PERFORMANCE

Done by: Aloysius Goh

 Formula Sheet

Section Formula

Climb Climb Gradient = [(Thrust - Drag) / Weight] x 100

● Sin y = Tan y = Climb Gradient

ROC (ft/min) = Tas (kt) x Still air Gradient (%)

Wind Effective Gradient = Still air gradient x (TAS/GS)
Gradient (%) - Altitude Difference (ft) x 100 / Ground Difference (ft)

Drag = T - W Sin Y
Lift = W Cos Y

Descent Drag = T +W Sin Y

Lift = W Cos Y

Power/Thrust Power Required = Drag x TAS

Power Available = Thrust x TAS

Fuel / Range SR (Air): TAS/ Fuel Consumption per hour (FF)

SR (Ground) = GS / Fuel Consumption per hour (FF)
SR = TAS/ (SFC x Drag) → for jets and assuming T = D

Load Factor Load Factor (n) = Lift / Weight

Load Factor (Turn) = 1/ CosΘ

Wind Headwind/Tailwind = Wind Speed x cos (angular difference between runway and wind)
Crosswind = Wind speed x sin (angular difference between runway and wind)

Hydroplaning TAKE OFF: 9 x SqRt (pressure in psi)

LANDING(non-rotating wheels) : 7.7 x SqRt (pressure in psi)
BARS: 34 x SqRt (pressure in bars)

Temperature TAT (K)= OAT (K) x (1 + 0.2 x Mach2)

 MUST KNOW REGULATIONS:

Class B

Take off Speeds VR

1.05 VMC or 1.10 VS1
● Speed at 50ft above the take off surface → 1.20 VS1
VREF
1.3 VSO or VMC

Take off Distances No Stopway or Clearway

1. 1.25 UTOD < TORA
When Stopway or clearway available
2. TORA
3. 1.15 UTOD < TODA
4. 1.3 UTOD < ASDA

Factorisation Landing Surface (Take off)

Surface Type Condition Factor

Grass (on firm soil) Dry 1.2

Grass (up to 20cm long) Wet 1.3

Paved Wet 1.0

Landing Surfance (Landing)
Surface Type Condition Factor

Grass (on firm soil) Dry 1.15

Grass (up to 20cm long) Wet 1.15

Grass + Wet Cumulative Factors (1.15)2

Multi Piston Engine Finding LDR. If finding LD, 1.43 (divide by 0.7)
factorisation not required

Wind: not more than 50% headwind or not less than 150% tailwind
Slope: 5% per 1% slope

Departure Sector Half Width = 60m + wingspan/2 + 0.125D

● Max 300m if flight conducted under conditions allowing visual course guidance

Net Take Off Flight Path (NTOFP) NTOFP = 0.77 x AEO Gradient (up to clouds)
NTOFP = OEI (from clouds to 1500ft)

Enroute En-route gradient (net gradient)= Gross Gradient +/- 0.5%

● Descent = increase 0.5%
● Climb = Decrease 0.5%
Max Enroute altitude
● ROC 300 fpm

Landing Class B → 0.7 x LDA = LDR

 General Concepts
Performance Legislation

Performance A 1. Multi-engined aeroplanes (Turbo Prop Engines) with MOPSC > 9 or MTOM > 5700
kg
2. Multi-engined Turbo-jet aeroplanes (see “jet” pick “jet”)
3. All jet aircraft belong to this performance class

Performance B 1. Propeller engines with MOPSC 9 or less and MTOM 5700kg or less

Measured Average set of data, achieved by the new aeroplane when flown by TEST PILOTS
Performance

Gross Performance Average performance by LINE PILOTS when flown in accordance with techniques described in the
flight manual
● Calculated performance with no safety factor

Net performance Gross Performance Minus Safety Factor

● Actual flight path of the aeroplane reduced by a safety margin
Obstacle Requirements for Take off Flight Path
● Min: 35 ft
● Turn exceeding 15o: 50 ft
 ETOPS (Extended Twin Operations)

Aircraft should be able to make it to its alternate airport within that timeframe in the case of an engine failure
● Starts at 60 mins, then 90, 120 and 180 hours
Specific Criteria
● Min two-engined aeroplane under conditions of Still air
○ Performance Class A with either:
■ MOPSC 20 or more
■ MTOM 45 360kg or more
■ Restriction: Distance flown in 60 mins at the One engine inoperative (OEI) cruising speed
○ Performance Class A with
■ MOPSC 19 or less
■ MTOM < 45 360kg
■ Restriction: distance flown in 120 mins or, subject to approval, up to 180 mins for turbo jet
aeroplanes, at OEI cruise speed
○ Performance Class B or C:
■ Restrictions: distance flown in 120 mins at OEI cruise speed or 300NM whichever is less
 General Performance Theory

VX= Max Gradient /Best angle of climb Vy= Max Rate / Best rate of climb

Graphs Where Thrust Curve and Drag Curve (furthest apart) Where Power Available and Power Required (Furthest
Apart)

Increased Mass Vx Increase Vy Increase

Increased Altitude Vx Increase (prop), Unchanged (jet) Vy decrease

Increased Temperature Vx Decrease Vy Decrease

Flaps Deployed Vx Decrease Vy Decrease

Max Horizontal Speed Max Thrust Intersect Total Drag Max thrust intersect Power Required
Thrust Lower Air Density = less thrust → less horizontal distance travelled
● Therefore, Climb gradient decreased

Backside of Thrust Curve: A lower airspeed requires more thrust

Specific Range (SR) SR (Air): TAS/ Fuel Consumption per hour (FF)
SR (Ground) = GS / Fuel Consumption per hour (FF)

