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261 lines
7.4 KiB
C++
261 lines
7.4 KiB
C++
//
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// FILE: temperature.cpp
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// AUTHOR: Rob Tillaart
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// VERSION: 0.3.7
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// DATE: 2015-03-29
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// PURPOSE: collection temperature functions
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// URL: https://github.com/RobTillaart/Temperature
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#include "temperature.h"
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float Fahrenheit(float celsius)
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{
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return 1.8 * celsius + 32; // 5.0 / 9.0 = 1.8
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}
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float Celsius(float Fahrenheit)
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{
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return (Fahrenheit - 32) * 0.55555555555; // 5.0 / 9.0 = 0.555...
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}
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float Kelvin(float celsius)
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{
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return celsius + 273.15;
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}
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// reference:
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// [1] https://wahiduddin.net/calc/density_algorithms.htm
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// [2] https://web.archive.org/web/20100528030817/https://www.colorado.edu/geography/weather_station/Geog_site/about.htm
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// dewPoint function based on code of [2]
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// calculation of the saturation vapour pressure part is based upon NOAA ESGG(temp)
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float dewPoint(float celsius, float humidity)
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{
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// Calculate saturation vapour pressure
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// ratio 100C and actual temp in Kelvin
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float AA0 = 373.15 / (273.15 + celsius);
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// SVP = Saturation Vapor Pressure - based on ESGG() NOAA
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float SVP = -7.90298 * (AA0 - 1.0);
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SVP += 5.02808 * log10(AA0);
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SVP += -1.3816e-7 * (pow(10, (11.344 * ( 1.0 - 1.0/AA0))) - 1.0 );
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SVP += 8.1328e-3 * (pow(10, (-3.49149 * (AA0 - 1.0 ))) - 1.0 ) ;
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SVP += log10(1013.246);
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// calculate actual vapour pressure VP;
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// note to convert to KPa the -3 is used
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float VP = pow(10, SVP - 3) * humidity;
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float T = log( VP / 0.61078); // temp var
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return (241.88 * T) / (17.558 - T);
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}
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// dewPointFast() is > 5x faster than dewPoint() - run dewpoint_test.ino
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// delta mdewPointFastax with dewPoint() - run dewpoint_test.ino ==> ~0.347
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// (earlier version mentions ~0.6544 but that test code is gone :(
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// http://en.wikipedia.org/wiki/Dew_point
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float dewPointFast(float celsius, float humidity)
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{
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float a = 17.271;
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float b = 237.7;
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float temp = (a * celsius) / (b + celsius) + log(humidity/100);
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float Td = (b * temp) / (a - temp);
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return Td;
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}
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// https://en.wikipedia.org/wiki/Humidex
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float humidex(float celsius, float dewPoint)
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{
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float e = 19.833625 - 5417.753 /(273.16 + dewPoint);
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float h = celsius + 3.3941 * exp(e) - 5.555;
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return h;
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}
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// 0.3.0 => https://www.wpc.ncep.noaa.gov/html/heatindex_equation.shtml
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// previous https://en.wikipedia.org/wiki/Heat_index
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// TF = temp in Fahrenheit
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// RH = relative humidity in %
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float heatIndex(float TF, float RH)
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{
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// Steadman's formula
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// float HI = 0.5 * (TF + 61.0 + ((TF - 68.0) * 1.2) + (RH * 0.094));
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// optimized to:
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float HI = TF * 1.1 - 10.3 + RH * 0.047;
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// Rothfusz regression
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if (HI >= 80)
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{
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const float c1 = -42.379;
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const float c2 = 2.04901523;
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const float c3 = 10.14333127;
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const float c4 = -0.22475541;
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const float c5 = -0.00683783;
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const float c6 = -0.05481717;
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const float c7 = 0.00122874;
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const float c8 = 0.00085282;
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const float c9 = -0.00000199;
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float A = (( c5 * TF) + c2) * TF + c1;
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float B = (((c7 * TF) + c4) * TF + c3) * RH;
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float C = (((c9 * TF) + c8) * TF + c6) * RH * RH;
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HI = A + B + C;
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if ((RH < 13) && (TF <= 112))
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{
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HI -= ((13 - RH) / 4) * sqrt((17 - abs(TF - 95.0)) / 17);
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}
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if ((RH > 87) && (TF < 87))
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{
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HI += ((RH - 85) / 10) * ((87 - TF) / 5);
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}
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}
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return HI;
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}
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// 0.3.0 => https://www.wpc.ncep.noaa.gov/html/heatindex_equation.shtml
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// previous https://en.wikipedia.org/wiki/Heat_index
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// TC = temp in Celsius
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// RH = relative humidity in %
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float heatIndexC(float TC, float RH)
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{
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if ( (TC < 27) || (RH < 40)) return TC;
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float TF = Fahrenheit(TC);
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return Celsius(heatIndex(TF, RH));
