Module 1

Aircraft Performance

Module 1

Where are we? Module 1 : Introduction to aircraft performance, atmosphere Module 2 : Aerodynamics, air data measurements Module 3 : Weights / CG, engine performance, level flight Module 4 : Turning flight, flight envelope Module 5 : Climb and descent performance Module 6 : Cruise and endurance Module 7 : Payload-range, cost index Module 8 : Take-off performance (1 of 2) Module 9 : Take-off performance (2 of 2) Module 10 : Enroute and landing performance Module11 : Wet and contaminated runways Module 12 : Impact of performance requirements on aircraft design

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Overview of aircraft performance  General  Certified versus non-certified data  Certification versus operational regulations  Role and responsibilities of the performance engineer – working for an aircraft manufacturer

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General  Performance is a branch of flight mechanics • F = ma applied to the aircraft • Consider the aircraft as a mass point

 Performance defines the operational capability of the aircraft  Performance requirements ensure that the aircraft can be operated safely, in particular in the event of an engine failure  Performance can be measured and predicted  Performance is a key factor for aircraft selection • Very competitive market requires aircraft with good performance • Speed, range, payload capability, airfield performance, …

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General (Cont’d)  Performance has a direct impact on operating costs • Fuel burn • Flight time

 Performance generates profits - a priority for operators • Payload and range capability translate into revenues

 The price of an aircraft is directly related to its performance as can be seen in the next slide

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General (Cont’d)  Performance is a function of the following parameters • • • • •

Aircraft weight Aircraft geometry (defines aerodynamic characteristics) Engine thrust Atmospheric properties Flight conditions

 Performance is a very important consideration during the aircraft design process • Aircraft design has to meet specific Marketing Requirements and Objectives (MR&O) • Operational field performance • Operational en route performance

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General (Cont’d) Situational Awareness

Pressurization

Op. Field Performance

Op. En route Performance

System Redundancy

Weights & Balance

Strength Margins

Flight Envelope & Placard Speeds

Stall & Speed Margins

Fatigue

Flutter

Introduction and atmosphere

Low-speed & High-speed Buffeting

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Certified versus non-certified performance data  Performance data can be classified in two main categories : certified and non-certified data  Certified data : • Approved by Transport Canada (TC) and other certification agencies • Contained in the Airplane Flight Manual (AFM) • Based on FAR/JAR 25 requirements • Mostly based on operation with one engine inoperative • Sometimes referred to as operational field performance • Defines performance levels that must be adhered to in order to ensure safety • Examples : stall speeds, take-off speeds and distances, climb gradients, landing speeds, landing distances, …

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Certified versus non-certified performance data (Cont’d)  Non-certified data : • Data contained in Flight Planning and Cruise Control Manual (FPCCM) • Not approved by certification agencies • Based on operation with all engines operating • Sometimes referred to as operational en route or mission performance • Used mainly for flight planning purposes, i.e. definition of the mission flight profile (time, speed and altitude) and mission fuel requirements • Examples : range, rate of climb, maximum cruise speed, fuel burn during all phases of flight (climb, cruise, descent, holding), …

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Certification versus operational regulations  Certification regulations (e.g. FAR Part 25 for large transport category airplanes) define how certified AFM performance data must be calculated • Example : The landing speed as specified in the AFM must not be less than 1.23 times the stall speed

 Operational regulations (e.g. FAR Part 121 for scheduled airline service with large transport category airplanes) define how AFM performance data must be used in order to define operational limitations • Example : For landing, the runway length available must not be less than 1.67 times the landing distance specified in the AFM.

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Certification versus operational regulations (Cont’d) FAR Certification Regulations

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FAR Operational Regulations

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Role and Responsibilities of the Performance Engineer working for an Aircraft Manufacturer  Extensive involvement in all phases of aircraft life • Development / Definition phase • Certification - Entry Into Service (EIS) • Operation  Support of conceptual design studies  Support of wind tunnel test programs  Definition of preliminary performance models  Support of flight tests  Calculation of certified and non-certified performance data  In-service support Introduction and atmosphere

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The atmosphere        

Introduction Standard atmosphere Non-standard day conditions Examples Altimeters Geometric altitude versus pressure altitude Certified altitude-temperature envelope Icing conditions

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Introduction

 The atmosphere is one of the most important item affecting the performance of an aircraft • Influences lift, drag, airplane stability, thrust, fuel consumption

 It is important to have a good understanding of the atmosphere • Need mathematical models in order to calculate air pressure, temperature and density

