Aerospace Vehicle Performance / Operational
Performance of Aircraft
Module 1
Introduction, Atmosphere
AERO446 / MECH 6241 – Winter 2021 - Module 1
Introduction
Jitendra Patel
§ B. Eng. - 1990 Mechanical Engineering
(McGill)
§ M. Eng. - 1994 Engineering (McGill)
§ 1990-1993 – CAE – Flight simulation
engineer
§ 1993 - to Present – Bombardier – Aircraft
Performance
§ Flight Testing
§ Conceptual Aircraft Design
§ Aircraft Development
§ Aircraft Certification
§ Flight Operations Engineering
§ 2018 – Present – Concordia - Part-time
lecturer
§ Aerospace Vehicle Performance
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Aerospace Vehicle Performance / Operational
Performance of Aircraft
§ January 19: Module 1
§ January 26: Module 2
§ February 2: Module 3
§ February 9: Module 4
§ February 16: Module 5
§ February 23: Module 6
§ March 2:
Mid-term Break
§ March 9:
Mid-term
§ March 16:
Module 7
§ March 23:
Module 8
§ March 30:
Module 9
§ April 6:
Module 10
§ April 13:
Module 11
§ April 20:
Module 12
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Aerospace Vehicle Performance / Operational
Performance of Aircraft
§ Module 1: Introduction to aircraft performance, atmosphere
§ Module 2: Aerodynamics, air data measurements
§ Module 3: Aircraft Propulsion
§ Module 4: Aircraft operational performance and limitations overview
§ Module 5: Climb & 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
§ Module 11: Wet & Contaminated Runways
§ Module 12: Impact of Performance requirements on aircraft design
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Introduction
Aircraft Performance is a branch of flight mechanics
F = ma
applied to the aircraft
Considers the aircraft as a point mass
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Introduction
§ 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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Introduction
§ Aircraft Performance is a function of the following parameters
§
§
§
§
§
Aircraft weight
Aircraft geometry (defines aerodynamic characteristics)
Engine thrust
Atmospheric properties
Flight conditions
§ Aircraft Performance is a very important consideration during the aircraft
design process
§ Aircraft design has to meet specific Marketing Requirements and Objectives
(MR&O)
§ Field performance (take-off and landing)
§ Enroute performance (climb, cruise, descent)
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Introduction
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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) / Computerized Airplane
Flight Manual (CAFM)
§ Based on following requirements:
§ Canadian Aviation Regulations - CAR 525 (Canada)
§ Federal Aviation regulation - FAR (United States)
§ Certification Standards - CS 25 (Europe)
§ 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 provided in the Flight Planning and Cruise Control Manual (FPCCM) or
the Computerized In-Flight Performance (CIFP) software
§ Not approved by certification agencies
§ Based primarily on operation with all engines operating (includes also one
engine inoperative data)
§ Sometimes referred to as operational enroute 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, climb and cruise ceiling, maximum cruise
speed, fuel burn during each phase 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 actual 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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The Atmosphere
§
§
§
§
§
Introduction
Standard atmosphere
Non-standard day conditions
Altimeter
Geometric altitude versus pressure
altitude
§ Certified altitude-temperature envelope
§ Icing conditions
Suggested Readings:
1) Jet Transport Performance Methods – Chapters 4 & 5.
2) Getting to grip with Aircraft Performance – Pages 11 to 22.
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The atmosphere - Introduction
§ The atmosphere is one of the most important items affecting the
performance of an aircraft
§ Influences lift, drag, airplane stability, thrust, fuel consumption, speed, range,
time, climb and cruise ceilings.
§ 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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The atmosphere - Introduction
§ 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 = rgRT
§ p = pressure (lb/ft2)
§ r = density (slugs/ft3)
§ g = gravitational acceleration = 32.174 ft/s2
§ R = gas constant = 96.036 ft / oK = 29.26 m/ oK = 53.3533 ft/ oR
§ T = ABSOLUTE temperature (oK)
§ Water vapor is present, but in varying amounts, usually less than 1% at the
earth’s surface
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The atmosphere - Introduction
§ 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 at an altitude where no more reduction in temperature
occurs:
§
This altitude is called the tropopause
§ The region below the tropopause is the troposphere
§ The region above the tropopause is the stratosphere
§ Temperature is constant up to 65 600 feet
§ The atmosphere is constantly changing. Pressure, temperature and density of
the air are affected by a number of factors including pressure patterns
associated with frontal systems, surface heating, seasonal effects and so on.
