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NASA Technical Memorandum 104316

Airdata Measurement
and Calibration

Edward A. Haering, Jr.

December 1995

National Aeronautics and

Space Administration
NASATechnicalMemorandum104316

Airdata Measurement
and Calibration
Edward A. Haering, Jr.
NASA Dryden Flight Research Center
Edwards, California

1995

National Aeronautics and

Space Administration

Dryden Flight Research Center

Edwards, California 93523-0273
 ABSTRACT

This memorandum provides a brief introduction to airdata measurement and calibration.

Readers will learn about typical test objectives, quantities to measure, and flight maneuvers and
operations for calibration. The memorandum informs readers about tower-flyby, trailing cone,
pacer, radar-tracking, and dynamic airdata calibration maneuvers. Readers will also begin to
understand how some data analysis considerations and special airdata cases, including high-
angle-of-attack flight, high-speed flight, and nonobtrusive sensors are handled. This
memorandum is not intended to be all inclusive; this paper contains extensive reference and
bibliography sections.

INTRODUCTION

Airdata are vital to successfully complete an aircraft's mission and are derived from the air
surrounding the aircraft. References 1-4 supply pertinent information regarding airdata
measurement and calibration. These airdata encompass indicated and true airspeed, pressure
altitude, ambient air temperature, angles of attack and sideslip, Mach number, and rate of climb.
Typically, pitot and static pressures are sensed and converted (by mechanical means in the
instruments themselves) into indications on the altimeter, vertical speed indicator, airspeed
indicator, and Machmeter. Similarly, measured local flow angles establish angles of attack and
sideslip, and the outside air temperature is measured and indicated in the cockpit. (Instruments
that can perform the conversion, such as airspeed indicators, altimeters, and Machmeters, do not
correct for errors in the input values.) These measured parameters are commonly input to the
airdata computer, which, using appropriate algorithms and correction factors (or calibrations, as
discussed later), can provide other parameters, such as true airspeed, required by the aircraft's
avionics or flight control system.

The presence of the aircraft in the airstream causes input errors to the measuring
instruments -- the aircraft disturbs the air that it flies through, thereby also disturbing the airdata
measurements. Figure 1 shows the airflow around an airplane wing. The air above the wing has
lower pressure than the ambient air, while the pressure below the wing is higher than the ambient
air. Compressibility and shock waves also disturb the air and affect the measurements.
Compressibility effects become important above approximately Mach number 0.3. As a result, the
static pressure around an airplane varies considerably with location. Local flow angles also differ
from the free-stream flow direction. In straight-and-level flight, the airflow rises to the wing
leading edge and falls below the trailing edge, causing errors in flow direction measurements. To
some extent these errors can be studied in wind tunnels, but wind-tunnel measurements cannot
replace in-flight measurements.

Accurate airdata are necessary for many purposes and applications. Obviously, the pilot
cannot safely fly the aircraft without knowing airspeed and pressure altitude. In civil aviation, the
small vertical separation between flight levels assigned by air traffic controllers is based on
accurate knowledge of pressure altitude. Numerous systems, such as autoflight controls, engine
controls, cockpit and cabin environmental control, weapons delivery, navigation, and air traffic
control, depend on accurate airdata. When an unproven airplane undergoes envelope expansion,
 940226

Figure I. Airflow around an aircraft wing.

careful attention must be paid to flight limits of equivalent airspeed to ensure flight safety. In
flight research, most measurands are referenced to airdata quantities, and many parameters are
normalized to dynamic pressure. The accuracy needed for a particular application dictates how
airdata should be measured and dictates the amount of calibration effort required. References 5
and 6 specify the accuracy levels required of the pitot-static system by civil and military
organizations. Flight research activities may require higher accuracies.

TEST OBJECTIVES

If the location of the static ports has not already been identified, then the first objective must
be to determine the best location for the static ports, that is, where the smallest or most constant
position errors occur. Once this location is established, the calibrations of the total and static
pressures, angles of attack and sideslip, and air temperature should be determined to account for
the disturbing presence of the aircraft in the flow field. The calibrations must be performed under
various flight conditions of airspeeds and altitude as well as aircraft attitudes and configurations
(combinations of flaps, gear, and external stores).

