From usc!howland.reston.ans.net!cs.utexas.edu!uunet!spstimes.sps.mot.com!mogate!newsgate!mark Thu Dec 1 11:15:08 PST 1994
Article: 44542 of rec.autos.vw
Newsgroups: rec.autos.vw
Path: usc!howland.reston.ans.net!cs.utexas.edu!uunet!spstimes.sps.mot.com!mogate!newsgate!mark
From: mark@wdc.sps.mot.com (Mark Shaw)
Subject: Power Corrections
Message-ID: <1994Nov30.000154.15533@newsgate.sps.mot.com>
Sender: news@newsgate.sps.mot.com
Nntp-Posting-Host: margay.sps.mot.com
Organization: Motorola Western MCU Design Center
Date: Wed, 30 Nov 1994 00:01:54 GMT
Lines: 241
I had mentioned a couple of weeks ago about some test data on my exhaust
system. Well, I've been pretty busy and that fell to the bottom of the
to-do list. Anyway, I'm back on track and had to do a power correction
investigation first to make sure that my individual tests would
correlate to each other. So this and a related post (called Correction
Tables) can be used for this purpose. Have fun with this stuff.
CORRECTING HP AND TORQUE FOR AMBIENT CONDITIONS
================================================
This document outlines how to correct observed horsepower of torque readings for
the differences in ambient air pressure, temperature, humidity and altitude from
the standard conditions. Correction is based on the procedure in SAE J1349 for
Net Power Ratings and the physical relationships the atmosphere as explained in
most physics, meteorology, or fluid mechanics texts.
TERMINOLOGY
The following variables are used:
Term Description Metric English
Ta Actual temperature C F
To Standard temperature 25C 77F
po Standard pressure (dry air) 99 kPa 29.23 inHg
pa Ambient pressure kPa inHg
pc Pressure, Corrected to ho kPa inHg
pa Actual pressure kPa inHg
pd Ambient Pressure (dry) kPa inHg
pv Vapor pressure of water kPa inHg
pw Partial pressure of water kPa inHg
ha Actual altitude meters ft
ho Sea Level 0 meters 0 ft
Pbc Brake power (corrected) kW hp
Pbo Brake power (observed) kW hp
Pfo Friction power (observed) kW hp
Pic Indicated power (corrected) kW hp
Pio Indicated power (observed) kW hp
CA Air correction factor dimensionless
e Efficiency % %
g Acceleration of gravity 9.81 m/sec2 32.15 ft/sec2
LM Lapse Rate (for n=1.235) -0.006507 K/m -0.003566 R/ft
M Mean molecular weight of air 28.966 28.966
n Polytropic exponent 1.235 1.235
R Gas Constant 8.314 J/mole-K 1715 ft-lbs/slug-R
RH Relative humidity % %
CONVERSIONS:
The following conversions will be useful in correcting readings:
Units Metric English Conversions
Temperature C F F= (9/5)C + 32 C=(5/9)(F-32)
Absolute Temp K R K=273 + C R=460 + F
Pressure kPa inHg 3.386 kPa = inHg
Length meter ft meter = 3.2808 ft
Power kW hp 0.746 kW = hp
Acceleration m/sec2 ft/sec2 m/sec2 = 3.277 ft/sec2
DETERMINING ALTITUDE
--------------------
The altitude at the test site is unimportant if you have a barometer and can
measure the ambient air pressure directly. Otherwise you will have to rely
on the locally reported barometric pressure, which is corrected to sea level
and must be converted back for the altitude of your test site.
The altitude at the test site can be measured with an altimeter, but usually
these need to be carefully corrected for the ambient pressure. A better method
is to determine the altitude of the test site from a topology map; or to run the
tests near an airport and use its official altitude.
DETERMINING TEMPERATURE
-----------------------
The ambient temperature at the test site can be easily measured with about any
thermometer. The ambient temperature should be measured outside the vehicle as
that is the temperature that determines the local air density. The ambient
temperature can also be heard on NOAH Weather Radio as an hourly update (see
resources at end).
DETERMINING PRESSURE
--------------------
The ambient pressure at the test site can be measured with a barometer. The
ambient pressure should be meaured outside the vehicle as that is the pressure
that determines the local air density. If a barometer is not available, then
the ambient pressure can be estimated from the barometric pressure reported at
a nearby airport or US Weather Service station. The ambient pressure, corrected
to sea level, can also be heard on NOAH Weather Radio as an hourly update (see
resources at end).
This reported barometric pressure is normally corrected to the pressure that
would appear at sea level, if the local pressure were present at an altitude
identical to that of the weather station. There are some assumptions made as
to the temperature at the theoretical sea level, but these are a minor error
source. This reported sea level corrected barometric pressure must be corrected
back to the actual pressure at the altitude of the test site. The ambient
pressure is related to the altitude in several ways dependent on what standard
conditions and assumptions are made.
