NASA Technical Memorandum 104316

.... j"

Airdata Measurement

and Calibration

Edward A. Haering, Jr.

December 1995

National Aeronautics and

Space Administration

https://ntrs.nasa.gov/search.jsp?R=19990063780 2018-05-11T19:21:34+00:00Z
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 highangle-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,
Figure I. Airflow around an aircraft wing.

940226

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 aircraftshocks,suchasthoseonnosebooms(ref.7), will not have

aircraft shock losses (ref. 2). Figure 2 shows a typical flight test noseboomthat measures

pitot-staticpressuresaswell aslocalflow 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

- Total pressure port _--,I

Static pressure/

port location -_

,F Angle-of-attack

I

!

vane

L-J_ Angle-of-sideslip vane

940227

Figure 2. Noseboom for measuring pitot and flow angles.

AP

--0

qc

-1

Pressure distribution

along this line

_2_

940228

Figure 3. Subsonic static pressure distribution.
with a referencesource,suchas a trailing cone.)This pressuredistributionchangeswith flight

condition,soacalibrationovertheflight envelopemaystill benecessary.

Location1 in figure 3 alsohaszerostaticpressureerror.A noseboomcanbeusedto placea

static-pressuresourcetoward this region. Structuralconsiderationsprevent a noseboomfrom

being long enoughto have identically zero static pressureerror. Somestatic pressureerrors

remainandneedtobecalibrated.Somenoseboomsandpitot-staticprobeshavecontoursdesigned

to compensatethemeasuredstaticpressurefor thepositionerrorinducedby thespecificairplane

(or probefor asupersonicnoseboom)(ref.2).

Evenwith theselectionof thebeststaticport position,somepressureerrorswill remain,and

theseerrorsmust be determinedin flight. The differencebetweenthe locally measuredstatic

pressureandtheambientstaticpressure,which is dependentuponangleof 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 measurementsmustalsobecorrectedfor

self-heating(resultingfrom the electricalexcitationof the heatingelement),radiation,and the

previouslymentionedrecoveryfactor.

The combination of theseerrors is often termed the recovery factor, which must be

determinedfrom indicatedtemperatureto TAT. The easiestway to determinethis factor is to

comparethe readingswith a referenceTAT probethat hasbeencalibratedin a wind tunnel.

Anothermethodis to comparetheindicatedtemperaturereadingswith thoseobtainedon another

aircraftin which thetemperaturesystemhasbeencalibrated.

Figure4 showsatypical temperaturecalibrationfor thecasein which areferenceprobeis not

available.Plotting total temperatureasa functionof Machnumbersquaredyieldsa lineartrend.

Theordinateinterceptis theambienttemperature.Theslopeandambienttemperatureareusedto

determinethe recoveryfactor (ref. 1). The datafor oneplot mustbe gatheredin a short timeand-distanceintervalandat aconstantaltitudesothattheambienttemperatureremainsconstant.

Anothermethodfor determiningthe recoveryfactor usesa direct measurementof ambient

temperature.This temperatureis obtainedusingathermometerin a towerfor low-altitude flight.

Still anothermethodusesmeteorologicaldata and true Mach numberto calculatetrue total

temperatureand,thereby,therecoveryfactor(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

Total

temperature,

oR

750

7O0

650

600

550

5OO

450

40O

Flight data

Least-squares curve fit

)/2

where Too--- Ambient temperature

J k = Recovery factor

-- / y -=Ratio of specific heats

/ for air (typically 1.4)

/

/

/

/

//-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

Figure 4. Total temperature calibration.

950444
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
dataispossiblebut generallydifficult. Thelocationof anangularrategyroscopeis unimportantif

theairplaneis inflexible andthelocationis subjectto experienceonly minorvibration.

Linear accelerometersshouldbe located as nearthe centerof gravity as possible. If a

significantoffsetexistsbetweentheaccelerometerlocationandthecenterof gravity,thenangular

rates and angularaccelerationswill affect the linear accelerationdata. Theseeffects can be

subtractedif the moment arm, angularrates, and angular accelerationsare known. Linear

accelerometersareaffectedby gravityandmayalsobeaffectedby 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 groundbased 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

Figure 5. Tower fly-by calibration method.

Fly-by line

940229

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

f (position) analysis

Weathermaps] [-- _t analysis Radar H Position velocity and I

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

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, Richardson, Norman R. and Pearson, Albin O., "Wind-Tunnel Calibrations of a Combined

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