MEASUREMENT AND CALIBRATION OF AIRDATA QUANTITIES

Pitot Pressures

The pitot, or total, pressure is the sum of the static pressure and the pressure rise resulting
from stagnation of the airflow (dynamic pressure) in the pitot tube. Total pressure is generally
easy to measure accurately; the location is not critical as long as the tube opening is outside the
aircraft's boundary layer and is oriented to the incoming flow. For well-sited or aligned probes,
the total pressure error is usually negligible. (This assumption can be checked by comparison with
a venturi pitot or by flying in formation with a calibrated pacer aircraft.) The shape of the pitot
tube opening dictates the flow angles at which the pitot tube works well. For supersonic flight

2
pitot tubesthatareforwardof aircraft shocks,suchasthoseon nosebooms(ref. 7), will not have
aircraft shock losses (ref. 2). Figure 2 shows a typical flight test noseboomthat measures
pitot-staticpressuresaswell aslocal flow angles.

Static Pressures

Static pressure can be measured with a pitot-static tube or a flush-mounted port on the
fuselage. Figure 3 shows a typical subsonic static pressure distribution on an aircraft fuselage
(ref. 2). The measured minus true static pressure, AP, normalized to compressible dynamic
pressure, qc' is plotted as a function of fuselage position. Zero static pressure error on the
fuselage exists at locations 2 through 5. One of these locations is chosen for the static port. To
keep pneumatic lag small, the static port is normally located as near the airdata instruments as
possible (or the other way around). (To determine this location precisely, several static ports are
made in this area. The optimum location is then selected as a result of comparing the various ports

vane
,F Angle-of-attack
- Total pressure port _--,I
I

Static pressure/
port location -_

! L-J_ Angle-of-sideslip vane

940227

Figure 2. Noseboom for measuring pitot and flow angles.

Pressure distribution
along this line

AP
--0
qc
_2_
-1 940228

Figure 3. Subsonic static pressure distribution.

with a referencesource,suchas a trailing cone.)This pressuredistributionchangeswith flight
condition,so a calibrationoverthe flight envelopemay still benecessary.

Location 1 in figure 3 alsohaszerostaticpressureerror. A noseboomcan beusedto placea

static-pressuresourcetoward this region. Structuralconsiderationsprevent a noseboomfrom
being long enoughto have identically zero static pressureerror. Some static pressureerrors
remainandneedtobe calibrated.Somenoseboomsandpitot-staticprobeshavecontoursdesigned
to compensatethe measuredstaticpressurefor thepositionerror inducedby the specificairplane
(or probefor a supersonicnoseboom)(ref. 2).

Evenwith the selectionof the beststaticport position,somepressureerrorswill remain,and

theseerrorsmust be determinedin flight. The differencebetweenthe locally measuredstatic
pressureandthe ambientstaticpressure,which is dependentupon angleof attack,airspeed,and
aircraftconfiguration,is calledposition error.

Three calibration types are generally used to determine position error: direct comparison,
altimetry, and velocimetry. The direct-comparison calibration type involves measuring the true
static pressure from a known source. The result is then compared with the static pressure of the
airplane being calibrated. Direct comparisons are completed using the trailing cone and pacer
methods described in later sections of this memorandum. The altimetry type adds one level of
complexity by first determining the true pressure altitude. This altitude is then converted to static
pressure. The tower-flyby and radar-tracking methods, also described in later sections of this
memorandum, use altimetry. The velocimetry type uses the ground speed of the airplane and
windspeed to determine true airspeed. If test maneuvers are conducted in opposite directions,
wind errors can be minimized. Temperature errors affect this calibration type. After the pitot and
static pressure system is calibrated, the flow angles and temperature may be calibrated.

Temperature

The undisturbed ambient outside air temperature (OAT) can only be directly measured on
board the aircraft at very low speeds. At the low speeds, temperature is typically measured
mechanically using a bimetallic strip that moves a needle indicator. At higher speeds the
stagnation or total air temperature (TAT) is measured and then corrected to ambient conditions to
provide better accuracy of OAT measurement. TAT is the sum of the OAT and the adiabatic
temperature rise resulting from the stagnation of the airflow. Because there is not 100 percent
stagnation (some airflow past the sensing element is required), a correction, termed the recovery
factor, has to be determined. OAT can be readily determined by the methods in reference 1 once
the true TAT and Mach number are known.

