new Performance

Jet Performance

Fundamental knowledge of performance principles for heavy, high-speed, high-altitude jet airplanes.

Generic guide to know Weight & Calculate Profit from Payload

used with the Airplane Operations Manual (AOM).

most basic parameters used in its calculations:

1. (Temperature—>1/∝)

2. (Altitude—>1/∝)

3. (Speed—>∝ Until Shockwave)

Ram Rise

Difference between TAT & SAT. ⇡ in Temp. due to Compressibility

• Negligible Until: 0.3 Mach speed

Main cause: Deceleration (stagnation) of air

Minor effect: Friction with probe surfaces

Compressibility

Change in the Volume when

External Force is Applied

Total Air Temperature (TAT)

“OAT”+ 100% of Ram Rise

• Determines N1 / EPR limits

• Obtained by TAT Probes including Ram Rise.

Comparison: TAT > SAT due to ram air stagnation.

MCQ Trap: In flight, the higher the Mach number, the greater the Ram Rise and the larger the difference between TAT and SAT.

Ram Air Temperature (RAT)

SAT + Certain % of Ram Rise.

If A/C is stationary→TAT = RAT = SAT.

In modern A/Cs: ADC accounts for compressibility, displays only→TAT, OAT

RAT → No longer displayed.

Outside Air Temperature (OAT) / Static Air Temperature (SAT)

Temp. of Free moving, Undisturbed Air Around A/C. Obtained from

• Ground meteorological Sources

• in-flight TAT Corrected by ;ADCs for: Instrument Errors & Ram Rise.

Altitude

Vertical measurement (Elevation) with respect to Specified Reference Level.

Barometric Altitude: as Altitude⬆→Pressure⬇

QFE (Height)

Altimeter setting that indicates

Height Above Ground Level (AGL)

Absolute Altitude

Height Above Terrain Measured by RA

calculating time delay of a radio signal to ground and back.

(used in Approach & Landing phases Only)

QNH ‘Local Altimeter Settings’

Altimeter setting Below Transition Layer

A/C flies with Reference to MSL

Giving Indicated Altitude

Provided by ATC

Indicated Altitude

Altitude on the Altimeter when set to QNH
indicating A/C Height above MSL

??? Local setting example: 1015 hPa or 30.00 inHg.???

• used for IFR flights below Transition altitude.

QNE

Altimeter setting used Above Transition Layer

A/C flies with reference to Flight Level
@1013.25Hpa (ISA press.)

Giving Pressure Altitude

Pressure Altitude (PA)

Altitude on the altimeter when set to; QNE

• @ ISA, which is 1013.25 (hPa) or 29.92 (inHg).

• Above: Standard Datum Plane (SDP).

PA = (Stndrd press.- Non stndrd press.) X 1000 + Elevation

Density Altitude

Press.Alt. Corrected for Non-Stndrd Temp.

120 feet for every 1°C Deviation from ISA

High DA →Occurs on hot days at high elevation airports; results in reduced air density, leading to longer takeoff rolls and reduced rates of climb.

Aircraft performance calculations are based on actual air density.

Density Altitude Equation

used for Perf. Calc.:
DA=[Non stndr temp. - ISA temp.(15°c) ] x 120 + PA

True Altitude

Actual Height of an object above Sea Level
Not Indicated by any instruments.

in ISA conditions

True Alt.= Indecated Alt.

In extreme cold weather, True Altitude is lower than Indicated Altitude.

Vs (Stall Speed)

Speed at which airflow Separation Begins

Highest point on (CL) vs AoA (α) curve.

V S1G

corresponds to CLmax→(just before the lift starts to decrease)

At this moment, Load Factor = One

Load Factor (or) G Factor

relation between Lift Produced to

Gross Weight Opposing it.

V MCG

Minimum Control speed on Ground

at which A/C Controllable using Maximum Rudder Deflection only in case of 😞 engine Failure rec. @ V1 & Other engine on T/O Thrust

Affected by:

Temp, Alt. —> Inversely proportional (1/∝)

V MCA

Minimum Control speed in Air (Flight)

at which A/C Controllable using Maximum Rudder Deflection only.

in case of 😞 engine failure @ V1

& Other engine on T/O Thrust

Minimum Unstick Speed (VMU)

Lowest speed where A/C can Safely; Lift Off Ground→Continue T/O

Without Encountering Tail Strike.

