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Aviation Flow Chart

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Aviation Flow Chart
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Aviation Flow Chart document sample

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PPC Requirements

 AR 95-1, para 5-2a tells us that the

aviator will evaluate:

 Aircraft performance

 Departure, enroute, and approach data

 Notices to Airmen (NOTAM)



 DA Form 5701-R may be used as an aid

to organize performance planning data

required for the mission

PPC Requirements

 This form will be used for:

 RL progression training

 Annual ATP evaluations

 When required during other training and

evaluations

 Forevaluation flights, the evaluator will

determine the blocks that will be filled

out

 Be safe and do it all

PLANNING CONDITIONS

 CURRENT  MAXIMUM

 PA = 2500 ft MSL  PA = 3000 ft MSL

 FAT = 25 deg C  FAT = 30 deg C

 GWT = 15000 lbs

 ETF #1 = 1.0  CRUISE

 ETF #2 = .98  PA = 6000 ft MSL

 FAT = 25 deg C

Engine Torque Factor

 ETF

 The comparison of an individual engines

torque available to a specification engines

(1.0 ETF) torque available at a reference

temperature of 35 deg C

 The ETF must be between .85 to 1.0

 The ETF indicates degradation of

performance based on engine usage

Aircraft Torque Factor

 ATF

 ATF is the average of the two ETF’s. It

indicates the aircraft’s total performance

capability based on the condition of the two

engines.

 ATF is also based on 35 deg C and is allowed

to range from .90 to 1.0

 If ATF is outside this range do not fly the

aircraft

2500/3000 25/30 15000





.99 1.0 .98









6000 25

Torque Ratio

 TR

 Torque factor chart indicates improved

engine and aircraft performance as

temperature decreases below +35 deg C

 Torque ratio will be written to three decimal

places

 Three instances when chart is not needed:

• If FAT is +35 degrees or above

• If FAT is -15 or below

• If ETF is 1.0

Chart Info

Torque Factor

100% RPM R

Page 7A-7









.982

Chart Info

Torque Factor

100% RPM R

Page 7A-7









.984

2500/3000 25/30 15000





.99 1.0 .98

.991 1.0 .982









6000 25



.992 1.0 .984

Max Torque Available

 This torque value represents the

maximum specification torque available

at zero airspeed and 100% RPM R for

the operational range of PA and FAT

 This value may or may not be continuous

due to Chapter 5 limitations

Max Torque Available

 The actual MTA figure should be

annotated on the PPC, regardless of

whether it is above the continuous torque

limits

 Conditions may arise when the pilot may

need transient power demands

 The pilot is responsible for ensuring that

Chapter 5 transient limits are applied

when using this value, if applicable

Max Torque Available

 Based on flight test data, the MTA chart

reflects the maximum torque the engines

can produce without exceeding the

maximum of any of your three 30 minute

engine operating limits:

 TGT = 851 deg C

 Ng = 102%

 Engine Oil Temperature = 150 deg C

Max Torque Available

 MTA is limited by the HMU through Ng

limiting

 A TGT limiter circuit within the DEC

causes the HMU to limit fuel to the Ng

engine section when TGT reaches 866 +/-

6 deg C (dual engine) and 891 +/- 5 deg C

(single engine)

Max Torque Available

 TGT limiting is what will most commonly

limit MTA for the PA and FAT

combinations that most aviators operate

in

 The HMU also limits fuel to the Ng

section during high ambient temperature

conditions

Max Torque Available

 At high ambient temperatures, the air

becomes less dense, causing the Ng

turbine section to operate at higher

speeds in order to deliver the same

volume of air output to the power turbine

wheels (Np)

 Fuel flow is limited to prevent excessive

operating speeds that could damage the

Ng turbine wheels

Max Torque Available

 The HMU also limits fuel flow to the Ng

section during very cold conditions

 Mach speeds decrease as temperature

decreases

 This limiting is to prevent compressible

air flow (mach speeds) from occurring

within the compressor inlet section

Max Torque Available

 IfMTA is more than 100% dual engine

(above 80 KIAS), 120% dual engine (80

KIAS or less), or 135% single engine,

then the aircraft is structurally limited

 The engines are capable of producing the

power, but components in the

transmission (main module for DE

torque and input modules for SE torque)

