AIRSPEED CALIBRATION SERVICE 

NIST Special Publication 250-79 

T.T. Yeh and J. M. Hall 

Fluid Metrology Group 

Process Measurements Division 

Chemical Science and Technology Laboratory 

National Institute of Standards and Technology 

Gaithersburg, MD 20899 
ii

Certain commercial equipment, instruments, or materials are identified in this paper to foster 

understanding. Such identification does not imply recommendation or endorsement by the 

National Institute of Standards and Technology, nor does it imply that the materials or equipment 

identified are necessarily the best available for the purpose 
iii

Table of Contents Page 

Abstract...........................................................................................................................................1 

1. Introduction ................................................................................................................................1 

2. Description of the Measurement Service...................................................................................2 

3. Procedures for Submitting an Airspeed sensor for Calibration ..............................................2 

4. Airspeed Calibration Facilities .................................................................................................3 

5. Primary Airspeed Standard -- LDA.........................................................................................5 

5.1 Operation Principle of Laser Doppler Anemometry ................................................5 

5.2. Spinning Disk Calibration of Laser Doppler Anemometer ....................................7 

5.3 NIST LDA Airspeed Uncertainty Analysis............................................................10 

5.3.1 The diameter of rotating cylinder, D.........................................................11 

5.3.2 The thermal expansion of the disk ............................................................11 

5.3.3 The thermal expansion of the probe..........................................................11 

5.3.4 The frequency counter of the rotating disk ..............................................12 

5.3.5 The motor speed variation .........................................................................12 

5.3.6 Variation of fringe spacing with position .................................................12 

5.3.7 The spectrum analyzer ...............................................................................14 

5.3.8 Angle Misalignment for LDA-Disk calibration........................................16 

5.3.9 Misalignment in LDA with wind tunnel installation..............................17 

5.3.10 Summary of the NIST airspeed standards uncertainty.........................17 

5.4 Uncertainty of Airspeed Calibration......................................................................20 

6. Check Standards ......................................................................................................................21 

6.1. Pitot-Static Tube .......................................................................................................21 

6.2. Thermal Anemometer...............................................................................................24 

References .....................................................................................................................................26 

Appendix A: Sample Calibration Report ....................................................................................1 
1

Abstract 

The National Institute of Standards and Technology (NIST) provides calibration services for 

airspeed instrumentation such as Pitot-static tubes, anemometers (ultrasonic, thermal or hot-wire, 

cup, and propeller types) as well as others. The NIST calibration system consists of a wind 

tunnel and a Laser Doppler Anemometer (LDA). The standard for airspeed measurement is a 

fiber optic LDA, which is calibrated with known velocities produced by a rotating disk. A Pitotstatic tube probe and thermal anemometer are used as check standards. The wind tunnel used for 

the calibration has a test cross section of 1.5 m by 2.1 m and water droplets injected into the wind 

tunnel from fine spray nozzles provide the light scattering particles necessary for the operation of 

the LDA. The range of the airspeed in the calibration service is from 0.15 m/s to 40 m/s. 

This document also describes the methods of operation and uncertainty of NIST airspeed 

standards. An extensive component analysis of the system was performed. Over the calibration 

range, the airspeed uncertainty is found to be a function of airspeed and the expanded 

uncertainty at 95 % confidence level, i.e. k = 2, in m/s can be expressed by the root-sum-square 

of 0.0064V and 0.0036 m/s, where V is airspeed in m/s. This gives a maximum uncertainty of 2.5 

% (0.0038 m/s ) at the lowest airspeed of 0.15 m/s and a minimum uncertainty of 0.65 % (0.26 

m/s ) at the highest speed of 40 m/s. 

1. Introduction 

The National Institute of Standards and Technology (NIST) provides calibration services for 

airspeed instrumentation such as Pitot-static tubes, anemometers (hot-wire, cup, and propeller 

types) as well as others. These calibration services provide traceability with a calibration report that 

documents the calibration procedure, the calibration results, and their uncertainties for airspeed 

sensor manufacturers, secondary airspeed calibration laboratories, and sensor users. The customer 

may use the sensor and its calibration results in different ways. It is often used as a transfer 

standard to compare the customer’s primary standards to the NIST primary standards so that the 

customer can establish traceability, validate their uncertainty analysis, and demonstrate proficiency.

Customers with no primary standards use their NIST calibrated airspeed sensors as working 

standards or reference standards in their laboratory to calibrate other airspeed sensors. 

NIST's airspeed calibration system consists of a dual test section wind tunnel and a LDA 

airspeed measurement system. The airspeed is measured with a Dantec LDA. A Pitot-static tube 

probe and thermal anemometer are used as check standards during every calibration. Routine 

calibrations are done by direct comparison of the averaged response of the instrument under test 

(IUT) with the response of the NIST LDA standard in the same air stream. 
2

2. Description of the Measurement Service 

Customers should consult the web address www.cstl.nist.gov/div836/Fluid Metrology Group to 

find the most current information regarding our calibration services, calibration fees, technical 

contacts, and flowmeter submittal procedures. 

NIST provides calibration services for various air speed instrumentations. The calibration 

facility is a dual section wind tunnel, which has two interchangeable test sections, together, spans a

velocity range of 0.15 m/s to 67 m/s (0.34 mph to 150 mph). Currently, NIST provides air speed 

calibration services over a range of 0.15 m/s to 40 m/s. NIST is working to incorporate additional 

setups so that the air speed calibration service will reach 67 m/s. Routine calibrations are done by 

direct comparison of the response of the instrument under test (IUT) with the response of a NIST 

standard instrument in the same air stream. Airspeed is measured with a calibrated Dantec laser 

Doppler anemometer (LDA). A Pitot tubes and a thermal anemometer are used as the check 

standards. The expanded uncertainties for the airspeed standard, in m/s as a function of air speed, is 

given as ( ) ( ) 2 2k .0 0032 VLDA + .0 0018 with a coverage factor of k = 2 where VLDA is the indicated 

airspeed from the LDA in the unit of m/s. It varies from 2.5 % at the lowest speed of 0.15 m/s to 

0.65 % to the highest speed of 40 m/s. 

The temperature, pressure, and the relative humidity in the airflow are also measured in the test 

section of the wind tunnel during the test. A normal airspeed calibration performed by the NIST 

Fluid Metrology Group consists of several speeds spread over the range of the given airspeed 

sensor. Two calibration cycles are done separated by a shutdown. In each calibration cycle, the air 

speed is measured five times at each airspeed set point. Therefore, the final data set consists of ten 

speed measurements made at each speed set point. The sets of five measurements can be used to 

assess repeatability, while the sets of ten can be used to assess reproducibility. For further 

explanation, see the sample calibration report in the Appendix A of this document. Variations on 

the number of speed set points, spacing of the set points, and the number of repeated measurements 

can be discussed with the NIST technical contacts. However, for data quality assurance reasons, we 

rarely will conduct calibrations involving fewer than five speed set points and two sets of three 

speed measurements at each set point. The Fluid Metrology Group prefers to present airspeed 

calibration results in a dimensionless format based on the speed ratio. 