The location for the TAT is not critical as long as the probe inlet openings are outside the
boundary layer and are aligned with the airflow when the aircraft is in its normal flight attitude. A
favorable location is on the aircraft nose, in the area where the flow is still attached.

Most modern aircraft use TAT probes with electrical resistance elements, or thermistors
(ref. 8), with a mechanical design that prevents liquid, ice, or dirt particles from affecting the
sensing element. Most probes also have housings that are electrically heated to prevent icing; the
sensorresultsmustbe correctedfor this heating.TAT measurements mustalsobe correctedfor
self-heating(resulting from the electricalexcitation of the heatingelement),radiation, and the
previouslymentionedrecoveryfactor.

The combination of these errors is often termed the recovery factor, which must be
determinedfrom indicatedtemperatureto TAT. The easiestway to determinethis factor is to
comparethe readingswith a referenceTAT probe that has beencalibratedin a wind tunnel.
Anothermethodis to comparethe indicatedtemperaturereadingswith thoseobtainedon another
aircraft in which the temperaturesystemhasbeencalibrated.

Figure4 showsa typical temperaturecalibrationfor thecasein which a referenceprobeis not

available.Plotting total temperatureas a functionof Mach numbersquaredyields a linear trend.
The ordinateinterceptis the ambienttemperature.The slopeandambienttemperatureareusedto
determinethe recoveryfactor (ref. 1). The datafor oneplot mustbe gatheredin a short time-
and-distanceinterval andat a constantaltitudesothatthe ambienttemperatureremainsconstant.

Anothermethodfor determiningthe recoveryfactor usesa direct measurementof ambient

temperature.This temperatureis obtainedusing a thermometerin a tower for low-altitude flight.
Still another methodusesmeteorologicaldata and true Mach number to calculatetrue total
temperatureand,thereby,the recoveryfactor(ref. 1).

Measurement of Flow Angles

The locations of the flow angle sensors greatly affect their measurement. At subsonic speeds
the local angle of attack is affected by flow around the body and wing of the airplane, which is

750
Flight data
Least-squares curve fit

7O0

650

600
Total
temperature, )/2
oR
550

where Too--- Ambient temperature

J k = Recovery factor
5OO
-- / y -=Ratio of specific heats

/ for air (typically 1.4)

450
/
/
/
/

40O
-T I//

I I I I I I I
0 .5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Mach number squared
950444

Figure 4. Total temperature calibration.

termed upwash. Upwash affects the sensors near a lifting surface much more than it affects
sensors on a noseboom. Wingtip-mounted sensors are greatly influenced by upwash and
sidewash; thus, they are rarely used. Flow angles are typically measured with one of three
sensors: flow vanes, fixed differential pressure probes, and null-seeking servoactuated differential
pressure probes (refs. 1 and 2). Flow vanes resemble small weather vanes and are connected to a
potentiometer or other angle-measuring transducers. These vanes should be mass-balanced to
remove biases and to improve precision in dynamic maneuvers. Flow vanes tend to be more
sensitive than the other two sensors, especially at low speeds. On the other hand these vanes are
more susceptible to damage than the other sensors are.

Fixed differential pressure probes generally are hemispherically or pyramidally headed probes
with two pressure ports for measuring the flow angle in each axis. When the two pressures are
equal, the probe is aligned with the flow. A nonzero differential pressure can be converted to the
angle of the flow to the probe.

The null-seeking probe is similar to the fixed probe, except that a servo rotates the probe to
achieve zero differential pressure. The angle to which the probe is rotated measures the local flow
direction relative to the aircraft body datum.

Angle-of-Attack Calibration

True angle of attack can be determined during steady flight as the difference between the pitch
attitude angle and flightpath climb angle of the airplane (ref. 1). (Measurement methods for these
quantities will be discussed in a later paragraph.) This analysis requires minimum effort, but the
result may not be valid during unsteady flight.

To obtain true angle of attack for unsteady flight, the winds aloft, airplane ground speed, and
true airspeed -- for which the position error must be known -- are combined. This combination
is known as trajectory or state reconstruction (refs. 9-13). Assuming that the vertical winds are
zero usually is valid for a nonturbulent atmosphere. Dynamic effects on the sensors must also be
considered, including the bending of the airplane structure and the effects on accelerometers and
flow vanes from angular rate and acceleration (ref. 12).