are incapable of sustaining these torque

loads continuously without damage

Max Torque Available

 In a structurally limited aircraft,

attempting to operate continuously above

the allowable torque value in Chapter 5

will result in structural damage to the

transmission

 Maximum torque for a structurally

limited aircraft is limited to a 10 second

time limitation

Max Torque Available

 IfMTA is below 100% dual engine

(above 80 KIAS), 120% dual engine (80

KIAS or less), or 135% single engine,

then the aircraft is environmentally

limited

 Due to environmental conditions the

engines are incapable of producing

maximum rated power and transmission

torque limits will not be reached

Max Torque Available

 In an environmentally limited aircraft,

attempting to demand more torque than

MTA, will result in rotor bleed-off

 Depending on how far the collective is

increased beyond this point, will

determine how far the rotor will droop

 The larger the excursion, the greater the

reduction in rotor

 The bigger the splat mark

Max Torque Available

 Itis important to understand what the

pilot will observe on the torque gauges

when maximum power is demanded

 One scenario would be an aircraft with

identical ETF’s, resulting in identical

MTA values for both dual and single

engine operations

Max Torque Available

 After doing our planning we find out that

out Dual Engine MTA is 114%

 When MTA is demanded the pilot would

observe 114% torque on both the #1 and

#2 engine torque gauges

 The respective TGT for each engine would

be at the dual engine limiting value (866

+/- 6)

 TGT limiting would prevent the pilot from

receiving more torque

Max Torque Available

A more common scenario would be

having different ETF’s (1.0 and .948)

resulting in a different MTA for each

engine

 In this situation when MTA is demanded,

the pilot would not see 114% on the

torque gauges, as this is only an averaged

number between the two engines

 As the pilot demanded power, torque on

both engines would rise evenly to 108%

Max Torque Available

 At this time the #2 engine would reach

it’s TGT limiter and would remain at

108% torque

 If the pilot continues to demand more

power, the stronger 1.0 engine would

produce up to 114% before reaching it’s

TGT limiter

Max Torque Available

 The pilot would observe 114% and 108%

respectively, with TGT on both engines at

the dual engine limiter

 Attempting to demand more power in

this case would result in rotor bleed-off

 A torque split will be induced by the pilot

when power demanded exceeds that of

the weakest engine

 This is considered normal

Max Torque Available

 With bleed-air extracted, adjust MTA as

follows:

 Eng. Anti-Ice On - Subtract 18% from MTA

 Heater On - Subtract 4% from MTA

 Both On - Subtract 22% from MTA



 Thiswill hold true for SE MTA except

the values are half of that stated

Max Torque Available

 These values are different for different

helicopter models

 See the -10 for the values for the UH-60A

 Also see the -10 if HIRSS is installed and

baffles removed

 This is not a normal configuration

Chart Info

Max TQ Avail

10 Min Limit

Bleed Air Off

100% RPM R

Zero Airspeed

Page 7A-10









112%

Chart Info

Max TQ Avail

30 Min Limit

Bleed Air Off

100% RPM R

Zero Airspeed

Page 7A-11









95%

2500/3000 25/30 15000





.99 1.0 .98

.991 1.0 .982

111 112 110







Spec Torque - 112% 112 X .982 = 110

Spec Torque - 95% 112 X .991 = 111

95 X .984 = 93

1/2 MTA = 46% 95 X .992 = 94



6000 25



.992 1.0 .984

94 95 93

Max Allowable GWT

OGE/IGE

 This is the most weight the aircraft is

able or allowed to pick up to a 10’ hover

height for IGE operations or to an OGE

altitude (70’ for UH60) for OGE

operation

 This weight is limited by either engine

capability or aircraft structural design

Max Allowable GWT

OGE/IGE

 The Max GWT for UH60A without

provisions for Engine Output Shaft

STUD BALANCE MWO or without the

wedge mounted pitot static probes is

20,250 lbs

 The Max GWT for UH60L or UH60A

with the MWO provisions and wedge

mounted pitot static probes is 22,000 lbs

Max Allowable GWT

OGE/IGE

 If the Max GWT IGE or OGE is

20,250/22,000 lbs (as applicable), then

your aircraft is structurally limited

 Although the engines may be capable of

lifting more weight, the airframe is not

 When the Max GWT value is

20,250/22,000 lbs, attempting to operate

at a weight above that value will result in

exceeding a structural design limitation

and airframe damage is likely

Max Allowable GWT

OGE/IGE

 If the Max GWT IGE or OGE is less than

20,250/22,000 lbs (as applicable), then

your aircraft is environmentally limited

 Although the airframe is capable of

lifting up to the Chapter 5 limit, the

engines cannot provide enough power to

lift that weight for the given

environmental conditions

Max Allowable GWT

OGE/IGE

 When the Max GWT value is less than

20,250/22,000 lbs, attempting to operate

at a weight above that value will result in

rotor droop (environmental limitation),

but no airframe damage should result

 Unless you crash from low rotor RPM!

