Universidad Autónoma de Nuevo León

Facultad de Ingeniería Mecánica y Eléctrica

Practica N°2 EFFECT OF ALTITUDE, MACH
NUMBER AND PRESSURE RATIO ON
PERFORMANCE PARAMETERS
Materia: Sistemas de Propulsión Y Laboratorio
Maestro: ALDO ENRQUE MARIÑO GAMEZ
Grupo: 507
NOMBRE MATRICULA PROGRAMA
EDUCATIVO
Luis Guillermo García 2008306 IAE
López

Fecha de entrega: 22/11/2024

OBJECTIVE

• Understand how altitude, Mach number and pressure ratio significantly

influence various aspects of performance in aircraft propulsion systems.

INTRODUCTION
As an aircraft moves through the air, the air molecules near the aircraft are disturbed
and move around the aircraft. If the aircraft passes at a low speed, typically less than
250 mph, the density of the air remains constant. But for higher speeds, some of the
energy of the aircraft goes into compressing the air and locally changing the density
of the air. This compressibility effect alters the amount of resulting force on the
aircraft. The effect becomes more important as speed increases. Near and beyond the
speed of sound, about 330 m/s or 760 mph, small disturbances in the flow are
transmitted to other locations isentropically or with constant entropy. But a sharp
disturbance generates a shock wave that affects both the lift and drag of an aircraft.
The Mach number is named after the physicist and philosopher Ernst Mach according
to a proposal by the aeronautical engineer Jakob Ackeret in 1929. The word Mach is
always capitalized since it derives from a proper name, and since the Mach number is
a dimensionless quantity rather than a unit of measure, the number comes after the
word Mach; the second Mach number is Mach 2 instead of 2 Mach (or Machs). This
is somewhat reminiscent of the early modern ocean-sounding unit mark (a synonym
for fathom), which was also unit-first, and may have influenced the use of the term
Mach. In the decade preceding faster-than-sound human flight, aeronautical engineers
referred to the speed of sound as Mach's number, never Mach 1.

The ratio of the speed of the aircraft to the speed of sound in the gas determines the
magnitude of many of the compressibility effects. Because of the importance of this
speed ratio, aerodynamicists have designated it with a special parameter called the
Mach number in honor of Ernst Mach, a late 19th century physicist who studied gas
dynamics. The Mach number M allows us to define flight regimes in which
compressibility effects vary.

The speed of sound (blue) depends only on the temperature variation at altitude (red) and
can be calculated from it since isolated density and pressure effects on the speed of sound
cancel each other. The speed of sound increases with height in two regions of the
stratosphere and thermosphere, due to heating effects in these regions.

Subsonic conditions occur for Mach numbers less than one, M < 1 . For the lowest
subsonic conditions, compressibility can be ignored.
As the speed of the object approaches the speed of sound, the flight Mach number is
nearly equal to one, M = 1, and the flow is said to be transonic. At some places on the
object, the local speed exceeds the speed of sound. Compressibility effects are most
important in transonic flows and lead to the early belief in a sound barrier. Flight faster
than sound was thought to be impossible. In fact, the sound barrier was only an
increase in the drag near sonic conditions because of compressibility effects. Because
of the high drag associated with compressibility effects, aircraft do not cruise near
Mach 1.
Supersonic conditions occur for Mach numbers greater than one, 1 < M < 3.
Compressibility effects are important for supersonic aircraft, and shock waves are
generated by the surface of the object. For high supersonic speeds, 3 < M < 5,
aerodynamic heating also becomes very important for aircraft design.
For speeds greater than five times the speed of sound, M > 5, the flow is said to be
hypersonic. At these speeds, some of the energy of the object now goes into exciting
the chemical bonds which hold together the nitrogen and oxygen molecules of the air.
At hypersonic speeds, the chemistry of the air must be considered when determining
forces on the object. The Space Shuttle re-enters the atmosphere at high hypersonic
speeds, M ~ 25. Under these conditions, the heated air becomes an ionized plasma of
gas and the spacecraft must be insulated from the high temperatures.
While the terms subsonic and supersonic, in the purest sense, refer to speeds below
and above the local speed of sound respectively, aerodynamicists often use the same
terms to talk about particular ranges of Mach values. This occurs because of the
presence of a transonic regime around flight (free stream) M = 1 where
approximations of the Navier-Stokes equations used for subsonic design no longer
apply; the simplest explanation is that the flow around an airframe locally begins to
exceed M = 1 even though the free stream Mach number is below this value.