Heavier aircraft → More fuel required + less distance travelled = SR reduces

Density Altitude Is the altitude in the standard atmosphere at which the prevailing density would be found
● Also the pressure altitude corrected for “non-standard” temperature
3 factors:
1. Altitude
a. Increase Altitude → Decrease Density
2. Temperature
a. Increase Temperature → Decrease Density
3. Humidity
a. Increase Humidity → Decrease Density

Load Factor Load Factor (n) = Lift / Weight

Load Factor (Turn) = 1/ CosΘ

Aerodynamic Ceilings Absolute Ceiling (Coffin Corner)

● Altitude where power required and power available curves are tangential to each other
● Only one speed is available
● Achievable ROC is 0 ft/min
Service Ceiling
● Altitude at which the aircraft is capable of a climb rate of 100 feet per min or about 0.5m / sec
● There is a reasonable, range of speed within which the aircraft can operate
Max Operating Altitude
● Highest pressure altitude certified for normal operation
Take-off

Critical Engine (Right hand prop)

● A left engine failure, with a left quartering wind

Climb Performance

Climb Gradient: Defined as the ratio of the increase of altitude gained to horizontal traveled (in still air) as a percentage
● Climb Gradient = [(Thrust - Drag) / Weight] x 100
● Sin y = Tan y = Climb Gradient

ROC (ft/min) = Tas (kt) x Gradient (%)

● Best ROC is obtained when the difference between Power Required and Power Available is at its maximum
● Gradient = Still air gradient

Increased Temperature → Reduces both Climb gradient and ROC

High Humidity → Reduce Climb performance

Drag = T - W Sin Y
Lift = W Cos Y
Glide Performance

Engines are off: no difference between Jet and Propeller aircraft

● Max Endurance: Ie Max Time in the air - Min possible ROD
○ VMP for both aircraft types
● Max Range: Greatest Distance Traveled
○ VMD for both aircraft types
ROD Factors (to increase/Decrease)
1. Speed
2. Descent Angle
a. Any change from optimum = reduced Glide distance
Drag = T +W Sin Y
Lift = W Cos Y

ROD/Glide Angle … If a plane loses weight and forward speed is kept constant
● It will be travelling faster than its optimum, causing it to fly a shallower glide path if no changes are made.
Hence, to maintain glide path
○ ROD Increase
○ Glide Angle Increase
○ CL/CD decrease

Flaps Deployed
● Drag increases = ROD increases
● ROD Increase = Descent Gradient Increase
Gradient (%) - Altitude Difference (ft) x 100 / Ground Difference (ft)
ROC = Still air Gradient x TAS
Wind Effects
Headwind Tailwind

Shorten distance to descend = steeper/Increase Glide Increase Distance to descend = shallower/ Decrease Glide
Path Angle Path Angle
● Counter: Increase Power ● Counter: Reduce Power
Decreases the ground distance flown Increases the ground distance flown
Lift Off Speed reached earlier Lift Off Speed reached later
Higher speed for maximum range Lower speed for maximum range
Descent Angle Constant Descent Angle Constant
ROC INDEPENDENT of any wind
Climb Angle Relative to air INDEPENDENT of any wind
Climb Angle Relative to Ground DEPENDENT of wind

Slope
Uphill Downhill

More Diff to Accelerate = Increase TOD + Lower TOM Easier to Accelerate = Decrease TOD + Higher TOM
● Increase ASD (acceleration portion greater ● Decrease ASD (acceleration portion greater
effect than Stop segment) effect than Stop segment)

EASA AIR OPS: 5% for 1% upslope

Runway Surface Condition TAKE OFF

Surface Type Condition Factor

Grass (firm soil) Dry 1.2

Up to 20 cm long Wet 2.3

Paved Wet 1.0

LANDING
Surface Type Factor

Grass (on firm soil up to 20cm 1.15

long)

Technique (Wet Runway)

● Positive Touchdown, full reverse and brakes as soon as possible
Dry Short Grass Vs Pavement
● Take off Distance → Increase
● Landing Distance → Increase
 Drag Curve (Jet) Power Required Curve (Prop)

Lowest Point: VMD Lowest Point: VMP

● VMD = best endurance (jet), best range (prop) ● VMP = best endurance (prop)
● Vx = min power off glide (Jet) ● Vx = min power off glide (prop)
Tangent: (1.32 VMD) Tangent:
● 1.32 VMD = best range (Jets) = Max Specific Range ● VMD = best endurance (jet), best range (prop)
Power Required = Drag x TAS → lower than VMD

Summary - JETS Vs PROPS

Category JETS PROP

Best Endurance VMD VMP

Best Range 1.32 VMD VMD

Vx: Max gradient VMD VMP

 Runway Lengths

Definitions TORA = Take-off Run Available

TODA = Take-off Distance Available (TORA + Clearway)
ASDA = Accelerate Stop Distance Available (TORA + Stopway)
● Includes TORA
● Includes Starter Extension
● Includes Stopway in direction of take off
LDA = Landing Distance Available (TORA - Displaced Threshold)
Stopway: An area on the ground beyond the end of TORA which is prepared and designated as a suitable area in which an aeroplane
can be stopped in the event of an abandoned take-off
Clearway: an area that may be provided beyond the end of TORA that is free from obstacles which may cause a hazard to airplanes
in flight
● Not least than 152 m (500ft) wide
● Upslope not exceeding 1.25%
● Threshold lights may protrude above the plane if their height is 0.66m (26 in) and located each side of the runway

Screen height → the height at the end of the TODR and at the beginning of the landing distance required

