With the arrival of highly accurate multi-port pressure measurement systems, conditions that previously did not affect overall system accuracy must now be scrutinized closely. Errors caused by elevation differences between pressure sensing elements and model pressure taps can be quantified and corrected. With multi-port pressure measurement systems, the sensing elements are connected to pressure taps that may be many feet away. The measurement system may be at a different elevation than the pressure taps due to laboratory space or test article constraints. This difference produces a pressure gradient that is inversely proportional to height within the interface tube. The pressure at the bottom of the tube will be higher than the pressure at the top due to the weight of the tube's column of air. Tubes with higher pressures will exhibit larger absolute errors due to the higher air density. The above effect is well documented but has generally been taken into account with large elevations only. With error analysis techniques, the loss in accuracy from elevation can be easily quantified. Correction factors can be applied to maintain the high accuracies of new pressure measurement systems

Panek, Joseph W.

Sorrells, Mark R.

English

NASA Technical Reports Server

NASA Technical Memorandum 107240
i--
Elevation Correction Factor for Absolute
Pressure Measurements
Joseph W. Panek and Mark R. Sorrells
Lewis Research Center
Cleveland, Ohio
Prepared for the
42nd International Instrumentation Symposium
cosponsored by the Aerospace Industries and Test Measurement
Divisions of the Instrument Society of America
San Diego, Califomia, May 5-9, 1996
National Aeronautics and
Space Administration
https://ntrs.nasa.gov/search.jsp?R=19960028558 2020-06-16T03:59:41+00:00Z
Trade names or manufacturers' names are used in this report for identification
only. This usage does not comtitute an official endorsement, either expressed
or implied, by the National Aeronautics and Space Administration.
Elevation Correction Factor for Absolute Pressure
Measurements
Joseph W. Panek
Electrical Operations Engineer
NASA - Lewis Research Center
Cleveland, OH 44135
Mark R. Sorrells
Electrical Operations Engineer
NASA - Lewis Research Center
Cleveland, OH 44135
KEYWORDS
Pressure Measurement, Elevation, Accuracy, Error Analysis
ABSTRACT
With the arrival of highly accurate multi-port pressure measurement systems, conditions that previously
did not affect overall system accuracy must now be scrutinized closely. Errors caused by elevation
differences between pressure sensing elements and model pressure taps can be quantified and corrected.
With multi-port pressure measurement systems, the sensing elements are connected to pressure taps that
may be many feet away. The measurement system may be at a different elevation than the pressure taps
due to laboratory space or test article constraints. This difference produces a pressure gradient that is
inversely proportional to height within the interface tube. The pressure at the bottom of the tube will be
higher than the pressure at the top due to the weight of the tube's column of air. Tubes with higher
pressures will exhibit larger absolute errors due to the higher air density.
The above effect is well documented but has generally been taken into account with large elevations
only. With error analysis techniques, the loss in accuracy from elevation can be easily quantified.
Correction factors can be applied to maintain the high accuracies of new pressure measurement systems.
INTRODUCTION
Thefollowing shallbepresented:
• thetheoreticalanalysiswhichproducestheappropriatecorrectionfactorbasedonelevation
(assumingconstantemperature);
• theeffectof air temperatureuponthecorrectionfactor;
• datawhich validatesthe elevation correction factor;
• the effect upon the overall accuracy of a typical PSI System 8400 with 15 PSI rackmount
modules calibrated by a 15 PSIA Pressure Calibration Unit (PCU).
THEORETICAL ANALYSIS
The following derivation shows the variation of pressure with elevation in the earth's atmosphere. It is
assumed that air density is proportional to air pressure, the change in gravity is negligible and the air
temperature is constant at all elevations. Rer.J (Some derivation values were changed for consistency
throughout the paper.)
The following equation shows how pressure varies with elevation in a fluid in static equilibrium.
dP
- pg
ay
dP
ay is the change in pressure per change in elevation while -Pg is the weight density of
air (air density * gravity). As the elevation, y, increases, the pressure, P, decreases.
At a constant temperature, air density, p, is proportional to air pressure, P, and we have
P _ P
Po Po
where Po and Po are known values of density and pressure.
2
Substituting dP _ -g9o-_-, sothat dP _ -g-_--dy.
dy o P o
Integrating this from the value Po at the elevation y = 0 to the value P at an elevation y, we obtain
P Po - (polPo)y
ln - g--y P = P exp
p p o
o o or
At 20 DegC,
g
9.80 m/s 2, Po = 1.205 kg/m 3 and Po = 1.01325x105 Pa,
so that POg_ =
P
O
4 _1 6 1
1.16546x10- m = 35.523x10- fi-.
