borasky@ogicse.cse.ogi.edu (M. Edward Borasky) (12/31/90)
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.
akcs.kevin@hpcvbbs.UUCP (Kevin Jessup) (01/02/91)
I am not much into thermodynamics and the like but I have always wondered why nothing in this equation deals with the moisture content of the air as well! Would that not affect the apparent temperature (WCI)?
fin@norge.unet.umn.edu (Craig A. Finseth) (01/03/91)
In article <2781f572:1544.1comp.sys.handhelds;1@hpcvbbs.UUCP> akcs.kevin@hpcvbbs.UUCP (Kevin Jessup) writes: >I am not much into thermodynamics and the like but I have always >wondered why nothing in this equation deals with the moisture >content of the air as well! Would that not affect the apparent >temperature (WCI)? Yes, it does, but so do many other factors. Besides, those of us who live in the colder areas (Minneapolis/St. Paul is warm for me) pretty much ignore the wind-chill numbers anyways. (Except for impressing our friends from down south. Personally, I find it much more impressive to say that if the air temperature is, say, -20 deg F so I can warm up by going into a freezer.) What factors do I use? More or less in order: - how long I am going to be outside, and where I'm going (putting out the garbage doesn't even rate a coat, regardless of temperature) - air temperature - amount of sun - type and amount of snowfall - wind speed, direction, gustiness, etc. - humidity (usually about 50% which equates to 5% or so when the air is warmed up) Craig A. Finseth fin@unet.umn.edu [CAF13] University Networking Services +1 612 624 3375 desk University of Minnesota +1 612 625 0006 problems 130 Lind Hall, 207 Church St SE +1 612 626 1002 FAX Minneapolis MN 55455-0134, U.S.A.
akcs.kevin@hpcvbbs.UUCP (Kevin Jessup) (01/04/91)
I agree. I live in Milwaukee.
akcs.joehorn@hpcvbbs.UUCP (Joseph K. Horn) (01/23/91)
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." |
+----------------------------------------+akcs.dnickel@hpcvbbs.UUCP (Derek S. Nickel) (01/24/91)
Joe,
I guess that would depend on whether it was a cool breeze or the Santa
Ana...
Derek S. Nickeltaber@ultnix.enet.dec.com (Patrick St. Joseph Teahan Taber) (01/24/91)
In article <279d5175:1544.4comp.sys.handhelds;1@hpcvbbs.UUCP>, akcs.joehorn@hpcvbbs.UUCP (Joseph K. Horn) writes: |> |>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... |> No mystery to me... remember it's *apparent* temperature. Hanging off a radio tower in the middle of winter with a wind blowing, it sure seems well below absolute zero. -- >>>==>PStJTT Patrick St. Joseph Teahan Taber, KC1TD If I was authorized to speak for my employer, I'd be too important to waste my time on this crap....
mcgrant@elaine23.stanford.edu (Michael Grant) (01/25/91)
In article <1991Jan24.082451@ultnix.enet.dec.com> taber@ultnix.enet.dec.com (Patrick St. Joseph Teahan Taber) writes: >In article <279d5175:1544.4comp.sys.handhelds;1@hpcvbbs.UUCP>, >akcs.joehorn@hpcvbbs.UUCP (Joseph K. Horn) writes: >|> >|>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... >|> > >No mystery to me... remember it's *apparent* temperature. Hanging off a radio >tower in the middle of winter with a wind blowing, it sure seems well below >absolute zero. > Gee, so what does it feel like to be in absolute zero? I mean, to have all of your atoms stop vibrating, so have all of your fluids turn solid, hmm... :-) Do you realize that when Mr. Horn writes 'absolute zero' he means -273C or so, the point where all random kinetic energy is eliminated? Where everything including helium freezes, where no life could possibly exist? I have a feeling when YOU said absolute zero you just meant 0F or 0C. Mike .