Regulation ASD ≤ ASDA

● Accelerate Stop distance must not exceed accelerate stop distance available
TOD ≤ TODA
● TOD must not exceed TOD available, wth clearway not exceeding half of TORA
TOR ≤ TORA
● Take off run must not exceed Take of Run Available

Reference 0 is a point 35 ft vertically beneath the aircraft: At the end of TODR

Take off Distance

1. Without stopway or clearway, when multiplied by a factor of 1.25, TOD should not exceed TORA
2. When stopway or clearway available, TOD should not exceed TORA
3. When stopway or clearway available, when multiplied by a factor of 1.15, TOD should not exceed TODA
 Level Flight, Range, Endurance

Specific Range

BELOW VMD
❖ Drag increases = Thrust Required Increases
ABOVE VMD
❖ Drag increases = Thrust Required Increases
Greatest SR : High Altitude + Low Temperature
● High Altitude: Lower air pressure = Less drag = Burn less fuel
● Low Temperature: Greater density = More thrust per unit fuel burnt
● High temperature = Specific Range decrease
● Increased Mass = SR decrease
● TAS high + SFC Low = SR increase
● *SR increases when approaching optimum Alt and Decreases as you diverge away
● SR Independent of Wind

Speed for Max Endurance is ALWAYS LOWER than Speed for Max Range
● JETS:
○ Max Range: 1.32 VMD
○ Max Endurance: VMD
● PROPS
○ Max Range: VMD
○ Max Endurance: VMP
● Max Endurance: Unaccelerated level flight with minimum fuel flow
● Higher Altitude = Higher Max Endurance Speed

*Every 1000ft deviation from optimum altitude = 2.5% reduction in range

Fuel Flow Directly proportional to the mass of the aeroplane

● E.g 5% Increase in mass = fuel flow increase by 5%
SFC: Specific Fuel Consumption
● Amount of fuel burnt to produce a specific unit of thrust (Jet) or Power (Piston)
● Inversely Proportional to SR
● High Alt + Low Temp = Increased SR = Decreased SFC
*As fuel is consumed throughout the flight
● IAS Decrease, Drag Decrease
 ● Optimum alt changes → the lighter the aircraft, the higher the optimum altitude

Optimum Performance Altitude

Engine Type Best Endurance Altitude

Non-turbocharged Propeller Aircraft (Piston Low Altitude (MSL)

Engine) ● TAS decreases with altitude as no
● “Propeller aircraft” supercharger to maintain thrust against the
reducing density
Maximum Achievable IAS (PISTON) : Decreases
steadily with altitude as density decreases

Turbo-prop Medium Altitude

Jet Engine High Altitude

● Endurance is max at High level, low OAT,
design RPM

Speed Performance

Maximum Speed (VMax) → where maximum thrust equals to total drag

2 Intersections = Vs and VMax

*Most Jet aircraft cruise at 85-90% of Max RPM

Climbing and Descending

Climb ROC = Sin y x TAS
● Faster the speed, the greater the ROC
● Heavier will climb faster (at faster Speed) but the Gradient and ROC will be the same
○ ROC speed higher
Sin y = [(T - D) /W] x 100 Or (T/W) - (D/L)
● Thrust is made up of all engines operating (be careful)
L = W Cos (y)
CosΘ = L/W
Climb Performance
● Worst: obtained at high Density Altitude
○ High OAT + High Pressure Altitude
○ Excessive Configuration (too much drag = lower L/D ratio)
● Best: obtained at low Density Altitude
○ Low OAT + Low Pressure Altitude
 ○ Best obstacle clearance = Vx + No High Life Devices
○ CL/CD max @ 4o AOA
● Maintain Climb Performance
○ Interchange between speed and Angle of climb (inversely proportional)
● Vx always < Vy
● Headwind: Maximum Range Speed increases (to move drag curve to the right) and speed of max angle
of climb (remains the same)

Descent

Headwind:
1. Ground Speed: Decrease; Countermeasure: ROD Decrease + Maintain IAS/CAS
2. Initial Glide range decrease → but after some time → Increase (pitch down gains higher speed at best
L/D ratio)
Best Glide Performance
● Headwind = Less GD = Less Range. Hence, need to increase speed to compensate
● Propellers → Feathered

Engine Failure Twin Engine Plane

● Thrust Required: Increase (due to increased drag)
● Thrust Available: reduced by 50%
● Excess Thrust: reduced more than 50%
● Vy Decreases (point of max excess power reduced)

● VXSE is higher than Vx; VYSE is lower than Vy

 CS-23/ Applicable Operational Requirements Performance Class B - Theory

Class B Aeroplane: Aeroplanes powered by propeller engines with a MOPSC of 9 or less and a MTOM of 5700kg or less

Airworthiness Requirements
Take off Obstacle Clearance Net take-off flight path shall be determined in such a way that the aeroplane clears all obstacles by a vertical distance of
at least 50ft or by a horizontal distance of at least 60 m +Wingspan/2+ 0.125 D
● Where D is the horizontal distance the aeroplane has traveled from the end of the TODA or the end of the TOD
Factors for Consideration
1. Mass of aeroplane
2. Pressure altitude
3. OAT
4. Not more than 50% Headwind OR not less than 150% Tailwind
Track changes → Not be allowed up till one half the wingspan but not less than 50 ft (whichever higher) above the
elevation of TORA is reached
● Up to 400 ft: Bank no more than 15o
● Above 400ft: greater than 15o but not more than 25o

Critical Speeds
VS stalling speed or minimum steady flight speed at which the aeroplane is controllable

V1 Take-off Decision Speed

● High Altitude → V1 Decreases as air is less dense, need more runway to stop (less
reverse thrust available)