For any measured pressure, Po, the actual pressure, P (at elevation y) can be found by
P = Poexp
-35.523x10-6y
Substituting, P = PoEy where Ey = exp
-35.523x10-6y
This gives us an elevation correction factor, Ey which can be applied to any measured pressure, Po, to
correct for a positive or negative elevation, y, between the transducer and the model pressure tap with
applied pressure, P at 20 DegC.
TEMPERATURE EFFECTS ON THE ELEVATION CORRECTION FACTOR
It is safe to assume constant gravity for a small change in elevation. The influence of temperature on the
elevation correction factor is shown in the following examples for a 20 Ft elevation.
The density of air, p, decreases with increasing temperature. The density of air is 1.293 kg/m 3 at 0 DegC
and 0.946 kg/m 3 at 100 DegC. The density of air, P0. at 14.696 Psia, for any temperature, T, can be
calculated from the following equation. Ref4
1.293 kg/m 3
P0 = (1 +(0.00367. T))
The following chart and table show the change in air density with temperature.
Temp Air Density
DegC kg/m^3 Air Density at 101.325 kPa (14.696 Psia)
-200 4.8609 5.1 T ........ -...................
8
-180 3.8097 4 6 _- ...... J ......... :......... ', ........ ; ......... :......... ',........ -;........
-160 3.1323
-140 2.6594 4.1 _-- -\- - - - - - ; ......... :......... ; ........ -' ......... ',......... : ........ ; ........
-120 2.3106
-100 2.0427 ,_" 3.6 -r ....... -, ......... ,......... , ........ , , , ,* • t 2 ......... _......... t ........ ..= ........
-80 1.8304
......!.........: ......:...............: ......:..............
. : : : _ • . ^
-20 1.3954 2.6 ........ _ ....... :......... _ ........ -,,.....0 1.2930
20 1.2046 _ ii i
40 1.1275 _ 2.1 ........ ! ........ ;......... i ........ i ......... ;......... ; ........ " ........
60 1.0597 1.6 ....................
80 0.9995
_ooo_,_ _ ........i.........::.........::........:...... _ ..............."........
120 0.8977 f140 0.8541 0.6 ; ;, ; ,,, ;,,, ; i ;
160 0.8146 -200 -150 -100 -50 0 50 100 150
180 0.7786 Temp. (DegC)
200 0.7457
200
Assuming Po = 1.01325 xl0 s Pa and g = 9.8 m/s:,
For po = 1.293 kg/m 3(0 DegC),
PO 4 _I 6 I
g-- = 1.25057x10- m = 38.118x10- ft-.
P
O
The pressure correction, Ey is Ey = exp -(38"118x 1°-6"2°) = 0.999238.
4
For po = 0.946 kg/m 3 (100 DegC),
Po 4 _1
g-- = 0.91496x10- m
P
6 I
= 27.888x10- fi-.
The pressure correction, Ey is -(27.888x I0-6"20) =Ey = exp 0.999442.
At 0 DegC, the correction factor, Ey, equals 0.999238. (-0.076%)
At 100 DegC, the correction factor, Ey, equals 0.999442. (-0.056%)
At 20 DegC, the correction factor, Ey, equals 0.999290. (-0.071%)
Assuming that Po is 14.7 PSIA, a temperature change from 0 to 100 DegC (32 to 212 DegF) would cause
an additional 0.020% (0.0029 PSIA) error. A change from 0 to 20 DegC (32 to 68 DegF) would add an
additional 0.005% (0.0008 PSIA).
To determine the elevation deviation needed to induce the same 0.020% correction factor change as the
100 DegC temperature shift,
0.99980 = exp -38'llSxlO-6*y
ln0.99980 = 38.118x10-6*y
-0.0002000
y = = 5.25fi
-38.118x10 -6
For _ 20 ft elevation differential, an additional 5.25 ft variation in elevation produces the same error as a
temperature change from 0 to 100 DegC (32 to 212 DegF). For many applications, temperature effects
upon pressure can be ignored since elevation produces the dominant error.
DATA TO VALIDATE THE THEORY
Data was acquired at various pressures and elevations by a 19 PSIA PSI Sonix pressure gage (Reference
Pressure) and a 19 PSIA Ruska pressure gage (Elevation Pressure). The ambient temperature was
704-5 DegF. The two gages are accurate to 4-0.003 PSIA but have much higher repeatability (approx-
imately 4-0.001 PSIA). Biases between the two standards were measured at the four measured pressures•
These were subtracted from the elevation pressure so that a true comparison could be made of the
elevation effects. Error bars of+0.001 PSIA are shown on the data points.
