• No results found

Calibration of the ultrasonic current meter UCM-40 MK II

N/A
N/A
Protected

Academic year: 2022

Share "Calibration of the ultrasonic current meter UCM-40 MK II"

Copied!
47
0
0

Laster.... (Se fulltekst nå)

Fulltekst

(1)

CALIBRATION OF THE ULTRASONIC CURRENT METER UCM-40 MK II

by

Eirik S0rgard

INSTITUTT FOR GEOFYSIKK

UNIVERSITETET I OSLO

llN§llllllUlliE iiEIPOill SIEiTIIE§

(2)

No: 78 December 1990

CALIBRATION OF THE ULTRASONIC CURRENT METER UCM-40 MK II

by

Eirik s0rgard

ABSTRACT

The velocities recorded by the current meter are calibrated, and the turbulence induced by the instrument at different orientations is investigated. The protection rings influence the vertical velocity and the measured conductivity. It is found that the wake effect induced by the conductivity cell is significant. The amount of turbulence induced by the instrument at moderate tilts obtains its smallest value when the protection rings are omitted, the wake effect of the conductivity cell is avoided, and the probe axes are positioned so that none of them become parallel with the mean flow. The conductivity cell is calibrated, and calibration curves for the salinity with and without the upper protection ring mounted are presented.

(3)

CONTENTS

1.

2.

3.

4.

5.

ABSTRACT.

CONTENTS.

...

INTRODUCTION.

INSTRUMENT .••

2.1 2.2 2.3 2.4 2.5 2.6 2.7

General description ... . Current velocity sensors.

Sound velocity sensor.

Temperature sensor •..••..

Pressure sensor •...••.

Conductivity sensor.

Tilt sensor ....•..•...

2.8 Compass . . . . CALIBRATION RESULTS.

3.1 Velocity calibration routines . . . • Calibration

3.2

3.3 Calibration of of

the the

horizontal velocity ... . ..•

vertical velocity .•...•

conductivity cell . . . . 3.4 Calibration of the

TURBULENCE INDUCED BY THE INSTRUMENT .•.•••...•

CONCLUSIONS ••.

ACKNOWLEDGEMENTS.

REFERENCES.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

TABLES ..

FIGURES.

1 2 3 4 4 4 5 6 6 6 7 7 7 7 8 10 13 15 17 17 18 19 32

(4)

1. INTRODUCTION

In the early 1970's Trygve Gytre constructed an ultrasonic current meter with the possibility of recording turbulent velocity fluctations as well as the mean flow. The instrument was developed at the Christian Michelsen Institute in Bergen.

The first versions of this instrument could only measure the velocity along two axes. Audunson and McClimans (1974) applied a field version of the instrument for turbulence measurements in a strongly stratified estuary. Later on an improved version with the possibility of measuring turbulent velocity fluctations along three axes was developed (T. Gytre, 1976).

The method of measurement was adapted by the company Simrad Optronics which developed an ultrasonic current meter (UCM-10) for commercial sale. A modified version of the instrument was calibrated by Sorgard et al. [1988], and its ability to measure turbulence was investigated. This instrument was applied by Sorgard et al. [1990] to measure the turbulent conditions in a salt wedge estuary.

The instrument has recently been rebuilt and made smaller. The probe configuration is changed and the instrument equiped with t i l t sensors. The new probe configuration gives a more accurate measure of the velocity and minimizes the turbulence produced by the instrument. This ultrasonic current meter

(UCM-40 Mk II) is produced by the new company SimTronix.

The aim of this study has been to calibrate the horizontal and vertical velocities, and to estimate the turbulence produced by the instrument itself at different velocities and orientations relative to the mean flow. The accuracy of the conductivity cell has also been investigated.

A general description of the instrument and some properties of the different sensors are given in Chapter 2. Calibration results are presented in Chapter 3, and the turbulence produced by the instrument is discussed in Chapter 4.

(5)

2. INSTRUMENT

2.1 General description

A sketch of the ultrasonic current meter (UCM-40 Mk II) is given in Figure 1. The instrument consists of a cylinder, which contains the electronics, with the sensors fixed at the lower end. It is equiped with sensors for current velocity, sound velocity, temperature, pressure, conductivity and tilt, in addition to a fluxgate compass. Two protection rings may be mounted above and below the sensors (Figure lc).

The instrument communicates with an external computer by means of a cable, the RS 232C port on the computer, and a terminal emulation program. A detailed description of the use and programming of the instrument is given in the UCM-40 Mk II reference manual. The maximum sampling frequency is 20 Hz, and the maximum data output frequency is 2 Hz. The power consumption by the instrument is 1.8 W.

In the following sections we shall give some key properties for the different sensors. These are range, resolution, response time (time spent to obtain 63% of change in value), repeatability and absolute accuracy. Some of the data are based on the calibration results discussed in Chapter 3, and some are given by the producer. The applied sensors are either sensors constructed by SimTronix, or rebuilt commercial sensors specially designed for the UCM-40 Mk II.