Meanwhile, the supersonic regime is usually used to talk about the set of Mach
numbers for which linearised theory may be used, where for example the (air) flow is
not chemically reacting, and where heat-transfer between air and vehicle may be
reasonably neglected in calculations.

In the following table, the regimes or ranges of Mach values are referred to, and not
the pure meanings of the words subsonic and supersonic.

Generally, NASA defines high hypersonic as any Mach number from 10 to 25, and
re-entry speeds as anything greater than Mach 25. Aircraft operating in this regime
include the Space Shuttle and various space planes in development.
True Airspeed (TAS) represents the actual speed of an aircraft relative to the air it
moves through. This differs from Indicated Airspeed (IAS), as TAS accounts for
changes in air density with altitude. The Local Speed of Sound (LSS) is the speed at
which sound propagates through a specific medium, which depends on temperature.
In the atmosphere, as temperature decreases with altitude, the LSS also reduces,
directly impacting Mach number calculations.
The high-speed buffet occurs when an aircraft approaches its critical Mach number
(M_critic), the speed at which airflow over a portion of the wing reaches Mach 1,
creating shockwaves and disrupting lift. This phenomenon generates significant
aerodynamic instability and vibrations, requiring careful flight management to avoid
structural or control issues.
True Airspeed is Calibrated Airspeed (CAS) corrected for altitude and nonstandard
temperature.
Because air density decreases with an increase in altitude, an aircraft has to be flown
faster at higher altitudes to cause the same pressure difference between pitot impact
pressure and static pressure.
Therefore, for a given CAS, TAS increases as altitude increases; or for a given TAS,
CAS decreases as altitude increases.
A pilot can find TAS by two methods. The most accurate method is to use a
conventional or electronic flight computer. A second method, which is a rule of
thumb, provides the approximate TAS. Simply add 2 percent to the CAS for each
1,000 feet of altitude. At 10,000 feet, you are flying approximately 20% faster than
your indicated airspeed.
In aerodynamics, the critical Mach number (Mcr or M*) of an aircraft is the lowest
Mach number at which the airflow over some point of the aircraft reaches the speed
of sound, but does not exceed it. At the lower critical Mach number, airflow around
the entire aircraft is subsonic. Supersonic aircraft such as the Concorde and combat
aircraft also have an upper critical Mach number at which the airflow around the entire
aircraft is supersonic.

For an aircraft in flight, the speed of the airflow around the aircraft differs
considerably in places from the airspeed of the aircraft; this is due to the airflow
having to speed up and slow down as it travels around the aircraft's structure. When
the aircraft's airspeed reaches the critical Mach number, the speed of the airflow in
some areas near the airframe reaches the speed of sound, even though the aircraft itself
has an airspeed lower than Mach 1.0. This creates a weak shock wave. As the aircraft
exceeds the critical Mach number, its drag coefficient increases suddenly, causing
dramatically increased drag, and, in an aircraft not designed for transonic or
supersonic speeds, changes to the airflow over the flight control surfaces lead to
deterioration in control of the aircraft.

In aircraft not designed to fly at or above the critical Mach number, the shock waves
that form in the airflow over the wing and tailplane cause Mach tuck and may be
sufficient to stall the wing, render the control surfaces ineffective, or lead to loss of
control of the aircraft. These problematic phenomena appearing at or above the critical
Mach number were eventually attributed to the compressibility of air. Compressibility
led to a number of accidents involving high-speed military and experimental aircraft
in the 1930s and 1940s.
 Transonic flow patterns on an aircraft wing, showing the effects at and above the critical Mach
number.

