Unit 5: Aircraft Performance in Accelerated Flight - Subjective Questions

Take-off performance describes the distance, time, and speed required for an aircraft to become airborne and clear a specified obstacle safely.

The principal phases are:

• Ground roll: The aircraft accelerates from rest to lift-off speed .
• Rotation: At rotation speed , the pilot raises the nose to establish the required lift coefficient.
• Lift-off: The aircraft leaves the runway when lift becomes sufficient for flight.
• Transition: The flight path changes from approximately horizontal to the required climb angle.
• Initial climb: The aircraft climbs at a specified speed and clears the screen or obstacle height.

Take-off performance is affected by aircraft weight, thrust, aerodynamic drag, runway slope, wind, air density, runway surface, flap setting, and ground effect.

During the ground roll, the longitudinal equation of motion is

where is thrust, is drag, is the rolling-friction coefficient, and is the normal reaction.

Using

the equation becomes

Therefore, the ground-roll distance is

If thrust is constant and

define

Then

For an approximately constant net accelerating force , this reduces to

The derivation assumes negligible runway slope and no wind unless their effects are separately included.

The important effects are:

• Aircraft weight: Greater weight raises stall and lift-off speeds and reduces acceleration, increasing ground roll.
• Thrust: Higher thrust produces greater acceleration and shortens the roll.
• Air density: Low density reduces engine thrust, propeller effectiveness, and aerodynamic lift, generally increasing take-off distance.
• Headwind: Reduces the ground speed needed to reach a given airspeed, shortening ground distance. A tailwind has the opposite effect.
• Runway slope: An upslope adds a resisting component of weight and increases distance; a downslope reduces it.
• Runway surface: Soft, wet, or contaminated surfaces increase rolling resistance and may reduce acceleration.
• Flap setting: Moderate flap can reduce lift-off speed, but excessive flap increases drag.
• Aerodynamic drag: Greater drag reduces net accelerating force.
• Ground effect: Reduced induced drag near the runway can improve acceleration and initial lift-off performance.

Using the work-energy relation,

Hence,

Substituting the given values,

Therefore, the estimated take-off ground-roll distance is .

This result assumes that the stated net force is constant and already includes the effects of drag and rolling resistance.

Assume that the aircraft follows a circular transition of radius from horizontal flight to a climb angle , followed by a straight climb.

For a circular transition, the horizontal and vertical displacements are

For an approximate constant load factor at small flight-path angles,

If the obstacle height exceeds , the remaining height is gained in a straight climb. Its horizontal distance is

Thus, the total airborne distance is

If the transition is neglected, a simpler estimate is

The total take-off distance is the sum

The method assumes constant speed, a constant climb angle, and no significant wind variation during the airborne segment.

Obstacle clearance depends on both ground and airborne performance:

• Lift-off position: A longer ground roll leaves less runway or horizontal distance for climbing.
• Climb gradient: It is approximately and depends primarily on excess thrust.
• Take-off speed: The selected speed affects lift, drag, transition radius, and climb capability.
• Aircraft weight: Higher weight increases required speed and reduces climb gradient.
• Available thrust: Engine condition, temperature, altitude, and engine failure directly affect excess thrust.
• Wind: A headwind reduces horizontal ground distance for a given altitude gain.
• Configuration: Flaps and landing gear affect both lift and drag.
• Obstacle height and location: A nearby obstacle may require a steep initial climb or a reduced take-off mass.

Safe clearance requires the calculated flight path, including regulatory margins, to remain above the obstacle-clearance surface.

Balanced field length is the runway length for which the accelerate-stop distance equals the accelerate-go distance following a critical engine failure.

The decision speed separates two actions:

• If a critical failure is recognized before , the take-off is rejected and the aircraft must stop within the available runway.
• If the failure is recognized at or after , the take-off is continued and the aircraft must lift off and clear the specified screen height.

At the balanced condition,

where is accelerate-stop distance and is accelerate-go distance.

Increasing generally increases accelerate-stop distance because braking begins later, but decreases accelerate-go distance because more acceleration has occurred before engine failure. Their intersection determines the balanced value of and the balanced field length.

Accelerate-stop distance consists of:

1. Acceleration from rest to the engine-failure or decision speed.
2. Distance travelled during recognition and pilot reaction.
3. Braking distance from the achieved speed to rest.

It may be represented as

Accelerate-go distance consists of:

1. Acceleration with all engines operating up to engine failure.
2. Continued acceleration with one engine inoperative.
3. Rotation and lift-off.
4. Airborne distance required to clear the specified screen height.

Thus,

To determine balanced field length, both distances are calculated for several values of . The selected balanced speed satisfies

Graphically, it is the intersection of the accelerate-stop and accelerate-go curves. Operational field-length requirements may also include regulatory safety factors.

Balanced field length is affected by:

• Take-off mass: A higher mass increases required speeds and usually lengthens both accelerate-stop and accelerate-go distances.
• Engine thrust: Greater thrust improves acceleration and one-engine-inoperative climb performance.
• Braking capability: Effective brakes, spoilers, and reverse thrust reduce accelerate-stop distance.
• Runway condition: Wet, icy, or contaminated runways reduce braking effectiveness and increase field length.
• Pressure altitude and temperature: High density altitude reduces thrust and aerodynamic performance.
• Wind: Headwind generally reduces ground distance, whereas tailwind increases it.
• Runway slope: Upslope assists stopping but opposes acceleration; downslope has the reverse effects.
• Obstacle or screen height: A greater required clearance height increases accelerate-go distance.
• Reaction time: Delayed recognition and braking increase accelerate-stop distance.
• Flap setting: It changes lift-off speed, drag, and one-engine-inoperative climb gradient.

