PERFROMANCE

The four forces of lift, weight, thrust and drag acting on an aircraft all induce stress into the airframe structural
members, with temperature factors leads to fatigue.

Fatigue, is a permanent loss of the physical properties of the materials comprising the structure. Fatigue will, if
left undetected or unattended, eventually cause the structure to fail altogether.

Based on this data, a Design Limit Load (DLL) is calculated for each member and for the complete structure.

The DLL is the maximum load that can be applied to the structure repeatedly during normal operations without
inducing excessive fatigue and the pilot must never deliberately exceed this value.

The DUL is the minimum load the structure must be able to absorb in an emergency without collapsing.

Structure subject to loads in excess of the DUL is likely to suffer some permanent damage and may even
collapse altogether.

Suitable mass limits are imposed so that the integrity of the structure is guaranteed throughout the aircraft’s
working life.

Definitions

Centre of Gravity

The centre of gravity (CG) is:

the point that the total weight of the aircraft is said to act through
the point of balance
that part of the aircraft that follows the flight path
the point that the aircraft manoeuvres about in the air
the point that the three axes of the aircraft pass through.
it affects the stability of the aircraft.

Centre of Gravity Limits

The CG is not a fixed point; it has a range of movement between a maximum forward position and a
maximum rearward position which is set by the aircraft manufacturer and cannot be exceeded. The CG
must be on or within the limit range at all times.
CG moves in flight as a result of fuel burn, flap positions, and crew and passenger movements.
The manufacturer sets down CG range of movement limits to ensure that the average pilot is able to
control the aircraft through all stages of flight safely, with normal piloting effort, free of fatigue.

CG position Stability Manoeuvrability Stick forces

Towards the nose of the increases decreases increases

aircraft

Towards the rear of the decreases increases decreases

aircraft
 Factors CG outside foward limit CG outside aft limit

Drag Increases decreases

fuel consumption increases decreases

endurance decreases increases

Longitudinal stability increases decreases

Take off speeds increase decrease

Range decrease increase

Stability increase decrease

manouvreability decrease increase

stick force increase decrease

Datum

A point along the longitudinal axis designated by the manufacturer as the zero or reference point from which all
balance arms (distances) begin.

Balance Arm

The distance from the aircraft’s datum to the CG position or centroid of a body or mass.

For the purposes of calculations, all balance arms ahead of (in front of) the datum are given a negative (-) prefix
and those behind (aft of) the datum are given a positive (+) prefix.

Weight

Weight also has pronounced effects on the aircraft’s performance, handling and aerodynamic properties.
 Factors Effect of increase of weight

Performance decrease

Take off and landing distance increase

ROD increase

Stall speed increase

Drag and fuel consumption increase

range and endurance decrease

Term Includes Excludes

Basic empty mass (BEM) Aircraft structure, unusable fuel, Usable fuel, crew, payload
oil

Dry operating mass (DOM) BEM + Crew + Catering + usuable fuel, payload
equipment

Operating mass (OM) DOM + usable fuel payload

Zero fuel mass (MZFM or ZFM) DOM + Payload usuable fuel

Ramp mass All onboard + fuel including taxi -

fuel

Take off mass Ramp mass minus taxi fuel -

Landing mass Take off mass minus fuel used -

during flight

All formulas

DOM = BEM + Crew + Crew Baggage + Catering + Operational Items

ZFM = DOM + Payload
Payload = Passengers + Baggage + Cargo
Ramp Mass = ZFM + Usable Fuel
or
Ramp Mass = DOM + Payload + Usable Fuel
Take-off Mass = Ramp Mass − Taxi Fuel
 Landing Mass = Take-off Mass − Trip Fuel
Payload = ZFM − DOM
Usable Fuel = Ramp Mass − ZFM
or
Usable Fuel = Total Fuel − Unusable Fuel
Total Mass = BEM + Crew + Payload + Usable Fuel
OM = DOM + Usable Fuel

Fuel Type Purpose

Start and Taxi Fuel From engine start to runway entry

Trip Fuel Take-off to landing at destination

Contingency Fuel Buffer for enroute variations

Alternate Fuel Destination to alternate airport

Final Reserve Fuel 30 min at 1,500 ft above alternate

Captain’s Discretion Fuel Extra fuel by PIC decision

Ramp / Block Fuel All fuel loaded onboard before start

Venting Fuel Fuel lost due to overfilling or thermal expansion

Fuel Policy Jet Aircraft Piston Aircraft

Final Reserve 30 min at 1,500 ft AGL 45 min at cruise (VFR)