Landing VREF: The speed of the aeroplane, in specified landing configuration, at the point where it descends
Approach through the landing screen height, used in the determination of the landing distance for manual
Speed (VREF) landings
1.3 VSO
● VSO: stall speed in landing configuration

Take-Off Twin-engined Aeroplanes

Speeds ● 1.10 VMC
● 1.20 VS1
Single-engined Aeroplanes
● 1.20VS1
VR Speed
● Twin-Engine
○ VR not less than the greater of 1.05 VMC or 1.10 VS1
● Single Engined Landplanes
○ VR must not be less than VS1
Screen Height
Class Phase Screen Height

A Take-off Dry/Wet 35 ft/ 15ft

A Landing Dry/Wet 50 ft

B Take-off Dry/Wet 50 ft

B Landing Dry/Wet 50 ft

Take off and Landing

Obstacle Accountability Area The area beyond the TODA within which obstacles are considered for the purposes of takeoff climb performance

Take off Distances Unaffected TOD (UTOD) specified in AFM shall not exceed
5. 1.25 UTOD < TORA
6. When Stopway or clearway available
a. TORA
b. 1.15 UTOD < TOD
c. 1.3 UTOD < ASDA

Flap Setting More Flaps Vs Clean Configuration (Good before lift off)
● Flaps produce induced drag → reduce performance / Climb gradient
● Provide shortest take off & landing distances
● Slower speed required for take off and landing

Landing Slopes EASA AIR OPS → states that take off and landing distance should be increased by 5% for 1% downslope

Actual Landing Distances MEP → 0.7 x LDA

Jet → 0.6 x LDA

Short Landing Operations Usable length of declared safe area does not exceed 90 m

Runway Surface Condition

Surface Type Condition Factor

Grass (on firm soil) Dry 1.2

Grass (up to 20cm long) Wet 1.3

Paved Wet 1.0

 Climb, Cruise and Descent
Calculation Question There is a single engine cruising aircraft at the altitude at 9000ft. Following an engine failure at this altitude, what is the
net glide distance given the following?
Elevation: 250 ft
True Airspeed: 101 kt
Tailwind: 3 kt
Gross Gradient 11%

Step 1: Note that net glide distance (engine failure en route gradient) = Gross Gradient + 0.5%
● Hence, net gradient = 11.5%

Step 2: Note NAM/TAS = NGM/GS and find as much information as you can
● TAS = 101 kt
● GS = 101 + 3 = 104 kt
● NAM = [(9000 - 250)/11.5] x100 = 76 087 ft (12.5NAM)
Step 3: Find the NGM using above formula
● 12.5/ 101 = NGM /104 → NGM = 12.9NM
* Finding Headwind/Tailwind:
● Wind speed x Cos (track difference from wind direction)

Take off Climb Steady gradient of climb after take off shall be at least 4% (if no specific gradient provided)

Operating Minima In the event of an engine failure → remaining engines operating within max continuous power conditions
● Shall be capable of continuing flight above relevant minimum altitudes to a point of 1000ft above an
aerodrome at which performance requirements can be met
● At the point of engine failure
○ Airplane not flying at an altitude that it is unable to reach a climb rate of at least 300ft/min with all
engines operating at max continuous power
○ Enroute gradient = gross gradient + 0.5%
 CS-23 / Applicable Operational Requirements Performance Class B - The Use of Aeroplane Perofmrance Data for Single
and Multi Engine Aeroplanes

Basic Graph

Note:
OAT: must be calculated yourself if they mention “ISA” conditions
Mass (lb): refers to FLTOM and reverse engineered FLTOM can be done using that section
Wind Component (HEADWIND): Use the formula Wind Speed x cos (angular diff between runway and wind)
Ground Roll and TOD: if you move horizontally to the right (1400ft), thats ground roll, if you interpolate upwards
1700ft), thats TOD (NOT TODA)
● Do not forget the 50ft obstacle adjustment
* If they are asking for TORA/TODA apply factorisation
** If use the appropriate factors to adjust the final answer

Factorisation Landing Surface (Take off)

Surface Type Condition Factor

Grass (on firm soil) Dry 1.2

Grass (up to 20cm long) Wet 1.3

Paved Wet 1.0

Landing Surfance (Landing)
Surface Type Condition Factor

Grass (on firm soil) Dry 1.15

Grass (up to 20cm long) Wet 1.15

Grass + Wet Cumulative Factors (1.15)2

Multi Piston Engine Finding LDR. If finding LD, 1.43 (divide by 0.7)
factorisation not required
 Slope:
1. Take OFF: increased by 5% for 1% upslope (downslope not calculated)
2. LANDING: increased by 5% for 1% downslope (upslope not calculated)

No Clearway or Stopway 1.25 TOD < TORA

With Clearway or Stopway TOD < TORA

1.15 TOD < TODA
1.3 TOD < ASDA

Reduce Distances by 7% if heavy duty brakes are fitted

Climb Questions Given:

Performance Class: B
Cloud base above reference 0: 300 ft
Wind: Calm
Obstacle Clearance: 15 000ft
Obstacle height above reference 0: 600 ft
ROC (AEI): 1830 ft/min CAAT 1630 fpm
ROC (OEI): 400 ft/min
TAS: 101 kt
Find the min obstacle clearance above the obstacle
Notes Before Starting:
1. All Engine Gradient x 0.77 → applied from 50ft to the cloud base
2. OEI ROC → after reaching cloud base
3. Screen height (50ft) always added to climb

1st Part: 50ft - 300ft (cloud base)