3. Procedures for Submitting an Airspeed sensor for Calibration 

The Fluid Metrology Group follows the policies and procedures described in Chapters 1, 2, 

and 3 of the NIST Calibration Services Users Guide [1]. These chapters can be found on the 

internet at the following addresses: 

http://ts.nist.gov/measurementServices/Calibrations/policy.cfm, 

http://ts.nist.gov/measurementServices/Calibrations/domestic.cfm, and 

http://ts.nist.gov/measurementServices/Calibrations/foreign.cfm 

Chapter 2 gives instructions for ordering a calibration for domestic customers and has the 

sub-headings: A.) Customer Inquiries, B.) Pre-arrangements and Scheduling, C.) Purchase 
3

Orders, D.) Shipping, Insurance, and Risk of Loss, E.) Turnaround Time, and F.) Customer 

Checklist. Chapter 3 gives special instructions for customers outside the United States. The web 

address www.cstl.nist.gov/div836/Fluid Metrology Group has information more specific to the 

airspeed calibration service, including the technical contacts in the Fluid Metrology Group, fee 

estimates, and turn around times. 

4. Airspeed Calibration Facilities 

 

NIST airspeed calibrations are done in a dual section wind tunnel [2] as shown in Fig. 1. The 

tunnel is a closed-circuit facility lying in a horizontal plane and has two interchangeable test 

sections. These two test section ducts ride "piggy back" on a cable hoisting arrangement. The 

upper test section is 12 m long and has a system of parallel arms along the sides which allow the 

side walls to be adjusted. The width of the test section is variable; however, the normal 

dimensions are 2.1 m high and 1.5 m wide. The top speed in the upper test section is 45 m/s. 

In the lower test section, the 2.1 m height at the entrance is gradually reduced in the flow 

direction to 1.2 m forming a venturi-like duct so that the top speed is 67 m/s. The effective 

working length is 3.0 m within the overall 12 m length. All sides of the lower test section are 

fixed. Currently the airspeed calibrations are done only in the upper test section over a range of 

0.15 m/s to 40 m/s. NIST is working to incorporate additional setups (e.g. a better seeding 

conditions) so that the airspeed calibration service will reach 67 m/s. 

The downstream end of the test sections is vented to the room establishing this point in the 

circuit as being near atmospheric pressure. From the test section, the flow passes into a 5o diffuser,

around two 90o bends containing turning vanes and into the drive section which measures 3.8 m by 

4.4 m at the location of a cooling coil used to stabilize the tunnel temperature. The cooling coil is 

situated between the drive motor and the fan so that the fan drive shaft passes through the center of 

the coil. A rectangular-to-round transition section makes the connection to the drive fan inlet. The 

entire drive mechanism, along with the cooling coil, is mounted on a large concrete slab, which is 

isolated from the building floor with springs to minimize the transmission of vibration. The main 

tunnel duct is attached to the drive section at each end by means of flexible boots. 

The fan is powered by a variable speed 300 kW direct current (DC) motor. The DC voltage is 

supplied by a 370 kW motor-generator set. The maximum fan speed is 600 revolutions per 

minute and is controlled by a feedback loop producing shaft revolutions stable to within ±0.1%. 

The fan is 2.4 m in diameter with two axial stages and manually adjustable-pitch blades. 

Downstream of the fan the flow passes through a circular-to-square transition section and into a 

five-degree diffuser followed by the two more special diffusers sets. The upstream diffuser 

consists of two sets of turning vanes, a 1 cm by 7.6 cm honeycomb, and the downstream wideangle diffuser containing 6 screens. After the diffuser, there is a 6.1 m by 7.5 m settling chamber 

having 9 screens. From the settling chamber the airflow passes through an entrance cone and into 

the 1.5 m by 2.1 m test section. 

The combined effects of the honeycomb, screens, and a contraction ratio of 14.5:1 provide 

test section longitudinal free-stream turbulence levels of 0.07 % over most of the speed range and 
4

a transverse velocity gradient less than 1 % within a "working window" of 90 % of the testsection areas. 

 

Figure 1 NIST Wind Tunnel for Airspeed Calibration Service. 

To provide the light scattering particles necessary for the operation of the LDA, water 

droplets, produced by several fine air-water spray nozzles, are introduced into the tunnel before 

the wide-angle diffuser and directed toward the honeycomb (see Fig. 1 for the nozzle location). 

Fig. 2 shows the fine water droplets with the spray nozzles. The spray can be adjusted to 

optimize the data rate for the LDA signal processor. 
5

Figure 2 Photo of fine water droplets with the air-water spray nozzles 

5. Primary Airspeed Standard -- LDA 

The primary standard for airspeed measurement at NIST is a fiber optic LDA. This instrument 

has been characterized by calibrating its indicated speed using particles of known speed as 

discussed below. 

5.1 Operation Principle of Laser Doppler Anemometry 

An LDA measures the velocity of a particle moving in a plane perpendicular to the bisecting 

plane of the two converging laser beams [3, 4]. The laser velocimetry operated in a differential 

mode is commonly used to generate the Doppler frequency of the scattered light and used to 

measure the particle/fluid speed. The NIST LDA is a differential laser velocimetry system. It 

splits a laser beam into two beams in a plane and then recombines them at a small intersection 

angle by using a transmitting focus lens. In the intersection volume, the two beams are mutually 

coherent, collimated of like polarization and of equal intensity. The interaction between these 

two laser beams results in a three-dimensional region (sensing volume) which contains an 
6

interference pattern that is composed of parallel light and dark fringes. Small particles, entrained 

in, and moving at the same speed as the air stream, scatter light as they pass through each bright 

fringe in the intersection volume. The NIST LDA operates in a backscattering configuration. 

Scattered light from the particle moving through the fringe pattern is collected by the same lens 

used to transmit the two laser beams and focused onto a fiber detector. Because of the periodic 

fringe pattern, the scattered light will be intensity modulated at a frequency proportional to the 

component of the particle velocity perpendicular to the fringe pattern. The correct airspeed is 

measured when the probe is properly aligned such that the bisecting plane of the two laser beams 

is perpendicular to the direction of the flow. 

The spacing between the bright fringes, d depends on the angle θ between the two laser 

beams and the laser wavelength λ as 













=

2

2sin θ

λ

d (1)

As shown in Fig. 3, when two parallel beams having a separation of h are combined by a lens 

having a focal length of fL, the beams intersect at the angle 

















=

−

L

f

h

2

2 tan 1

θ (2) 

In the context of airspeed measurement, the spacing d between the bright fringes serves as the 

length scale. 

To resolve the sign of the velocity, a frequency offset generated by a Bragg cell is used to 

move the fringe pattern through the measuring volume and across the scattering particle. Fiber 

optic cables transmit laser light to the probe through a transmitter probe system. The transmitter 

system includes color separation, beam splitter, and frequency shifter. The output ends of the 

optical cables are arranged at the fixed positions so the laser beams are parallel to the probe body. 

The NIST LDA is a two velocity component system. The laser source is an Argon ion laser 

operated in multi-color mode. One velocity component uses green light (λ = 514.5 nm) and the 

second velocity component uses the blue light (λ = 488.0 nm). However, the green light 

component is used predominately, while the blue light component is used only occasionally for 

checking the system. Table 1 shows the nominal optical parameters of the LDA probe. 
7

Figure 3 Laser Beams and Their Intersection Angle for 1D Component. 