It can be seen that the elevation effects are greater at higher pressures due to the higher air density.
0.001
•_ 0.000
_mc_o.O01
_0.002
g
gl
_o.oo3
n
Elevation Effects on 4 Psia Air
+
T i l -- Pressure Change (Calc.)
...-I-.-i--L • PressureChange (Actual)]..
........ : ....... ; ........ i. .....
........ , ........ J ........ J ........
-0.004 1 i i =
0 5 10 15 2O 25
Elevation (Ft)
Elevation Effects on 14.3 Psia Air
0+002 .
I_ i I- Pressure Change (Calc.)
¢.0002 1_.J • Pressure Change (Actual) .
6-°°°_ ............. _.....
1 i .'--.q i
-0.olo _....... : ..... ; ...... ".... _---- _.--
+ t i
-0 014 , ,
0 5 10 15 20 25
Elevation (Ft)
0.002
. 0.000
-0.002
t-
O
-0004
gl
gl
-ooo6
[Z
-0.008
Elevation Effects on 9 Psia Air
! I --Pressure Change (Calc.)
_t.. : Pro::S::: :h.:n:: (:c:::,: . . .
:!iiiiii :::
i , , , ,
5 10 15 20 25
Elevation (Ft)
0.004
Elevation Effects on 18 Psia Air
, , I I
'=_" . it -- Pressure Change (Calc.) I
---.tV_r_0.000 _ ......... • Pressure Change (Actual) ["
-" -0.004 ........ • ...... ., ........ , ........ • ......
8
__ -0.008 ....... , ....... ., ......................
-0.o12 ....... ; ....... -:........ :..... :- ......
n
-0,o16 ....
0 5 10 15 20 25
Elevation (Ft)
This data matches the theoretical curves to within 4.0.001 PSIA; the repeatability of our instrumentation.
This error is not significant for a PSI System 8400 with 15 PSI Rackmount Modules calibrated with a 15
PSIA Digiquartz PCU.
6
ERROR ANALYSIS OF A PSI SYSTEM 8400 AT VARIOUS ELEVATIONS
An error analysis has been done on the PSI System 8400 to determine system performance. Samples of
typical analyses are shown with 0 ft, 20 _ and 40 ft elevations from the system to the model pressure
ports. The PCU has an elevation difference of 6 ft from the rackmount modules. The largest error
occurs at the highest measured pressure, 15 PSIA. The following equations show the method used to
calculate the uncertainty. Ref2
URss = _ B'2 + _(2"S'/2N t
URSS = +Uncertainty (PSI)
N = Number of Data Sets Averaged
B' = Root-Sum-Square of all Bias (fixed) Errors
S' = Root-Sum-Square of all Precision (random) Errors
The following tables show all bias and precision errors as well as the final uncertainties.
For a system at the same elevation as the model pressure ports, the uncertainty is ± 0.05% of FS.
I DIGIQUARTZ :
Range 15 PSI
Temp Change from Calib. 10.0 DegF
Calibration Lab Error 0.0120 % FS
, MODULE
Range 15 PSI
Serial Number (Ignore B) 2037
Temp Change between Calibs. 1.5 DegF
Scale Factor 1000 Cnts/PSI
ThermalZero Shift 0.02 % FS
Thermal Span Shift 0.02 % FS
, SYSTEM
Number of Data Sets Averaged 8
Elevation from PCU to Modules 6.00 Feet
Elevation from Module to Ports 0.00 Feet
Highest Measured Pressure 15.00 PSI
DIGIQUARTZ ERRORS : ...... : I
i
Cal Lab Calibration Error B1 0.0018 PSI
Temp Error B2 0.0007 PSI
Time Base Error B3 0.0008 PSI
Curve Fit Error B4 0.0008 PSI
Repeatibility $1 0.0008 PSI
Hysteresis $2 0.0008 PSI
;ounter Resolution $3 0.0001 PSI
RACKMOUNT MOD. ERRORS, _; :. ;_
Repeatability $4 0.0015 PSI
Hysteresis $5 0.0008 PSI
ThermaIZero Shift B6 0.0045 PSI
Thermal Span Shift B7 0.0045 PSI
Non-Linearity Curve Fit Error B8 0.0008 PSI
ND Converter Resolution $6 0.0005 PSI
Computer Output Resolution $7 0.0010 PSI
SP/Module Elev. Span Error B9 0.0032 PSI
Module/Port Elev. Span Error B10 0.0000 PSI
I TOTAL DQ ERROR
Bias Errors
Random Errors
+1- Uncertainty (PSI)
+1- Uncertainty
ooo  PS;.......I
0.0011 PSI I
0.0023 PSI I
0.0154 % FS I
otal Bias Errors B' 0.0075 PSI ITotal Random Errors S' 0.0023 PSI
I+1- Uncertainty (PSI) 0.0075 PSI I/- rt i t (% Module FS) . 501%FS I
For a system with a 20 ft elevation to the model pressure ports, the uncertainty is 4- 0.087% of FS (an
increase of 74% in the uncertainty).