• No Longer Published in Flight Manual

Liftoff Speed (VLOF)

Actual speed at which the airplane Lifts Off. Depends on:

1. Weight,

2. (AoA) angle of attack,

3. Configurations.(flaps settings)

Must be Below:

Maximum Tire Speed.

Maximum Tire Speed

Strength of Tires determines this speed due to the Exposure to

⬆Centrifugal forces @⬆Speeds

✈Matters more@High-Elevation A/P:

• As Altitude ⬆, Density⬇

• To generate same Lift

• Higher True Airspeed (TAS) is needed.

• Indicated airspeed (IAS) might be normal,

but True Airspeed may Exceed Tire limit

Maximum Brake Energy Speed (V MBE)

Maximum Speed for Full Braking to a Complete Stop,

within Braking System's Heat Limitations

Must be Higher Than Vlof

Depends on:

1. Temp.

2. Press.

3. Weight,

4. Wind

5. RWY Slope
   Operational Significance: Higher TAS/ground speed at high-elevation airports (e.g., Addis Ababa at 7,600 ft) requires increased attention to V MBE.

Engine Failure Speed (V EF)

@ which Critical Engine Assumed to Fail.

Selected to allow 1 to 2 seconds before reaching V 1.
to allow pilots to react to 😞engine failure.

V 1 (Decision Speed)

Maximum speed whether you Reject or Continue T/O,

where 1st Braking Action must be Applied in case of Rejected T/O

limits:

1. > VMCG

2. < VR & VMBE

Rotation Speed (VR)

Calibrated speed at which pilot initiates Nose-Up Rotation for liftoff.

Ensures V2 @ Screen Height

Not Lower than >;

1. 1.05 Vmca

2. V1

Takeoff Climb Speed (V 2)

T/O Safety Speed, Reached @ Screen Height
& Maintained for Entire Climb with T/O Flaps,
in an 😞engine failure at or after V1. Not Lower Than>;

• 1.1Vmca,

• 1.2 Vs,

In All‑Engine takeoff;

• Climb is made 10–15 Kts Above V2

Screen Height

35’ for Dry,

15’ for Wet RW, above T/O surface

After an E.F. @ V1,
at which V2 Must be Reached & Maintained.

Take off Performance

Determining 3 things during this initial phase:

1. Capabilities and Limitations of aircraft

2. Minimum RW Length Required for Safe Takeoffs,

3. Best Fuel Consumption
   which

   -Ensuring passenger Safety

   -Reducing A/C Wear
   -Optimizing flight Schedules.

Crtical Engine

in ↔Multi-engine aircraft with the Most

Adverse Effects on A/C Handling & Performance
in case of its 😞Failure.

Takeoff Distance Required (TODR)

• Horizontal distance starting from; Ground Roll until reaching 35’

above T/O surface in case of 😞Engine Failure @V1

• with All engines operating →115% of horizontal distance, starting from ground roll to screen height,

Accelerate-Stop Distance Required (ASDR)→(1+2)

Sum of the Distances required to:
1) Accelerate with All Engines @ V1
2) Decelerate to a Full Stop with EF

Takeoff Run Required (TORR)

(2 R fel Nos ya 7mar)

The greater of:

1. Horizontal dis from ground roll until reaching a point Equidistant to Vlof & V2
   Assuming😞EF @ V1, Must not exceed Runway Length

2. 115% of distance to a point equidistant between V LOF and screen height (all engines).

Takeoff Run Available (TORA)

Length of runway declared available and suitable for ground run of an airplane.

Clearway

rectangular Area Clear from any Objects.
Beyond RWY, Above its Extended Centerline, Under A/P Authorities,

Might Not be a a Load-bearing Surface.

Min. Width of 500 feet,

Upward Slope not exceeding 1.25%

Inc. ⇡Weight & Dec. ⇣V1
to enhance Accelerate Stop Distance.

Takeoff Distance Available (TODA)

Runway length + Clear Way

Stopway

prepared rectangular Area Beyond RWY, Above its Extended Centerline, Under A/P Authorities,

Must be Rigid surface.

As Wide As RWY,

Increasing A/C’s Weight,

that’s Able to Support during Rejected T/O.