Table 1 Nominal Optical Parameters of the LDA Probe 

Laser wavelength λ , nm 514.5 

Laser beam separation h, mm 72.5 

Focal length fL, mm 1200 

Beam intersection angle θ , deg. 3.46 

Fringe spacing d, μm 8.52 

Probe diameter dm, mm 0.3 

Probe length lm, mm 9.9 

In the context of airspeed measurement, the average frequency of the scattered light serves as 

the timer. The particle speed seen by the LDA is 

LDA D V = d f (3)

where Df is the average Doppler frequency. NIST's LDA system uses a Dantec burst spectrum 

analyzer (BSA) to determine the Doppler frequency of the scattered light. 

At NIST, the light scattering particles used for the airspeed measurements are water droplets 

injected from the fine air-water sprays located just upstream of the settling chamber of the wind 

tunnel, as shown in Fig. 1 and Fig. 2. 

5.2. Spinning Disk Calibration of Laser Doppler Anemometer 

In principle, the speed obtained from Eqn. (3) can be used as primary standard for airspeed 

measurement if both the fringe spacing d (length scale) and the frequency fD (timer) are 

fL 

h θ

Fiber optic 

cables

Laser 

beams

LDA Probe
8

calibrated at specified uncertainty levels. The value of d can be calculated from the laser 

wavelength λ and the beam angle θ if both θ and λ are calibrated. However, the calibration of 

the measured Doppler frequency is still needed to ensure the accuracy of the indicated frequency 

fD, which is determined by a Burst Spectrum Analyzer (BSA). 

In this work, instead of measuring d and fD separately, we calibrate the entire LDA system 

directly by comparing the speed indicated by the LDA to the known speed of a wire attached to a 

spinning disk unit [5], as shown in Figs. 4 and 5. Similar calibration techniques have been used 

by others. Dopheide, et al. [6] used the particles on the surface of a thick rotating glass wheel to 

generate the known tangential velocity. Kurihara, et al. [7] used a rotor with a single wire to 

simulate the trace particle. Park, et al. [8] used sand paper on a rotating disk to create a known 

velocity. At NIST, a 5 μm diameter wire is mounted on the rim of a disk of known diameter D. 

The disk and the light-scattering wire rotate at a measured rotation frequency fDisk, thus enabling 

the calculation of the tangential speed of the wire from 

V f D 2/ Disk = Disk (4) 

collet hole

chopper

clamping screws

light trap

wire

light sensor for

rotating speed

fDisk

LDA laser

Light beam

D 

Disk

Disk Spin Axis

collet hole

chopper

clamping screws

light trap

wire

light sensor for

rotating speed

fDisk

LDA sensing volume, fringe spacing d

LDA laser

Light beam

D 

Disk

Disk Spin Axis

collet hole

chopper

clamping screws

light trap

wire

light sensor for

rotating speed

fDisk

LDA laser

Light beam

D 

Disk

Disk Spin Axis

collet hole

chopper

clamping screws

light trap

wire

light sensor for

rotating speed

fDisk

LDA sensing volume, fringe spacing d

LDA laser

Light beam

D 

Disk

Disk Spin Axis

Figure 4 Schematic Diagram of the Spinning Disk for Calibrating the LDA. 

The LDA is aligned so that the bisecting plane of the intersecting light beams is parallel to 

and passes through the axis of the disk and the wire passes through the intersection volume as the 

disk rotates. In this way, the LDA measures the known speed VDisk produced by the spinning 

disk. The calibration factor, CLDA is determined from the disk’s speed and the speed indicated by 

the LDA using 

f d

D f

V

V

C C

D

Disk

LDA

Disk

LDA 2

= = (5)
9

where C

D

f is the frequency measured by the LDA system when it is scattering from the disk 

moving at the velocity VDisk . The NIST standard speed thus becomes 

C

D

D

NIST LDA LDA Disk f

f

f

D

V C V

2

= = (6) 

Thus, the NIST LDA airspeed system is traceable to the length ( D ) and time standards 

( fDisk ) used in the spinning disk calibration. 

Figure 5 Photo of the Spinning Disk Unit. 
10

5.3 NIST LDA Airspeed Uncertainty Analysis 

Here we follow the guidelines for evaluating and expressing uncertainty provided in 

NIST TN 1297 [9], the ISO Guide [10], and elsewhere [11]. In general, if a measurement 

quantity, y is a function of variables ix , 

y x(f x, ,....., x ) = 1 2 n (7) 

 its first-order Taylor series approximation is, 

∑ ∂

∂

=

i

i

i

dx

x

y

dy (8) 

Thus, the propagation of uncertainty yields 

r x(u x(u) )

x

y

x

y

u x( )

x

y

x(u )

x

y

u )y(

ij i j

n

j i j

n

i i

i

n

i i

n

i

i

i

c

∑ ∑ ∑

∑

= +

−

= =

=

















∂

∂

















∂

∂

+

















∂

∂

=

































∂

∂

=

1

1

1

2

1

2

2

1

2

2

 (9) 

where u ( )y c is the combined standard uncertainty of the measurement result y , ( )i u x is the 

standard uncertainty of the variable ix , the partial derivatives i∂ /y ∂x are the dimensional 

sensitivity coefficients of ix on y , and ij r is the cross correlation coefficient between variables 

i

x and j

x . An alternative form of Egn.(9), which expresses the uncertainty propagation in a 

dimensionless form, is shown below and it is often more useful. 

i i i j i j

ij x x

n

j i

x y,

n

i

x x y,

n

i

uy ∑cx y, u ∑c ∑c r u u

= +

−

= =

= +

1

1

1

2

1

2 2

2 (10) 

In Eqn.(10), u u ( /)y y y = c is the combined dimensionless standard uncertainty of the 

measurement result y , c ( /y x )x / y x y, i i

i

= ∂ ∂ are the dimensionless sensitivity coefficients of ix

on y , and ( ) x i i u u x / x

i

= is the dimensionless uncertainty of the variable ix . Equation (10) is 

used here to estimate the combined uncertainty of the measurement. In many cases, the 

uncertainty of ix could not be measured directly. For those cases, the same uncertainty 

propagation given by Eqn.(10) is used for a sub-measurement process to estimate the combined 

uncertainty of the sub-measurement. This process is propagated throughout all the measurement 

components needed until the desired measured quantities are obtained. 

According to [9], the sources of uncertainty used in assessing the combined standard 

uncertainty of the measurement process can be classified according to two types: Type A - those 

which are evaluated by statistical methods, and Type B - those which are evaluated by other 

means. Following this convention, each measured quantity has been classified accordingly as a 
11

u A or uB. 

Referring to Eqns.(6) and (10), the airspeed uncertainty depends on the uncertainties of the 

variables of the diameter of the rotating cylinder D , the rotating frequency fDisk , and the 

Doppler frequencies measured by the LDA system C

D

f and Df . Although not shown in Eqn. (6) 

explicitly, many other variables could affect the uncertainties of the airspeed measurements. 

Based on the theory for the uncertainty propagation given above, the uncertainty from the subvariable components is estimated and included in the uncertainty of the NIST airspeed 

measurement. In addition, the result given in Eqn. (6) is based on the assumption of a perfect 

alignment. The misalignment of the LDA and disk will produced additional uncertainty. These 

sub-variables and additional uncertainties are discussed in detail in following sections. The 

sources and values of the uncertainties of these variables are summarized in Table 2, as well as 

their classification as either u A or uB. The corresponding airspeed uncertainties due to these 

sources are also given in Table 2. 