I .... DIGIQUARTZ . '
Range 15 PSI
Temp Change from Calib. 10.0 DegF
Calibration Lab Error 0.0120 % FS
,;, _ MODULE
Range 15 PSI
Serial Number (Ignore B) 2037
Temp Change between Calibs. 1.5 DegF
Scale Factor 1000 Cnts/PSI
ThermaIZero Shift 0.02 % FS
Thermal Span Shift 0.02 % FS
.... SYSTEM , ,
INumber of Data Sets Averaged 8
I Elevation from PCU to Modules 6.00 Feet
IElevation from Module to Ports 20.00 Feet
IHighest Measured Pressure 15.00 PSI
',:,_'_ DIGIQUARTZ ERRORS ........
Cal Lab Calibration Error B1 0.0018 PSI
TempError B2 0.0007 PSI
Time Base Error B3 0.0008 PSI
Curve Fit Error B4 0.0008 PSI
Repeatibility $1 0.0008 PSI
Hysteresis $2 0.0008 PSI
Counter Resolution $3 0.0001 PSI
RACKMOUNT MOD. ERRORS , ......
Repeatability $4 0.0015 PSI
Hysteresis $5 0.0008 PSI
Thermal Zero Shift B6 0.0045 PSI
Thermal Span Shift B7 0.0045 PSI
Non-Linearity Curve Fit Error B8 0.0008 PSI
ND Converter Resolution $6 0.0005 PSI
Computer Output Resolution $7 0.0010 PSI
SPIModule Elev. Span Error B9 0.0032 PSI
Module/Port Elev. Span Error B10 0.0107 PSI
I TOTAL DQ ERROR
Bias Errors
Random Errors
+/- Uncertainty (PSI)
+/- Uncertainty
0.0022 PSI
0.0011 PSI
0.0023 PSI
0.0154 % FS
Total Bias Errors B' 0.0130 PSI
Total Random Errors S' 0.0023 PSI
+/- Uncertainty (PSI)I tainty % Module FS) 0.0130 PSI I869 %FS
For a system with a 40 ft elevation to the model pressure ports, the uncertainty is 4- 0.15% of FS. This
error is three times larger than a pressure measurement system that has the model on the same level.
, DIGIQUARTZ
Range 15 PSI
Temp Change from Calib. 10.0 DegF
Calibration Lab Error 0.0120 % FS
,; : , ' : : MODULE ;
Range 15 PSI
Serial Number (Ignore B) 2037
Temp Change between Calibs. 1.5 DegF
Scale Factor 1000 CntslPSI
Thermal Zero Shift 0.02 % FS
Thermal Span Shift 0.02 % FS
:_ _' , ::,_,:_ SYSTEM
Number of Data Sets Averaged
Elevation from PCU to Modules
Elevation from Module to Ports
Highest Measured Pressure
8
6.00 Feet
40.00 Feet
15.00 PSI
i TOTAL DQ ERROR
Bias Errors
Random Errors
+/- Uncertainty (PSI)
+/- Uncertainty
0.0022 PSI
0.0011 PSI
0.0023 PSI
0.0154 % FS
DIGIQUARTZ ERRORS ..... , : : ":_:_"_:
Cal Lab Calibration Error B1 0.0018 PSI
Temp Error B2 0.0007 PSI
Time Base Error B3 0.0008 PSI
Curve Fit Error B4 0.0008 PSI
Repeatibility $1 0.0008 PSI
Hysteresis $2 0,0008 PSI
Counter Resolution $3 0.0001 PSI
RACKMOUNT MOD. ERRORS : ...... ': .......
