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." | +----------------------------------------+