5.3.1 The diameter of rotating cylinder, D 

In the NIST facility, the light-scattering wire is a tungsten wire 5 μm in diameter. The wire is 

mounted by clamping screws to the curved surface of the short right circular cylinder shown in 

Fig. 4 and 5. The wire is parallel to the axis of the cylinder. The wire spans a groove machined 

into the cylinder, shaped to serve as a light trap to eliminate unwanted reflected laser light. A 

hole along the axis of the cylinder is shaped to receive a small collet to facilitate mounting the 

cylinder on the shaft of gear motors. Care was exercised in the machining process to assure that 

the collet hole and the curved surface of the cylinder are coaxial. The cylinder is mounted on the 

output shaft of a gear motor such that the cylinder rotates in a horizontal plane. The entire 

assembly is mounted on an x-y translation stage. The diameter of the cylinder was measured to be 

136.522 mm with a standard uncertainty of 0.005 mm or 0.0037 % using a triple axis coordinate 

measuring machine (see uncertainties in Table 2 ). This will give 0.0037 % uncertainty in speed 

measurements. 

5.3.2 The thermal expansion of the disk 

The diameter of the disk D changes with the temperature. The temperature at which the 

diameter was measured might be different from the temperature where the diameter is used for 

LDA calibration. When the linear thermal expansion of the disk is assumed to be 1.7x10-5 /K, the 

change in D is 0.0116 mm or 0.0085 % for a 5 K difference in the temperature change. This 

contributes 0.0085 % uncertainty in speed. 

5.3.3 The thermal expansion of the probe 

Although fringe spacing d is not explicitly shown in Eqn. (6), its uncertainty will affect the 

uncertainty of the burst frequency measurement. The dimension of the probe and the beam 

separation h and the fringe spacing d will change with the temperature. The housing of the probe 
12

is made from aluminum and its linear thermal expansion is assumed to be 1.7x10-5 /K. Referring 

to Eqns. (1) and (2), and the optical parameters of the probe given in Table 1, for a 5 K difference 

in temperature, the change in h is 0.0062 mm and in d is 0.00071 μm or 0.0085 %. Here, we have 

assumed that the temperature change does not affect the alignment of the two laser beams and 

that the beams are kept parallel to the probe body all the time. Since the uncertainty of d affects 

both the uncertainties of C

D

f and Df , the total uncertainty on speed due to d is 2 × 0.0085 % = 

0.012 %. Here the Type A variations of C

D

f and Df are assumed to be independent.

5.3.4 The frequency counter of the rotating disk 

Calculation of the wire speed requires the measurement of the rotation frequency of the disk. 

This frequency is measured by counting the pulses produced by an optical signal modulated by 

the rotating disk. As shown in Fig. 4 or 5, the top surface of the disk was hollowed out so that 

the disk resembles a straight-sided bowl with a thick bottom. The side wall of the bowl has two 

holes, one centered on each end of a diameter through the axis. These holes serve as an optical 

chopper for a helium-neon laser, positioned so its light beam strikes a photo diode when the 

holes are aligned with the laser and the photo diode. This setup produces two pulses for each 

rotation. The output of the photo diode is counted with a frequency counter that determines the 

rotation rate of the disk. The frequency counter has a Type A uncertainty of 0.31 parts in 106 and 

a Type B uncertainty of 1.55 parts in 106. For a clock frequency of 1 MHz, this will give a Type 

A uncertainty of 3.2x10-5 % for a typical measurement time of 60 s and Type B uncertainty of 

0.0002 %. 

5.3.5 The motor speed variation 

A single Animatics Smart Motor, Model SM2315D with Animatics power supply Model 

PS42V6AG-110 was used to drive the calibration disk. The motor is digitally integrated motion 

controlled. It provides stable rotation rates in very large rotating range and has an encoder with a 

resolution of 2000 counts per revolution. The standard deviation of the disk rotation speed is 

found to be 0.038 % in the operation range. 

5.3.6 Variation of fringe spacing with position 

When the Gaussian laser beam is focused by a lens, the minimum beam diameter (the waist) 

is found at the back focal plane of the lens only if a waist also exists at the front focal plane. 

Interference fringes are formed in the volume where both laser beams intersect. If both beam 

waists are not located at this intersection, an enlarged probe volume at some part in the volume 

will result [3, 4]. Since the waists do not occur exactly at the intersection usually, the spacing of 

the interference fringes is not constant throughout the sensing volume as shown in Fig. 6. This 

error can be significant when the frequencies of the observed ‘Doppler’ signals are related to the 

speed of the scattering particles passing through the different parts of fringes. When fringe 

spacing is not constant throughout the probe volume, a constant wire speed will produce different 

LDA Doppler frequencies when the wire is located at different locations (see the value xw in Fig. 

9). Fig. 7 shows an example of the variation of the measured indicated velocity as a function of 
13

the wire location. The data show that the measured velocity is a linear function with the wire 

location within the sensing volume (-3 mm to +3 mm on the graph). Therefore, particles passing 

through different locations will produce different speeds indicated by the LDA, even when their 

speeds are the same just as the rotating disk does (Fig. 4). In the NIST standard, the averaged 

speed indicated for all particles passing the sensing volume is assumed to be the system speed for 

the LDA calibration. This assumption is reasonable because: (1) the variation of the speed ratio 

is linear, and (2) the particle concentration is uniform throughout the sensing volume so the 

probability of the LDA signals produced by particles is symmetric about the center point. 

Figure 6 Fringe Spacing Variations in an Improperly Aligned System 

To determine the mean value of the calibration, a least square error linear curve was obtained 

for each tested speed. The straight line shows the fitting of the data. From the fitted curve, both 

the mean value and the standard deviation of the LDA-disk calibration are obtained. The standard 

deviation obtained from the fitting will be discussed in the next section. The mean value is the 

speed calibration factor, CLDA as described in Eqn. (5). The variation of the mean values at 

different time and different speeds are mainly due to the uncertainty of locating the wire position 

with respect to the probe volume. The variation of the mean value is particularly true when the 

fringe spacing is not constant throughout the probe volume as discussed above. The standard 

deviation of this mean value is found to be 0.13 %. This is classified as the uncertainty from the 

fringe space variation. 
14

0.97

0.98

0.99

1.00

1.01

1.02

1.03

-4 -3 -2 -1 0 1 2 3 4

Wire Position, mm

VDisk / VLDA [-]

Figure 7 LDV Calibration Results vs Wire Position. 

5.3.7 The burst spectrum analyzer 

Frequency, C

D

f or Df , is determined by a burst spectrum analyzer (BSA). The uncertainty of 

the BSA consists of the uncertainty resulting from the clock (oscillator) used for time scale and 

the uncertainty from the BSA designed to interpret the burst frequency. The sensitivity 

coefficients of C

D

f and Df for airspeed are -1 and +1, respectively. So that the systematic 

uncertainty of the BSA will be cancelled out on the airspeed uncertainty while the Type A 

uncertainty on the airspeed will be enlarged by a factor of 2 . 

The clock used for the frequency or time scale has a Type A uncertainty of 0.5 parts in 106

and a Type B uncertainty of 2 parts in 106. For the nominal fringe space of 8.52 μm, the Type A 

and B uncertainties are 5x10-5 % and 0.0002 %, respectively. Thus the resulting uncertainty on 

speed due to the clock is 2 x 5x10-5 % =7.1x10-5 % for the Type A uncertainty and is zero for 

the Type B uncertainty due to cancellation. 