● AEO ROC = 1830 x 0.77 = 1409 ft/min
● Time to Climb = 250 / 1409 = 10.65 sec
● As Winds are calm → TAS = GS
● Distance Travelled → 1817ft
Remaining distance = 15 000 - 1817 = 13 183ft
Part 2: Cloud base onwards
● Time to cover remaining distance → 77.3 sec
● Vertical Distance climbed → (77.3/60) x 400 = 515 ft
Summary: 515 + 300 = 815 ft (total vertical height climbed)
● Obstacle clearance → 815 - 600 = 215ft
Other Graphs Mixture Graph

Things to Note:
1. Longer line refers to Mixture Full Rich
2. Shorter lines adjacent refers to Mixture Leaned to 25% of Peak EGT

MSTOM Graph

Notes:
1. Always pay attention to the corrections below and apple them to get the correct OAT and GO value
2. STOP normally limited by ASDA and GO limited by the Lowest of the following:
a. TORA
b. TODA/ 1.15
c. ASDA/ 1.3
 3. ROC (ft/min) = Tas (kt) x Gradient (%)
4. Wind Effective Gradient = Still air gradient x (TAS/GS)

*** Minimum Gross Gradient of Climb: 2.5%

 CS-25 Applicable Operational Requirements Performance Class A - Theory

Take off
Segments TAKE OFF: horizontal distance along the take-off path from the start of the TO to a point equidistant between the point at which VLOF is
reached and the point at which the aeroplane is 35 ft above the TO surface
One Engine Take Off Run: is the distance between the brake release point and the middle of the segment between VLOF point and 35 ft
TAKE OFF FLIGHT PATH: actual take off distance with no safety margins included
G-G-C-C Get Up (VLOF)
Gear Up
Clean Up (flaps up, accelerate VFTO)
Climb Up (Max continuous thrust in climb)

1st Segment I4nitial Airborne Phase

● Accelerating from Lift off to V2
● Minimum Climb Gradient
2 Engine Positive Climb Gradient

3 Engine 0.3%

4 Engine 0.5%
●
● TOGA thrust, flaps take off position + gear down
● Bank Angle Limit: 0o
● End of Segment: Once +ve ROC → gear comes up

2nd Segment Best possible climb gradient

● TOGA thrust and V2 and Flaps maintained
● Bank Angle Limit: 15o
● End of Segment → Extends to min 400ft AGL but may extend higher (if terrain requires)

3rd Segment Transition or Acceleration Segment

● To change aircraft from take off configuration to clean configuration
● Accelerate to min 1.25 VS / best engine out ROC (clean speed)
● Only level acceleration required
● Required Gross Gradient (2,3,4 Engines): 2.4%, 2.7% and 3.0% with flaps in take off configuration
● Max acceleration height depends on the maximum time take off thrust maybe applied
● End of segment → thrust reduced to max continuous thrust on operating engines

4th Segment Max Continuous Thrust

● Speed is minimum 1.25 VS / Clean speed (FINAL CLIMB SPEED)
● End of Segment: Transition to the en-route altitude is reached at least at 1500ft

Engine Time interval between VEF and V1 is approximately 2 seconds (recognition time)
Failure
Regulation: aircraft must be able to maintain a straight flight (no need altitude) without
● Use of exceptional pilot skill
● Angle of bank exceeding 20o
● No requirements to maintain a specific ROC

Critical Speeds
V1 Rule of Thumb: Bad conditions = decrease and vice versa
Take-off Decision Speed: Maximum speed during take off at which a pilot can safely stop without
leaving the runway
● Procedure - Engine Failure
○ At/ Before V1: Abort the take off
○ At/ After V1: continue the take off
 Criteria
1. Not less than VMCG
2. Not greater than
a. VR
b. VMBE: Minimum Brake Energy Speed

V2 Take-off Safety Speed: Minimum speed which the aircraft is legally required to achieve on
reaching the screen height (35ft Class A)
● Higher V2 → Improved climb capability
● V2 maintained until at least 400ft above ground

V2MIN: Minimum Take off safety speed→ May not be less than
●
1.13 VSR Turbojets and 2 and 3 engined turboprops

1.08 VSR Turbojets with provisions for obtaining a significant reduction

OEI power on stall speed

1.1 VMCA Or 10% more - usually limiting at low altitudes

VR Speed at which rotation should be initiated during take-off → May not be less than
●
V1

105% of VMC 1.05 VMC

110% of VMU AEO

105% of VMU OEI

● Speed at which rotation to lift off AOA is initiated

VSRO Reference stall speed in landing configuration

VSR1 Reference stall speed in a given configuration

VLOF Maximum tire speeds in terms of ground speed

● Affected by Wind and Runway Elevation

VFTO Final Take Off Speed.

● May not be less than 1.18 VSR

VSR Reference stall speed

● May not be less than 1g stall speed (VS1g)

VLO Maximum speed for landing gear operation

Vs1g Lowest speed at which level flight can be maintained

Sequence of Speeds: VMCG, V1, VR, V2
 V1 is speed D (or A in another qn) → intersection between TOD (OEI) and ASD

Factors High Air Density

Affecting ● Increased V2MIN/ V2
Speeds Downhill Slope
● Decrease take off speed V1
Anti-skid inoperative
● V1 Decreases
Stopway added
● V1 Increases
Mass Increase
● VMU Increases

Take-off Obstacle clearance area

Obstacle ● Wingspan (> 60m): 90m + 0.125 D
Clearance ● Wingspan (< 60m): 60m + ½ Wingspan + 0.125 D