Accelerate-Stop Distance Available (ASDA)

Runway Length + Stopway

Minimum Airworthiness Takeoff Requirements

Available distances must be ≥ Required distances.

1. ASDR ≤ ASDA,

2. TODR ≤ TODA,

3. TORR ≤ TORA.

Balanced vs Unbalanced Field Length

Balanced: TODR = ASDR (No clearway/stopway).

Unbalanced: TODR ≠ ASDR (Utilizes clearway or stopway).

Balanced Field Length occurs when ASDR = TODR.

Balanced Field Length

TODR=ASDR
Clearway or Stopway are 'Not Used'

Unbalanced Field Length (mtkawesa)

TODR ≠ ASDR
Clearway or Stopway Used

Climb Gradient

expressed in Percentage (%)

Height Gained to Horizontal Distance Traveled.

Used for: Obstacle Clearance

Height Gained / Horizontal Distance × 100.

Factors Affecting Net & Gross Gradients

•Config. (Flaps Settings)
• ⇡V1 ; ⇣T/O Dis.
• ⇡V2 ; ⇡T/O Dis.

Improved Climb Performance Technique

Using Excess RW

Accelerating to higher Speeds,
Achieving higher Climb Gradient,
Resulting in higher Take Off Weights

Takeoff Path

.actual flight path from 35ft to at least 1,500ft above T/O Surface in case of 😞Engine Failure @ V1

.or transition to en-route climb, whichever is higher.

1st Sigment

From 35’ till Landing Gear Fully Retracted, @constant V2 speed

using

• T/O Thrust + T/O Slats & Flaps,

• with +ve Minimum Climb Gradient

Second Segment of Takeoff Path

From Landing Gear fully Retracted to at least 400’ AGL (Min. Acceleration Height)

@constant V2 speed

using

• T/O Thrust, T/O Slats & Flaps,

• 2.4% Gross

• 1.6% Net

Min. Climb Gradient

• Most limiting segment for weight.

Climb Limit

Maximum allowable takeoff weight that satisfies the minimum 2nd segment climb gradient requirements following an engine failure at or after V1 .

Third Segment of Takeoff Path

Begins at Min. 400 ft (EgyptAir uses 800 ft)

→Horizontal Distance to Accelerate to Final Climb Speed, using

• T/O Thrust

• while Retracting Flaps & Slats

• 1.2% Minimum Climb Gradient

Maximum height limited by engine-out thrust time limit→ 10 minutes.

Fourth Segment of Takeoff Path

From End of Third segment to

At Least 1500ft

@ Final Climb Speed using

• MCT

• Retracted Slats & Flaps (Clean Config.)

• 1.2% Minimum Climb Gradient

Approach Climb Gradient

2.1% for 2-engine A/C

@Approach Config.

Landing Gear Retracted

With an Engine Failure

Landing Climb Gradient

3.2% for all engines A/C

Full landing Config.

Landing Gear Extended

Without an Engine Failure

Minimum Takeoff Path Gradients (2-Engine)

1. First segment: Positive,

2. Second segment: 2.4%,

3. Final segment: 1.2%.

Items Affecting T/O Performance

✅ Controllable Factors:

• Config.: A/C & Wheel Brake

• Engine Thrust Setting

• Weight

❌ Uncontrollable Factors:

RWY:

• Length

• Condition

• Environment

& Obstacles

Runway Slope Effects

Maximum Certified Slope Limit is ±2%

Downhill:

• Faster acceleration → shorter TOD,

• slower deceleration → longer ASD.

Uphill:

• Slower acceleration → longer TOD;

• faster deceleration → shorter ASD.

Wind Effects on Takeoff

For performance calculations, regulations require reported wind component up to: 50%→Headwind and

at least 150%→Tailwind.

Headwind:

• Reduces ground speed at V LOF → shorter TOD

• improves braking → shorter ASD.

Tailwind:

• Higher ground speed for V LOF → longer TOD

• diminishes braking → longer ASD.

Wet and Contaminated Runway Performance

⬇V1 to provide more Stopping Distance.

Screen height is reduced to 15 ft (instead of 35 ft).

If wet runway calculation allows higher weight than Dry

→More Limiting dry weight must be used.

