Supersonic Airfoils & Wind Speed Supersonic Airfoils

52 Pages·2011·2 MB·English

Revised Edition: 2016
ISBN 978-1-283-50490-4
© All rights reserved.
Published by:
White Word Publications
48 West 48 Street, Suite 1116,
New York, NY 10036, United States
Email: [email protected]
Table of Contents

Introduction

Chapter 1 - Airspeed Indicator

Chapter 2 - Equivalent Airspeed & Calibrated Airspeed

Chapter 3 - True Airspeed

Chapter 4 - V Speeds
Chapter 5 - Mach Number
Chapter 6 - Sound Barrier
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Chapter 7 - Indicated Airspeed & Position Error
Chapter 8 - Supersonic Airfoils & Wind Speed

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Introduction

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An airspeed indicator is a flight instrument that displays airspeed. This airspeed indicator
has standardized markings for a multiengine airplane
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Aircraft have pitot probes for measuring airspeed
Airspeed is the speed of an aircraft relative to the air. Among the common conventions
for qualifying airspeed are: indicated airspeed ("IAS"), calibrated airspeed ("CAS"), true
airspeed ("TAS"), equivalent airspeed ("EAS") and density airspeed.
The measurement and indication of airspeed is ordinarily accomplished on board an
aircraft by an airspeed indicator ("ASI") connected to a pitot-static system. The pitot-
static system comprises one or more pitot probes (or tubes) facing the on-coming air flow
to measure pitot pressure (also called stagnation, total or ram pressure) and one or more
static ports to measure the static pressure in the air flow. These two pressures are
compared by the ASI to give an IAS reading.
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Indicated airspeed
Indicated airspeed (IAS) is the airspeed indicator reading (ASIR) uncorrected for
instrument, position, and other errors. From current EASA definitions: Indicated airspeed
means the speed of an aircraft as shown on its pitot static airspeed indicator calibrated to
reflect standard atmosphere adiabatic compressible flow at sea level uncorrected for
airspeed system errors.
Outside of the former Soviet bloc, most airspeed indicators show the speed in knots i.e.
nautical miles per hour. Some light aircraft have airspeed indicators showing speed in
miles per hour.
An airspeed indicator is a differential pressure gauge with the pressure reading expressed
in units of speed, rather than pressure. The airspeed is derived from the difference
between the ram air pressure from the pitot tube, or stagnation pressure, and the static
pressure. The pitot tube is mounted facing forward; the static pressure is frequently
detected at static ports on one or both sides of the aircraft. Sometimes both pressure
sources are combined in a single probe, a pitot-static tube. The static pressure
measurement is subject to error due to inability to place the static ports at positions where
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the pressure is true static pressure at all airspeeds and attitudes. The correction for this
error is the position error correction (PEC) and varies for different aircraft and airspeeds.
Further errors of 10% or more are common if the airplane is flown in “uncoordinated”
flight.
Calibrated airspeed
Calibrated airspeed (CAS) is indicated airspeed corrected for instrument errors, position
error (due to incorrect pressure at the static port) and installation errors.
Calibrated airspeed values less than the speed of sound at standard sea level (661.4788
knots) are calculated as follows:
minus position and installation error correction.
Where
is the calibrated airspeed,
is the impact pressure (inches Hg) sensed by the pitot tube,
is 29.92126 inches Hg; static air pressure at standard sea level,
is 661.4788 knots;, speed of sound at standard sea level.
Units other than knots and inches of mercury can be used, if used consistently.
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This expression is based on the form of Bernoulli's equation applicable to a perfect,
compressible gas. The values for P and A are consistent with the ISA i.e. the conditions
0 0
under which airspeed indicators are calibrated.
Equivalent airspeed
Equivalent airspeed (EAS) is defined as the speed at sea level that would produce the
same incompressible dynamic pressure as the true airspeed at the altitude at which the
vehicle is flying. An aircraft in forward flight is subject to the effects of compressibility.
Likewise, the calibrated airspeed is a function of the compressible impact pressure. EAS,
on the other hand, is a measure of airspeed that is a function of incompressible dynamic
pressure. Structural analysis is often in terms of incompressible dynamic pressure, so that
equivalent airspeed is a useful speed for structural testing. At standard sea level pressure,
calibrated airspeed and equivalent airspeed are equal. Up to about 200 kts CAS and
10,000 ft the difference is negligable, but at higher speeds and altitudes CAS must be
corrected for compressibility error to determinine EAS. The significance of equivalent
airspeed is that at Mach numbers below the onset of wave drag, all of the aerodynamic
forces and moments on an aircraft scale with the square of the equivalent airspeed. The
equivalent airspeed is closely related to the Indicated airspeed speed shown by the
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airspeed indicator. Thus, the handling and 'feel' of an aircraft, and the aerodynamic loads
upon it, at a given equivalent airspeed, are very nearly constant and equal to those at
standard sea level irrespective of the actual flight conditions.
True airspeed
True airspeed (TAS) is the physical speed of the aircraft relative to the air surrounding
the aircraft. The true airspeed is a vector quantity. The relationship between the true
airspeed and the speed with respect to the ground (V )is:
g

Where:
V = Windspeed vector
w
Aircraft flight instruments, however, don't compute true airspeed as a function of
groundspeed and windspeed. They use impact and static pressures as well as a
temperature input. True airspeed is equivalent airspeed that is corrected for pressure
altitude and temperature (which define density). The result is the true physical speed of
the aircraft plus or minus the wind component. True Airspeed is equal to calibrated
airspeed and equivalent airspeed at standard sea level conditions.
The simplest way to compute true airspeed is using a function of Mach number:
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Where:
a = Speed of sound at standard sea level (661.4788 knots)
0
M = Mach number
T = Temperature (kelvins)
T = Standard sea level temperature (288.15 kelvins)
0
Or if Mach number is not known:

Where:
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a = Speed of sound at standard sea level (661.4788 knots)
0
q = Impact pressure (inHg)
c
P = Static pressure (inHg)
T = Temperature (kelvins)
T = Standard sea level temperature (288.15 kelvin)
0
The above equation is only for Mach numbers less than 1.0.
True airspeed differs from the equivalent airspeed because the airspeed indicator is
calibrated at SL, ISA conditions, where the air density is 1.225 kg/m³, whereas the air
density in flight normally differs from this value.

Thus

Where
is the air density at the flight condition.
The air density may be calculated from:

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Where
is the air pressure at the flight condition,
is the air pressure at sea level = 1013.2 hPa,
is the air temperature at the flight condition,
is the air temperature at sea level, ISA = 288.15 K.
Source: Aerodynamics of a Compressible Fluid. Liepmann and Puckett 1947. Publishers
John Wiley & Sons Inc.
Groundspeed
Groundspeed is the speed of the aircraft relative to the ground rather than through the air,
which can itself be moving.
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Chapter 1
Airspeed Indicator

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Diagram showing the face of a true airspeed indicator typical for a faster single engine
aircraft
The airspeed indicator or airspeed gauge is an instrument used in an aircraft to display
the craft's airspeed, typically in knots, to the pilot.
Use
The airspeed indicator is used by the pilot during all phases of flight, from take-off,
climb, cruise, descent and landing in order to maintain airspeeds specific to the aircraft
type and operating conditions as specified in the Operating Manual.
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