2.2 current velocity sensors

The current meter is based on a precise measurement of the difference in transit time between an ultrasonic wave that is propagated along a defined distance through the water, and another ultrasonic wave that is simultaneously transmitted in the opposite direction over the same distance. The transit time for a pulse along a path is dependent upon the fluid

(6)

velocity along the same path. The difference in transit time for the two pulses transmitted simultaneously in opposite directions will therefore be a function of the average current velocity along the same axis. By means of 8 crystals mounted on 4 probes {Figure 1) the current velocity along 4 directions may be measured. The three "best" directions are used to calculate the velocity along three orthogonal axes. The selection is made on the basis of which direction that is least influenced by wake effects. The wake effects are compensated for in the internal software of the instrument.

The range is programmable and may be chosen as 0-3 mjs or 0-6 mjs, with corresponding resolutions of 1 mmjs and 2 mmjs, respectively. The software enables corrections for offset values to be made. The response time is far less than the time given by the maximum sampling frequency. The standard deviation may be taken as a measure of the repeatability.

Consequently the repeatability is a function of the turbulence

i~duced by the instrument itself. Data are given in Table 3.

The calibration results seem to indicate that the absolute accuracy of the measured mean velocity is about 2%, but not less than 0.5 cmjs. This value is valid at moderate tilts

(within 20°), for the horizontal velocity both with and without mounted protection rings, and for the vertical velocity without protection rings. The rings induce wake effects, and it was found necessary to give a separate calibration curve for the vertical velocity when the rings are mounted. With this curve the absolute accuracy of the mean vertical velocity is estimated to be about 7%. However, the conductivity cell may cause wake effects that increase the uncertainty.

2.3 Sound velocity sensor

The sound velocity is measured by the time used by an ultrasonic wave to travel a defined distance through water.

(7)

The range is 1380-1580 mjs, with a resolution of 2.5 mjs, and an absolute accuracy of 5 mjs. The repeatability was found to be better than the resolution. The response time is far less than the time given by the maximum sampling frequency.

2.4 Temperature sensor

The temperature is measured by means of a platinum resistance, with range from -5

°c

to 45

°c.

The software enables correction values for each 5

°c

intervall to be given. The absolute accuracy is 0.1

°c

with a resolution of 0.01

°c.

The repeatability was found to be better than the resolution. The response time is 1 second.

2.5 Pressure sensor

The pressure is measured . with a piezoelectric crystal. The range is 0-106 Pa (0-100 m depth), with an absolute accuracy corresponding to 0.5 m in depth. However, the software enables changes in offset or atmospheric pressure to be corrected for.

The resolution corresponds to 0.04 m in depth, but the digital output values limit the resolution to 0.1 m. The repeatability was found to be better than the resolution. The response time is 0.05 s.

2.6 Conductivity sensor

The conductivity is measured by an inductive cell with a range of 2-77 mmhojcm and a resolution of 0.01 mmhojcm. The response time is 0.1 sec. The calibration results showed significant discrepancy between "true" and measured values.

linear calibration curve is suggested, and absolute accuracy should be about 0.1 psu. The was found to be 0.02 psu.

A piecewise with this the repeatability

(8)

2.7 Tilt sensor

An electrolytic t i l t sensor is applied to measure the orientation of the instrument relative to the vertical. The range is ±30° with a resolution of 1°. The absolute accuracy is within 10% of the reading and the response time is 0.3 sec.

The repeatability was found to be better than the resolution.

2.8 Compass

The flow direction is measured by means of a 3-axes fluxgate compass. The absolute accuracy is better than 2° with a resolution of 1°. The response time is 0.05 s. The repeatability was found to be better than the resolution.

3. CALIBRATION RESULTS

3.1 Velocity calibration routines

The velocity calibration took place in the tank of the company Marintek in Trondheim. The tank is about 200 m long, 10 m wide, 10 m deep through 120 m of its length, and 6 m deep through 80 m of its length. The instrument was mounted to a

lorry of the same width as the tank and of 7 m length. By dragging the instrument at different speeds through the water at rest, the measured speed as compared with the speed of the lorry and the turbulence generated by the instrument itself could be investigated. The instrument was positioned at 1 m depth to avoid effects of the surface lee-waves on the measurements.

The instrument was mounted on a steel frame which enabled runs to be made at different t i l t angles ~ and rotation angles g. ~

is defined as the angle between the mean flow and the horizontal plane of the sensor (Figure 2), and positive angles are defined when the lower end of the instrument points

(9)

towards the mean flow. g is defined as the rotation angle between a defined direction on the instrument (positive axis marked with a 'N') and the mean flow (Figure 3).

In order to calibrate both the horizontal and vertical velocity the usual corrections for compass and t i l t made by the internal software were excluded. Consequently the measured velocities Ym and ~m refer to the horizontal and vertical planes of the instrument. The vertical velocity could be measured when the instrument was tilted. "True" horizontal and vertical velocities Ye and ~e are calculated from the known speed Yt of the lorry and the t i l t angle ~:

The sampling frequency was 20 Hz, with a data output frequency of 2 Hz. The record length was typically 60 seconds for velocities below 1 mjs, and 30 seconds for velocities above 1 m/s and for the runs made without protection rings. The accuracy of the speed of the lorry is of the order 2 mmfs. ~

was measured with an accuracy of 1° or better, and g with 2°.