Regulated Takeoff Weight (RTOW)

Maximum Takeoff Weight limited by:

1. Climb limit

2. Tire speed limit

3. Runway limit

4. Brake energy limit

5. Obstacles limit

6. Structure limit

Gross vs Net Gradient

Gross→Actual demonstrated performance;

real aircraft capability without safety margins.

Net→Gross Reduced to ensure obstacle clearance.

Certified climb performance after applying safety margins

2-Engine: Net = Gross - 0.8% reduction (e.g., 2.4% - 0.8% = 1.6%).

• 2-engines: 0.8%,

• 3-engines: 0.9%,

• 4-engines: 1.0%.

Net flight path must clear all obstacles by at least 35 ft.

Obstacle Clearance Limit→based on→Net flight path Gradients

Factors Affecting Net & Gross Gradients

•Config. (Flaps Settings)
• ⇡V1 ; ⇣T/O Dis.
• ⇡V2 ; ⇡T/O Dis.

Departure Sector (Buffer Area)

Defined airspace for obstacle consideration starting at Runway End.

where→(Gross & Net Gradients Applied)

• Initial width 300’ each Side;

• Divergence angle 7.1° (12.5% of distance).

Limitations:

• Max Width VMC Day🔆: 1,000 ft total (2,000 ft if turn > 15°).

• Max Width IMC/Night🌑: 2,000 ft total (3,000 ft if turn > 15°).

Flap Setting Compromise

Large Flaps:

• More lift → higher runway-limited weight;

• more drag → reduced climb gradient (climb-limited).

Small Flaps:

• Less drag → improved climb gradient

• less lift → requires higher speed → likely runway-limited.

Optimum T/O Flaps Settings

Compromisation between 2 values
if Runway's the problem, More flaps are useful.
if it’s Climb Gradient, Fewer flaps are useful.

V1 and V2 Effects

V1 affects TOD/ASDR but not climb gradient.

Higher V2 improves climb gradient but increases TOD.

Flat Rated Power

Max. Thrust Output based on Ambient Temp.

Provided by Engine (thermally limited not mechanically)

based on HPT blade Temp. limits.

High-Pressure Turbine (HPT) Blade Temperature Limit

Maximum temperature HPT blades can tolerate without structural damage

Damage Risk:
• Melting
• Cracking

This limit determines the engine flat-rated thrust

Tref

highest Temperature engine can provide Flat rated power.

Power starts to Decrease After, due to Temp. increase

T MAX

Max. Temp. at which the engine Can provide Thrust.

Above it→Turbine Inlet Temperature (TIT) Exceed Safe Limits.

Engine’s Thrust

Pushing force exerted by A/C’s Engine
Affected by: (ptha)🏠
1.Pressure→α
2.Temperature→1/α
3.Humidity→1/α (slight/negligible)
4.Airspeed→α (Ram Recovery)

Environmental Factors on Thrust

-Press.⬆→Density⬆→Mass Airflow⬆ →Higher Thrust⬆

-Temp⬆→ Density⬇→Mass Airflow⬇ → Lower Thrust⬇

-Humidity⬆→Density⬇→ slight/negligible ⬇ in Thrust.

-Speed⬆→Ram Recovery⬆→inlet Density⬆→ higher thrust⬆

Reduced Takeoff Thrust

• Allowed by Regulations, but:

  • Must not exceed 25%

  • Min.= 75% of Full-Rated takeoff thrust

• Two methods

  1. -(ATM) for Boeing

     -(Flex) for Airbus

  2. De-rate Only For Boeing

Reducing Cost by:

• ⬇Stress on Turbine,

• ⬆Engine Life & Fuel Efficiency

(FLEX) Flexible temperature (Airbus)

ATM Assumed Temprature Method Boeing

Imputting Fictional (Higher) Temp.

Limiting Actual T/O Thrust

but VMCG calculated based on Full Rated Thrust

D-Rate for Boeing

Replacing the Full Rated engine with another

Less Thrust, Entirely Diff. Engine

Through the FMC.

VMCG is lower because yawing moment is reduced.