Typically, production angle-of-attack sensors are mounted on the side of the fuselage forward
of the wing. Upwash caused by wing lift should not affect the sensor in supersonic flow; however,
the sensor may be affected by other local shock waves (ref. 12).

Angle-of-Sideslip Calibration

In theory, angle of sideslip can be calibrated in the same manner as angle of attack. In
practice, however, wind variability makes steady flight angle-of-sideslip calibration difficult
because calculated true angle of sideslip is very sensitive to lateral winds (ref. 1). Obtaining bias
errors for angle of sideslip through trajectory reconstruction presents similar difficulties (ref. 12).
This problem increases in difficulty as aircraft speed decreases. In a similar way that upwash
affects angle of attack, sidewash affects angle of sideslip. Sidewash and shock wave effects can
be determined through trajectory reconstruction.
 PARAMETERS REQUIRED FOR AIRDATA CALIBRATION

Quantities used to calibrate airdata parameters include velocity, attitude, angular rates,
angular and linear accelerations and atmospheric data. During steady-state flight, most of these
quantities can be recorded using pencil and paper. For greater accuracy, however, especially
during dynamic maneuvers, digital recording is used.

Position, Velocity, and Attitude

Several of the calibration calculations require Earth-relative position or velocity components.

These data can be determined by an inertial navigation system (INS); ground-based radar, laser,
or optical tracker; or global positioning system (GPS). Euler angles for aircraft attitude (roll,
pitch, and yaw) can be measured using INS and some GPS units [11-14].

An INS generally provides a complete Earth-relative data set, self-contained in the airplane,
but these data are subject to drift errors. These drift errors are aggravated by maneuvering flight.
An INS that uses ring-laser gyroscopes generally has less drift than one that uses mechanical
gyroscopes. Altitude from an INS typically uses airdata to stabilize its integration loop. Some INS
units have significant transport delays or lags because of filtering, or both, that should be taken
into account.

Ground-based radar, laser, or optical trackers can be used to determine aircraft position and
velocity. These trackers are not subject to the kinds of drift that INS experience, but they are
susceptible to errors, such as atmospheric refraction (ref. 15). Where an INS determines velocity
from integrated acceleration, systems using radar, laser, and optical trackers determine velocity
from differentiated position. Radars can track aircraft to much greater distances than laser or
optical trackers.

A GPS receiver can determine the time, position, and velocity of an airplane without drift
errors. Position data from a GPS receiver may be degraded by selective availability when a
nonmilitary receiver is used. Velocities are not affected by this problem. Using differential GPS
greatly increases position accuracy, but a reference ground receiver is needed. These GPS data are
typically received on the order of 1 sample per second. The Euler angles of the airplane can be
measured using multiple GPS antennae on the airplane and the carrier phase of the GPS signal.

Another type of inertial reference blends INS and GPS. This reference has all the benefits of
an INS with GPS used to remove the drift error associated with INS.

Rates and Accelerations

The angular rates, angular accelerations, and linear accelerations of the airplane are used in
the calibration analyses of dynamic maneuvers. Linear accelerometers can also be used in steady
flight to measure the pitch and roll attitude of the airplane (ref. 1).

An angular rate may be measured by a rate gyroscope. Angular accelerations can be

determined by differentiating the angular rate data. Direct measurement of angular acceleration

7
datais possiblebut generallydifficult. Thelocationof an angularrategyroscopeis unimportantif
the airplaneis inflexible andthe locationis subjectto experienceonly minorvibration.

Linear accelerometersshould be located as near the center of gravity as possible. If a

significantoffsetexistsbetweenthe accelerometer locationandthe centerof gravity, thenangular
rates and angularaccelerationswill affect the linear accelerationdata. Theseeffects can be
subtractedif the moment arm, angularrates, and angular accelerationsare known. Linear
accelerometers areaffectedby gravityandmay alsobeaffectedby aircraftbending(ref. 12).