Max Width of Obstacle Clearance Area

● Change of track ( < 15o)
○ Suff Nav Accuracy can be maintained: 300m
○ All other Conditions: 600m
● Change of track ( > 15o)
○ Suff Nav Accuracy can be maintained: 600m
○ All other Conditions: 900m
Factors for consideration:
● Not more than 50% headwind or less than 150% tailwind component
● Bank Limits:
○ Not more than 20o bank angle between 200ft and 400ft
○ Not more than 30o when above 400ft
● Planned Track changes, can be assumed that
○ Clearing an obstacle by vertical distance of at least 50ft - 400ft: Bank > 15o
○ Above 400ft: Bank angles greater than 15o but not more than 25o
Allowed TOM
Factors Climb Limited TOM MTOM at which minimum climb gradients are met for each climb segment
● Performance limited
● Not affected by wind

Field Length Limited MTOM that allows for a take off within that runway at certain specific conditions
TOM ● Ground distance available limited

Obstacle Limited TOM MTOM at which obstacle clearance can be demonstrated

● Increased V2 speed = Increased OLTOM

Runway line-up correction Anytime positioning of the aircraft on the runway does not permit the aircraft to start the take off roll a
the start of the threshold

Temperature of brakes: need to be checked as overheated brakes will not perform adequately in the event of a rejected Take off
● Brake absorb more energy = Increase MTOM
1. Maximum Brake Energy Limits: capable of absorbing only a limited amount of energy and convert it to heat
2. Slope of Runway: will Degrade/ help the aeroplane stop (Upslope Good, Downslope bad)
3. OAT: if outside is cold, assist in brake’s transfer of heat
4. Pressure Altitude: low PA = higher TAS required for the same lift = hinder amount of heat the brake can absorb
5. Wind Component: Headwind = less TAS needed for take off (IAS matters more) = brakes need to absorb less

ACN-PCN
● ACN may exceed PCN by up to 10%

Field Lengths
Balanced Field Length No clearway, No Stopway TOD = ASD
● V1 = Balanced (1 single V1 Value)
● OEI TODR = OEI ASDR
● Gives minimum required field length in the event of an engine failure

Unbalanced Field Length Clearway, no Stopway TOD > ASD

● V1 < V1BALANCED
● V1 Decreases

Unbalanced Field Length Stopway, no clearway TOD < ASD

● V1 > V1BALANCED

Distances and Factors and Masses

Increase V1 TOM limited by TODA: increase; TOM limited by ASDA: Decrease

Compressed Snow TODR: remains the same; ASDR: Increases

Increased OAT Field Length Limited TOM: decrease; Climb Limited TOM: decrease

Inclusion of Clearway Field Length Limited TOM: Increase

Inclusion of Stopway ASDR: Increases

Lower Flap Setting + Climb Limited TOM: Increased

Higher V2

Anti Skid Inoperative ASDR: Increases

Contaminated Runway TOD: Increase ASD: Increase

Take off Takeoff Runway Performance Requirements → based upon failure of critical engine or all engines operating which ever gives the
Distance greater TOD
Dry Runway
Greater of the following:
1. Distance to TO and Climb to 35ft with AEI +15%
2. Distance to TO and Climb with Critical Engine Inoperative

Reduced Purpose: reduce maintenance costs, save engine life, noise abatement
Take-Off Permitted only if the actual TOM is lower than the field length limited TOM
Thrust ● MJRT 1: max assumed temperature for calculation +55oC
● Max reduction 25%
● TOGA allowed anytime
Prohibited Criterias:
1. Windshear conditions
2. Contaminated runway
3. Anti Skid Inoperative

Derated Thrust Lower thrust means lower VMCG and thus, allowing for lower V1 for runways that are ASDA limited as less distance needed to stop
Penalty: TODR will increase
● TOGA prohibited unless absolutely necessary (E.g Windshear)
● Better performance

Improved Increasing TOD to trade for increased VR to use the excess speed to outclimb limiting obstacles
Climb ● Requires the runway to be long and obstacles not too close to the runway
Procedure

Gross/Net NET GRADIENT: the maximum height that will be attained by an aircraft flown in accordance with the AFM after failure of the critical
Gradient power unit

Net Gradient + 0.8% = Gross Gradient (2 Engines)

Net Gradient + 0.9% = Gross Gradient (3 Engines)
Net Gradient + 1.0% = Gross Gradient (4 Engines)

Net gradient < Gross Gradient

Hydroplaning TAKE OFF: 9 x SqRt (pressure in psi)

LANDING : 7.7 x SqRt (pressure in psi)
BARS: 34 x SqRt (pressure in bars)

Non-rotating wheels have lower aquaplaning speeds (Hence, landing < Take off)

Runway Contamination
Contaminated Runway More than 25% of runway surface area within the required length and width covered by:
1. Surface water more than 3mm deep or equivalent to more than 3mm of water
2. Compacted snow
3. Ice including wet ice

Damp Runway Runway where the surface is not dry, but when the moisture on it does not give it a shiny appearance

Dry Runway Runway which is neither wet nor contaminated

Wet Runway Runway which the surface is covered with water. Sufficient moisture on the runway surface to cause it to
appear reflective but without significant areas of standing water

Runway Surface Condition

Descriptors
Wet Ice Ice with water on top of it or ice that is melting

Wet Snow snow that contains enough water to be able to make a well compacted, solid snowball, but
 water will not squeeze out
● Max allowed depth = 30mm

Dry Snow Sticks to the bottom of a shoe and falls off when the shoe is raised. if compacted by hand
to form a snow ball, will fall apart upon release

Compacted Snow that has been compacted into a solid mass such that aeroplane tyres, will run on the
Snow surface without significant further compaction or rutting of the surface

Slush Saturated snow, which when hit in a heel-to-toe, slap down manner, will splatter around
FLUID CONTAMINATION DRAGS:
1. Impingement Drag: caused when water spray strikes an aircraft’s landing gear/ airframe
2. Displacement Drag: Drag created by standing water resisting the forward motion of the wheels
 Climb
Cabbage Tikka Masala (coz i am vege
boy)