No runs were made before the movements in the tank had calmed down to give velocities below 1 cmjs. No significant oscillations by the instrument could be detected for speeds below 1 mjs. At speeds above 1.5 m/s some transversal movements were seen, and these movements were strongest at the speeds of 2 m/s and 2.5 mjs.

3.2 Calibration of the horizontal velocity

The calibration results obtained in Marintek's tank are presented in Table 1 and Figures 4-B. The uncertainty in the

"true" value due to the uncertainty of 1° in the t i l t angle ~

is given in Table 1. The two solid lines in the figures indicate the range of uncertainty due to both the inaccuracy

(10)

of ~ (1°) and the water movements in the tank (1 cmjs). since this uncertainty is not due to the instrument but to the set- up of the test, i t may be denoted the test uncertainty. The results may be summarized as follows:

1) There is an almost perfect match between measured and

"true" velocity with the protection rings mounted and a zero degree t i l t (~=0°) (Figure 4).

2) The conductivity cell induces wake effects when i t is positioned before the current meter relative to the mean flow direction. This is clearly seen for ~=9.5° and g=45° (Figure 5).

3) At ~=±19° the values obtained without the protection rings lay perfectly within the range of test uncertainty, while the values obtained with the protection rings are more spread but close to the range of test uncertainty (Figure 6).

4) The wake effect induced by the instrument cylinder is clearly seen at large negative t i l t angles (~=-39°,-59°)

(Figure 7, 8). These values are obtained without the protection rings mounted. There are also discrepancies between measured and "true" values when the lower end of the instrument points towards the mean flow. The response is, however, very linear in both cases.

If the instrument is oriented so that the conductivity cell is not situated in front of the current meter relative to the mean flow, there should be no need for any correction of the measured values. However, at large t i l t angles the following calibration curves are proposed (Figure 7, 8):

u = 1. 053

urn ~ = 39°

3.3 u = 1.374

urn ~ = -39°

u

=

1.123

· •

urn ~ = 59°

u = 4.221

urn ~ = -59°

where y and Yrn are "true" and measured values, respectively.

(11)

The calibration curves are estimated by means of the method of least squares. The number of data is not sufficient to give a calibration curve as a continuous function of ft.

Note that no run was made with the orientation which probably has the strongest influence of the conductivity cell (e.g.

~=-9.5°, g=45°). One would then expect the discrepancy between measured and "true" velocity to be even larger than the discrepancy observed for ft=9.5° and g=45o.

The absolute accuracy at moderate tilts (within 20°) may be estimated by the relative rest deviation. Omitting values obtained at large tilts (~=±39°,±59°) and the series influenced by the conductivity cell, the relative rest deviation was found to be 3%. However, some of the scattering may be due to the test uncertainty. The range of this uncertainty is indicated in Figures 4-8 by the two solid lines. A relative rest deviation based on the difference between measured velocity and the range of test uncertainty gives a value of 1%. The difference was set to zero if the measured value lay within the range of test uncertainty. The uncertainty in the mean horizontal velocity may lie somewhere in between these two values, and the mean value of 2% is probably a reasonable estimate of the absolute uncertainty due to the instrument. However, the producer states that the uncertainty of the mean value is not less than 0.5 cmjs.

3.3 Calibration of the vertical velocity Calibration values for the vertical Table 1 and in Figures 9-13. As

velocity are given in for the horizontal velocities, the uncertainty caused by the inaccuracy of the t i l t angle ~ (1°) is given in Table 1, and the range of uncertainty is indicated by the two solid lines in Figures 9-13. The results may be summarized as follows:

1) The measured vertical velocities are within the test

(12)

uncertainty range for positive t i l t angles (~ > 0°) when the protection rings are omitted (Figures 9 -13).

2) The measured vertical velocities are within the test uncertainty range for negativ t i l t angles (~ <

o

0) down to 200 when the protection rings are omitted (Figures 9, 10). The wake effect induced by the cylinder of the instrument is clearly seen at large negative t i l t angles (~=-39°,-59°)

(Figures 11 and 12).

3) The conductivity cell induces wake effects that may result in considerable discrepancies between measured and "true"

values (Figures 9, 10). This is the case when the conductivity cell is positioned ahead of the current meter relative to the mean flow (e.g. Q=45°, ~=9.5o).

4) The measured values are within the range of test uncertainty for positive values up to 20 cmjs when the protection rings are mounted and the t i l t is within 20°. Due to the wake effect, the corresponding negative values fall within the range of test uncertainty only down to -7 cmjs

(Figures 9 and 10).

If the conductivity cell is not situated in front of the current meter relative to the mean flow, and the t i l t is moderate (within 20°) and the protection rings omitted, there should be no need for any correction of the measured vertical velocity (Figures 9,10) . At large t i l t angles (~=±39°, ±59°) i t was found necessary to calibrate only for the negative tilts (Figures 11,12), and the following calibration curves are proposed:

3.4 w

=

1.233 • wm

w =

1.437 •

wm

where ~ and ~m are "true" and measured values, respectively.