Atmospheric Data

To convert the Earth-referenced data from such sources as INS or radar into airdata, the state
of the atmosphere must be known. Measurements of the atmosphere can be made from ground-
based devices, upper-air weather balloons, and satellite data. If direct atmospheric measurements
cannot be made -- for example, for a vehicle flying in near-space -- a first-order approximation
can be made using a standard atmosphere (ref. 16).

Weather balloons employ radio tracking for wind measurements by the rawinsonde method.
The balloon carries an instrumentation package and telemeters the data to a ground station that
also tracks the location of the balloon to determine the wind. The processed data include
temperature, humidity, pressure, and windspeed and direction as a function of altitude. These
balloons are released from many locations around the world at least twice a day. Data from a
single balloon may have significant errors, so an atmospheric analysis may be required (ref. 17).

TYPICAL CALIBRATION TECHNIQUES

This subsection describes typical maneuvers and methods for most airdata calibrations.
Tower-flyby, trailing static or trailing cone, pacer aircraft, radar tracking, and dynamic maneuvers
are included.

Tower Flyby

The tower-flyby method is the most accurate of the altimetry type of calibrations; however,
only subsonic data can be taken. In addition, only a few calibration points can be flown during
one flight. Figure 5 illustrates the tower-flyby method (refs. 1, 4, and 12). The airplane is flown at
a steady airspeed and altitude near the flyby tower. Passes by the tower are flown at various
subsonic Mach numbers. At the same time, the airplane is sighted from the tower through an
eyepiece or camera and grid, and the true geometric altitude of the airplane is determined by
geometry. Then, the hydrostatic equation is used to adjust the pressure at the tower for the height
of the airplane above the tower. This new pressure is the free-stream static pressure at the altitude
of the airplane. The total pressure is assumed to be correct.

Trailing Static or Trailing Cone

A direct-comparison type of calibration is the trailing static or trailing cone method (refs. 1, 2,
and 18). Location 6 in figure 3 shows a region of nearly zero static pressure error. By trailing a
 Fly-by tower Fly-by line
940229

Figure 5. Tower fly-by calibration method.

long tube behind the airplane, a nearly free-stream static pressure measurement can be taken
(fig. 6). A perforated cone at the end of the tube acts as a drag device to keep the tube stable.
Because of the long tube length, only steady level calibration points are possible. A differential
pressure measurement between the trailing tube and airdata system static source measures
position error directly. Some trailing cones have pressure transducers within them; these do not
have pneumatic lag problems.

Although in principle a trailing cone may be used throughout the envelope of an airplane, its
trailing tube may have some regions of dynamic instability. A method to extend and retract the
tube is preferred to prevent damage of the apparatus during takeoff and landing and to adjust the
length and thereby ensure stability of the tube. The optimum extension length varies with aircraft
and speed but may typically be two wingspans.

Pacer Aircraft

Another direct-comparison calibration method involves a second airplane, known as a pacer

airplane (refs. 1 and 4). An accurately calibrated airdata system aboard the pacer is used to
calibrate the test airplane. Both aircraft fly at nearly the same altitude, so the calibrated static
pressure, or pressure altitude, from a pacer airplane is the free-stream static pressure, or pressure
altitude, for a test airplane (fig. 6). In this way, a direct-comparison calibration is done. If some
altitude difference exists between the two aircraft, an altimetry calibration can be performed using
optical measurements of the altitude difference.

Although it is desirable for a pacer airplane to have performance similar to a test airplane, test
aircraft can perform flybys in the same fashion as tower flybys. Position error is determined by

9
 Pacer aircraft

Trailing cone --_

940230

Figure 6. Trailing cone and pacer aircraft.

the difference in static pressure, or pressure altitude, between the two aircraft. The accuracy of the
resulting calibration cannot be better than the accuracy of the airdata system of the pacer airplane.

Radar Tracking

Figure 7 shows the radar-tracking method. As in the tower-flyby method, free-stream static
pressure is calculated for the airplane (refs. 1, 4, and 12). For a calibration run, the airplane flies
with wings level, on a constant heading, and at a constant geometric altitude. The airplane begins
the run at a low airspeed and accelerates at a slow rate to its peak speed. The pilot then begins to
decelerate slowly back to the original airspeed. The entire maneuver is completed at radar
elevation angles above 10 degrees to minimize radar refraction errors and below 80 degrees to
avoid high radar antennae slew rates. Time-coded radar data are processed to give geometric
altitude. Weather data from balloons and other sources are analyzed to determine the true static
pressure as a function of altitude and lateral distance. These data are combined to give the true
static pressure at the airplane during the entire maneuver.