* Can add ‘EAS’ on the left of CAS → Expensive Cabbage Tikka Masala

Tropopause: If mach constant + temp constant (isothermal) = TAS constant

Climbing with constant IAS → as thrust available constant, Climb Angle and Pitch angle: Decrease
Climb with constant Mach = Lower IAS/CAS = More CL to maintain steady climb

Cross Over Altitude At the cross over altitude during climb with a constant speed, a constant IAS/CAS is changed to a constant
Mach Number
● Expect the ROC to increase when constant IAS replaced by Constant mach climb
○ ROC = Tas x Sin Climb Angle → sudden increase in climb angle results in momentary
increase in ROC

Lower Cost Index Lower speeds across the board

E.g Standard climb speeds for a jet transport aircraft are 250kt below 10 000ft and thereafter 300kt. This
switches to 0.80M on passing the crossover altitude. How would these speed change if you were to enter a
lower cost index into the FMC

Vx (best angle of climb)

Tangent = ratio between ROC and forward speed is maximum / Speed of which excess of thrust available
over thrust required is the greatest
● Ensures Best obstacle clearance
 Cruise
Cost Index Cost Index (Dimensionless Number) = Hourly Operating Cost / Fuel Cost
● CI = 0: Max Range / Min trip fuel / High Trip Time
● CI = Max: Min Range/ Max Trip Fuel / Min trip time
○ Fastest Speeds

Optimum Altitude The altitude at which the maximum range will be achieved if flown at the appropriate speed
● Max specific Range (NM/kg of fuel)
○ SR = TAS/ (SFC x Drag)
● Mass & Mach Number are inversely proportional to the altitude
Aeroplanes sometimes flies above the optimum cruise altitude, because ATC normally does not allow to fly
continuously at the optimum cruise altitude
● Fly lower: if lower altitude either less headwind or more tailwind

Aerodynamic Ceiling → Is the altitude at which the speeds for low speed buffet and for high speed buffet
are the same
● Flying with Low speed/ High speed buffet: Limits the manoeuvering load factor at high altitudes
● Determined by aerodynamics
Stepped Climb Procedure (fuel economy)
● Used to remain as close to optimum altitude as possible or to avoid severe turbulence
○ As mass is not constant throughout the flight, optimum altitude changes during flight
○ As semicircular rules means that there are designated flight levels to adhere to, → cannot
always fly at optimum altitude
○ Therefore, always request for a higher cruise altitude whenever optimum altitude
exceeds current cruise altitude by 1000ft
● 1.3g buffet onset requirements (Buffet margin)
○ Must not be at any altitude at which any maneuver results in 1.3g load factor reached
○ Hence, performing a step climb based on economy can be limited by 1.3g buffet onset
requirements

Long Range Cruise (LRC)- Fly Faster LRC Speed higher speed than 1.32 VMD (max range)
for lesser increase in FF ● But if one flies 4% faster than 1.32 VMD, gets one to destination faster with range penalty of only
1% → 99% Max Specific Range and higher cruise speed
● Efficient to fly slightly faster than max range speed (in terms of time)
○ Overall lower cost (Operating cost)
● Long range speed: Higher cost index than 1.32VMD

Minimum Fuel Consumption If range involved: Max Range speed

No Range involved: Max endurance
 Enroute One-Engine-Inoperative
Net Flight Path Shall clear vertically, by at least 2000ft, all terrain and obstructions along the route 9.3 km (5NM) on either
side of the intended track

Drift Down 3 Strategies

Standard Strategy Used to assist engine relight → High speed descent carried out

Obstacle Strategy Provide greatest vertical margin over obstacles

● Requires shallowest Flight path = highest CL/CD ratio (VMD)
● Decelerating to Jet VMD = VX (Jet) or Vy (Prop)
● Fuel Jettison to begin before start of drift down

Fixed Mach Number Used in case of ETOPS

Strategy (ETOPS) ● Required for adequate separation

Factors affecting Drift Down:

● OAT
● Altitude
● Weight At the time of the engine failure
● Engine Thrust
● Obstacle clearance

TAT from OAT TAT (K)= OAT (K) x (1 + 0.2 x Mach2)

 Descent
General Graph

Context + Procedure
Context Procedure

Above GP + Too Fast Decrease airspeed to below VLO and extend the landing gear, followed by flaps, to
increase drag and get back on the descent path and speed profile

Constant Mach Beware as it might: Exceed VMO

Descent Benefits:
1. As IAS increase, AOA decrease = increased margin to stall
2. Margin between High and Low speed buffet increase

Gliding Manoeuvre As engines are not working → NO DIFF between Jet and Prop
(max Endurance) ● Max Endurance: VMP (jets and prop)
● Max Range: VMD (jets and prop)

Descent Procedure

1st Part: Descent flown at Constant Mach Number

2nd Part: Descent flown at Constant IAS
Continuous Descent Arrival (CDA): To stay higher for longer and operate at a lower engine thrust

**** ‘No Power My Jet’ → ‘NE’ Piston, ‘Mo’ Jet (NPMJ)

VNE: refers to piston engine
VMO: refers to Jets
 Approach and Landing
Landing Field Length Jet: 60% LDR (or multiply 1.67)
Required (Memory) Prop: 70% LDR (or multiply 1.43)
Wet Factor: multiply 1.15 (or 15%)

Jet = 1.15 / 0.6 Or 1.15 x 1.67 → 1.92 Factor (92%)

Prop = 1.15 / 0.7 Or 1.15 x 1.43 → 1.64 Factor

Missed Approach 2 Problems to be addressed → Obstacle Clearance and Maneuvering Capability