If protection rings are mounted and the t i l t is moderate

(13)

(within 20°) 1 the following calibration curves are proposed (Figure 13) :

3.5 w

=

1. 073

wm

w

=

1.155

wm

The calibration curves are estimated by means of the method of least squares. Although the calibration factor is clearly a function of tilt, the number of data is insufficient to estimate this function. For the same reason no attempt was made to obtain a calibration curve as a function of the rotation angle g.

Note again that no run was made when the wake effects of the conductivity cell could be expected to have their strongest influence (e.g. ~=-9.5o, g=45o).

The absolute uncertainty of the mean vertical velocity is estimated by the relative rest deviation from the calibration line. By omitting the values measured without protection rings and with the conductivity cell ahead of the current meter relative to the mean flow, a value of 12 % is obtained both for positive and negative velocities. However, the test uncertainty is significant, and the value of the relative rest deviation is influenced by this uncertainty. As for the horizontal velocities, a relative rest deviation based on the distance between the measured velocity and the range of test uncertainty was calculated, and a a value of 3% was obtained.

The absolute uncertainty may lie between these values, and the mean value of 7% is probably a reasonable estimate . . However, at absolute vertical velocities below 25 cmfs all values but five fall within the range of test uncertainty when the calibration curves are applied. That is, for absolute vertical velocities below 25 cmfs, 94% of the values fall within the range of test uncertainty.

Without the protection rings mounted all values fall within the range of test uncertainty. The relative rest deviation is

(14)

3%, and since this value also incorporates the test uncertainty, the absolute accuracy is probably about 2%.

3.4 Calibration of the conductivity cell

The "true" conductivity of water samples was measured by a Yea-Kal salinometer, model 601 Mk1v. The instrument was checked by diluting standard sea water with destilled water to a known salinity. The accuracy of the experiment was found to be about 0.03 psu. The conductivity ~ of different water samples of known salinity ~ was then measured with the UCM-40 Mk II. The measuring frequency was 20 Hz with a data output

frequency of 2 Hz. The record length was about 1 minute.

Measurements were made both with and without the upper protection ring mounted, because this ring is very close to the conductivity cell (Figure 1c) and can be expected to influence the conductivity.

The results are given in Table 2 and Figures 14 and 15, and may be summarized as follows:

1) Conductivity measured with the protection ring mounted is larger than when i t is omitted.

2) The discrepancy between measured and true conductivity is large and may amount to 1 mmhofcm, corresponding to 0.8 psu.

3) There is not a linear relation between measured and ''true"

conductivity.

The salinity is calculated.by means of the Practical Salinity Scale 1978 (e.g. Lewis, 1980). However, different values for the conductivity of standard sea water at zero pressure and 15

0

c

are reported. Poisson [1980] gives a value of 42.933 mmhofcm. The value applied in the software of the UCM-40 Mk II

is 42.906 mmhofcm, which is somewhat less than the commonly used . value of 42.914 mmhofcm (Culkin and Smith, 1980). The uncertainty in this value will only affect the calculated

(15)

salinity to the second decimal, but may be corrected for by calibration.

Due to the limited number of data and the large discrepancy between measured and "true" values a calibration curve was made for the salinity

found necessary to calibration curves,

rather than for the conduct ivity. It was give two

depending

different piecewise linear on whether the uppermost protection ring was mounted or not. ~m and ~ denote measured and "true" salinity, respectively.

The calibration curve with the protection ring mounted is:

3.6 s = 0.47 + 0.844•Sm 1.60 ~ sm ~ 3.59 s = 0.05 + 0.961•Sm 3.59 ~ sm ~ 23.40 s =-2.15 + 1.055•Sm 23.40 ~ sm ~ 32.50 s =-5.79 + 1.167 •Sm 32.50 ~ sm

The calibration curve with the protection ring dismounted is:

3.7 s = 0.41 + 0.873•Sm 1. 60 ~ sm ~ 2.84 s = 0.22 + 0.940•Sm 2.84 ~ sm ~ 12.61 s =-0.36 + 0.986•Sm 12.61 ~ sm ~ 24.63 s =-2.01 + 1. 053 •Sm 24.63 ~ sm ~ 32.93 s =-7. 41 + 1.217•Sm 32.93 ~ sm

The rest deviations from the calibration curves for mounted and dismounted protection r ing were found to be 0.09 psu and 0. 07 psu, respectively, with a maximum deviation from "true"

values of 0.21 and 0.10 (Table 2) . An overall value of 0.1 psu may be taken as a representative estimate of the absolute accuracy. The repeatability was found to be 0.02 psu

(Table 2).

(16)

4. TURBULENCE INDUCED BY THE INSTRUMENT

In addition to the accuracy and resolution of the sensors, the ability of an instrument to measure turbulence depends on the measuring length scale ~ and the amount of turbulence induced by the instrument itself. The distance between the probes limits the turbulent scale which can be measured. The turbulent length scale 1 and the turbulent time scale 1 are commonly related by Taylor's hypothesis:

4. 1 A

=

Ut

where ~ is the mean velocity. Soulsby (1980] states that 90%

of the turbulence with length scale 1=6.0•~ can be measured, but only 50% of the turbulence with length scale 1=2.2•~, and no turbulence with length scale 1 ~ 1.4·~·

The distance between the probes may be taken as the measuring length scale, and consequently ~ equals 15 em. The limit of the turbulent time scale which i t becomes possible to measure at different current speeds may then be calculated by means of 4.1. The results are shown in Figure 16. The length scale ~

limits the turbulent time scale possible to measure, and the measuring frequency has to be increased with increasing current speed.

