generic optimized formula (save ram and execution time). added explan…

…ation to

reconstruct our thoughts.

docs/README.md

@@ -338,9 +338,9 @@ or
 #### float HeatIndex(float temperature, float humidity, TempUnit tempUnit = TempUnit_Celsius)
 
  Calculate the heat index based on the temperature and humidity with the specified units. 
- The NWS algorithm is used.
+ The U.S. NWS algorithm is used.
 ```
- return: float heat index
+ return: float heat index in TempUnit
 
  * Temperature: float
  values: any float related to TempUnit

examples/Environment_Calculations/Environment_Calculations.ino

@@ -136,6 +136,7 @@ void printBME280Data
  client->print("\t\tHeat Index: ");
  float heatIndex = EnvironmentCalculations::HeatIndex(temp, hum, envTempUnit);
  client->print(heatIndex);
+ client->print("°"+ String(envTempUnit == EnvironmentCalculations::TempUnit_Celsius ? "C" :"F"));
 
  client->print("\t\tAbsolute Humidity: ");
  client->println(absHum);

src/EnvironmentCalculations.cpp

@@ -51,7 +51,7 @@ float EnvironmentCalculations::Altitude
  if (!isnan(pressure) && !isnan(referencePressure) && !isnan(outdoorTemp))
  {
  if(tempUnit != TempUnit_Celsius)
- outdoorTemp = (outdoorTemp - 32.0) * (5.0 / 9.0); /*conversion to [�C]*/
+ outdoorTemp = (outdoorTemp - 32.0) * (5.0 / 9.0); /*conversion to [°C]*/
 
  altitude = pow(referencePressure / pressure, 0.190234) - 1;
  altitude *= ((outdoorTemp + 273.15) / 0.0065);
@@ -96,6 +96,7 @@ float EnvironmentCalculations::AbsoluteHumidity
 
 
 /****************************************************************/
+//FYI: https://ehp.niehs.nih.gov/1206273/ in detail this flow graph: https://ehp.niehs.nih.gov/wp-content/uploads/2013/10/ehp.1206273.g003.png
 float EnvironmentCalculations::HeatIndex
 (
  float temperature,
@@ -114,27 +115,32 @@ float EnvironmentCalculations::HeatIndex
  {
  temperature = (temperature * (9.0 / 5.0) + 32.0); /*conversion to [°F]*/
  }
-
+ // Using both Rothfusz and Steadman's equations
+ // https://www.wpc.ncep.noaa.gov/html/heatindex_equation.shtml
  if (temperature <= 40) 
  {
- heatIndex = temperature;
+ heatIndex = temperature; //first red block
  }
  else
  {
- heatIndex = 0.5 * (temperature + 61.0 + ((temperature - 68.0) * 1.2) + (humidity * 0.094));
+ heatIndex = 0.5 * (temperature + 61.0 + ((temperature - 68.0) * 1.2) + (humidity * 0.094)); //calculate A -- from the official site, not the flow graph
 
  if (heatIndex >= 79) 
  {
- // Using both Rothfusz and Steadman's equations
- // https://www.wpc.ncep.noaa.gov/html/heatindex_equation.shtml
+ /*
+ * calculate B 
+ * the following calculation is optimized. Simply spoken, reduzed cpu-operations to minimize used ram and runtime. 
+ * Check the correctness with the following link:
+ * https://www.wolframalpha.com/input/?source=nav&i=b%3D+x1+%2B+x2*T+%2B+x3*H+%2B+x4*T*H+%2B+x5*T*T+%2B+x6*H*H+%2B+x7*T*T*H+%2B+x8*T*H*H+%2B+x9*T*T*H*H
+ */
  heatIndex = hi_coeff1
  + (hi_coeff2 + hi_coeff4 * humidity + temperature * (hi_coeff5 + hi_coeff7 * humidity)) * temperature
  + (hi_coeff3 + humidity * (hi_coeff6 + temperature * (hi_coeff8 + hi_coeff9 * temperature))) * humidity;
-
+ //third red block
  if ((humidity < 13) && (temperature >= 80.0) && (temperature <= 112.0))
  {
  heatIndex -= ((13.0 - humidity) * 0.25) * sqrt((17.0 - abs(temperature - 95.0)) * 0.05882);
- }
+ } //fourth red block
  else if ((humidity > 85.0) && (temperature >= 80.0) && (temperature <= 87.0))
  {
  heatIndex += (0.02 * (humidity - 85.0) * (87.0 - temperature));
@@ -148,7 +154,7 @@ float EnvironmentCalculations::HeatIndex
  }
  else 
  {
- return heatIndex;
+ return heatIndex; //fifth red block
  }
 }
 
@@ -167,7 +173,7 @@ float EnvironmentCalculations::EquivalentSeaLevelPressure
  if(!isnan(altitude) && !isnan(temp) && !isnan(pres))
  {
  if(tempUnit != TempUnit_Celsius)
- temp = (temp - 32.0) * (5.0 / 9.0); /*conversion to [�C]*/
+ temp = (temp - 32.0) * (5.0 / 9.0); /*conversion to [°C]*/
 
  if(altUnit != AltitudeUnit_Meters)
  altitude *= 0.3048; /*conversion to meters*/

src/EnvironmentCalculations.h

@@ -70,6 +70,8 @@ namespace EnvironmentCalculations
  /////////////////////////////////////////////////////////////////
  /// Calculate the heatindex based on the humidity and temperature
  /// in tempUnit.
+ /// The formula based on the Heat Index Equation of the US National Weather Service
+ /// https://www.wpc.ncep.noaa.gov/html/heatindex_equation.shtml
  /// @param temperature in tempUnit
  /// @param humidity in percentage
  /// @param temptUnit in °C or °F. default=TempUnit_Celsius