The estimation of the other uncertainties for the BSA is more complicated. We have 

estimated these uncertainties from the uncertainty of the disk-LDA calibration. This uncertainty 

is identified by the standard deviation obtained from the curve fitting as discussed in section 
15

5.3.6 and shown in Fig. 7. The uncertainty as a function of the calibrated speed is plotted in Fig. 

8. Diamond symbols shown in Fig. 8 are the combined uncertainty of the disk-LDA calibration 

data. This uncertainty is mainly due to both the disk rotation speed and BSA uncertainties. Since 

the systematic uncertainty is cancelled out for the final speed measurement and is not the issue 

here, the data shown is only for the Type A uncertainty. The disk-LDA uncertainty data can be 

represented by two independent terms: a constant speed term and a constant ratio term. These 

two terms were found by fitting curve to the data in Fig. 8 and the result of the fitting, ((0.13 

/V)2 + (0.21)2)

1/2, in %, is shown as the solid curve. The constant speed term (the speed 

uncertainty for any speed) is 0.0013 m/s (corresponding to a 150 Hz on the BSA for an 8.52 μm 

fringe spacing) and the constant ratio term is 0.21 % of the speed. The constant speed term 

(0.0013 m/s) results from the resolution of the BSA while the constant ratio term results from the 

combined effect of the motor speed variation and the conversion factor of the BSA. 

0.1

0.2

0.3

0.4

0.5

0.6

0 10 20 30 40

V , m/s

u

A of LDA-Disk [%]

Data

fitting

Figure 8 Type A Uncertainty of LDA-Disk Calibration. 

The fitting is ( (0.13 /V)

2

 + (0.21)2)

1/2 in %. 

The BSA uncertainty can be estimated by subtracting the motor speed uncertainty of 0.038 %, 

found in Section 3.5, from the combined uncertainty (accounting for the RSS relationship). Here 

we have assumed that the motor speed uncertainty is independent of the BSA uncertainty. The 

resulting BSA uncertainty for the constant percentage term is thus 0.207 % (= (0.212 – 0.0382)

1/2

%). It is the uncertainty of the conversion factor of the BSA. 
16

The Type A uncertainty of the BSA affects both C

D

f and Df independently and thus the 

resulting speed uncertainty is 2 x 0.0013 m/s = 0.0018 m/s for the constant speed term and 

2 x 0.207 % = 0.29 % for the constant percentage term. 

5.3.8 Angle Misalignment for LDA-Disk calibration 

As noted above, the result given in Eqn. (6) is based on the assumption of a perfect 

alignment. The misalignment of the LDA and disk will produce additional uncertainty. The 

rotating disk is mounted on the output shaft of a gear motor such that the disk rotates with a 

vertical spin axis. The entire assembly is mounted on an x-y translation stage. The alignment of 

LDA probe with the direction of the wire velocity is another parameter to be examined. As noted 

above, the LDA must be aligned so that the plane bisecting the intersection angle is parallel to 

and passes through the axis of the cylinder. Fig. 9 shows the local coordinates for the disk and 

the laser beams intersection during the LDA-Disk calibration. The laser beams are on an x-y 

plane and z is normal to the x-y plane. The center of the probe volume is assumed to be at the 

coordinate origin, (0,0,0). The light scattering wire is located at xW, oriented in the z direction 

and moves in the y direction when the disk is rotating. n is a unit vector normal to the bisecting 

plane (x-z plane). The fringes are parallel to the bisecting plane. φ is the angle between the wire 

velocity VDISK and the unit vector, n. C is the axis of the rotating disk. 

To help making the alignment of the LDA with the disk, an acrylic rod having a 1 mm 

diameter hole drilled along the axis of the rod is mounted vertically in the hole on top of the 

collet of the disk. The LDA is aligned with the axis by x-y translations of the cylinder assembly 

so that the intersection volume is centered on the axis of the acrylic rod (C in Fig. 9). The 1 mm 

hole scatters light and makes the laser light visible on the axis. The x-y translations are adjusted 

for maximum brightness of the scattered light. The traversing system on which the fiber optic 

probe is mounted is then backed away a distance equal to the radius of the cylinder and lowered 

so that the wire passes through the intersection volume as the cylinder rotates. To ensure the 

bisecting plane of the laser beams is always in line with the disk axis when the traversing system 

is moved, the bisector of the laser beams (the optical probe) must be aligned with the traversing 

system correctly. The alignment can be checked by turning the probe 90o to have a vertical 

bisecting plane and then checking the intersection while moving the traversing system. Final 

adjustment is done by turning the lead screw of the traverser slowly while watching the input to 

the signal processor on an oscilloscope. When the system is misaligned, the observed speed is 

given by ) VDisk cos(φ . The uncertainty of the calibration speed is the cosine effect of the 

misalignment. It is 1-cos(φ ) for an angle of φ. The misalignment angle φ can be decomposed 

into two orthogonal angles, φx and φz. The uncertainties of the misaligned angles are estimated to 

be 0.5 deg. and thus a speed uncertainty of 0.004 % for both φx and φz.
17

Axis of the rotating disk.

R is the distance between 

the wire and the axis

x

y

Light scattering wire

Laser

VDISK

φz

xw

yb

C R

rotation

n is an unit vector normal to the bisecting plane, 

φ is the angle between VDISK and n. φx(not 

shown) and φz, are the components of the angle φ

rotated around x and z axes respectively. 

n

Axis of the rotating disk.

R is the distance between 

the wire and the axis

x

y

Light scattering wire

Laser

VDISK

φz

xw

yb

C R

rotation

n is an unit vector normal to the bisecting plane, 

φ is the angle between VDISK and n. φx(not 

shown) and φz, are the components of the angle φ

rotated around x and z axes respectively. 

n

Figure 9 Local Coordinates for the Spinning Disk and the Laser Beam Intersection. 

5.3.9 Misalignment in LDA with wind tunnel installation 

The sources of the uncertainties discussed above are only for the LDA airspeed standards 

system. However, additional uncertainties must be added if the LDA probe is not aligned with 

respect to the airspeed direction in the test section of the wind tunnel or if the device under test is 

misaligned. Ideally, the unit vector of the bisecting plane should be in the direction of the 

airspeed (y). That is, the laser bisecting plane should be in vertical direction (z) and parallel to 

the x direction (horizontal and normal to y). αx and αz denote the angles of misalignment rotated 

around the x and z axes, respectively. The airspeed uncertainty due to the cosine effect varies 

with 1-cos(αx) and 1-cos(αz). The uncertainties of these misaligned angles are estimated to be 1 

deg. and thus a speed uncertainty of 0.015 % for both αx and αz. 

5.3.10 Summary of the NIST airspeed standards uncertainty 

Table 2 lists the sources and values of the uncertainties. Table 3 lists the effect of the source 

uncertainties on the uncertainty of the NIST airspeed standards. As shown in Table 3, the major 

uncertainty of the airspeed standards is due to the BSA uncertainty given in section 5.3.7 and the 

variation of fringe spacing given in section 5.3.6. 

The airspeed uncertainty is classified into two types: a constant speed term and a constant 

percentage term as shown in Table 2. The uncertainty for each group is then combined and given 

in Table 3. 
18

Table 2 Summary of Sources and NIST Airspeed Uncertainties. 