Chart Info

Hover

Clean Config.

100% RPM R

Zero Wind

Page 7A-15



21,250 lbs

2500/3000 25/30 15000





.99 1.0 .98

.991 1.0 .982

111 112 110

21250/22000









6000 25



.992 1.0 .984

94 95 93

GO/NO GO Torque OGE/IGE

 This value is essentially a weight check

 At a 10’ hover height, this is the torque

that will determine if you are at or below

your maximum weight that the engines

are capable of lifting to an IGE or OGE

altitude

 Bottom line…GNG is the hover torque

for Max Allowable GWT for the day

GO/NO GO Torque OGE/IGE

 If your Max GWT OGE is at the Chapter

5 maximum (ie. 20,250/22000), then only

one GNG value will be needed and this

will represent both IGE and OGE

capability

 If you can lift maximum weight to OGE

altitudes, then you can obviously do it at

IGE altitudes

GO/NO GO Torque OGE/IGE

 Inthis scenario, if the torque required to

maintain a stationary hover is at or below

the GNG IGE/OGE value, the pilot has

confirmed aircraft weight to be at or

below Max GWT and any maneuver

requiring OGE power or less may be

attempted

GO/NO GO Torque OGE/IGE

 If the torque required to maintain a

stationary hover is above the GNG

IGE/OGE, you cannot operate in

compliance with the -10 because you are

exceeding the aircraft’s maximum

structural gross weight

 This requires an entry to made to DA

Form 2408-13

 The helicopter shall not be flown until

corrective action is taken

GO/NO GO Torque OGE/IGE

 If your Max GWT is less than the

Chapter 5 maximum (20,250/22,000),

then a GNG value is required for both

IGE and OGE

 If the torque required to maintain a

stationary hover exceeds the GNG OGE,

but does not exceed the GNG torque

IGE, then only IGE maneuvers may be

attempted

GO/NO GO Torque OGE/IGE

 Maneuvers requiring OGE power are:

 Perform fast rope insertion

 Perform rappelling procedures

 Perform rescue-hoist operations

 Perform STABO operations

 Perform external load operations



 Basically, if it hangs under the aircraft

don’t do it

GO/NO GO Torque OGE/IGE

 Theoretically,if the torque required to

hover exceeds the GNG OGE, you should

not be able to exceed the GNG IGE for

and environmentally limited aircraft since

your MTA will equal your GNG IGE and

rotor bleed off will develop when engines

hit the TGT limiter at 866 +/- 6

GO/NO GO Torque OGE/IGE

 Remember, all hover checks are done at

an altitude of 10’

 If you are performing external load

operations plan a GNG value that will

place the load at 10’ AGL (usually 30’ or

40’)

GO/NO GO Torque OGE/IGE

 GNG is computed using maximum

forecast conditions

 When the actual temperature is less than

maximum, the torque required to hover

at a given GWT is less

 To ensure that OGE capability exists

and/or structural limitations are not

exceeded, reduce GNG by 1% for each

10C that actual temperature is less than

maximum forecast

GO/NO GO Torque OGE/IGE

 The colder temperatures would allow the

same 20,250/22,000 pound aircraft to

hover at these weights with less torque

 Therefore operating at the higher

(original) GNG torque value would mean

you are actually hovering an aircraft

weighing more than the Chapter 5 limits

allowed

Chart Info

Hover

Clean Config.

100% RPM R

Zero Wind

Page 7A-15









92%

Chart Info

Hover

Clean Config.