This radar-tracking method is of the altimetry type and has the advantage of being able to
handle large amounts of data at all speeds. This method is less accurate than the tower-flyby
method because meteorological and radar errors propagate into the analysis.

Dynamic Maneuvers

An extension of the radar-tracking method uses radar, or another Earth-relative data source,
during dynamic maneuvers to perform a trajectory reconstruction. Typical flight maneuvers

10
 Weather
balloon

Weather
balloon
station

IStaticpressure: H Weather IL_ I Weathermaps] [-- _t analysis

Radar H velocity and
Position I
f (position) analysis
940231

Figure 7. Radar-tracked calibration method.

include windup turns, climbs, descents, roller coasters, pushover-pullups, and rudder sweeps
(refs. 1 and 12). Windup turns can be used to get data at elevated normal force or angles of attack.
Roller coaster and pushover-pullup maneuvers are used for angle-of-attack calibration. Rudder
sweeps are used for angle-of-sideslip calibration. One benefit of dynamic maneuver analysis is
that any maneuver done with sufficient data collection can be analyzed for airdata calibration.
Note, however, that keeping the varying quantities to a minimum number is desirable because it
simplifies interpretation of the results.

DATA PROCESSING AND ANALYSIS

Items of concern for airdata calibrations include data tares, atmospheric references, trajectory
reconstruction, and pneumatic lag and attenuation.

Data Tares

The use of data tares, or zeros, greatly improves the quality of a calibration. These readings
should be taken while the airplane is stationary, and no personnel are climbing around it.
Readings of all the instruments and transducers are taken before and after the flight. The resulting
data can be used to determine if the transducers have drifted and to adjust the flight data if a
change has occurred. Some designs of differential pressure transducers can measure tares while in
flight and then be returned to a data-gathering mode for the test maneuver. This capability can
give highly accurate readings of small differential pressures.

Collecting data during stabilized flight before and after a dynamic maneuver is also a form of
a tare. For trajectory reconstruction efforts where accurate wind data are needed, the airplane can

11
perform slow stabilized tums. Ground speed, true airspeed, and heading are used to measure the
winds in flight. Often an airplane will perform calibration maneuvers along a track in opposite
directions. A wind tare can be gathered while putting the airplane on a reciprocal heading on the
original track.

An airdata calibration can be no more accurate than the sensors used to measure airdata and
other calibration parameters. End-to-end calibration of all transducers is highly desirable. This
procedure involves calibrating the sensor, signal conditioning, analog-to-digital conversion, data
telemetry, and recording systems as a whole unit. Some transducers need accurate placement or
alignment, such as accelerometers, INS units, nosebooms, and flow vanes. On flexible aircraft
with nosebooms or bendable flow vanes, the alignment should be checked periodically.

Atmospheric References

Climatological data must sometimes be used instead of measured weather data. Common
examples include situations in which the airplane is flown great distances from any weather
station or at altitudes above those in which measurements are taken. Using monthly
climatological data instead of collocated measurements will degrade the quality of the calibration,
but that is preferable to simply using the standard atmosphere or other annual reference statistics.

Atmospheric data may be needed for a calibration, but data from a single weather balloon may
have significant errors. See the section entitled Atmospheric Data. An atmospheric reference
analysis may be required (ref. 17). For this analysis data from multiple balloons are collected at
different locations and times. Then, these data are merged with satellite and weather map data.
The resulting data are checked for consistency and are interpolated to the flight time and location
of the airplane.

Trajectory Reconstruction

The simplest way to reconstruct a trajectory is to use one measurement of each needed input
parameter. A more complicated method that increases accuracy is to combine all available data
sources and then blend them. This method assumes that each data source has some random error,
and these errors cancel each other out when blended with similar data from an independent source
(refs. 9-12).