§ Because of this variation from place to place and from day to day, it’s difficult
to define the performance of an airplane in constant terms.
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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 = - rg dh
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Standard atmosphere (cont’d)
§ ISA is based on standard values of Sea Level (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 ( ro )
= 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
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Standard atmosphere (cont’d)
§ Equation of state (p = rgRT) knowing po = rogRTo and dividing
leads to:
p
r T
=
po r o To
§ Can be written as
d =
s
q
§ Pressure, density and temperature ratios
§ d = p/ po = air pressure / air pressure at SL standard day
§ s = r/ ro = air density / air density at SL standard day
§ q = T/ To = air temper. / air temper. at SL standard day (use oK or
oR)
§ Knowing pressure and temperature ratios, the density ratio is
derived from s = d / q
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Standard atmosphere (cont’d)
§ ISA assumes a linear drop in
temperature of approximately 2oC per
1000 ft from SL to an altitude of
36,089 ft (11 km), the tropopause
§ T = To - lh
§ l = lapse rate = 0.0019812 oC/ft
(0.003566 oR/ft or 6.5 oC/km)
§ h = altitude in ft or km
§ ISA assumes a constant temperature
at altitudes from 36,089 ft (11 km) to
65,617 ft (20 km), the stratosphere
§ T = -56.5oC or 216.65 oK
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Standard atmosphere (cont’d)
§ The variation of pressure is determined from the equation of state (p = rgRT) and from the
integration of the hydrostatic equation (dp = - rg dh )
§ 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
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Standard atmosphere (cont’d)
§ Below the tropopause (SL - 36,089 ft) :
§
§
§
§
§
§
§
§
§
§
§
§
dp = - rg dh (hydrostatic equation)
p = rgRT (equation of state)
Dividing the two equations: dp/p = -dh / RT
From T = To - l h,
Differentiating, we can obtain dT = - l dh or dh = -dT/ l
dp/p = dT/ lRT
can be integrated between SL (subscript o) and an altitude h, :
p/po = (T/To) 1/lR = (1- (l/To)h) 1/ lR = (T/To) 5.2559
q = 1 - 6.87535 x 10-6 h
d = (1 - 6.87535 x 10-6 h)5.2559
d = q5.2559
s = q4.2559
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(note : h in ft)
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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:
§ ∫
=−
∫ ℎ
§ ln (p/ptr) = -(h-htr)/RTtr
§ p/ptr = e -((h- htr)/RTtr)
§ From equations on previous page, d = q5.2559
§ ptr = 0.22336 po
q = 0.7519
d = 0.22336 e -((h-36089)/20806)
s = 0.29707 e -((h-36089)/20806)
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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
q
1.0000
0.9656
0.9313
0.8969
0.8626
0.8282
0.7939
0.7595
0.7519
0.7519
Pressure ratio
d
Density ratio
s
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 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
§ Pressure altitude can be derived from ambient pressure or d using
equations defining the standard atmosphere
§ Below 36,089 ft : hp = (1 - d1/5.2559)/6.87535 x 10-6
§ Above 36,089 ft : hp = 36089 - 20806 ln(4.477 d)
(ft)
(ft)
§ Temperature ratio can differ from ISA at any pressure altitude but is
always calculated as
§ q = T/ To
§ Density can also differ from standard conditions but can be derived
from
§ s=d/q
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Non-standard day conditions
§ Example 1: Calculate d, hp, temperature deviation from ISA, q, s and r for
ambient conditions of 35 oC and 84.31 kPa
§ d = p/ po = 84.31 / 101.325 = 0.8321
§ From standard atmosphere table, d = 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 oC or ISA +
29.9
§ Note : unless stated otherwise, deviations from ISA are in oC
§ q = T/ To = (273.15oK + 35) / 288.15oK = 1.0694
§ s = d / q = 0.8321 / 1.0694 = 0.7781
§ r = s ro = 0.7781 x 0.002377 = 0.001850 slugs / ft3
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Non-standard day conditions
§ 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
§ d = (1 - 6.87535 x 10-6 x 35,000)5.2559 = 0.2353
§ p = d po = 0.2353 x 2116.22 = 498.0 lb / ft2
§ Tstd = To - l 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
§ q = 238.8 / 288.15 = 0.8287
§ s = d / q = 0.2353 / 0.8287 = 0.2839
§ r = s ro = 0.2839 x 0.002377 = 0.000675 slugs/ft3
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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
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Altimeters (Cont’d)
§ Consider following graph.