100% RPM R

Zero Wind

Page 7A-15









96%

2500/3000 25/30 15000





.99 1.0 .98

.991 1.0 112

111 112 110

21250/22000

92/96









6000 25



.992 1.0 .984

94 95 93

Predicted Hover Torque

 With current conditions at takeoff, and at

takeoff GWT, this is the estimated torque

required for a stationary 10’ hover in

zero wind conditions

 For external load operations, record the

predicted torque required to hover at a

height that will place the load at 10’ AGL

(usually 30’ or 40’)

Predicted Hover Torque

 Ifactual hover torque does not agree

with predicted hover torque it is not a

non-flying condition

 As long as you are still below GNG OGE

or IGE you may still fly

Predicted Hover Torque

 Oneof the following conditions has

occurred:

 Your actual weight is more or less than you

predicted

 Current conditions have changed since you

computed your PPC (FAT, PA, GWT, Wind,

etc.)

• Remember, your hover values are based on a no

wind condition

error was made during computation of

 An

PPC

Chart Info

Hover

High Drag

100% RPM R

Zero Wind

Page 7A-16









58%

2500/3000 25/30 15000





.99 1.0 .98

.991 1.0 .982

111 112 110

21250/22000

92/96

58









6000 25



.992 1.0 .984

94 95 93

Velocity Never to Exceed (Vne)

 The maximum permitted airspeed as a

function of temperature, pressure

altitude, and aircraft weight

 Exceeding this airspeed may cause the

rotor system to encounter the effects of

retreating blade stall

 Stall has not been encountered in one G

flight up to the airspeeds shown on the

Vne chart in the -10

Velocity Never to Exceed (Vne)

 Exceeding this airspeed may also cause

advancing blade compressibility (-10C

and colder), and/or aircraft structural

damage

 This airspeed cannot be obtained in level

flight

Velocity Never to Exceed (Vne)

 If Vne minus 15 KIAS is a lesser value

than MAX RANGE IAS, this lower value

will be the recommended maximum

turbulence penetration airspeed

 The 15 knot speed reduction reduces the

likelihood of the pilot exceeding Vne due

to airspeed fluctuations associated with

turbulence

Chart Info

Airspeed

NO ESSS

100% RPM

Page 5-14









180 KIAS

2500/3000 25/30 15000





.99 1.0 .98

.991 1.0 .982

111 112 110

21250/22000

92/96

58









6000 25 180



.992 1.0 .984

94 95 93

Cruise Speed IAS/TAS

 These airspeeds are dictated by the

mission or chosen by the pilot within

aircraft limits

 Indicated airspeed is the airspeed shown

on the pitot static airspeed indicator that

has been calibrated for standard sea level

pressure and is uncorrected for airspeed

system errors

Cruise Speed IAS/TAS

 Calibrated airspeed is the indicated

airspeed corrected for position and

instrument error

 Calibrated airspeed would be equal to

true airspeed (TAS) at standard pressure

at sea level

 The error is usually small and may be

computed with reference to the -10

Cruise Speed IAS/TAS

 TAS is calibrated airspeed corrected for

error due to density altitude

 Since the airspeed indicator is calibrated

for the dynamic pressures corresponding

to airspeeds at sea level conditions,

variations in air density must be

accounted for

Cruise Speed IAS/TAS

 When determining the IAS to be used for

the PPC, the pilot should use the speed

that the aircraft will be at for the

majority of the flight profile

 When determining single engine (SE)

cruise speed, the pilot has the option of

choosing any speed that falls within the

MIN/MAX SE envelope.