Procedure
Landing Climb Requirement: Covers the few seconds at the beginning of the go-around manoeuvre
● Climb rate must not be less than 3.2%
● Configuration:
○ Landing Flaps
○ Gear Down
○ All engines at go-around thrust

Approach Climb Requirement:

● Configuration:
○ Approach Flap
○ Gear Up
○ 1 Engine out, remaining engines at go-around thrust

Overall Climb Gradient (OEI):

2 Engines 2.1%

3 Engines 2.4%

4 Engines 2.7%

Landing Climb: AEI

● Not less than 3.2% with engines at power or thrust available at approx 8 seconds after initiation of power
MLM: Could be limited by
● Climb requirements with OEI in the approach configuration (most restrictive)

Maximum Quick Maximum mass corresponding to the minimum time you need to wait before commencing another take off
Turnaround Mass (Brake
Temperature) Factors Influencing: (1,2,3,4,5,6,7)
1. OAT
2. Altitude
3. Runway Slope (only taken into account when it exceeds +/- 2%)
4. Aircraft Mass
5. Flap Setting
6. Thrust Reverse (influence but is not a limitation)
7. Runway Length
8. NO air conditioning packs
Context + Procedure
Context Procedure

Landing on a Flooded Objective: stick the landing

Runway + heavy rain ● Increase approach speed (prevent stall)
● Land firmly in order to obtain a firm contact of the wheels with the runway
and immediately land your nose gear
● Use systematically all life dumper devices

Landing Must be in landing configuration

Stabilised Approach:
● CAS not less than VREF down till 50ft , where VREF must not be lower than
○ 1.23 VSR0
○ VMCL

Minimise hydroplaning Make a positive landing + max reverse thrust and brakes ASAP
during landing
 CS-25 Applicable Operational Requirements Performance Class A - Use of Airplane Perofrmance Data

Take off
Basic Graph

Notes:
1. Left input weight is the Limited TOM → has already applied the corrections
a. Qn might need you to work backwards from the Limited TOM so apply the corrections in the opp manner
(ie. subtract 900kg when Packs Off instead of adding it)
2. Corrections
a. Packs OFF: Increased Limited TOM by 900kg
b. Anti-Ice ON: subtract 190kg (PA at or below 8000kg) or subtract 530kg (PA above 8000ft)
c. PMC OFF → read from the table at the bottom
d. If flaps 5o → no need for correction and the left horizontal line need not be slant and can remain horizontal
Note:
1. Top of the Graph ‘if intersection outside shaded area, check VMBE’
a. Final product of the graph is VMBE
2. Apply corrections (as per the table) to determine the regulated VMBE
3. Compare VMBE with the V1 and correct the planned mass to obtain Allowed TOM
4. If VMBE is limiting (by qn) → assume the highest brake release mass (if none provided = 68 000kg)
a. VMBE = V1 → Limiting TOM (68 000kg) = MTOM (no corrections needed)
b. VMBE < V1 → Limiting TOM (68 000kg) > MTOM
c. VMBE > V1 → Limiting TOM (68 000kg) < MTOM
Notes:
1. ‘REF LINE’ is the point which after it the line has to follow the trend of the graph and before it, the line continues as
per normal
a. See the vertical line after brake release → remains vertical until OAT ‘REF LINE’
2. Correction
a. Refer to the PMC off table and apply the correction to determine the limit
Notes:
1. REF line is the point of change until intersection with the appropriate data then vertical line downwards
a. E.g OAT + 25oC → follow the slant line after REF PT and then once crossing 25oC , vertical line
downwards
2. Brakes on Speed → apply correction specified in the question / CAP 698
a. Subtract 3 kt from VREF
b. E.g subtract 3 kt from approach speed and you may consider 150% for a tailwind and 50% for a headwind
3. Max Manual Braking → follow the slant line until intersecting autobrake specified and then vertical downwards
4. CAP 698: each mile of taxi, add 1 million foot pounds
Notes:
1. Determine Headwind/ Tailwind by using trigo
2. Left Column refers to ‘Assumed/Flex To → IGNORE OAT unless only OAT present
3. 3 numbers at the bottom of each box e.g ‘38-38-43’ refer to V1, VR, V2 → 138kt, 138 kt, 143kt
a. These are the values before correction
4. NO INTERPOLATION
a. Use the most restrictive values for calculation / correction
5. E.g 2/4 refers to which performance limitation is in force (use the limitation code at the bottom)
6. Correction
a. Refer to the table for all
b. If QNH > Standard → NO CORRECTION needed
 Drift down and stabilising altitude
Basic Graph

Notes:
1. Correction for temperature (top right graph) only for ISA + 10oC and above
2. Find Equivalent Gross Mass
a. Require corrections from top left table applied to the gross mass
3. Use ‘drift down to’ pressure altitude for the graph
4. Dotted vertical lines refer to fuel burn from engine failure
5. Calculate Ground Distance
a. Extend the vertical line down until the REF LINE
b. Follow the shape of the graph (interpolate) until the appropriate tailwind intersects then vertical down

Equivalent Gross Weight Is the actual gross weight corrected for OAT higher than ISA + 10oC
at Engine Failure
 Landing
Basic Graph

Note:
1. Be careful to note whether you are working backwards (top-down) or going via the normal route (bottom-up)
a. Working backwards: only start following the shape of the graphs after intersecting the values
b. Working upwards: follow the shape until intersecting the values
c. E.g Refer to Runway Condition (WET) → After intersecting, the graph then followed the shape and vice
versa
2. Identify if anti-skid is OPERATIONAL (Top left) or INOPERATIONAL (Top right)