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Introduction (Cont’d)  Large jet transport aircraft fly from Sea Level (SL) up to as much as 51,000 ft (15.5 km)  Air is a mixture of a number of gases • Normal composition of clean, dry air (SL to 90 km) :78.10 % N2, 20.95 % O2, 0.93 % Ar, 0.02 % other gases • Air can be considered as a uniform gas for aerodynamic calculations • Equation of state applies : p = ρgRT p = pressure ρ = density g = gravitational acceleration = 32.174 ft/s2 R = gas constant = 96 ft / oK = 29.26 m/ oK T = ABSOLUTE temperature (oK)

 Water vapor is present, but in varying amounts, usually less than 1% at the earth’s surface Introduction and atmosphere

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Introduction (Cont’d)  The sun is responsible for heating the atmosphere • Only little energy is transferred directly from the sun to the air • Sun heats the earth’s surface, which in turn heats the air • Warm air near the surface rises, expands due to decreasing pressure and is cooled • An equilibrium is reached where no more reduction in temperature occurs : the tropopause

 The region below the tropopause is the troposphere  The region above the tropopause is the stratosphere • Temperature is constant in the stratosphere

 Seasonal changes have an important effect on the temperature, pressure and density of the air

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Introduction (Cont’d)

Variation of temperature with altitude - mean and 1 % extremes Introduction and atmosphere

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Standard atmosphere  To provide a basis for estimating and comparing airplane and engine performance, a standard atmosphere must be defined  The International Standard Atmosphere (ISA) has been defined by the International Civil Aviation Organization (ICAO)  ISA represents the average atmospheric conditions in North America and Europe and it is based on the following assumptions : • Air is a perfect gas • Air is dry • Gravitational acceleration does not vary with altitude • Hydrostatic equilibrium exists : dp = - ρg dh

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Standard atmosphere (Cont’d) 

ISA is based on standard values of SL density, pressure and temperature • Standard pressure at SL = po = 2116.22 lb/ft2 = 101.325 kPa (kN/m2 ) = 29.92 in Hg • Standard temperature at SL = To = 15oC (288.15oK) = 59oF (518.67oR) • Standard density at SL = ρ o = 0.002377 slugs/ft3 = 1.225 kg/m3 • Slugs ??? 1 lbf = 1 lbm x 32.174 ft/sec2 1 lbf = 1 slug x 1 ft/sec2 1 slug = 32.174 lbm Introduction and atmosphere

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Standard atmosphere (Cont’d)

p ρ T = po ρ o To

 Equation of state leads to

 Can be written as

δ =

σ

θ

• useful equation

 Pressure, density and temperature ratios ∀ δ = p/ po = air pressure / air pressure at SL standard day ∀ σ = ρ/ ρ o = air density / air density at SL standard day ∀ θ = T/ To = air temper. / air temper. at SL standard day

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Standard atmosphere (Cont’d)  Variation of temperature in ISA is defined as follows  ISA assumes a linear drop in temperature of approximately 2 oC per 1000 ft from SL to an altitude of 36,089 ft (11 km), the tropopause • T = To - λ h λ = lapse rate = 0.0019812 oC/ft (0.003566 oR/ft or 6.5 oC/km) h = altitude in ft

 ISA assumes a constant temperature at altitudes from 36,089 ft (11 km) to 65,617 ft (20 km), the stratosphere •

T = -56.50 oC or 216.65 oK

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Standard atmosphere (Cont’d)

Variation of temperature with altitude in the standard atmosphere Introduction and atmosphere

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Standard atmosphere (Cont’d)  Variation of pressure and density in the standard atmosphere • The variation of pressure is determined from the equation of state (p = ρgRT) and from the integration of the hydrostatic equation (dp = - ρg dh ) using appropriate boundary conditions • Unlike temperature, pressure continues to decrease at altitudes above the tropopause • Variation of pressure with altitude below the tropopause is not the same as above the tropopause due to the influence of temperature - different equations are used

Hydrostatic pressure

• Knowing pressure and temperature ratios, the density ratio is derived from σ = δ / θ Introduction and atmosphere

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Standard atmosphere (Cont’d)  Below the tropopause (SL - 36,089 ft): • dp = - ρg dh (hydrostatic equation) • p = ρgRT (equation of state) • Dividing the two equations: dp/p = -dh / RT • From T = To - λ h we can obtain dT = - λ dh or dh = -dT/ λ • dp/p = dT/ λRT • can be integrated between SL (subscript o) and an altitude h : •

p/po = (T/To)1/ λR = (1- (λ/To)h) 1/ λR

θ = 1 - 6.87535 x 10-6 h

(note : h in ft)