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/*
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const float c1 = -8.78469475556;
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const float c2 = 1.61139411;
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const float c3 = 2.33854883889;
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const float c4 = -0.14611605;
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const float c5 = -0.012308094;
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const float c6 = -0.0164248277778;
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const float c7 = 0.002211732;
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const float c8 = 0.00072546;
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const float c9 = -0.000003582;
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float A = (( c5 * Celsius) + c2) * Celsius + c1;
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float B = (((c7 * Celsius) + c4) * Celsius + c3) * humidity;
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float C = (((c9 * Celsius) + c8) * Celsius + c6) * humidity * humidity;
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return A + B + C;
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*/
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}
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// https://carnotcycle.wordpress.com/2012/08/04/how-to-convert-relative-humidity-to-absolute-humidity/
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// Absolute Humidity (grams/m3) = 6.112 × e^[(17.67 × T)/(T+243.5)] × rh × 2.1674
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// -----------------------------------------------
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// (273.15+T)
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float absoluteHumidity(float Celsius, float relHumidity)
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{
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float TC = Celsius;
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float AH = (2.1674 * 6.112) * relHumidity;
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AH *= exp((17.67 * TC)/(243.5 + TC));
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AH /= (273.15 + TC);
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return AH;
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}
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// https://en.wikipedia.org/wiki/Wind_chill
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// US = Fahrenheit / miles / hour
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// METRIC = Celsius / meter / hour (sec)
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// wind speed @ 10 meter,
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// if convert is true => wind speed will be converted to 1.5 meter
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// else ==> formula assumes wind speed @ 1.5 meter
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// US
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float WindChill_F_mph(const float Fahrenheit, const float milesPerHour, const bool convert)
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{
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if ((milesPerHour < 3.0) || (Fahrenheit > 50)) return Fahrenheit;
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float windSpeed = milesPerHour;
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if (convert) windSpeed = pow(milesPerHour, 0.16);
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return 35.74 + 0.6125 * Fahrenheit + (0.4275 * Fahrenheit - 35.75) * windSpeed;
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}
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// METRIC - standard wind chill formula for Environment Canada
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float WindChill_C_kmph(const float Celsius, const float kilometerPerHour, const bool convert)
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{
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if ((kilometerPerHour < 4.8) || (Celsius > 10)) return Celsius;
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float windSpeed = kilometerPerHour;
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if (convert) windSpeed = pow(kilometerPerHour, 0.16);
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return 13.12 + 0.6215 * Celsius + (0.3965 * Celsius - 11.37) * windSpeed;
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}
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float WindChill_C_mps(const float Celsius, const float meterPerSecond, const bool convert)
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{
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return WindChill_C_kmph(Celsius, meterPerSecond * 3.6, convert);
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}
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// https://www.engineeringtoolbox.com/air-altitude-pressure-d_462.html
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// Does not have the temperature correction ==> it has almost the -5.257 exponent
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// https://www.omnicalculator.com/physics/air-pressure-at-altitude
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// similar to https://en.wikipedia.org/wiki/Barometric_formula
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//
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// Note: altitude in meters.
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float baroToSeaLevelC( float pressure, float celsius, float altitude)
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{
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float altitudeFactor = 0.0065 * altitude;
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float kelvin = celsius + 273.15;
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return pressure * pow( 1 - (altitudeFactor / (kelvin + altitudeFactor)), -5.257);
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}
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// https://www.omnicalculator.com/physics/air-pressure-at-altitude
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// temperature (Celsius) at altitude (meter)
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float seaLevelToAltitude( float pressureSeaLevel, float celsius, float altitude)
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{
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float kelvin = celsius + 273.15;
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// P = P0 * exp( -g.M.h / (R.T));
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float factor = -9.80655 * 0.0289644 / 8.31432;
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factor /= kelvin;
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return pressureSeaLevel * exp(factor * abs(altitude));
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}
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float altitudeToSeaLevel( float pressure, float celsius, float altitude)
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{
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float kelvin = celsius + 273.15;
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// P = P0 * exp( -g.M.h / (R.T));
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float factor = 9.80655 * 0.0289644 / 8.31432;
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factor /= kelvin;
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return pressure / exp(factor * abs(altitude));
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}
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// https://en.wikipedia.org/wiki/High-altitude_cooking
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float boilingFahrenheit(float feet)
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{
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if (feet >= 0) return 212.1309 - feet * 1.86176954e-3;
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return 212;
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}
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float boilingCelsius(float meter)
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{
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if (meter > 0) return 100.08143 - meter * 3.39670635e-3;
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return 100;
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}
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// Celsius = 80..100
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float boilingMeter(float Celsius)
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{
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if (Celsius >= 100) return 0;
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return 29458.542 - Celsius * 294.34149;
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}
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// -- END OF FILE --
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