Sources Speed 

Variable Sources Section Uncertainty 

Mean uA uB uA % uB %

Diameter of rotating 

disk, D [mm] 5.3.1 136.5 0 0.005 0 0.0037

Thermal expansion of 

D, [mm] 5.3.2 136.5 0.0116 0 0.0085 0 

Fringe spacing 

expansion, d [μm] 5.3.3 8.52 0.0007 0 0.012 0 

Timer for rotating disk 

[parts in 106] 5.3.4 - 0.31 1.55 3.2x10-5 0.0002

Rotation speed, [%] 5.3.5 - 0.038 0 0.038 0 

Fringe spacing with 

position, [%] 5.3.6 - 0 0.13 0 0.13 

Clock for BSA [parts in 

106] 5.3.7 - 0.5 2.0 7.1x10-5 0 

BSA constant speed 

term [m/s] 5.3.7 - 0.0013 0 0.18/VLDA 0 

BSA constant ratio term 

[%] 5.3.7 - 0.207 0 0.29 0 

LDA-disk, φx , [deg] 5.3.8 0 0 0.5 0 0.004

LDA-disk, φz, [deg] 5.3.8 0 0 0.5 0 0.004 

LDA-wind tunnel, αx, 

[deg] 5.3.9 0 0 1.0 0 0.015 

LDA-wind tunnel, αy , 

[deg] 5.3.9 0 0 1.0 0 0.015 

Table 3 Combined Airspeed Uncertainty 

uA % uB % 

Constant ratio term 0.29 0.13 

Constant speed term 0.18/VLDA 0 

Based the data in Table 3, the results for the total combined standard uncertainty for the NIST 

airspeed, in m/s can be given as 

( )2 2 2( ) = .00029 + .0( 0013 ) + .0( 0018)

c VNIST VLDA VLDA u (11) 

where VLDA is in m/s. The approximate confidence level of the result given above is 68 %. 

Following the guidelines of [9], the expanded uncertainty with a coverage factor k is given as 
19

( )2 2

( ) = .0 0032 + .0( 0018) NIST VLDA U V k (12) 

When a coverage factor of k = 2 is used to convert the combined standard uncertainty to an 

expanded uncertainty, with an approximate 95 % level of confidence, the expanded uncertainty, 

in m/s, becomes: 

( ) ( ) 2 2 U(VNIST ) = .0 0064 VLDA + .0 0036 (13) 

Based on Eqn. (13), the NIST airspeed expanded uncertainty is plotted in Fig. 10 in the unit 

of m/s for the coveraged airspeed range of 0.15 m/s to 40 m/s. This gives a minimum uncertainty 

of 0.0038 m/s at the lowest airspeed of 0.15 m/s and a maximum uncertainty of 0.26 m/s at the 

highest speed of 40 m/s. The uncertainty from the spinning disk can be obtained by removing the 

BSA uncertainty given in section 5.3.7 and alignment uncertainty given in section 5.3.9 and is 

shown as dashed line in Fig. 10 for reference. The same uncertainty data are plotted in Fig. 11 in 

the unit of %. This gives a maximum uncertainty of 2.5 % at the lowest airspeed of 0.15 m/s and 

a minimum uncertainty of 0.65 % at the highest speed of 40 m/s. 

0.0

0.1

0.2

0.3

0.1 1 10 100

Airspeed , m/s

Airspeed Uncertainty, k=2, m/s

Dashed line - Spinning disk

Figure 10 NIST Airspeed Uncertainty in m/s versus Airspeed 
20

0

1

2

3

0.1 1 10 100

Airspeed , m/s

Airspeed Uncertainty, 

k =2, %

Dashed line - Spinning disk

Figure 11 NIST Airspeed Uncertainty in % versus Airspeed 

5.4 Uncertainty of Airspeed Calibration 

The uncertainty analysis reported here is for the NIST airspeed standards. To obtain the 

uncertainty for an airspeed meter calibration additional uncertainties, such as the alignment 

uncertainty of the meter should also be included. The LDA measures the airspeed directly in 

varying environmental conditions ( temperature, pressure, and humidity). Some airspeed sensors 

might be greatly affected by the environmental conditions and they require corrections of the 

environmental effects on the indicated speed. The uncertainty for the IUT results will also 

depend on the airspeed sensor type, and the associated instruments used during the airspeed 

calibration. In addition, the quality of the water drop seeding used for LDA could also affect the 

LDA data rates and uncertainty. To account for these additional uncertainties, the expanded 

uncertainty of the calibration of the instrument under test, U , can be calculated by 

 

2 2

R

2 U = k uV +u Acq u

NIST

+ (14) 

The quantity VNIST

u , as given in Eqn. (14), is the standard uncertainty of the airspeed 

measurements made with the LDA as discussion in section 5 above. The quantity Acq u is the 

standard uncertainty of the data acquisition system and instrumentation used to obtain the 

readings from the instrument under test. In this case, the uncertainty due to data acquisition is 

considered negligible. The quantity uR is the reproducibility [12] of the test. Reproducibility is 

herein defined as the closeness of agreement between measurements with the airspeed changed 
21

and then returned to the same nominal value. To measure the reproducibility of the test, uR, the 

standard deviation of the air speed ratio at each of the nominal air speeds was used to calculate 

the relative standard uncertainty. By using this method, the total uncertainty of the calibration 

data for the test meter will include both contributions from the calibration system and IUT. 

6. Check Standards 

Beside the LDA used as the primary airspeed standard, NIST maintains the airspeed check 

standards: the Pitot-static tube probe (pst) and thermal anemometer (Ta). Current check standard 

results are compared to prior results as a means of verifying the continued proper operation and 

performance of all of the air speed calibration service systems (instrument calibrations, software, 

operating procedures, the check standards themselves, etc.). The check standards are also used if 

there is any significant change made to the system or before a critical calibration. 

6.1. Pitot-Static Tube 

Henri de Pitot first described the instrument that bears his name in 1732 [13, 14]. Currently, the 

Pitot-static tube, or Pitot tube, is still widely used to measure the speed of gas and liquid streams.

The operation principle of a pst is based on the well known Bernoulli’s equation. For an 

incompressible flow, the Bernoulli's equation [15] gives 

2

2

1

Pt = Ps + ρ V (15) 

where Pt is the total pressure, Ps is the static pressure, and 2

2

1

ρ V is the dynamic pressure for a 

fluid of density of ρ and flow speed of V. Solving for the velocity, we have 

ρ

∆P

V CD

2

= (16) 

where CD is added to denote the pitot-static meter constant, and ∆P = Pt − Ps

 is the differential 

pressure between the total pressure and the static pressure, or the dynamic pressure. 

