Path: utzoo!utgpu!news-server.csri.toronto.edu!cs.utexas.edu!uunet!ogicse!ogicse.cse.ogi.edu!borasky
From: borasky@ogicse.cse.ogi.edu (M. Edward Borasky)
Newsgroups: comp.sys.handhelds
Subject: Wind Chill Index
Message-ID: <15458@ogicse.ogi.edu>
Date: 31 Dec 90 02:27:55 GMT
Sender: borasky@ogicse.ogi.edu
Organization: Oregon Graduate Institute (formerly OGC), Beaverton, OR
Lines: 47

A week or so ago, someone requested a formula to compute the Wind Chill
Index.  I hope no one has frozen to death waiting for this reply.

The Wind Chill Index was developed in Little America (Antarctica) between
1939 and 1941.  The primary developer was Dr. Paul Siple, who is well-
known among Boy Scouts -- he was an Eagle Scout who was chosen to go
to Little America with Byrd.  Anyhow, Siple came up with the following
empirical formula by experiments at Little America:

	H = (A + B*SQRT(V) + C*V)*DT

where H is the heat loss in kg. cals./m^2/hr.  V is the wind velocity 
in meters/second and DT is the difference between "neutral body"
temperature" (33 degrees Celsius) and the air temperature.  A, B and C
are constants, equal respectively to 10.45, 10 and -1.  The Wind Chill
Index is the Fahrenheit (it gets MORE complicated, hang on) temperature
that has the same heat loss at a wind speed of 4 miles per hour as the
heat loss at the current wind speed and temperature.  So what you have
to do is take the current wind speed and temperature, convert to 
meters per second and degress Celsius, then compute the heat loss H.
Then you take the equation, substitute this value of H and 4 MPH, 
which you must convert to meters per second, for the velocity and 
solve for the temperature, which you then need to convert to 
Fahrenheit to get the Wind Chill Index.  In principle, you can do this
using the built-it numerical solver, but it doesn't take much work to
come up with a closed-form expression for the Wind Chill Index.

Well, you've got a HP-28S or HP-48SX, don't you?  I've got the HP-28S,
so I've done all the hard work FOR you!  The formula is

	WCI = 48.05 + 0.3034*SQRT(MPH)*TF - 0.02029*TF*MPH - 27.73*SQRT(MPH)
	    + 0.4743*TF + 1.854*MPH

where WCI is the Wind Chill Index in degrees Fahrenheit, TF is the
Fahrenheit temperature and MPH is the wind speed in miles per hour.

Given this form for the equation, I thought it would be a neat trick
to take the Wind Chill Index table from the World Almanac and do a least-
squares fit to try and re-create THEIR constants.  It turns out that you
get slightly different numbers:

	WCI = 48.16 + 0.2977*SQRT(MPH)*TF - 0.02010*TF*MPH - 27.86*SQRT(MPH)
	    + 0.4932*TF + 1.887*MPH

I like the second version better because it gives you numbers that 
correspond to what you will see on TV weather reports -- they use the
table from the World Almanac, which actually comes from NOAA.