Contingency 5% of Trip Fuel 10% of Trip Time

Alternate Planning Often long distance Close alternates preferred

CG = Total Moment / Total Mass

Moment = Mass x arm length

Take off distances

Term Definition / Use

Take off roll (TOR) Ground roll to liftoff

Take off distance (TOD) Distance to reach 35 ft/ screen height after brake release

TORR (Take off run required) Ground distance required to get airborne

TODR ( Take off distance Full distance needed to reach 35 ft under actual conditions
required )

Take-off Path Total climb profile from brake release to 1,500 ft

ASDA/ EMDA - Accelerate-stop TORA + stopway

Distance Available or Emergency
If no stopway, then ASDA = TORA
Distance Available

Accelerate-Go Distance to continue take-off after engine failure at V1

TORA Runway length usable for take-off run/the length of the runway from
threshold to threshold.

TODA TORA + Clearway

If no clearway, then TORA and TODA are same.

Clearway Clearways are an area beyond the runway, not less than 152 m (500 ft)
wide, centrally located about the extended centre line of the runway,
and under the control of the airport authorities.

The clearway is expressed in terms of a clearway plane, extending from

the end of the runway with an upward slope not exceeding 1.25%,
above which no object or terrain protrudes.

Stopway Stopways are an area beyond the take-off runway, no less wide than
the runway and centred upon the extended centre line of the runway,
able to support the aeroplane during a Rejected Take-off (RTO),
without causing structural damage to the aeroplane.

Paved structure, not as strong as main runway length

Balanced field length TODA= ASDA

V-Speed Definition When It’s Used Conditions / Notes

V1 Max speed at which pilot Take-off roll Below V1 → Reject

can decide to abort the At/Above V1 →
Take off decision Continue
take-off safely
speed Depends on
balanced field
length

Vr Speed at which the pilot End of take-off roll Must be ≥ Vmc

initiates nose-up pitch to Chosen so that V2 is
Rotation Speed achieved at 35 ft
lift off
AGL

Vlof Speed at which aircraft Immediately after Vr May equal or

actually lifts off the runway slightly exceed Vr
Lift-off Speed
(wheels leave ground)

V2 Speed that ensures safe 2nd Segment Climb Must be achieved at

OEI (One Engine 35 ft AGL
Take-off Safety Provides positive
Inoperative) climb after
Speed climb gradient with
take-off
1 engine

Vmu Minimum speed where Test/certification Determined during

aircraft can lift off safely flights flight test
Minimum Unstick Not operationally
without tail strike or stall
Speed referenced by
pilots

Vmca Minimum speed at which Multi-engine aircraft Vr must always be ≥

aircraft is controllable with take-off Vmc
Minimum Control No rudder
critical engine failed
Speed in air authority below
Vmc

Vmcg Lowest speed at which Determines Rudder not effective;

aircraft is controllable on minimum safe V1 only nosewheel steering
Minimum control
the ground with engine / asymmetric thrust
speed on ground failure

Vne Max airspeed that must Structural integrity Marked with red line on
never be exceeded in any protection ASI
Never exceed speed
flight condition

Vs1g Stall speed in clean Load factor Used to compute

configuration at 1g level calculations, maneuvering speed (Va =
Stall Speed at 1g flight maneuver margins √n × Vs1g)

Vs Minimum steady flight All flight phases Base value for other
speed in clean performance
Stall Speed (Clean speeds
configuration (gear/flaps
configuration) up)

Vs0 Minimum steady flight Landing approach Flaps down, gear

speed in full landing down
Stall speed in landing
configuration
configuration

Vref Approach speed used for Final approach Must not be less
landing, typically 1.3 × Vs0 than 1.23 Vsr
Reference landing (certification rule)
speed

Vx Speed for max altitude gain Obstacle clearance Steeper climb

per horizontal distance after take-off Used to clear close-
Best Angle of Climb in obstacles
Speed

Vy Speed for max altitude gain Normal climb More efficient climb
per unit time Less steep than Vx
Best Rate of Climb
Speed

Vfe Highest speed at which a Take-off & landing Exceeding this can
given flap setting can be phases damage flap system
Max Flap Extended
safely used
Speed

Vle Max speed with landing Approach, go-around Do not exceed with
gear extended gear down
Max Landing Gear
Extended Speed

Vlo Max speed for extending or Gear Lower than Vle to

retracting landing gear extension/retraction prevent damage
during movement
 Max Landing Gear

Vmd The speed at which the To achieve maximum Flying at Vmd gives:
total drag on the aircraft is aerodynamic
Minimum drag speed Maximum
at its minimum during efficiency
endurance for jet
steady, level flight. (Max
aircraft
L/D ratio) Minimum power
required for level
flight.