In aerodynamics, the critical Mach Number (Mcr or Mcrit) of an aircraft is the lowest
Mach number at which the airflow over any part of the aircraft reaches the speed of
sound.

Discussion
For all aircraft in flight, the speed of the airflow around the aircraft is not exactly the
same as the airspeed of the aircraft due to the airflow speeding up and slowing down
to travel around the aircraft structure.

At the Critical Mach number, local airflow near some areas of the airframe reaches
the speed of sound, even though the aircraft itself has an airspeed lower than Mach
1.0. This creates a weak shock wave. In aircraft not designed for transonic or
supersonic flight, speeds greater than the Critical Mach number will cause the drag
coefficient to increase suddenly causing a dramatic increase in total drag and changes
to the airflow over the flight control surfaces will lead to deterioration in control of
the aircraft.
In aircraft not designed to fly at the Critical Mach number, shock waves in the flow
over the wing and tailplane can be sufficient to stall the wing, make control surfaces
ineffective, or lead to loss of control.

The relationship between TAS and Mach number lies in their dependency on the LSS.
Mach number is calculated as the ratio of TAS to LSS, meaning that for a given TAS,
the Mach number increases as LSS decreases with altitude. Similarly, the LSS directly
influences the Mach number; colder temperatures at higher altitudes lower the LSS,
increasing the Mach number for the same TAS.
The coffin corner is a flight condition where the margin between the stall speed and
MMO narrows to nearly zero at high altitudes. This critical point occurs because as
altitude increases, stall speed rises due to lower air density, while MMO decreases
due to reduced LSS. Operating near the coffin corner demands precise control to avoid
exceeding aerodynamic limits.
The machmeter is an instrument in aircraft cockpits that displays the current Mach
number, providing pilots with essential information for managing speeds relative to
compressibility effects and flight envelope constraints. It ensures safe operation by
helping maintain speeds within safe bounds, particularly in transonic and supersonic
flight regimes.
The ratio between the true air speed (TAS) and the local speed of sound (LSS). This
ratio, which equals one when the TAS is equal to the LSS, is known as the Mach
Number (M) and is very important in aircraft operating at high speed.

Coffin corner (also known as the aerodynamic ceiling or Q corner) is the region of
flight where a fast but subsonic fixed-wing aircraft's stall speed is near the critical
Mach number, at a given gross weight and G-force loading. In this region of flight, it
is very difficult to keep an airplane in stable flight. Because the stall speed is the
minimum speed required to maintain level flight, any reduction in speed will cause
the airplane to stall and lose altitude. Because the critical Mach number is the
maximum speed at which air can travel over the wings without losing lift due to flow
separation and shock waves, any increase in speed will cause the airplane to lose lift,
or to pitch heavily nose-down, and lose altitude.

The "corner" refers to the triangular shape at the top of a flight envelope chart where
the stall speed and critical Mach number are within a few knots of each other. The
"coffin" refers to the possible death in these kinds of stalls. The speed where they meet
is the ceiling of the aircraft. This is distinct from the same term used for helicopters
when outside the auto-rotation envelope as seen in the height-velocity diagram.
Consideration of statics shows that when a fixed-wing aircraft is in straight, level
flight at constant-airspeed, the lift on the main wing plus the force (in the negative
sense if downward) on the horizontal stabilizer is equal to the aircraft's weight and its
thrust is equal to its drag. In most circumstances this equilibrium can occur at a range
of airspeeds. The minimum such speed is the stall speed, or VSO. The indicated
airspeed at which a fixed-wing aircraft stalls varies with the weight of the aircraft but
does not vary significantly with altitude. At speeds close to the stall speed the aircraft's
wings are at a high angle of attack.

