Weather Math
By Stephen Scott

Atmospheric pressures are listed in millibars. Local weather forecasts are Kilopascals. Just adjust the decimal to the right one place. 103.56 kPa becomes 1035.6 millibars. Local barometric pressure forecasts from Environment Canada are also sea level adjusted. Calgary’s forecast come from the airport which is at 3500 feet. Race city actually sits at 3350 feet however the track is officially listed at 3500 feet. The more decimal places you go the closer the accuracy of the formulas.

Forecast: (a good race day) - used for examples
Pressure = 1035.6 millibars
Temp = 16c
Humidity = 30%
Dew point = -1.544
Altitude of forecast = 3500 feet

Conversions:
millibars = inches x 33.8653
inches = millibars / 33.8653
meters = feet x 0.3048
temp Kelvin = Celsius + 273.15

Station Pressure: Formula for Station Pressure
=((sea level pressure ^ 0.190284)-(8.4288e-05 x altitude in meters))^5.2553026+0.3
=((1035.6^0.190284)-(8.4288e-05 x 1066.8))^5.2553026+0.3
=(3.7475-0.0899)^5.2553026 +0.3
=3.6576^5.2553026+0.3
=911.52+0.3
=911.82 millibars or 26.9249 inches of mercury.

Pressure Altitude: Formula for Pressure Altitude
=(1-(station pressure/1013.25)^0.190284) x 145366.45
=(1-(911.82/1013.25)^0.190284) x 145366.45
=(1-0.899896373^0.190284) x 145366.45
=(1-.980129737) x 145366.45
=.019870263 x 145366.45
=2888.469 feet above sea level

Density Altitude: Formula for Density Altitude (This is what really affects your ET)
=145366 x (1-((0.28424 x station pressure) / ((temp Kelvin / (1-0.379 x (6.1078 x 10 ^ ((dew point x 7.5) / temp Kelvin)) / station pressure) - 273.15) + 273.15)) ^ 0.235)
=145366 x (1-((0.28424 x 911.82) / ((289.15 / (1-0.379 x (6.1078 x 10 ^ ((-1.544 x 7.5) / 289.15)) / 911.82) - 273.15) + 273.15)) ^ 0.235)
=145366 x (1-(259.1757168 / ((289.15 / (1-0.379 x (6.1078 x 10 ^ (-11.58 / 289.15)) / 911.82) - 273.15) + 273.15)) ^ 0.235)
=145366 x (1-(259.1757168 / ((289.15 / (1-0.379 x (6.1078 x 10 ^ -0.04) / 911.82) - 273.15) + 273.15)) ^ 0.235)
=145366 x (1-(259.1757168 / ((289.15 / (1-0.379 x 5.570379805 / 911.82) - 273.15) + 273.15)) ^ 0.235)
=145366 x (1-(259.1757168 / ((289.15 / .997684659 - 273.15) + 273.15)) ^ 0.235)
=145366 x (1-(259.1757168 / (16.67103452 + 273.15)) ^ 0.235)
=145366 x (1-(259.1757168 / 289.8210345) ^ 0.235)
=145366 x (1-.894261236 ^ 0.235)
=145366 x .025921101
=3768 feet above sea level