Vmp Vmp is the speed at which To give maximum This is not the same
minimum engine power is endurance in as Vmd (minimum
Minimum Power drag) because
required to maintain propeller aircraft
Speed power required ≠
steady, level flight.
drag — power
depends on both
drag and speed.
P=D⋅V
So, even if drag is
low (as at Vmd), if
the speed is high,
power required can
still be greater.
Thus: Vmp < Vmd
Minimum drag ≠
minimum power

Ceiling

Service Ceiling

Max altitude where aircraft can still climb at 100 ft/min

Practical operational limit
For twins: 50 ft/min with one engine inoperative
Minimal excess power remains
Used in performance planning

Absolute Ceiling

Max altitude where rate of climb = 0

No further climb possible, even at full power
No excess thrust or lift margin
Not used operationally
Aircraft can only level off, not climb

Factors affecting take off distance

 Factor Effect on Take-off Distance

Aircraft Weight ↑ Weight = ↑ Distance

Air Density (DA) ↓ Density = ↑ Distance

Wind Headwind ↓, Tailwind ↑

Runway Slope Upslope ↑, Downslope ↓

Surface Condition Wet/grass ↑, Paved ↓

Flap Setting Optimum (10 degree flap) ↓, Too much (40 degree flap) ↑

Engine Performance More thrust ↓, Less thrust ↑

Obstacle Height Higher obstacle = ↑ distance to clear

Temperature & Humidity Higher = ↑ Distance

Configuration Errors Improper trim/flaps = ↑ Distance

Airframe Contamination Severely ↑ Distance / May prevent lift-off

Take off segment

First Segment (Liftoff to 35 feet AGL)

Starts at: Aircraft becomes airborne (main wheels leave the ground)
Ends at: Aircraft reaches 35 feet above runway surface
Configuration:
1. Gear down
2. Take-off flaps/slats extended
3. Take-off thrust (All engines or OEI)
Speed: ≥ V2 (take-off safety speed)
Minimum Climb Requirement: Positive climb gradient
Purpose: Safely establish the aircraft in a stable climb post-liftoff

Second Segment (35 feet AGL to ~400 feet AGL)

Starts at: 35 ft AGL

Ends at: Aircraft reaches 400 feet AGL
Configuration:
1. Gear retracted as soon as climb is positive
2. Flaps/slats remain extended
3. Take-off thrust (maximum rated OEI thrust)
Speed: Maintain V2 to V2 + 10 kt
Minimum Climb Gradient:
 4. 2.4% (twin-engine)
5. 2.7% (three-engine)
6. 3.0% (four-engine)
Purpose: This is the most critical OEI segment, ensuring obstacle clearance and adequate climb
performance

Third Segment (Transition Segment / Acceleration Segment)

Starts at: 400 ft AGL (or manufacturer-defined acceleration altitude)

Ends at: When clean configuration is achieved and aircraft is accelerating
Configuration:
1. Flaps/slats retracted gradually
2. Aircraft transitions from take-off to climb configuration
3. Engine at take-off or max continuous power (depending on phase)
Speed: Aircraft accelerates from V2 to final segment climb speed
Minimum Climb Gradient: None specified
Purpose: Allows pilot to accelerate and reconfigure aircraft safely before resuming steady climb

Fourth Segment (Final Segment Climb – Clean Climb)

Starts at: End of configuration/acceleration phase

Ends at: Aircraft reaches 1,500 ft AGL
Configuration:
1. Clean (gear and flaps retracted)
2. Engine at Maximum Continuous Thrust (MCT) (OEI)
Speed: Final segment speed (usually VySE or manufacturer-recommended OEI climb speed)
Minimum Climb Gradient:
3. 1.2% (twin-engine)
4. 1.5% (three-engine)
5. 1.7% (four-engine)
Purpose: Continue safe OEI climb to a height where normal flight and procedures can resume

Rate of Climb (ROC)

Rate of Climb (RoC) is the vertical speed at which an aircraft gains altitude, usually expressed in feet per minute
(fpm) or meters per second (m/s).

Rate of Climb=Excess Power/ aircarft weight

​RoC=TAS×Climb Gradient

Vy- best rate of climb speed , max ROC

Angle of climb (AOC)

The Angle of Climb is the angle between the horizontal ground and the aircraft’s flight path during a climb.