The contribution to the Reynolds stresses from the turbulence induced by the instrument itself was calculated from the same series as applied for the velocity calibration. y and y now refer to horizontal velocities in directions parallel and transversal to the mean flow, respectively. H denotes vertical velocity, positive upwards. y', y', and H' refer to perturbations from the respective mean values. The calibration curves given in Chapter 3 were applied. The results are given in Table 3.

The record length was commonly 60 seconds for velocities below 1 m{s, and 30 seconds for velocities above 1 m/s and the

(17)

series obtained without the protection rings. The transversal movements of the instrument at speeds above 1 mjs influence the correlations including y'.

An additional series with the lorry at rest was made, to estimate the turbulence from the water movements in the tank.

The results from a 1 minute mean in the most turbulent part of this series (no. 233) and the results from a 10 minutes mean

(no. 234) are presented in Table 3. The contribution from the turbulence in the tank is very small, and close to the resolution of 0.01 cm2js2.

No attempt has been made to give the turbulence induced by the instrument as a function of the rotation angle g, t i l t angle

~' and the speed of the lorry Yt• The present results are offered only as an aid to those who use the instrument for turbulence measurements. The user may then compare the measured turbulence values with the ones given in Table 3, to clearify if there is a significant difference.

However, a few general and important characteristics of the turbulence induced by the instrument may be listed:

1) The turbulence increases with increasing velocity, and increases more rapidly for velocities above 1 mjs.

2) The turbulence level is increased when the conductivity cell is situated in front of the current meter relative to the mean flow (g=45°) .

3) The turbulence level increases when one of the probe axes becomes parallel ~ith the mean flow (g=45o,135°,225°,315°).

4) The turbulence level decreases when the protection rings are omitted.

(18)

5. CONCLUSIONS

The results show that this is an accurate current meter suitable for measurements of both mean velocities and turbulence. When the protection rings are mounted, a separate calibration curve is needed for the vertical velocity (equation 3.5). The wake effect induced by the conductivity cell is significant, and the instrument should be positioned so that the conductivity cell does not become situated in front of the current meter relative to the mean flow. A large discrepancy between measured and "true'' conductivity was found, and a calibration curve for the salinity should be applied (equation 3.6 and 3.7). The upper protection ring affects the conductivity measurements and may at most give a difference corresponding to 0.1 psu. The repeatability of the sensors was commonly found to be better than or equal to the resolution, except for the velocity where the repeatability is a function of the turbulence induced by the instrument. When applying the instrument for turbulence measurements the protection rings should be omitted, the wake effect from the conductivity cell should be avoided, and the instrument should be positioned so that none of the probe axes become parallel with the mean flow. The turbulence induced by the instrument will then obtain its smallest value.

ACKNOWLEDGEMENTS

I gratefully acknowledge Terje L¢yning for his assistance during the calibration in Marintek's tank in Trondheim. I am due thanks to Eyvind Aas for valuable advices throughout this investigation, and to the Norwegian Council for Science and the Humanities for financial support to the calibration of the instrument. The study was supported by a research fellowship from the Royal Norwegian Council for Scientific and Industrial Research.

(19)

Audunson, T. and McClimans, T.A., 1974, Some observations of velocity fluctuations in a strongly stratified estuary using an ultrasonic transit-time-difference current meter, Int. Wat.

Res. Ass., Measuring and sensing methods, 1, 90-108.

Culkin, F. and Smith, N.D., Determination of the conductivity of potassium chloride solution having the same electrical conductivity, at 15

°c

and infinity frequency, as standard seawater of salinity 35.0000 °j00 (chlorinity 19.37394 °j00 ) , IEEE J . Oceanic Eng. OE-5, 1, 22-23.

Gytre, T., 1976, The use of a high sensitivity ultrasonic current meter in oceanographic data acquisition systems. The Radio and Electr. Eng., 46, 617-623.

Lewis, E.L., 1980, The practical salinity scale 1978 and its antecedents, IEEE J. Oceanic Eng., OE-5, 1, 3-8.

Poisson, A., 1980, Conductivity/ salinity/ temperature raltionship of diluted and concentrated standard seawater, IEEE J. Oceanic Eng., OE-5, 1, 41-50.

Soulsby, R.L., 1980, Selecting record length and digitization rate for near bed turbulence measurements, J. Phys. Oceanogr., 10, 208-219.

S0rgard, E., Martinsen T. and Aas, E., 1988, Calibration of an ultrasonic current meter, Rep. Inst. Geophys. Univ. Oslo, 72, 46 pp.

S0rgard, E., Martinsen T. and Aas, E., 1990, Drag coefficient at a stationary salt wedge, J. Geophys. Res., 95, 7337-7345.

(20)

Table 1. Calibration data for the horizontal and vertical velocity

g and ~ denote horizontal and vertical velocities relative to the instrument.