Repeatability $4 0.0015 PSI
Hysteresis $5 0.0008 PSI
ThermaIZero Shift B6 0.0045 PSI
Thermal Span Shift B7 0.0045 PSI
Non-Linearity Curve Fit Error B8 0.0008 PSI
ND Converter Resolution $6 0.0005 PSI
Computer Output Resolution $7 0.0010 PSI
SP/Module Elev. Span Error B9 0.0032 PSI
Module/Port Elev. Span Error B10 0.0213 PSI
Total Bias Errors B' 0.0226 PSI ITotal Random Errors S' 0.0023 PSI
+/- Uncertainty (PSI) 0.0226 PSI I/- rt i t (% Module FS) .150 %FS I
8
CONCLUSIONS
It has been shown that the elevation between a transducer and the test article pressure port causes an
error in the absolute pressure measurement. The derivation for an elevation correction factor has been
shown and proven to be valid from the acquired data. Temperature effects have been presented. The
effects upon the accuracy of a typical PSI System 8400 Pressure Measurement System have been
demonstrated.
This can also be used to correct errors from elevation differences from a pressure standard to a
transducer being calibrated. This would be the case for a PSI System 8400 using remote miniature ESP
Modules. (The modules would be on the same elevation as the pressure taps with the pressure calibrator
at a different elevation.)
This information can be easily integrated into future testing or be used to re-process old data to yield
higher accuracy pressure measurements.
9
REFERENCES
1. Physics, Parts I and II; David Halliday and Robert Resnick, Copyright 1978, John Wiley and Sons,
New York, NY.
2. NASA Contractor Report 198361, AIAA-95-3072, "A PC Program for Estimating Measurement
Uncertainty for Aeronautics Test Instrumentation"; Philip Z. Blumenthal, July, 1995.
3. The Bell and Howell Pressure Transducer Handbook; CEC/Instruments Division, Copyright 1974,
Bell and Howell Company.
4. CRC Handbook of Chemistry and Physics, 66th Edition 1985-1986; Editor-in-Chief, Robert C.
Weast, Ph.D., Copyright 1985, CRC Press, Inc., Boca Raton, Florida.
ACKNOWLEDGMENT
We would like to thank Phil Blumenthal for his assistance with the error analysis portion of this paper.
10

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1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED
June 1996 Technical Memorandum
4. TITLE AND SUBTITLE
Elevation Correction Factor for Absolute Pressure Measurements
6. AUTHOR(S)
Joseph W. Panek and Mark R. Sorrells
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)
National Aeronautics and Space Administration
Lewis Research Center
Cleveland, Ohio 44135-3191
9. SPONSORING/MONITORINGAGENCYNAME(S)ANDADDRESS(ES)
National Aeronautics and Space Administration
Washington, D.C. 20546-0001
5. FUNDING NUMBERS
WU-505--62-82
8. PERFORMING ORGANIZATION
REPORT NUMBER
E- 10285
10. SPONSORINGRAONITO_NG
AGENCY REPORT NUMBER
NASA TM- 107240
11. SUPPLEMENTARY NOTES
Prepared for the 42nd International Instrumentation Symposium cosponsored by the Aerospace Industries and Test Measurement
Divisions of the Instrument Society of America, San Diego, California, May 5-9, 1996. Responsible person, Joseph W. Panek,
organization code 2850, (216) 433-5670.
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Unclassified - Unlimited
Subject Categories 35, 38, 33, 35, and 09
This publication is available from the NASA Center for AeroSpace Information, (301) 621-0390.
12b. DISTRIBUTION CODE
13. ABSTRACT (Maximum 200 words)
With the arrival of highly accurate multi-port pressure measurement systems, conditions that previously did not affect
overall system accuracy must now be scrutinized closely. Errors caused by elevation differences between pressure sensing
dements and model pressure taps can be quantified and corrected. With multi-port pressure measurement systems, the
sensing elements are connected to pressure taps that may be many feet away. The measurement system may be at a
different elevation than the pressure taps due to laboratory space or test article constraints. This difference produces a
pressure gradient that is inversely proportional to height within the interface tube. The pressure at the bottom of the tube
will be higher than the pressure at the top due to the weight of the tube's column of air. Tubes with higher pressures will
exhibit larger absolute errors due to the higher air density. The above effect is well documented but has generally been
taken into account with large elevations only. With error analysis techniques, the loss in accuracy from elevation can be
easily quantified. Correction factors can be applied to maintain the high accuracies of new pressure measurement systems.
14. SUBJECTTERMS
Pressure measurement; Elevation; Accuracy; Error analysis
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Elevation correction factor for absolute pressure measurements

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