The common method to calculate the standard atmospheric pressure and temperature
is based on the NACA (NASA) approach, which relies on a polytropic exponent, n,
with an associated rate of change in temperature with altitude that is called
the lapse rate, LM. The equations for the standard pressure and standard
temperature at any altitude are as follows (substituting in values for the
constants and letting the corrected barometric pressure be the new reference
pressure):
(1) pa = po ( 1 - ha/(280.3(460+To)) ) ** 5.255
(2) Ta = To - 0.00357 ha
We do not know the temperature at the reference altitude, ho, but we do know
the temperature at the test site altitude, ha. Therefore, we can solve for
To and insert back into the pressure equation (1) to use the ambient
temperature, Ta.
(3) pa = pc (1 - ha/(280.3 Ta + 1.001 ha + 128938) ) ** 5.255
DETERMINING WATER PARTIAL PRESSURE
----------------------------------
The actual barometric pressure and oxygen density needs to be corrected for the
water vapor partial pressure. Determining the local humidity requires a fairly
good hygrometer, which is not cheap. The local weather station can be called or
the ambient humidity can also be heard on NOAH Weather Radio as an hourly update
(see resources at end).
For low values of humidity and/or temperature, this correction is small, but for
tropical hot and humid conditions the power loss can be significant. By
definition the partial pressure of the water vapor, pw, is related to the
saturated vapor pressure of water, pv, and the Relative Humidity (%) as follows:
(4) RH = 100 pw/pv
Therefore, if you have the humidity and temperature, you can calculate the
partial pressure attributed to the water vapor. This partial pressure of the
water vapor is then substracted from the ambient barometric pressure to yield
the dry ambient barometric pressure used for correcting horsepower readings.
The calculation of the dry pressure is as follows:
(5) pd = pa - pv RH/100
The vapor pressures for water are usually found in tabular form versus ambient
temperature. There is also a mathematical form relating vapor pressure of water
to temperature that is a good first approximation (derived by O. Tetens, 1930).
This form is easier to use in a calculation than a table lookup. It gives about
a 0.5% accurate result with most of the error being at temperatures below freezing.
Its form is as follows:
(6) pv = 6.11 x 10 ** (7.5 Ta/(Ta + 237.3))
and is in C and mbar. It can be converted to F and inHg as follows:
mbar = 0.75006 mmHg = 0.02953 inHg C = (5/9)(F - 32)
(6) pv = 0.1804 x 10 ** ((4.167 Ta - 133.3)/(0.5556 Ta + 219.5))
Combining with equation (5) above the dry ambient temperature is:
(7) pd = pa - RH (0.001804 x 10 **((4.167 Ta - 133.3)/(0.5556 Ta + 219.5))
AMBIENT TEMPERATURE AND PRESSURE CORRECTION
-------------------------------------------
The general case for the brake horsepower of an engine is defined as what is left
over after subtracting out the frictional losses as follows:
(8) Pbo = Pio - Pfo
So the indicated horsepower (which cannot generally be measured directly) is
always higher than the brake horsepower available. Also, since the friction
horsepower is generally unaffected by the ambient air conditions, then only the
indicated horsepower needs to be corrected for ambient air conditions.
If the friction horsepower is measured then the corrected brake horsepower can
be found by applying the air correction factor to the indicated power as follows:
(9) Pbc = Ca Pio - Pfo
where the correction factor is calculated as follows (in English units):
(10) Ca = p0/pa sqrt((Ta+460)/To)
This supports the normally recognized concept that colder, more dense air gives
more power. The European DIN standards use an absolute pressure, po, of 101.3 kPa;
and an absolute temperature of 273K [reference: Bosch Automotive Handbook, 3rd
Edition, pages 394-405]. Other test procedures may also vary, so the SAE approach
will be chosen for convenience.
Humidity also has some effect in that moist air has less oxygen, but the effect is
negligible for low humidity as mentioned above. As a side note, the A/F mixture
will become richer as the atmospheric pressure drops [reference: Bosch Automotive
Handbook, 3rd Edition, pages 394-405].
In equations (8) and (9) above, we normally cannot measure the frictional horsepower
in a vehicle test, but we can assume an overall engine efficiency, e, which is the
percentage of the frictional horsepower, Pfo, with respect to the indicated
horsepower, Pio. Therefore we can assume that the brake horsepower is composed
of two terms:
(11) Pio = Pbo ( 1 + e/100 )
(12) Pfo = Pbo ( e/100 )
But only the Pio term can be corrected for ambient conditions, therefore:
(13) Pic = Ca Pbo ( 1 + e/100 )
and therefore the corrected brake horsepower will be:
(14) Pbc = Pbo ( Ca ( 1 + e/100 ) - ( e/100 ) )
>From equation (14) it can be seen that a portion of power has the ambient air
correction factor applied and then a constant amount subtracted that is the
estimated frictional losses in the engine. The correction factor equation (10)
and the values of the SAE standard ambient conditions can now be applied to
equation (14) using English units.