At higher altitudes, the air density is lower than at sea level. Because of the
progressive reduction in air density, as the aircraft's altitude increases, its true airspeed
is progressively greater than its indicated airspeed. For example, the indicated
airspeed at which an aircraft stalls can be considered constant, but the true airspeed at
which it stalls increases with altitude.
Air conducts sound at a certain speed, the "speed of sound". This becomes slower as
the air becomes cooler. Because the temperature of the atmosphere generally
decreases with altitude (until the tropopause), the speed of sound also decreases with
altitude. (See the International Standard Atmosphere for more on temperature as a
function of altitude.)

A given airspeed, divided by the speed of sound in that air, gives a ratio known as the
Mach number. A Mach number of 1.0 indicates an airspeed equal to the speed of
sound in that air. Because the speed of sound increases with air temperature, and air
temperature generally decreases with altitude, the true airspeed for a given Mach
number generally decreases with altitude.

As an airplane moves through the air faster, the airflow over parts of the wing will
reach speeds that approach Mach 1.0. At such speeds, shock waves form in the air
passing over the wings, drastically increasing the drag due to drag divergence, causing
Mach buffet, or drastically changing the center of pressure, resulting in a nose-down
moment called "mach tuck". The aircraft Mach number at which these effects appear
is known as its critical Mach number, or MCRIT. The true airspeed corresponding to
the critical Mach number generally decreases with altitude.
 Graph of altitude/speed region envelope for Lockheed U-2 depicting coffin corner

A machmeter is an instrument which provides an indication of the Mach Number,

(M), which is the ratio between the aircraft true air speed (TAS) and the local speed
of sound (LSS). This ratio, which equals one when the TAS is equal to the local speed
of sound, is very important in aircraft operating at high speed.
The machmeter uses the aircraft pitot-static system to generate M and usually portrays
this on a simple needle and dial instrument, such as that shown below.
Alternatively, the machmeter may be combined with the Air Speed Indicator (ASI),
in which case it is often referred to as a Combined Speed Indicator (CSI).
High speed aircraft, including airliners and business jets, have limiting mach numbers
which must not be deliberately exceeded. If the aircraft is deliberately or accidentally
allowed to exceed its limiting mach, shock waves are likely to form on the aerofoils
and can result in buffet or mach tuck.
Some aircraft use a constant mach number (rather than constant speed) technique for
cruise operations. Constant mach technique may be used to separate aircraft on the
same track and at the same altitude whilst in a non radar environment.

MATERIAL AND EQUIPMENT

• Laboratory manual
• Projector
• Laptop
• Speakers

WORKING PROCEDURE
In this practice, we will pay attention to the crucial importance of altitude, Mach number and pressure
ratio in affecting performance parameters in aircraft propulsion systems. Understanding how these
factors affect the performance of an aircraft is essential to ensure safe flights. Pilots and engineers
must have a thorough understanding of how altitude and Mach number can influence aircraft
operation, especially in critical situations. The performance of an aircraft is also related to its payload
capacity. Understanding how altitude and Mach number affect payload capacity is essential for
effective flight and load planning. Aerospace engineers must have a thorough understanding of these
effects in order to design aircraft that can perform optimally in different conditions. This is essential
for developing more advanced and efficient aircraf
THEORETICAL FRAMEWORK
• • If the true airspeed of the aircraft with respect to the air is known to be 438 kts and the local speed
of sound with respect to the recorded flight conditions is 638 kts, calculate the actual Mach number
of the aircraft.
𝑇𝐴𝑆
𝑀𝑎𝑐ℎ =
𝑆𝑃𝐸𝐸𝐷 𝑂𝐹 𝑆𝑂𝑈𝑁𝐷
438
𝑀𝑎𝑐ℎ = = 0.6865
638

QUESTIONS
Write the questions according to the practice performed.
1. What phenomenon occurs when the airflow over certain parts of an aircraft
reaches Mach 1?
Shock wave
2. According to the schematic in Figure 1, indicate the region where the subsonic
flow is located.