§ Two values of non-standard sea
level pressure:
§ for a high-pressure day :
§ 30.42 inches of mercury, and
§ for the low-pressure day: 29.42 in.
Hg.
§ For a given elevation, the actual static pressure could be either higher or
lower than the standard pressure for that elevation.
§ This indicates how much altitude error can be introduced by an altimeter
which uses only the standard day relationship.
§ On high pressure day, at 26 in Hg, for an elevation of 4400 feet and
Altimeter would read 3800 feet based on ISA.
§ On low pressure day, at 26 in Hg, for an elevation 3400 feet and Altimeter
would read 3800 feet based on ISA.
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Altimeters (Cont’d)
§ Look again at a diagram of pressure versus
elevation for three different conditions, as
shown in figure to the right.
§ For an airport at an elevation of 1000 feet, a
high pressure day like the one shown on right
would cause the standard day-calibrated
altimeter to display an altitude of
approximately 550 feet – an error of 450 feet.
§ Similarly, on a low-pressure day, the altimeter
will read approximately 1450 feet, again an
error of 450 feet.
§ Since takeoff and landing safety requires the flight crew to know accurately
their height above the airport and the local terrain, or above sea level, this
inconsistency is obviously unacceptable
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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)
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The QNH is calculated through the measurement
of the pressure at the airport reference point
moved to Mean Sea Level, assuming the
standard pressure law. With the QNH setting, the
altimeter indicates the altitude above Mean Sea
Level (if temperature is standard)
34
Altimeters (Cont’d)
§ Altimeter Setting – Example
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Altimeters (Cont’d)
§ 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]
§ Note QNH is in inches of mercury.
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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
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Altimeters (Cont’d)
§ Another real, and potentially dangerous, inaccuracy in altimeters is due to
variation in air density.
§ As we have said previously, all altimeters necessarily assume some
relationship between air pressure and altitude. The ISA relationship is
normally used for this purpose.
§ However, in atmospheric conditions which are colder or warmer than ISA,
the relationship between pressure and actual altitude will not follow the
standard atmosphere.
§ This is because the air density will be different from the standard density
when the temperatures are above or below the standard temperature. In
those cases, the density compared to the standard would be less or
greater respectively.
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Altimeters (Cont’d)
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Altimeters (Cont’d)
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Geometric Altitude Versus Pressure Altitude
§ Relationship between change in geometric altitude and change in
pressure altitude:
§ For temperature > ISA, geometric altitude is greater than hp
§ For temperature < ISA, geometric altitude is lower than hp
D Pressure altitude
(ft)
0
500
1000
1500
2000
D Geometric altitude
ISA
(ft)
0
500
1000
1500
2000
D Geometric altitude
ISA + 20
(ft)
0
535
1070
1605
2140
D 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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Geometric Altitude Versus Pressure Altitude
§ Flight Manuals will
provide corrections
geometric altitude for
non-standard
temperature.
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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 (example)
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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 when operating anti-ice systems
Ice may accumulate on non-protected surfaces (drag and weight increase)
Several accidents have been attributed to icing conditions
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Appendix – The Hydrostatic Equation
§ Air is composed of gases, and these gases have weight, however
small.
§ The air pressure at any point in the atmosphere is a function of the
weight of the air above that point.
§ The hydrostatic equation expresses the relationship between
weight, pressure and height in this static situation.
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Appendix – The Hydrostatic Equation
§ Picture a column of air, extending
from the earth’s surface to the
upper limit of the atmosphere, as
shown in figure to the right. Let’s
assume this column of air has a
cross-sectional area of A.
§ We take an extremely thin slice
through the column; the slice has a
height of dh. At the top of the slice,
let’s assume the pressure is equal
to some unknown pressure p.
§ The weight of the slice is equal to
its mass density ρ multiplied by the
acceleration of gravity g and by the
volume of the slice, which is A ×
dh..
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Appendix – The Hydrostatic Equation
§ The pressure at the bottom of the slice which we will call p + dp (dp being
some as yet unknown change in pressure as we move downward) is then
equal to the pressure at the top of the slice, PLUS the weight of the slice
itself. If this slice of air is not moving (i.e. static) we can equate the vertical
forces on the slide as follows:
( p + dp ) × A = ( p × A ) + ( ρ × A × g × dh )
§ which leads to:
dp = ρ g dh
Note that in this case, dh is positive in the downward direction. If we were
taking dh as an upward change, then the equation would be:
dp = – ρ g dh
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