The density of the air, in kg/m3, is calculated with the expression [16] 

















= −

−

T

C

P c H c e

T

c

3

1 2

0

ρ (17) 

where the constants c0 = 0.003 484 8, c1 = 0.003 796, c2 = 1.7526x1011, and c3 = 5315.56, T is 

the absolute air temperature in °K, P is the barometer pressure in Pa, and H is the relative 

humidity expressed as a percent. 
22

Fig. 12 is a sketch of a typical version of the device. It is comprised of two concentric tubes. The 

center tube is open; the annular space between the tubes is sealed at one end. There is a band of 

small, radial holes through the wall of the outer tube located about eight outer tube diameters 

from the sealed end. The tubes are oriented parallel to the direction of the flow with the sealed 

end facing into the flow. The other ends of the tubes are connected to instrumentation to measure 

the differential pressure between that in the center tube and that in the annular space. The center 

tube senses the total pressure that is the sum of the static ambient pressure and the pressure due 

to the motion of the fluid. The radial holes sense only the static, ambient pressure. The 

differential pressure is due to the motion of the fluid. Often, the multi-port averaging Pitot-static 

tube is an appropriate choice as the primary element for measuring the differential pressure. 

Figure 12 Sketch of a Pitot tube. 

A Pitot-Static tube provides the measurement of dynamic pressure allowing calculation of the 

flow velocity. However, a Pitot-static tube alone can not provide the air speed information. The 

airspeed is only calculated from the measured dynamic pressure (∆P) and the air density. The pst 

velocity error is mainly due to inaccurate sensing of static pressure. It is usually not possible to 

find locations for the static ports which accurately sense static pressure at all speeds and angles of

attack. The pst is a square root device, meaning the square root of the ∆P is proportional to the 

flow speed. Thus it produces a very small ∆P and a large speed uncertainty at low velocity (< 1

m/s for air). 
23

The NIST pst system is calibrated periodically with the LDA system. The sample calibration data 

for the air speed ratio, Y = VNIST / Vpst , taken in a period of a year, are shown in Fig. 13. Without 

calibration, the typical standard uncertainty of Pitot-static probes is about 1.5 %. Based on the 

calibration, a curve fitting of Y = 0.992 011 + 5.001 x 10-5 Vpst is obtained and shown as solid line 

in the Fig. 13. The deviation of the speed ratio from the fitting is shown in Fig. 14. The typical 

standard uncertainty of the calibrated pst probe is about 0.35 %. 

Traditionally, uncalibrated psts were often used as airspeed standards. The calibrated pst can also 

be used as an airspeed transfer standard. Currently, NIST uses the pst as a check standard. 

0.97

0.98

0.99

1.00

1.01

0 10 20 30 40

V pst (m/s)

V NIST

/V pst

Figure 13 NIST Pitot Static airspeed vs. NIST Standard airspeed. Data taken between 

4/12/05 and 2/1/06. Solid line is a curve fit. 
24

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

0 10 20 30 40

V pst (m/s)

100(

V NIST

/V pst-fit)

Figure 14 Deviation of the speed ratio Y for the pst probe from the curve fit. Data taken 

between 4/12/05 and 2/1/06. 

6.2. Thermal Anemometer 

A thermal anemometer (Ta) is an instrument for determining fluid velocities by measuring heat 

transfer from a small, electrically-heated wire or film sensor immersed in the fluid [14, 17]. The 

rate at which heat is removed from the sensor is related to the velocity of the fluid flowing over 

the sensor. Therefore, the fluid velocity is related to the current or voltage required to maintain 

the sensor at a constant temperature. Since the heat transfer rate depends on many details of the 

construction of the sensor, it is difficult to get an analytical expression for this relationship. 

Therefore, NIST periodically calibrates the Ta that is used as a check standard for the airspeed 

measurements. These calibrations use the LDA system. The calibration data for the air speed 

ratio, Y = VLDA / VTa are shown in Fig. 15. At constant airspeed, the typical standard deviation is 

approximately 1 %. But the nonlinearity with the speed could contribute a larger airspeed 

uncertainty of about 4 %, especially at low speeds. From the calibration data, a curve fitting 

based on the format y = (a + c x + e x2 + g x3)/(1 + b x + d x2 + h x3), where x = log(VTa) is 

obtained and shown as a solid line in the Fig. 15. The deviation of the speed ratio from the 

fitting is shown in Fig. 16. The typical standard uncertainty of the calibrated Ta probe is about 

1.2 %. 
25

0.96

1.00

1.04

1.08

1.12

0 10 20 30 40

V Ta (m/s)

V LDA / 

V Ta

Figure 15 NIST Ta airspeed vs. NIST Standard airspeed. Data taken between 4/12/05 and 

4/5/06. Solid line is a curve fit. 

-4

-2

0

2

4

0 10 20 30 40

V Ta (m/s)

100(

V LDA / 

V Ta-fit)

Figure 16 Deviation of the speed ratio Y for the Ta probe from the curve fit. Data taken 

between 4/12/05 and 4/5/06.
26

References 

[1] NIST Calibration Service Users Guide 1998, J.L. Marshall, Editor, NIST Special 

Publication 250, January 1998, National Institute of Standards and Technology, Gaithersburg, 

MD. 

[2] Mease, N.E., Cleveland, W.G., Mattingly, G.E. and Hall, J.M., "Airspeed Calibrations at 

the National Institute of Standards and Technology", Proceedings of the Measurement 

Science Conference, Anaheim, CA 1992. 

[3] Durst, F., Melling, A. and Whitelaw, J.H. "Principles and Practice of Laser-Doppler 

Anemometry", Academic Press, NY, 1976 

[4] Thompson, H. and Stevenson, W.H. "Laser Velocimetry and Particle Sizing", Hemisphere 

Publishing Corporation, NY, 1979 

[5] Bean, V.E. and Hall, J.M., "New Primary Standards for Air Speed Measurement at NIST", 

Proceeding of the 1999 NCSL Workshop and Symposium, Charlottle, NC. 

[6] Dopheide, D., Taux, G. and Narjes, L. "Accurate Flow Rate Measurements by Means of 

Laser Doppler Anemometry", 3rd Conference of the IMEKO Technical Committee on Flow 

Measurements TC9, FLOMEKO '83, September 20 - 22, 1983, pp. 51-59 

[7] Kurihara, N., Terao, Y. and Takamoto, M. "LDV Calibrator for the Air Speed Standard 

between 1.3 to 40 m/s", 5th International Symposium on Fluid Flow Measurement, Arlington, 

Virginia April 2002 

[8] Park, J.T., Cutbirth, J.M. and Brewer, W.H. "Hydrodynamic Perfomance of the Large 

Cavitation Channel", 4th ASME_JSME Joint Fluids Engineering Conference, Honolulu, 

Hawaii, July 2003 

[9] Taylor, B. N., and Kuyatt, C. E., Guidelines for Evaluating and Expressing the Uncertainty 

of NIST Measurement Results, NIST Technical Note 1297, 1994 Edition, National Institute 

of Standards and Technology, Gaithersburg, Maryland. 

[10] International Organization for Standardization (ISO), “Guide to Expression of 

Uncertainty in Measurement, Geneva, Switz., 1993 edition. 

[11] Coleman, H. W. and Steele, W. G., “Experimentation and Uncertainty Analysis for 

Engineers,” 2nd ed., John Wiley and Sons, NY, 1999. 

[12] ISO, “International Vocabulary of Basic and General Terms in Metrology, 2nd ed.,” 

International Organization of Standardization, Geneva, Switzerland, 1993. 

[13] Benedict, R.P., Fundamentals of Temperature, Pressure, and Flow Measurement, (John 

Wiley and Sons, New York, 1969), p. 245. 