Indices m and g denote mean measured and "true" value, respectively. g denotes

rotation angle and ~ denotes t i l t angle. The speed of the lorry is gt and the record-length ~. Series marked with * are obtained with the protection rings dismounted.

No. a ~ T urn wm ut ue we

deg. deg. s cmfs cm/s cm/s cm/s em/a

001 225 0.0 83 11.5 0.0 11.3 11.3 ± 0.0

o.o

± 0.2 002 225

o.o

68 21.2 0.0 21.4 21.4 ± 0.0 0.0 ± 0.4 003 225 0.0 74 40.6 -0.6 41.6 41.6 ± 0.0

o. o

± 0.7 004 225 0.0 67 60.7 -0.5 61.9 61.9 ± 0.0 0.0 ± 1.1 005 225 0.0 43 80.8 -0.5 81.9 81.9 ± 0.0 0.0 ± 1.4 006 225 0.0 39 100.7 -0.5 101.8 101.8 ± 0.0

o.o

± 1.8 007 225

o.o

24 150.7 -0.8 152.5 152.5 ± 0.0

o.o

± 2.7 008 225 0.0 25 201.1 0.0 202.6 202.6 ± 0.0 0.0 ± 3.5 009 45

o.o

118 10.5 -0.2 9.7 9.7 ± 0.0 0.0 ± 0.2 010 45 0.0 69 20.3 -0.1 19.7 19.7 ± 0.0 0.0 ± 0.3 011 45

o.o

74 40.1 -0.7 39.8 39.8 ± 0.0 0.0 ± 0.7 012 45 0.0 65 60.2 -0.6 59.9 59.9 ± 0.0 0.0 ± 1.0 013 45 0.0 66 79.9 -1.2 79.8 79.8 ±

o. o o.o

± 1.4 014 45 0.0 38 99.6 -1.5 99.5 99.5 ± 0.0

o.o

± 1.7 015 45 0.0 26 148.9 -2.2 149.9 149.9 ± 0.0 0.0 ± 2.6 016 45 0.0 23 201.3 -4.5 199.7 199.7 ± 0.0 0.0 ± 3.5 017 195 0.0 53 11.6 0.2 11.3 11.3 ± 0.0

o.o

± 0.2 018 195 0.0 63 22.2 0.2 21.4 21.4 ± 0.0 0.0 ± 0.4 019 195 0.0 69 42.3 0.5 41.5 41.5 ± 0.0 0.0 ± 0.7 020 195 0.0 64 61.6 0.8 61.9 61.9 ± 0.0

o. o

± 1.1 021 195 0.0 56 80.2 1.0 79.8 79.8 ±

o.o

0.0 ± 1.4 022 195

o.o

30 102.1 1.3 101.7 101.7 ± 0.0 0.0 ± 1.8 023 195 0.0 35 152.4 2.3 152.4 152.4 ± 0.0

o.o

± 2.7 024 195 0.0 19 200.1 1.2 202.5 202.5 ± 0.0 0.0 ± 3.5 025 15

o.o

62 10.1 -0.3 9.6 9.6 ± 0.0

o.o

± 0.2 026 15 0.0 62 19.4 0.0 19.7 19.7 ±

o.o

0.0 ± 0.3 027 15 0.0 66 39.5 -0.1 39.8 39.8 ± 0.0 0.0 ± 0.7 028 15

o.o

63 58.8 -0.4 59.9 59.9 ± 0.0

o.o

± 1.0 029 15 0.0 65 77.6 -0.8 79.8 79.8 ± 0.0 0.0 ± 1.4 030 15 0.0 34 98.6 0.4 99.5 99.5 ± 0.0

o. o

± 1.7 031 15

o.o

33 147.2 0.6 149.9 149.9 ± 0.0

o.o

± 2.6 032 15 0.0 17 195.6 -2.4 199.8 199.8 ± 0.0

o.o

± 3.5 033 165

o.o

61 11.6 0.1 11.3 11.3 ± 0.0 0.0 ± 0.2 034 165 0.0 66 21.8 0.0 21.4 21.4 ± 0.0

o.o

± 0.4 035 165 0.0 65 42.4 0.4 41.5 41.5 ± 0.0

o.o

± 0.7 036 165 0.0 67 62.3 0.5 61.8 61.8 ± 0.0 0.0 ± 1.1 037 165 0.0 72 82.4 0.9 81.8 ·81.8 ± 0.0

o.o

± 1.4 038 165 0.0 33 103.0 2.0 101.8 101.8 ± 0.0

o.o

± 1.8 039 165 0.0 23 153.6 3.3 152.4 152.4 ± 0.0

o.o

± 2.7 040 165 0.0 32 202.4 3.4 202.6 202.6 ± 0.0 0.0 ± 3.5

(21)