(15) Pbc = Pbo (( 1 + e/100 ) (po/pa) (sqrt((Ta+460)/To)) - ( e/100) )
and substituting the SAE standard conditions into equation (15) converts to:
(15) Pbc = Pbo (( 1 + e/100 ) (29.23/pa) (sqrt((Ta+460)/537)) - ( e/100) )
and using the typical efficiency of 18% recommended in SAE Standard J1349, the
equation simplifies further to:
(15) Pbc = Pbo ( (34.491/pa) (sqrt((Ta+460)/537)) - ( 0.18 ) )
Having said all that, what is the easy answer? Look at the three separate files
which are tables for looking up the typical range of factors.
LOCAL CONDITIONS AND REFERENCES
-------------------------------
National Weather Service also broadcasts the local weather conditions, with
updates every hour on:
NOAH Weather Radio at 162.55 MHz
Radio Weather Cube receives this well in most areas.
Hourly update usually includes the hourly temperature, dew point,
relative humidity, barometric pressure and wind conditions:
Weather reference book:
Saucer, Walter J., рPrinciples of Meteorological Analysisс Dover
Publications, NY, 1955, 1983, ISBN 0-486-65979-A
From usc!howland.reston.ans.net!pipex!uunet!spstimes.sps.mot.com!mogate!newsgate!mark Thu Dec 1 11:15:23 PST 1994
Article: 44543 of rec.autos.vw
Newsgroups: rec.autos.vw
Path: usc!howland.reston.ans.net!pipex!uunet!spstimes.sps.mot.com!mogate!newsgate!mark
From: mark@wdc.sps.mot.com (Mark Shaw)
Subject: Correction Tables
Message-ID: <1994Nov30.001040.15842@newsgate.sps.mot.com>
Sender: news@newsgate.sps.mot.com
Nntp-Posting-Host: margay.sps.mot.com
Organization: Motorola Western MCU Design Center
Date: Wed, 30 Nov 1994 00:10:40 GMT
Lines: 81
Here's the lookup tables to assist in determining correction factors for power
and torque for ambient conditions other than SAE standard.
Mark
Correction Factors for Various Ambient Conditions
=================================================
SAE Standard Conditions: 29.23 inHg, 77║F, 18% Efficiency
Determine ambient barometric pressure (Pa), ambient temp (Ta), and
ambient relative humidity (RH).
Using Table 1, find the vapor pressure correction for the RH and Ta
of the test conditions. SUBTRACT this correction from the Pa.
Then use the newly correctec dry ambient pressure (Pd) and Ta in
Table 2 to find the correction factor to multiple times the observed
power or torque readings.
For ordinates not in tables, interpolation is acceptable.
-----------------------------------------------------------------------------------
TABLE 1 - Vapor Pressure Correction vs. Humidity and Temperature:
RH Ambient Temperature (║F)
(%), 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120
0,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00
10,0.00,0.01,0.01,0.02,0.02,0.04,0.05,0.07,0.10,0.14,0.19,0.26,0.34
20,0.01,0.01,0.02,0.03,0.05,0.07,0.10,0.15,0.21,0.28,0.39,0.52,0.69
30,0.01,0.02,0.03,0.05,0.07,0.11,0.16,0.22,0.31,0.43,0.58,0.78,1.03
40,0.02,0.03,0.04,0.07,0.10,0.15,0.21,0.30,0.41,0.57,0.77,1.04,1.38
50,0.02,0.04,0.05,0.08,0.12,0.18,0.26,0.37,0.52,0.71,0.97,1.30,1.72
60,0.03,0.04,0.07,0.10,0.15,0.22,0.31,0.44,0.62,0.85,1.16,1.56,2.07
70,0.03,0.05,0.08,0.12,0.17,0.25,0.37,0.52,0.72,1.00,1.35,1.82,2.41
80,0.04,0.06,0.09,0.13,0.20,0.29,0.42,0.59,0.83,1.14,1.55,2.08,2.76
90,0.04,0.06,0.10,0.15,0.22,0.33,0.47,0.67,0.93,1.28,1.74,2.34,3.10
100,0.04,0.07,0.11,0.17,0.25,0.36,0.52,0.74,1.03,1.42,1.93,2.60,3.45