Blending multiple data sources can be accomplished with a multiple-state linear Kalman
filter. This filter blends data from multiple sources to estimate the minimum variance of the
trajectory of the airplane. The observations and dynamics equations are selectively weighted
using a matrix determined by physical intuition about the system. The linear Kalman-filter
algorithm consists of prediction and correction steps. The prediction step extrapolates the
measured data to the next time point using the dynamics equations. The correction step adjusts the
extrapolated state using measured data at that point to give the minimum variance estimate
(ref. 12).

By necessity or for a lack of resources, some aircraft have no airdata sensors. In these cases,
trajectories must be reconstructed for every data flight. Such reconstruction provides a basis for
inferring the airdata parameters of the airplane (ref. 13).

12
 Pneumatic Lag and Attenuation

During unsteady flight, pneumatic lag and attenuation may affect pressure measurements.
Pressure variations propagate as waves through the pneumatic tubing to the pressure transducer.
The wave propagation is damped by frictional attenuation along the walls of the tubing and fluid
viscosity. This damping produces a magnitude attenuation and a phase lag. After the wave
reaches the transducer, it is reflected back up the tube. Depending upon frequency distribution of
the incoming wave energy and tubing length, the reflected wave may cancel or reinforce
incoming pressure wave. If the waves cancel each other out, further spectral attenuation occurs. If
the waves reinforce each other, the power of the incoming wave is amplified and resonance
occurs.

The response of a pneumatic system can be approximated by a second-order model whose

time response lag and natural frequency are functions of tube length, tube diameter, entrapped
volume, local pressure, and local temperature (refs. 19-23). The classic treatment of pneumatic
lag assumes a first-order model as well as a very large entrapped volume (refs. 1, 24, and 25).
These assumptions are only valid for step pressure inputs in an overdamped system. Then, the
classical lag calculations agree with the second-order calculations.

Lag and attenuation can be estimated or measured experimentally. Criteria can be set for how
quickly pressure can change in the pneumatic system without affecting the airdata. Such
calibration methods as the trailing cone may have very large pneumatic lags and may have to be
used in steady flight.

SPECIAL CASES

Airdata measurement and calibration for three special cases are discussed next. These cases
are high-angle-of-attack flight, high-speed flight, and nonobtrusive sensors. The measurements
and calibration techniques previously described were developed for aircraft flying at low angles
of attack and low-to-moderate speeds. As aircraft envelopes expand into previously unknown
regions, some of the initial assumptions made for the typical methods are no longer valid.

High Angle of Attack

High-angle-of-attack flight, which is arguably above 30-degrees angle of attack, complicates

the measurement and calibration of airdata (ref. 26). The typical assumption about total pressure
being measured correctly without calibration may not hold. Some total pressure sensors are more
suited for high-angle-of-attack flight, such as Kiel or self-aligning probes (refs. 27 and 28).
Typical total temperature sensors also suffer because of the high angularity of the flow.

The characteristics of the nose of an airplane become very important at high angles of attack,
and flight characteristics can be adversely affected by use of a noseboom. Wingtip-mounted
booms suffer from a great deal of upwash and sidewash. A flush airdata sensing (FADS) system
can be used over a large range of flow angles without disturbing the flow about the nose of an
airplane. FADS systems will be discussed in more detail in a following section entitled
Nonobtrusive Sensors.

13

• tlcbt: tiab_ib UiaJl t)_ bllUll_ LIIIULII_II i:l. IILISII WIIItlOW in the airplane.
 REFERENCES

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Sensors," AGARD-AG-300, vol. 1, Sep. 1983.

2. Wuest, W., et al., "Pressure and Flow Measurement- Flight Testing," AGARD-AG-160,
vol. 11, Jul. 1980.

3. Gracey, William, "Measurement of Aircraft Speed and Altitude," NASA RP-1046, May 1980.

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Jun. 1981.

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Part 25, "Airworthiness Standards: Transport Category Airplanes," U.S. Government Printing
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6. U.S. Navy, Bureau of Aeronautics, "Instrument Systems, Pitot Tube and Flush Static Port
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, Richardson, Norman R. and Pearson, Albin O., "Wind-Tunnel Calibrations of a Combined

Pitot-Static Tube, Vane-Type Flow-Direction Transmitter, and Stagnation-Temperature
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8. Holman, J.P. and Gajda, W.J., Jr., Experimental Methods for Engineers, 4th ed., McGraw-
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