No. a ~ T um wm ut ue we

deg. deg. a em/a emjs em/a em/s em/a

041 345 0.0 74 9.4 -0.2 9.7 9.7 ± 0.0 0.0 ± 0.2 042 345 0.0 65 9.2 0.0 19.7 19.7 ± 0.0 0.0 ± 0.3 043 345 0.0 66 39.6 0.3 39.8 39.8 ± 0.0 0.0 ± 0.7 044 345 0.0 63 59.5 0.2 60.0 60.0 ± 0.0 0.0 ± 1.0 045 345 0.0 86 78.9 0.3 79.9 79.9 ± 0.0 0.0 ± 1.4 046 345 o.o 33 98.7 0.6 99.7 99.7 ± 0.0 0.0 ± 1.7 047 345 0.0 26 149.9 1.6 150.1 150.1 ± 0.0 0.0 ± 2.6 048 345 0.0 33 198.8 -0.2 200.1 200.1 ± 0.0 0.0 ± 3.5 049 135 o.o 63 12.0 -0.4 11.3 11.3 ± 0.0 0.0 ± 0.2 050 135 0.0 70 22.2 -0.1 21.4 21.4 ± 0.0 0.0 ± 0.4 051 135 0.0 68 42.3 -o.5 41.5 41.5 ± o.o 0.0 ± 0.7 052 135 0.0 68 63.1 0.3 61.8 61.8 ± 0.0 0.0 ± 1.1 053 135 0.0 70 83.1 0.0 81.8 81.8 ± 0.0 0.0 ± 1.4 054 135 o.o 34 104.1 3.0 101.7 101.7 ± 0.0 0.0 ± 1.8 055 135 0.0 33 154.1 4.6 152.4 152.4 ± 0.0 o.o ± 2.7 056 135 0.0 21 204.6 3.3 202.5 202.5 ± 0.0 0.0 ± 3.5 057* 135 0.0 18 254.6 -0.5 253.2 253.2 ± 0.0 0.0 ± 4.4 058* 135 0.0 20 307.3 -4.3 303.2 303.2 ± 0.0 0.0 ± 5.3 059 315 0.0 65 9.8 -0.1 9.7 9.7 ± o.o o.o ± 0.2 060 315 0.0 64 20.5 -0.2 19.7 19.7 ± 0.0 0.0 ± 0.3 061 315 0.0 67 40.9 -0.7 39.8 39.8 ± 0.0 0.0 ± 0.7 062 315 o.o 66 60.9 0.4 59.9 59.9 ± 0.0 0.0 ± 1.0 063 315 0.0 86 80.6 o.o 79.8 79.8 ± 0.0 0.0 ± 1.4 064 315 0.0 38 101.3 0.1 99.6 99.6 ± 0.0 0.0 ± 1. 7 065 315 0.0 25 151.4 0.9 150.0 150.0 ± 0.0 0.0 ± 2.6 066 315 0.0 33 200.8 -2.2 199.9 199.9 ± 0.0 0.0 ± 3.5 067* 315 0.0 13 249.8 -7.3 250.1 250.1 ± o.o 0.0 ± 4.4 068* 315 0.0 21 403.2 -19.0 400.5 400.5 ± 0.1 0.0 ± 7.0 069 225 -9.5 62 12.7 -1.3 11.3 11.1 ± 0.0 -1.9 ± 0.2 070 225 -9.5 65 22.3 -2.8 21.5 21.2 ± 0.1 -3.5 ± 0.4 071 225 -9.5 69 42.1 -6.7 41.6 41.0 ± 0.1 -6.9 ± 0.7 072 225 -9.5 63 62.3 -8.0 61.9 61.1 ± 0.2 -10.2 ± 1.1 073 225 -9.5 61 81.7 -10.7 81.9 80.8 ± 0.3 -13.5 ± 1.4 074 225 -9.5 31 102.9 -12.5 101.7 100.3 ± 0.3 -16.8 ± 1.7 075 225 -9.5 17 152.5 -19.3 152.4 150.3 ± 0.5 -25.2 ± 2.6 076 225 -9.5 27 254.8 -29.8 253.2 249.7 ± 0.7 -41.8 ± 4.3 077 45 9.5 68 9.6 0.9 9.7 9.6 ± 0.0 1.6± 0.2 078 45 9.5 67 18.9 2.3 19.7 19.4 ± 0.0 3.3 ± 0.3 079 45 9.5 64 37.5 5.2 39.8 39.3 ± 0.2 6.6 ± 0.7 080 45 9.5 64 56.7 6.2 60.0 59.2 ± 0.2 9.9 ± 1.0 081 45 9.5 69 73.7 7.8 79.8 78.7 ± 0.2 13.2 ± 1.3 082 45 9.5 30 92.2 10.4 99.5 98.1 ± 0.3 16.4 ± 1.7 083 45 9.5 18 137.7 15.6 149.9 147.8 ± 0.4 24.7 ± 2.6 084 45 9.5 26 245.8 30.3 250.1 246.7 ± 0.8 41.3 ± 4.3

(22)

No. a p T um wm ut ue we

deg. deg. a em/a em/a em/a em/a em/a

085 195 -9.5 63 11.1 -1.3 11.3 11.1 ± 0.0 -1.9 ± 0.2 086 195 -9.5 63 21.1 -3.0 21.4 21.1 ± 0.1 -3.5 ± 0.4 087 195 -9.5 64 39.5 -6.3 41.5 40.9 ± 0.1 -6.8 ± 0.7 088 195 -9.5 65 58.9 -8.7 61.8 61.0 ± 0.2 -10.2 ± 1.1 089 195 -9.5 66 77.6 -10.7 81.8 80.7 ± 0.3 -13.5 ± 1.4 090 195 -9.5 30 97.8 -12.9 101.7 100.3 ± 0.3 -16.8 ± 1.7 091 195 -9.5 23 147.4 -19.7 152.4 150.3 ± 0.5 -25.2 ± 2.6 092 195 -9.5 25 195.6 -24.7 202.5 199.7 ± 0.6 -33.4 ± 3.5