A landing consists of:

• Approach: The aircraft descends toward the runway at a selected approach speed and glide angle.
• Flare: The descent rate is reduced and the flight path becomes nearly horizontal.
• Touchdown: The main landing gear contacts the runway at the touchdown speed.
• Ground roll: Aerodynamic drag, wheel braking, spoilers, and reverse thrust decelerate the aircraft.

Major variables include aircraft mass, approach speed, touchdown speed, glide angle, lift and drag coefficients, flare technique, runway slope and condition, wind, air density, braking coefficient, reverse thrust, spoiler effectiveness, and pilot reaction time.

Because kinetic energy is proportional to , even a small excess in touchdown speed can cause a substantial increase in landing distance.

For a straight approach at a constant glide angle , the geometry gives

where is screen height and is horizontal approach distance. Therefore,

For and ,

Thus, the approach distance is approximately .

If the flare begins at height , the straight-approach portion should instead be calculated from

Wind changes the distance measured over the ground, although it does not directly change the geometric air-path angle when defined relative to the surrounding air mass.

Model the flare as a circular arc of radius that changes the flight-path angle from a descent angle to zero.

The horizontal flare distance is

and the height lost during the flare is

If the aircraft flies at approximately constant speed and constant load factor , the normal equation gives

For a shallow approach angle, , so

Consequently,

A larger flare radius gives a smoother maneuver but requires more horizontal distance. Excess speed also increases flare distance because varies approximately with .

After touchdown, the principal retarding forces are aerodynamic drag , wheel-braking friction, and reverse thrust .

The normal reaction is

so the braking force is

The longitudinal equation is

Using ,

Therefore, the landing ground roll from touchdown speed to rest is

If the average retarding force is constant,

where is the average total retarding force.

Deploying spoilers reduces lift, increases the normal reaction, and therefore improves wheel-braking effectiveness.

Using the work-energy relation,

Therefore,

Substituting,

Hence, the estimated landing ground-roll distance is .

The result assumes a constant average retarding force and no runway slope or wind correction. A wet runway or delayed brake application would increase the actual distance.

Take-off ground roll:

• Thrust acts in the direction of motion.
• Drag and rolling resistance oppose acceleration.
• Increasing lift reduces wheel reaction and rolling resistance.
• The objective is to reach lift-off speed in the shortest safe distance.
• The governing force is .

Landing ground roll:

• Drag, wheel braking, spoilers, and reverse thrust oppose motion.
• Residual lift reduces the normal reaction and can weaken wheel braking.
• Spoilers are used to destroy lift and transfer weight to the wheels.
• The objective is to dissipate kinetic energy and stop safely.
• The retarding force is .

Both distances are strongly affected by speed because kinetic energy is

Thus, excessive lift-off or touchdown speed produces a disproportionately large increase in runway distance.

Ground effect occurs when an aircraft flies within approximately one wingspan of the ground. The ground interferes with the formation of wingtip vortices and restricts the downward motion of the airflow.

Its principal consequences are:

• Downwash at the wing is reduced.
• The induced angle of attack becomes smaller.
• Induced drag decreases for a given lift.
• The effective lift-curve slope may increase.
• The aircraft can produce the required lift at a lower geometric angle of attack.

Since induced drag is associated with vortex strength and downwash, the wing behaves as though it has a higher effective aspect ratio near the ground. Ground effect is strongest at very small wing heights and gradually disappears as height increases.

During take-off, reduced induced drag can allow the aircraft to lift off at a speed that is too low for satisfactory climb outside ground effect. If the pilot climbs abruptly, induced drag increases and the aircraft may settle back toward the runway.

During landing and flare:

• Reduced induced drag causes the aircraft to retain energy and float farther along the runway.
• Flare distance may increase, especially when approach speed is excessive.
• The descent rate may reduce more readily near the surface.

After touchdown, continued aerodynamic lift can reduce the wheel normal force:

This lowers the available braking force

Spoilers shorten the ground roll by reducing lift and increasing wheel loading. Thus, ground effect may aid lift-off but can also increase float and delay effective braking during landing.

Resolving forces along the flight path gives

where is the climb angle. Since ,

The aircraft accelerates when

For a steady climb at constant speed,

and therefore

If , the aircraft decelerates while climbing. Thus, available excess thrust must be divided between overcoming the component of weight along the climb path and producing acceleration.

The specific mechanical energy of the aircraft is

Differentiating with respect to time gives

The excess power is

Dividing by weight gives specific excess power:

Therefore,

This equation shows that excess power may be used to:

• Increase altitude through .
• Increase speed through .
• Produce a combination of climbing and acceleration.

For a steady climb, , so

For level acceleration, , and all excess power increases kinetic energy.

1. Flare height:

2. Straight-approach distance:

3. Flare distance:

4. Landing ground roll:

5. Total landing distance:

Therefore, the approximate total landing distance is . Regulatory margins, wind, runway slope, braking delay, and runway condition would need to be included in an operational calculation.