Cruise Speed IAS/TAS

 The pilot may wish to consider using at

least 80 KIAS or higher. 80 KIAS

provides the minimum rate of descent for

autorotation and would ensure sufficient

airspeed available to arrest the rate of

descent should the other engine become

inoperative

Cruise Speed IAS/TAS

 Autorotative decelerations initiated at

speeds below 80 KIAS will most likely

result in aircraft damage

 Although it will not always be possible,

an airspeed should be used that will

maintain cruise flight at or below your

continuous torque available SE

 Torques above your continuous value will

limit you to 30 minutes of operation if

that power setting is maintained

Chart Info

Cruise

Clean Config

6000ft. PA

30 deg C

Page 7A-60

115 KTAS

Chart Info

Cruise

Clean Config

6000ft. PA

30 deg C

Page 7A-60









96 KTAS

2500/3000 25/30 15000





.99 1.0 .98

.991 1.0 .982

111 112 110

21250/22000

92/96

58









6000 25 180



.992 1.0 .984

94 95 93

100 115 80 96

Cruise Torque

 Thisis the torque required to maintain

the Cruise Speed (IAS or TAS) that you

have selected for the mission

Chart Info

Cruise

Clean Config

6000ft. PA

30 deg C

Page 7A-60









44%

Chart Info

Cruise

Clean Config

6000ft. PA

30 deg C

Page 7A-60









38 X 2 = 76%

2500/3000 25/30 15000





.99 1.0 .98

.991 1.0 .982

111 112 110

21250/22000

92/96

58









6000 25 180



.992 1.0 .984

94 95 93

100 115 80 96

44 76

Cruise Fuel Flow

 This is the predicted fuel flow (burn rate)

that the aircraft will have at Cruise

Torque

 With bleed-air extracted, adjust fuel flow

as follows:

 Eng. Anti-Ice On - Add 100 lbs/hr

 Heater On - Add 12 lbs/hr

 Both On - Add 112 lbs/hr

Cruise Fuel Flow

 This will hold true for SE MTA Fuel

Flow except the values are half of that

stated

 These values are different for different

helicopter models

 See the -10 for the values for the UH-60A

 Also see the -10 if HIRSS is installed and

baffles removed

 This is not a normal configuration

Chart Info

Cruise

Clean Config 775 lbs/hr

6000ft. PA

30 deg C

Page 7A-60

Chart Info 1100/2 = 550 lbs/hr

Cruise

Clean Config

6000ft. PA

30 deg C

Page 7A-60

2500/3000 25/30 15000





.99 1.0 .98

.991 1.0 .982

111 112 110

21250/22000

92/96

58









6000 25 180



.992 1.0 .984

94 95 93

100 115 80 60

44 76

775 550

Continuous Torque Available

 This is the most torque the engines can

produce and remain out of all of your 30

minute engine operating limits

 You will be at the top of one or more of

your continuous limitations:

 TGT - 810C

 NG - 99%

 Eng Oil Temp - 135C

Continuous Torque Available

 As far as pre-mission flight planning, this

torque value is pretty limited in it’s

application

 A more practical value would be a

continuous airspeed which could be used

for determining times enroute and flight

plan speeds

Continuous Torque Available

 As a technique, the pilot may obtain a

continuous airspeed by tracing the

Continuous Torque available line upward

until you intersect your aircraft GWT

 Read horizontally to indicated airspeed

 This will provide the pilot with a speed

value to fly as quickly as possible to

his/her destination, while remaining

outside of any 30 minute limits

Continuous Torque Available

 Notice that unlike the ATF lines, there is

only one Continuous Torque line on your

cruise charts

 The Continuous Torque line in the cruise

chart represents an averaged ATF of .95

or greater

 If the aircraft ATF is lower than .95, the

Continuous Torque value will be less

than the PPC indicates, but we have no

means to compute how much less

Continuous Torque Available

 Notice also that the Continuous Torque

line stops at approximately 70-80 KIAS

 For torques below these speeds, read

vertically down from where the

Continuous Torque line terminates to

obtain this value

 DO NOT interpolate below the line

Continuous Torque Available

 Both the Continuous Torque and ATF

lines are slanted to the right as you move

upward

 This is to show the increase in torque

produced by the engines as the aircraft

increases speed

 With faster speeds, each engine intake

will receive a larger volume of air per

unit of time to work on, which results in

more power output available

Continuous Torque Available

 Notice also, the PA and Temp

combination of 30C and zero feet PA

shows that the Continuous Torque line

disappears off the cruise charts

 This is because when operating in colder

temperatures, the 100% Dual Engine

Torque limit will be reached before the

engines enter a 30 minute limit

 Continuous Torque available will then be

the same as MTA

Continuous Torque Available

 The pilot should be aware that operating

while bleed-air is being extracted from

the engines will result in a lower

Continuous Torque Available value than

shown on the PPC

 When bleed air is taken from the engines,

they operate less efficiently and result in

higher turbine temperatures to produce

the same amount of torque as without

bleed air usage

Continuous Torque Available

 Just as MTA is reduced with bleed air

extracted , Continuous Torque Available

is also going to be lower due to reaching

the Continuous TGT value earlier (810C)

