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., ÒPrinciples of Meteorological AnalysisÓ 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.