III
3. According to the schematic in Figure 2, indicate the region where the supersonic
flow is located.
I
4. Indicate the effects that may occur on aircraft that are not designed for supersonic
flight:
Increased resistance
High-speed milling
Mach Tuck
Reduced effectiveness of flight controls
5. What term describes a fairly sharp pitch down trend in an aircraft?
Mach Tuck
6. How does aerodynamic drag affect fuel consumption in an aircraft?
Increases it by requiring more thrust to overcome resistance
7. What term is used to describe vibrations caused by turbulent flow behind the shock
wave in an aircraft?
High-speed milling
8. What is the value of the Mach number at which the airflow over a certain part of
an aircraft reaches the speed of sound (Mach 1) called?
Critical Mach number
9. What is the main purpose of setting a maximum operating Mach number (MMO)
on an aircraft?
Avoiding the negative effects of shock waves
10. According to the schematic in Figure 3, indicate the region where the critical Mach
(Mcritic) is located.

2
Results
Isotropic Non Isotropic
Temperature Temperature
1 -40 -40
2 267 255
3 515 491
4 1366
5 1118
6 619

Isoentropic Vs Non Isoentropic

(Temperature)
1500
Temperature (°K)

1000

500

0
0 1 2 3 4 5 6 7
-500
Engine Stages

Isotropic Temperature Non Isotropic Temperature

Conclusion
The relationships between altitude, Mach number, and pressure are critical and have a significant
impact on aircraft performance parameters and propulsion systems. As altitude increases, air density
decreases, which reduces the availability of oxygen for combustion. This reduction in air intake can
lead to a decline in the power and efficiency of engines designed for airflow and combustion,
particularly in air-breathing propulsion systems.
These variations also influence aerodynamic and thermodynamic performance, playing a key role in
the design and operation of aircraft operating in transonic and supersonic regimes. Changes in Mach
number affect pressure distribution across the airframe, potentially altering stability and requiring
careful consideration in both design and operation. Modifications to engine and airframe systems,
aimed at managing these effects, can enhance overall performance by redistributing pressure more
effectively and maintaining stability.
Engine efficiency and fuel consumption are closely tied to these dynamics, as the engine’s ability to
adapt to varying conditions determines its thermal performance and fuel economy. Advanced
materials are often necessary to manage the increased thermal and mechanical stresses associated
with higher temperatures and pressures, ensuring durability and operational reliability.
Understanding the interplay of these factors is essential for optimizing performance, maintaining
safety, and ensuring efficient energy management during flight operations. This step-by-step
approach enables precise control over propulsion and aerodynamic systems to meet the demands of
high-altitude and high-speed flight.

References:
1. Mach number. (s. f.). https://www.grc.nasa.gov/www/k-12/airplane/mach.html

2. Young, Donald F.; Munson, Bruce R.; Okiishi, Theodore H.; Huebsch, Wade W. (21
December 2010). A Brief Introduction to Fluid Mechanics (5th ed.). John Wiley & Sons.
p. 95. ISBN 978-0-470-59679-1. LCCN 2010038482. OCLC 667210577.

3. Pilot Institute. (2024, 9 agosto). 6 Different Types of Airspeed: How to Calculate

Each. https://pilotinstitute.com/airspeed-types/

4. L. J. Clancy (1975) Aerodynamics, Pitman Publishing Limited, London ISBN 0-273-

01120-0
5. Critical Mach Number. (2022, 19 junio). SKYbrary

6. Aviation Safety. https://skybrary.aero/articles/critical-mach-number

7. Swatton, Peter J. (2011), "14.11", Principles of Flight for Pilots, Chichester, UK: Wiley &
Sons Ltd, ISBN 978-0-470-71073-9

8. ^ Clancy, L.J. (1975), Aerodynamics, Section 1.2, Pitman Publishing Limited, London, ISBN
0-273-01120-0
9. ^ Jump up to:a b Federal Aviation Administration (2003-01-02), AC 61-107B – Aircraft
Operations at Altitudes Above 25,000 Feet Mean Sea Level or Mach Numbers Greater
Than .75, retrieved 2015-10-31

10. Machmeter. (2022, 19 junio). SKYbrary Aviation Safety.

https://skybrary.aero/articles/machmeter