093 15 9.5 64 9.4 1.1 9.6 9.5 ±

o.o

1.6± 0.2

094 15 9.5 64 18.9 2.3 19.7 19.4 ±

o. o

3.3 ± 0.3 095 15 9.5 63 38.8 4.6 39.7 39.2 ± 0.1 6.6 ± 0.7 096 15 9.5 64 57.9 7.7 59.9 59.1 ± 0.2 9.9 ± 1.0 097 15 9.5 78 77.3 10.7 79.8 78.7 ± 0.2 13.2 ± 1.3 098 15 9.5 33 97.7 15.0 99.5 98.1 ± 0.3 16.4 ± 1.7 099 15 9.5 22 146.0 22.1 149.9 147.8 ± 0.4 24.7 ± 2.6 100 15 9.5 24 193.6 24.6 199.7 197.0 ± 0.6 33.0 ± 3.4 101 165 -9.5 63 11.4 -1.8 11.3 11.1 ± 0.0 -1.9 ± 0.2 102 165 -9.5 65 21.0 -3.1 21.4 21.1 ± 0.1 -3.5 ± 0.4 103 165 -9.5 65 40.1 -6.5 41.5 39.9 ± 0.1 -6.9 ± 0.7 104 165 -9.5 76 60.1 -8.6 61.8 61.0 ± 0.2 -10.2 ± 1.1 105 165 -9.5 75 79.2 -10.9 81.8 80.7 ± 0.3 -13.5 ± 1.4 106 165 -9.5 31 100.7 -12.3 101.7 100.3 ± 0.3 -16.8 ± 1.7 107 165 -9.5 27 150.5 -17.8 152.4 150.3 ± 0.5 -25.2 ± 2.6 108 165 -9.5 33 197.3 -23.0 202.5 199.7 ± 0.6 -33.4 ± 3.5 109 345 9.5 63 9.2 1.0 9.7 9.6 ± 0.0 1.6 ± 0.2 110 345 9.5 64 19.2 2.5 19.7 19.4 ± 0.0 3.3 ± 0.3 111 345 9.5 66 39.8 5.4 39.8 39.3 ± 0.1 6.6 ± 0.7 112 345 9.5 66 58.3 8.7 60.0 59.2 ± 0.2 9.9 ± 1.0 113 345 9.5 63 77.1 11.8 79.8 78.7 ± 0.2 13.2 ± 1.3 114 345 9.5 32 97.2 15.4 99.6 98.2 ± 0.3 16.4 ± 1.7 115 345 9.5 32 146.2 23.1 150.0 147.9 ± 0.4 24.7 ± 2.6 116 345 9.5 32 194.1 27.4 200.0 197.3 ± 0.6 33.0 ± 3.4 117 135 -9.5 63 11.6 -1.8 11.3 11.1 ±

o.o

-1.9 ± 0.2

118 135 -9.5 67 21.3 -3.4 21.4 21.1 ± 0.1 -3.5 ± 0.4 119 135 -9.5 68 42.3 -6.4 41.5 39.9 ± 0.1 -6.9 ± 0.7 120 135 -9.5 67 60.3 -9.1 61.8 61.0 ± 0.2 -10.2 ± 1.1 121 135 -9.5 72 79.9 -10.4 81.8 80.7 ± 0.3 -13.5 ± 1.4 122 135 -9.5 39 105.0 -13.9 101.7 100.3 ± 0.3 -16.8 ± 1.7 123 135 -9.5 26 155.5 -20.2 152.4 150.3 ± 0.5 -25.2 ± 2.6 124 135 -9.5 20 204.7 -28.0 202.5 199.7 ± 0.6 -33.4 ± 3.5

Referanser

RELATERTE DOKUMENTER

In April 2016, Ukraine’s President Petro Poroshenko, summing up the war experience thus far, said that the volunteer battalions had taken part in approximately 600 military

This report documents the experiences and lessons from the deployment of operational analysts to Afghanistan with the Norwegian Armed Forces, with regard to the concept, the main

Based on the above-mentioned tensions, a recommendation for further research is to examine whether young people who have participated in the TP influence their parents and peers in

The particle size distributions were characterized by the means of a disc centrifuge, and the effect of dispersion time, power density, and total energy input, for both bath

From the above review of protection initiatives, three recurring issues can be discerned as particularly relevant for military contributions to protection activities: (i) the need

Overall, the SAB considered 60 chemicals that included: (a) 14 declared as RCAs since entry into force of the Convention; (b) chemicals identied as potential RCAs from a list of

An abstract characterisation of reduction operators Intuitively a reduction operation, in the sense intended in the present paper, is an operation that can be applied to inter-

The political and security vacuum that may emerge after conflict can be structured to be exploited by less than benign actors such as warlords, criminal networks, and corrupt