CHILL \ Takes degC and speed(mph) of stack &
\ returns effective human still air degC
<< DEPTH
IF \ something on the stack DO WINDCHILL
THEN 4 MAX 60 MIN \ bound windspeed to 4-60mph
.447 * -> t v \ change mph to m/s
'33-(10.45+10*SQRTv-v)
*(33-t)/22.03405' \ transform equation
ELSE
"WindChill: deg$C mph -> deg$C" \ if stack is empty print helpful data
1 DISP
END
>>
SYMBOL KEY:
SQRT 131:-Square_root_symbol
-> 141:-Right_hand_arrow
deg$ 145:-Degree_symbol
<< 146:-Start_program_construct
>> 147:-End_program_construct *
BACKGROUND INFORMATION:
From borasky@ogicse.cse.ogi.edu Mon Dec 31 02:27:55 1990
Relay-Version: version Notes 2.8.4 1990/05/09; site hpqtdla.sqf.hp.com
From: borasky@ogicse.cse.ogi.edu (M. Edward Borasky)
Date: Mon, 31 Dec 1990 02:27:55 GMT
Date-Received: Thu, 3 Jan 1991 14:40:34 GMT
Subject: Wind Chill Index
Message-ID: <15458@ogicse.ogi.edu>
Organization: Oregon Graduate Institute (formerly OGC), Beaverton, OR
Path: hpqtdla!hpsqf!hpcuhb!hpda!hplabs!ucbvax!tut.cis.ohio-state.edu!att!emory!ogicse!ogicse.cse.ogi.edu!borasky
Newsgroups: comp.sys.handhelds
Sender: borasky@ogicse.ogi.edu
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.
From akcs.joehorn@hpcvbbs.UUCP Wed Jan 23 09:40:15 1991
Relay-Version: version Notes 2.8.4 1990/05/09; site hpqtdla.sqf.hp.com
From: akcs.joehorn@hpcvbbs.UUCP (Joseph K. Horn)
Date: Wed, 23 Jan 1991 09:40:15 GMT
Date-Received: Wed, 23 Jan 1991 20:13:21 GMT
Subject: Re: Wind Chill Index
Message-ID: <279d5175:1544.4comp.sys.handhelds;1@hpcvbbs.UUCP>
Path: hpqtdla!hpsqf!hpcuhb!hpda!hplabs!hp-pcd!hpcvra.cv.hp.com!rnews!hpcvbbs!akcs.joehorn
Newsgroups: comp.sys.handhelds
References: <15458@ogicse.ogi.edu> <27838cb8:1544.3comp.sys.handhelds;1@hpcvbbs
Lines: 32
M. Edward Borasky posted two equations for the Wind Chill Index
recently. It reminded me of the BURR (as in "Brrrrrr!!!") routine
that was in the VOYAGER program written by Dr. Robert Wilson for
the HP-71 onboard the historic round-the-world Voyager aircraft
flight in 1986. Here's that subprogram rewritten in 48 RPL:
-------------- CHILL in --------------
%%HP:T(3)F(.);
\<< 3.4759 MAX 50 MIN 4.63 * 9 / SWAP 32 - 5 * 9 / \-> v t
'33-(10.45+10*\v/v-v)*(33-t)/22.03405' 9 * 5 / 32 + 1 RND \>>
-------------- CHILL out -------------
This takes a Fahrenheit temperature in level 2, and a wind speed
in knots in level 1. (Change it to mph if you want.) The result
is not a Wind Chill Index, but the "apparent temperature" with
the wind chill factor already figured in.
So if you're skiing downhill on a 15 degree day with a 30 knot wind
sanding your face, this program says that it'll FEEL like it's
27.5 degrees below zero! Until frostbite sets in, of course.
What I find odd is that if it's cold and windy enough, the result
can be far below absolute zero. We must ponder this mystery...
Also, 91.4 degrees seems to be a turning point; above that, and
wind makes it seem HOTTER, not cooler! Seems to me that the magic
number should be 98.6 ("... when it's difficult to tell where you
end and the night begins."); I'd LOVE a breeze on a 95 degree day!
-- Joseph K. Horn -- (714) 858-0920 -- Peripheral Vision, Ltd. --
+----------------------------------------+
| "Many are cold, but few are frozen." |
+----------------------------------------+