-----------------------------------------------------------------------------------
TABLE 2 - Correction to Power/Torque at Ambient Temperature and Pressure:
Pd Ambient Temperature (║F)
("Hg), 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120
24.00,1.150,1.165,1.179,1.193,1.207,1.221,1.234,1.248,1.261,1.274,1.288,1.301,1.314
24.25,1.136,1.151,1.165,1.179,1.192,1.206,1.220,1.233,1.246,1.259,1.272,1.285,1.298
24.50,1.123,1.137,1.151,1.165,1.178,1.192,1.205,1.219,1.232,1.245,1.258,1.270,1.283
24.75,1.110,1.124,1.138,1.151,1.165,1.178,1.191,1.204,1.217,1.230,1.243,1.256,1.268
25.00,1.097,1.111,1.124,1.138,1.151,1.165,1.178,1.191,1.204,1.216,1.229,1.241,1.254
25.25,1.084,1.098,1.111,1.125,1.138,1.151,1.164,1.177,1.190,1.202,1.215,1.227,1.240
25.50,1.072,1.085,1.099,1.112,1.125,1.138,1.151,1.164,1.176,1.189,1.201,1.214,1.226
25.75,1.060,1.073,1.086,1.100,1.113,1.125,1.138,1.151,1.163,1.176,1.188,1.200,1.212
26.00,1.048,1.061,1.074,1.087,1.100,1.113,1.125,1.138,1.150,1.163,1.175,1.187,1.199
26.25,1.036,1.049,1.062,1.075,1.088,1.100,1.113,1.125,1.138,1.150,1.162,1.174,1.186
26.50,1.025,1.038,1.051,1.063,1.076,1.088,1.101,1.113,1.125,1.137,1.149,1.161,1.173
26.75,1.013,1.026,1.039,1.052,1.064,1.077,1.089,1.101,1.113,1.125,1.137,1.148,1.160
27.00,1.002,1.015,1.028,1.040,1.053,1.065,1.077,1.089,1.101,1.113,1.125,1.136,1.148
27.25,0.991,1.004,1.017,1.029,1.041,1.054,1.066,1.077,1.089,1.101,1.113,1.124,1.135
27.50,0.981,0.993,1.006,1.018,1.030,1.042,1.054,1.066,1.078,1.089,1.101,1.112,1.123
27.75,0.970,0.983,0.995,1.007,1.019,1.031,1.043,1.055,1.066,1.078,1.089,1.101,1.112
28.00,0.960,0.972,0.985,0.997,1.009,1.020,1.032,1.044,1.055,1.067,1.078,1.089,1.100
28.25,0.950,0.962,0.974,0.986,0.998,1.010,1.021,1.033,1.044,1.056,1.067,1.078,1.089
28.50,0.940,0.952,0.964,0.976,0.988,0.999,1.011,1.022,1.034,1.045,1.056,1.067,1.078
28.75,0.930,0.942,0.954,0.966,0.978,0.989,1.001,1.012,1.023,1.034,1.045,1.056,1.067
29.00,0.921,0.933,0.944,0.956,0.968,0.979,0.990,1.002,1.013,1.024,1.035,1.045,1.056
29.25,0.911,0.923,0.935,0.946,0.958,0.969,0.980,0.991,1.002,1.013,1.024,1.035,1.045
29.50,0.902,0.914,0.925,0.937,0.948,0.959,0.971,0.982,0.992,1.003,1.014,1.025,1.035
29.75,0.893,0.905,0.916,0.927,0.939,0.950,0.961,0.972,0.983,0.993,1.004,1.014,1.025
30.00,0.884,0.896,0.907,0.918,0.929,0.940,0.951,0.962,0.973,0.984,0.994,1.005,1.015
30.25,0.875,0.887,0.898,0.909,0.920,0.931,0.942,0.953,0.963,0.974,0.984,0.995,1.005
30.50,0.867,0.878,0.889,0.900,0.911,0.922,0.933,0.943,0.954,0.964,0.975,0.985,0.995
30.75,0.858,0.869,0.880,0.891,0.902,0.913,0.924,0.934,0.945,0.955,0.965,0.976,0.986
31.00,0.850,0.861,0.872,0.883,0.894,0.904,0.915,0.925,0.936,0.946,0.956,0.966,0.976
-----------------------------------------------------------------------------------
EXAMPLE: Ambient pressure (Pa) = 29.04 inHg
Ambient temp (Ta) = 50 degF
Ambient humidity (RH) = 80%
>From Table 1, the vapor pressure correction is 0.29 inHg.
The dry ambient pressure (Pd) is therefore 29.04 - 0.29 = 28.75 inHg.
>From Table 2, the power correction is 0.989; or the observed power is
about 11% higher than standard conditions.
icelord blog
мотозапчасти :: ПВД от Производителя: ПВД. Полиэтилен, Полипропилен. :: С целью обеспечения дополнительной устойчивости наши вышки туры комплектуются стабилизаторами.