 The -10 or ATM does not discuss this

situation, but the pilot may want to

consider subtracting the applicable

torque for heater and/or anti-ice

operation when in use

Chart Info

Cruise

Clean Config

6000ft. PA

30 deg C

Page 7A-60









81%

Chart Info

Cruise

Clean Config

6000ft. PA

30 deg C

Page 7A-60









80%

2500/3000 25/30 15000





.99 1.0 .98

.991 1.0 .982

111 112 110

21250/22000

92/96

58









6000 25 180



.992 1.0 .984

94 95 93

100 115 80 96

44 76

775 550

81 80

Max Endurance IAS

 Max Endurance IAS is based on drag

data

 This figure correlates to the maximum

lift to drag ration (L/D max) and will

result in the most aerodynamically clean

airspeed for flight at a given GWT and

environmental condition

Max Endurance IAS

 Max Endurance will allow you to fly

straight and level for the longest period

of time (time aloft) due to the lowest fuel

burn rate

 This airspeed will produce Max

Endurance only when operating at a

torque value that provides level flight

 This associated torque value can be

derived off the cruise chart is desired

Chart Info

Cruise

Clean Config

6000ft. PA

30 deg C

Page 7A-60









62 KIAS

2500/3000 25/30 15000





.99 1.0 .98

.991 1.0 .983

111 112 110

21250/22000

92/96

58









6000 25 180



.992 1.0 .984

94 95 93

100 115 80 96

44 76

775 550

81 80

62

Max Range IAS

 This is the airspeed which will take you

the farthest distance for a given amount

of fuel

 This is the best miles per gallon airspeed

under zero wind conditions

 This airspeed can also be used as

Turbulence Penetration Airspeed

provided it is less than Vne minus 15

knots

Max Range IAS

A method of estimating Max Range IAS

in winds is to increase Max Range IAS by

2.5 knots for each 10 knots of effective

headwind (which reduces flight time and

minimizes loss in range)

 You can also decrease Max Range IAS by

2.5 knots for each to knots of effective

tailwind due to economy

Chart Info

Cruise

Clean Config

6000ft. PA 122 KIAS

30 deg C

Page 7A-60

2500/3000 25/30 15000





.99 1.0 .98

.991 1.0 .982

111 112 110

21250/22000

92/96

58









6000 25 180



.992 1.0 .984

94 95 93

100 115 80 96

44 76

775 550

81 80

62

122

Single-Eng Capability IAS

(MIN/MAX)

 These are the minimum and maximum

airspeeds possible without losing altitude

with a single engine operating

 Operating between these airspeeds will

maintain RPMR within limits

 If the derived airspeed is less than 40

KIAS, the airspeed indicators will be

unreliable

Single-Eng Capability IAS

(MIN/MAX)

 Ifthe derived airspeed exceeds 130 KIAS

the SE max airspeed is still 130 KIAS

 Remember that the accuracy of these

values depends on which engine becomes

inoperative

 These figures are based on your lowest

ETF engine operating and at takeoff

GWT

Chart Info

Cruise

Clean Config

6000ft. PA

30 deg C

Page 7A-60 25 to 106 KIAS

2500/3000 25/30 15000





.99 1.0 .98

.991 1.0 .982

111 112 110

21250/22000

92/96

58









6000 25 180



.992 1.0 .984

94 95 93

100 115 80 96

44 76

775 550

81 80

62

122

25 106

Max Allowable GWT

Single Engine

 Thisis the maximum amount of weight

the remaining engine is capable of

powering for level flight

Chart Info

Cruise

Clean Config

6000ft. PA

30 deg C

Page 7A-60









19,000 lbs

2500/3000 25/30 15000





.99 1.0 .98

.991 1.0 .982

111 112 110

21250/22000

92/96

58









6000 25 180



.992 1.0 .984

94 95 93

100 115 80 96

44 76

775 550

81 80

62

122

25 106

19,000

Arrival Data

 Arrival data will be computed when the

conditions differ significantly from

departure conditions

 This is defined as an increase of:

 10degrees C in FAT

 2000 ft PA

 1000 lbs GWT



 Complete data on your own

 6000 PA, 25 FAT, 14000 GWT

6000 25 14000





.99 1.0 .985

100 101 99

19,500/22,000

54

62

Recomputation of PPC Data

 PPC will be recomputed whenever a

significant change in the mission’s

conditions occurs as discussed earlier

QUESTIONS??


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