δ = (1 - 6.87535 x 10-6 h)5.2559 δ = θ 5.2559 σ = θ 4.2559

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Standard atmosphere (Cont’d)  Above the tropopause (36,089 ft - 65,617 ft): • Since T is constant, dp/p = -dh / RT can be integrated directly between the tropopause (subscript tr) and an altitude h: • ln (p/ptr) = -(h-htr)/RTtr • p/ptr = e -((h- htr)/RTtr) • From equations on previous page, ptr = 0.22336 po

θ = 0.7519 δ = 0.22336 e -((h-36089)/20806) σ = 0.29707 e -((h-36089)/20806) Introduction and atmosphere

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Standard atmosphere (Cont’d)  The equations developed on the last two pages are valid for standard atmosphere only  A table can be made to summarize parameters of the standard atmosphere as a function of altitude  Airplane and engine manufacturers have adopted the international standard and are using it for all engineering and performance analyses  A simplified ISA table is presented on the next page

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Standard atmosphere (Cont’d) Pressure altitude (ft)

Temperature (o C)

0 5000 10000 15000 20000 25000 30000 35000 36089 40000

15 5.1 -4.8 -14.7 -24.6 -34.5 -44.4 -54.3 -56.5 -56.5

Temperature ratio θ 1.0000 0.9656 0.9313 0.8969 0.8626 0.8282 0.7939 0.7595 0.7519 0.7519

Pressure ratio δ

Density ratio σ

1.0000 0.8321 0.6875 0.5641 0.4595 0.3711 0.2969 0.2353 0.2233 0.1851

1.0000 0.8616 0.7383 0.6293 0.5326 0.4480 0.3741 0.3098 0.2971 0.2462

Atmospheric properties – ISA conditions

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Non-standard day conditions  Major reason for defining ISA is to permit performance and operation to be stated in forms which may be compared • Performance data may be presented for ISA temperature conditions or for deviations from ISA temperature conditions • At any geometric or tapeline altitude, measured pressure may be different than the standard value • Pressure altitude (hp) is the altitude corresponding to a given pressure in the standard atmosphere – hp is used as THE reference when defining temperature deviations from ISA conditions • Knowing pressure altitude (i.e. pressure) and temperature deviation from ISA (i.e.temperature), density can be calculated and, therefore, atmospheric properties are fully defined

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Non-standard day conditions (Cont’d)  Pressure altitude can be derived from ambient pressure or δ using equations defining the standard atmosphere • Below 36,089 ft : hp = (1 - δ 1/5.2559)/6.87535 x 10-6

(ft)

• Above 36,089 ft : hp = 36089 - 20806 ln(4.477 δ)

(ft)

 Temperature ratio can differ from ISA at any pressure altitude but is always calculated as ∀ θ = T/ To

 Density can also differ from standard conditions but can be derived from ∀ σ=δ/θ Introduction and atmosphere

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Non-standard day conditions (Cont’d) 

Example 1: Calculate δ, hp, deviation from ISA, θ, σ and ρ for ambient conditions of 35 oC and 84.31 kPa ∀ δ = p/ po = 84.31 / 101.325 = 0.8321 • From standard atmosphere table, δ = 0.8321 at an altitude of 5,000 ft. Therefore, pressure altitude hp is equal to 5,000 ft. • From standard atmosphere table, standard temperature at 5,000 ft is equal to 5.1 oC . Deviation from ISA is 35 – 5.1 = 29.9 o C or ISA + 29.9 - Note : unless stated otherwise, deviations from ISA are in o C ∀ θ = T/ To = (273.15oK + 35 oK) / 288.15oK = 1.0694 ∀ σ = δ / θ = 0.8321 / 1.0694 = 0.7781 ∀ ρ = σ ρ o = 0.7781 x 0.002377 = 0.001850 slugs / ft3 Introduction and atmosphere

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Non-standard day conditions (Cont’d)  Example 2: Using basic equations, define atmospheric properties at a pressure altitude of 35,000 ft under ISA + 20 conditions • Equations for altitude < 36,089 ft apply ∀ δ = (1 - 6.87535 x 10-6 x 35,000)5.2559 = 0.2353 • p = δ po = 0.2353 x 2116.22 = 498.0 lb / ft2 • Tstd = To - λ h = 15 - 0.0019812x35000 = -54.35 oC or 218.8 oK • T at ISA+20 = -54.35 + 20 = -34.35 oC or 238.8 oK ∀ θ = 238.8 / 288.15 = 0.8287 ∀ σ = δ / θ = 0.2353 / 0.8287 = 0.2839 ∀ ρ = σ ρ o = 0.2839 x 0.002377 = 0.000675 slugs/ft3 Introduction and atmosphere