Vx - best angle of climb speed, max AOC

 Factor Effect on Rate of Climb (RoC) Effect on Angle of Climb (AoC)

Aircraft Weight ⬇ Heavier = ⬇ RoC ⬇ Heavier = ⬇ AoC

Altitude (Density) ⬆ Altitude = ⬇ RoC (lower ⬆ Altitude = ⬇ AoC (reduced
power/thrust) thrust/lift, longer distance)

Temperature (ISA dev) ⬆ Temp = ⬇ RoC (hot air = less ⬆ Temp = ⬇ AoC (less thrust =
power) shallower climb)

Engine Power/Thrust ⬆ Power = ⬆ RoC (more excess ⬆ Thrust = ⬆ AoC (steeper

power) climb)

Drag / Configuration ⬆ Drag = ⬇ RoC (more power ⬆ Drag = ⬇ AoC (less net thrust
needed) = flatter angle)

Wind Minimal direct effect ⬆ Headwind = ⬆ AoC (shorter

ground run)⬇ Tailwind = ⬇ AoC

Flaps / Gear ⬇ RoC if extended (due to drag) ⬇ AoC if extended (due to

thrust/drag imbalance)

Aircraft Cleanliness ⬆ Clean = ⬆ RoC (less drag) ⬆ Clean = ⬆ AoC

Propeller / Jet Type Prop: performance drops rapidly Jet: maintains thrust longer —
with altitude better AoC at higher altitudes

Endurance

Endurance is defined to be the ratio of airborne time to fuel used for that time.

ENDURANCE = TIME (hr) ÷ FUEL (kg)

SPECIFIC ENDURANCE (hr/kg) = 1 ÷ FUEL FLOW

Jet Aeroplane Endurance

FUEL FLOW = FUEL FLOW PER UNIT THRUST × TOTAL THRUST

Fuel used per unit thrust is most commonly known as specific fuel consumption.

FUEL FLOW = SFC × TOTAL THRUST or

FUEL FLOW = SFC × TOTAL DRAG

To minimize drag, the jet aeroplane simply flies at the velocity for minimum drag. Therefore Vmd is the speed to
fly for maximum endurance for a jet aeroplane.

Propeller Aeroplane Endurance

FUEL FLOW = FUEL FLOW PER UNIT POWER × TOTAL POWER

FUEL FLOW = SFC × TOTAL POWER

For piston engines specific fuel consumption is a minimum at lower altitudes, whereas for turbo-propeller
engines specific fuel consumption is a minimum at middle to high altitudes.

For a propeller aeroplane, it is Vmp that is the speed for maximum endurance, whereas for a jet it is Vmd.

Factor Endurance (Prop) Vmp Vmd

Weight ↑ ↓ ↑ ↑

Altitude ↑ ↑ ↑ (TAS) ↑ (TAS)

Flaps/Gear ↓ ↓ ↓

Dirty Airframe ↓ ↑ ↑

Forward CG ↓ ↑ ↑

Load Factor (Turns) ↓ ↑ ↑

Colder Temp (ISA↓) ↑ ↓ ↓

Range

Maximum range can be defined as being the maximum distance an aeroplane can fly for a given fuel quantity
consumed or to put it another way, the minimum fuel used by an aeroplane over a given distance.

RANGE = DISTANCE (NM) ÷ FUEL (kg)

SPECIFIC RANGE (SR) = TAS ÷ FUEL FLOW

JET SPECIFIC RANGE (SR) = TAS ÷ (SFC × DRAG)

PROPELLER SPECIFIC RANGE (SR) = TAS ÷ (SFC × POWER REQUIRED)

Jet Aeroplane Range

1.32VMD that is the speed for maximum range for a jet aeroplane.

Propeller Aeroplane Range

VMD that is the speed for maximum range for a propeller aeroplane.

Factors affecting range

Factors Effect

Weight increases Specific range decreases

Flaps and gears deployed Range decreases

Headwinds Range decreases

Tailwinds Range increases

Altitude increases range increases, but above a specific altitude, range decreases.

Optimum altitude

The pressure altitude which provides the greatest specific range or fuel mileage at a given weight and speed.
Flying higher or lower than the optimum altitude will decrease the range of the aeroplane.

Over time, as the weight decreases with fuel burn, the optimum altitude increases.

Cross over altitude

Crossover Altitude is the altitude at which you switch from climbing at IAS (Indicated Airspeed) to climbing at
Mach number.

1. At lower altitudes, aircraft climb using constant IAS (e.g., 280 KIAS), because:
It gives good climb performance.
It prevents exceeding structural limits.
2. At higher altitudes, Mach number becomes limiting, because:
As you climb, TAS increases at constant IAS.
Eventually, you'll reach a critical Mach number (risk of shock waves).
So you switch to constant Mach climb (e.g., Mach 0.74).

The altitude where IAS equals Mach climb target (at standard atmosphere) is called the Crossover Altitude.

Long range cruise (LRC)

Long Range Cruise (LRC) is the airspeed that gives you the greatest range per unit of fuel burned — not the
absolute maximum range, but 95–99% of it, with a slight increase in fuel flow to allow higher cruise speeds.