Improved Climb Performance

Using Excess RW

Accelerating to higher Speeds,
Achieving higher Climb Gradient,
Resulting in higher Take Off Weights

(better climb gradient to lift a weight restriction on Hot days)

Engine Thrust Ratings

Takeoff/Go-Around: typically 5 minutes (10 min. in case of E.F.)
MCT: highest setting usable Indefinitely
Max Climb Thrust: typically Below MCT (except @ High Altitudes)

Climb Performance

Angle of Climb→Altitude per Distance (For→Gradient),

Rate of Climb→Altitude per unit Time

Best Angle used for distance constraints;

Best Rate used to minimize time to cruise.

Regulatory constraint:

• 250Kt below 10,000’ (Constrained Speed)
• 300Kt until Switching to Mach Number

Angle Of Climb

Gaining of Altitude per unit of Distance

Best Angle Of Climb 'Vx'

Speed @ which Shortest Distance is required for reaching a Specific Altitude.

used to meet ATC clearance constraints related to distance

such as crossing a specific point at or above a certain altitude.

Rate Of Climb

Gaining of Altitude per unit of Time.

Best Rate Of Climb "Vy"

Speed @ which Shortest Time is required for reaching a Specific Altitude.

used when time is a constraint, such as for traffic separation.

In case of Emergency from

Initial Climb —> Top of Climb (TOC)

• 250Kt below 10,000’ (Constrained Speed)
• 300Kt until Switching to Mach Number

Cruise

From Top Of Climb to Top Of Decent (TOC→TOD)

Main pilot's Task in this phase is Saving Fuel as much as possible

Maneuver Margin

Ability of Air Surrounding the Wings to Support the A/C’s Weight

Safety buffer between Low-speed & High-speed buffet.

Altitude increases → air density decreases → maneuver margin reduces.

• The higher the load factor, the smaller the maneuver margin .

• For any given weight and speed, the maneuver margin decreases as altitude increases.

This margin dictates

• Available bank angles

• turn capabilities

Load Factor

Ratio between Total Aerodynamic Force acting on A/C to Actual Weight of it.

Straight-and-level flight=1.0G

30° bank ≈ 1.15 G

Equivalent Weight

Effective weight the wings must support is the  actual weight multiplied by the load factor. Equivalent Weight = Actual Weight × Load Factor

Buffet Boundaries

Low & High speeds for Initial Buffets
@ Any Given Altitude & Weight

Mechanism (Low-Speed): Airspeed decrease → AoA increase → airflow separation → buffet → stall.
Mechanism (High-Speed): Speed approaches critical Mach → shockwaves form → turbulent airflow separation → buffet.

Low Speed Buffet

caused by Air-flow Separation before Stall.

High Speed Buffet

caused by Shockwaves Formation

Aerodynamic Ceiling (Coffin Corner)

Altitude where low-speed and high-speed buffet boundaries converge.
Limitations: Maximum achievable load factor is 1.0 G; zero margin for maneuvering.

Optimum Altitude

Altitude Providing: best Specific Range  for a given aircraft weight.

It increases as fuel burns off and the aircraft becomes lighter..

Optimum Altitude and LRC

Best compromise for maximum range while maintaining adequate maneuver margin.

• Typically a load factor of at least 1.3 G (allows approx. 40° bank).

• LRC provides 99% of maximum possible range.

Cruising above the optimum altitude

-Reduce flight Safety & Maneuverability: Lower load factor limits the ability to deviate around weather.

-Greater Turbulence Vulnerability: Aircraft is less able to withstand Vertical Gusts.

-Thunderstorm risk: Tops & Anvils extension Above jet cruise altitudes, making Avoidance Difficult.

-Reduces fuel efficiency (range per fuel).

Endurance ‘How Long You Last?’

Maximum Time Engine can Operate on Given Fuel quantity.

Best endurance speed

Speed Resulting in Min. Fuel Flow

Range ‘How Far Can You Go?’

Max. Distance Engine can Operate on Given Fuel quantity

Endurance vs Range

Endurance is maximum time (min fuel flow/min drag speed).

Range is maximum distance (tangent to drag curve).

• Maximum range speed is always higher than best endurance speed.

Specific Range (SR)

Distance traveled per unit of fuel consumed.

Formula: SR = True Airspeed (TAS) / Total Fuel Flow.

1. ∝ Altitude

2. 1/∝ Weight

3. Speed

Lower weight → less lift & drag → less thrust → better specific range.

Climbing from 10,000 ft to 30,000 ft can:

• double specific range due to higher TAS and lower fuel flow.