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Altimeters  An altimeter is a device that measures ambient pressure and converts it into an altitude  In transport category airplanes, altitude is measured and calculated as follows • Pressure is measured with a pressure transducer • The Air Data Computer (ADC) converts pressure into an altitude using basic altitude-pressure relationships • The resulting altitude is displayed to the flight crew

 In smaller airplanes, altitude is obtained from mechanical altimeters • Pressure acting on an aneroid assembly moves levers and gears so as to indicate the corresponding altitude to the crew

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Altimeters (Cont’d)  Altimeters can be adjusted with a trim knob to set reference pressure • The barometric correction (QNH or altimeter setting) is a bias that allows to correct altimeter indications for non-standard pressure conditions • When the proper barometric correction is set by the pilot, the altimeter displays an altitude indication which is close to geometric or true altitude • The altimeter reads pressure altitude when properly calibrated and set to 29.92 inches of mercury (I.e. po , standard conditions)

 Calculation of altitude is based on hp plus a term reflecting the barometric correction QNH h = hp + (QNH – po)(∂h/ ∂p) h = hp + (QNH – 29.92)[924.9(1–6.87535 x 10-6 hp) -4.2561] hp = h + 145442 [1- (QNH/ po)0.19026] Introduction and atmosphere

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Altimeters (Cont’d)  Regulations require that altimeters be manually set with a barometric correction during flight below 18,000 ft • Barometric correction allows a reasonable correlation between pressure altitude and geometric altitude during take-off, flight below 18,000 ft and landing • Barometric correction must be readjusted as the flight progresses

 Altimeters are set to 29.92 in Hg during flight above 18,000 ft • Altitude is calculated based on ISA definitions, I.e. pressure altitude is displayed • Allows aircraft to cruise at flight levels calculated on the same basis • Essential to maintain a safe vertical separation between aircraft flying at different altitudes • Pressure altitudes are defined as Flight Levels • For example, FL 210 and FL 350 correspond to pressure altitudes of 21,000 ft and 35,000 ft respectively Introduction and atmosphere

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Geometric Altitude Versus Pressure Altitude  Relationship between change in geometric altitude and change in pressure altitude follows from : • dh / dp = - RT/p • For temperature > ISA, geometric altitude is greater than hp • For temperature < ISA, geometric altitude is lower than hp Pressure altitude ∆ (ft) 0 500 1000 1500 2000

Geometric altitude ∆ ISA (ft) 0 500 1000 1500 2000

Geometric altitude ∆ ISA + 20 (ft) 0 535 1070 1605 2140

Geometric altitude ∆ ISA – 20 (ft) 0 465 930 1395 1860

Use of pressure altitude for vertical navigation may result in collision with obstacles on a cold day !

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Certified altitude- temperature envelope  Airplanes are certified to operate in a defined pressure altitude - temperature envelope  The airplane, including all systems, must be designed to operate normally within the certified envelope  Take-off and landing limits • Pressure altitude limits range typically from -1000 ft to 10,000 ft • This limit can be increased to 13,000 - 14,000 ft in order to allow operation at very high airfields such as Lhasa (11,700 ft), La Paz (13,200 ft) or Bangda (14,200 ft) • Temperature limits range typically from -40 oC to ISA + 35 (50 oC at SL) • Cold-weather testing is also required in order to demonstrate proper airplane operation in extremely cold conditions

 Maximum certified altitude • Performance (ceiling) and systems (pressurization) considerations

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Certified altitude- temperature envelope

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Icing conditions  Icing conditions may be present when • The air contains moisture such as clouds, fog, rain, snow • AND temperature is close to or below the freezing point

 Operation in icing conditions is an important part of the airplane certification process • Icing certification is optional for the airplane manufacturer but it is essential for most large airplanes • Flight in icing conditions is prohibited if airplane is not certified for operation in icing conditions

 Icing has a major impact on airplane operation and performance • Ice protection systems must be operated • Engine thrust may be significantly reduced • Ice may accumulate on non-protected surfaces (drag and weight increase) • Several accidents have been attributed to icing conditions

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