
  • Smaller flap settings improve obstacle clearance and climb gradient.