[14] Ower, E. and Pankhust, R.C. The Measurement of Air Flow, 4th ed. Pergamon Press, 

1966 

[15] Dryden, H., Murnaghan, F.D., and Bateman, H., Hydrodynamics, Dover Publication, Inc., 

1956 

[16] Jaeger, K. B. and Davis, R. S., A Primer for Mass Metrology, NBS Special Publication 

700-1, November 1984, National Bureau of Standards, Gaithersburg, MD. 

[17] Melnik, W.L. and Weske, J.R. Advances in Hot-wire Anemometry, Proceedings of the 

International Symposium on Hot Wire Anemometry, 1967 
1

Appendix A: Sample Calibration Report 

REPORT OF CALIBRATION 

FOR 

AIR SPEED INSTRUMENTATION 

May 01, 2007 

Shortridge Model ADM 870C Airdata Multimeter Serial Number M03327 with Airflow 

Technical Products Pitot-Static Tube Serial Number T12 

submitted by 

ABC Scientific 

1234 ABC Drive 

Any City, Any State xxxxx 

(Purchase Order Number 1234-07 dated April 2, 2007)

The calibration of the instrument described above, was performed in the 1.5 m by 2.1 m 

rectangular test section of the NIST Dual Test Section Wind Tunnel. The instrument under test 

(IUT) was supported near the center of the tunnel in a manner that presented negligible 

interference with the flow (see Figure 1). 

The air speed was measured by the NIST Laser Doppler Anemometer (LDA). The NIST LDA 

and its support were located about 0.5 m upstream of the anemometer under test so that the flow 

measured by the LDA was not perturbed by the presence of the instrument under test. 

The temperature, pressure, and the relative humidity were measured in the test section of the 

wind tunnel during the test. Two calibration cycles were done separated by a shutdown. In each 

calibration cycle, the air speed was measured five times at each air speed set point. The output 

(VIUT) from the instrument under test was gathered visually and recorded. 

The results for the instrument presented in Table 1 and in Figure 2 were calculated using the 

means of the 10 measurements at each speed. Table 1 lists the air speed from the NIST LDA 

(VNIST), the air speed from the instrument under test (VIUT), the temperature, pressure, and 

relative humidity of the air at the wind tunnel test section, the air speed ratio (VIUT VNIST ), and 

the expanded uncertainty values for the air speed ratio The uncertainties of the instruments that 

measure temperature, pressure, and relative humidity values listed in the Table 1 are 1 K, 0.1 

kPa, and 5 % respectively. 

The air speed ratio, VIUT VNIST , is plotted in Figure 2 with error bars that represent the expanded 
NIST Test No.: 836-123456-07 Service ID Number: 19020C

Calibrated April 12-14, 2007 by Mike Hall and T. T. Yeh 2 of 34 

uncertainty calculated as described below. 

Figure 1. Instrument under test in NIST Wind Tunnel, viewed from upstream and the readout. 

 The expanded uncertainty of the calibration of the instrument under test, U , can be calculated 

by1, 2

2

R

2

Acq

2 U = k uV +u u NIST

+ , (1) 

where the quantity k is the coverage factor, taken to be 2.0 to convert the combined uncertainty 

(67 % confidence level) to the expanded uncertainty (95 % confidence level). The quantity 

 

1

B. N. Taylor and C. E. Kuyatt, Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement 

Results, NIST Technical Note 1297, National Institute of Standards and Technology, January 1993.

2

Coleman, H. W. and Steele, W. G., Experimentation and Uncertainty Analysis for Engineers, 2nd ed., John Wiley 

and Sons, Inc., 1999. 
NIST Test No.: 836-123456-07 Service ID Number: 19020C

Calibrated April 12-14, 2007 by Mike Hall and T. T. Yeh 3 of 34 

VNIST

u is the standard uncertainty of the air speed measurements made with the LDA. The 

expanded uncertainty of the LDA is ( ) ( ) 2 2.0 0036 / .0 0064 VLDA m s + and the standard 

uncertainty is half of the expanded uncertainty.3

Table 1. Shortridge Model ADM 870C Airdata Multimeter Serial Number M03327 with Airflow 

Technical Products Pitot-Static Tube Serial Number T12 in the NIST Wind Tunnel 

NIST 

Air Speed 

(VLDA) 

[m/s] 

IUT 

Output 

(VIUT) 

[m/s] 

Tunnel 

Static 

Temperature 

[K] 

Tunnel 

Static 

Pressure 

[kPa] 

Tunnel 

Relative 

Humidity 

[%] 

Airspeed 

Ratio 

VIUT/VLDA

Expanded 

Uncertainty 

[%] 

0.279 0.292 297.9 99.9 59 1.045 7.44 

0.411 0.424 297.6 99.9 62 1.030 4.09 

0.641 0.652 297.4 99.9 64 1.017 1.66 

0.837 0.849 297.4 99.9 65 1.014 1.87 

0.976 0.986 297.2 99.9 68 1.010 1.54 

1.557 1.569 296.5 99.9 69 1.008 0.96 

1.988 2.002 296.8 99.9 69 1.007 0.78 

3.129 3.146 296.6 99.9 69 1.006 0.72 

4.056 4.081 295.9 99.9 72 1.006 0.65 

5.910 5.946 296.3 99.9 69 1.006 0.67 

8.052 8.107 297.2 99.8 65 1.007 0.63 

10.20 10.27 297.0 99.8 65 1.007 0.64 

12.09 12.17 296.7 99.8 65 1.007 0.65 

14.01 14.11 296.7 99.8 65 1.007 0.64 

16.11 16.23 297.1 99.8 64 1.008 0.69 

18.05 18.20 297.5 99.8 62 1.008 0.65 

20.10 20.30 297.8 99.8 61 1.010 0.70 

 

3

Yeh, T.T.and Hall,J.M., Air Speed Calibration Service, NIST Special Publication 250-79, National Institute of 

Standards and Technology, Gaithersburg, Maryland.
NIST Test No.: 836-123456-07 Service ID Number: 19020C

Calibrated April 12-14, 2007 by Mike Hall and T. T. Yeh 4 of 34 

The quantity Acq u is the standard uncertainty of the data acquisition system and instrumentation 

used to obtain the readings from the instrument under test. In this case, the uncertainty due to 

data acquisition is less than or equal to 0.1 % and can be considered negligible. To measure the 

reproducibility4 of the test, uR, the standard deviation of the air speed ratio at each of the nominal 

air speeds was used to calculate the relative standard uncertainty (the standard deviation divided 

by the mean and expressed as a percentage). 

0.95

1.00

1.05

1.10

1.15

0 5 10 15 20

NIST Air Speed, V NIST (m/s)

VIUT / VNIST

Figure 2. Graph of current and previous calibration results.

 

4 Closeness of the agreement between the results of measurements of the same measurand carried out under changed 

conditions of measurement. Defined in the ISO, “International Vocabulary of Basic and General Terms in

Metrology, 2nd ed.,” International Organization of Standardization, Geneva, Switzerland, 1993. Reproducibility is 

herein defined as the closeness of agreement between measurements with the air speed changed and then returned 

to the same nominal value. Data collected on two different days are considered in this report.
NIST Test No.: 836-123456-07 Service ID Number: 19020C

Calibrated April 12-14, 2007 by Mike Hall and T. T. Yeh 5 of 34 

For the Director, 

National Institute of Standards and Technology 

Fluid Metrology Group 

Process Measurements Division 

Chemical Science and Technology Laboratory