akcs.joehorn@hpcvbbs.UUCP (Joseph K. Horn) (01/25/91)
Omigosh, you won't believe this. In the Teacher's Edition of Addison Wesley's "Algebra and Trigonometry" high school textbook (1988), page 305, it gives the same formula for "windchill temperature" as we've seen above, but it leaves the units in the SI base: degrees Celsius, and windspeed in m/s. But they stupidly thought that m/s means miles per second! Here's what it says: "... where T is the actual temperature given in degrees Celsius and v is the wind speed in mi/sec." Wow, that's fast wind! Problem 50 then asks the student to calculate the windchill temperature given T=7 and v=8. Let's see; 8 mi/sec = 28,800 mph, according to the HP 48. Some wind! Hey - at that speed, wouldn't the temperature RISE due to air friction? No wonder our kids are graduating from high school totally innumerate...
taber@ultnix.enet.dec.com (Patrick St. Joseph Teahan Taber) (01/25/91)
In article <1991Jan25.004430.19802@portia.Stanford.EDU>, mcgrant@elaine23.stanford.edu (Michael Grant) writes: |> |>In article <1991Jan24.082451@ultnix.enet.dec.com> taber@ultnix.enet.dec.com (Patrick St. Joseph Teahan Taber) writes: |>>In article <279d5175:1544.4comp.sys.handhelds;1@hpcvbbs.UUCP>, |>>akcs.joehorn@hpcvbbs.UUCP (Joseph K. Horn) writes: |>>|> |>>|>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... |>>|> |>> |>>No mystery to me... remember it's *apparent* temperature. Hanging off a radio |>>tower in the middle of winter with a wind blowing, it sure seems well below |>>absolute zero. |>> |> |>Gee, so what does it feel like to be in absolute zero? I mean, to have all |>of your atoms stop vibrating, so have all of your fluids turn solid, hmm... |>:-) |> |>Do you realize that when Mr. Horn writes 'absolute zero' he means -273C |>or so, the point where all random kinetic energy is eliminated? Where |>everything including helium freezes, where no life could possibly exist? |> |>I have a feeling when YOU said absolute zero you just meant 0F or 0C. |> |>Mike |>. |> No, Mike, I meant -273C. It's something we earth people call humor. Maybe someone will explain it to you. -- >>>==>PStJTT Patrick St. Joseph Teahan Taber, KC1TD Too bad you can't buy a sense of humor... then more yuppies would have one.
edp@jareth.enet.dec.com (Eric Postpischil (Always mount a scratch monkey.)) (01/25/91)
In article <1991Jan25.004430.19802@portia.Stanford.EDU>, mcgrant@elaine23.stanford.edu (Michael Grant) writes: >Do you realize that when Mr. Horn writes 'absolute zero' he means -273C >or so, the point where all random kinetic energy is eliminated? Where >everything including helium freezes, where no life could possibly exist? The sentence as written does not describe a logical impossibility. It refers not to the person feeling like they are at absolute zero but the air feeling to the person as if the air were absolute zero. To see how this is possible, consider the rate at which heat would be lost from a person's body if the air were still but it were at absolute zero. There would be some finite rate at which heat would be conducted away from the person. Now consider that if air is moving, it is possible that heat might be transferred from the person at an even higher rate. Thus, the feeling of cold moving air is even colder than still air at absolute zero. -- edp (Eric Postpischil) "Always mount a scratch monkey." edp@jareth.enet.dec.com
rrd@hpfcso.HP.COM (Ray Depew) (01/25/91)
Michael Grant writes: > Do you realize that when Mr. Horn writes 'absolute zero' he means -273C > or so, the point where all random kinetic energy is eliminated? Where > everything including helium freezes, where no life could possibly exist? > > I have a feeling when YOU said absolute zero you just meant 0F or 0C. Umm... I think Mr. Taber was making a joke. When you're talking about a wind so cold that it freezes your boogers and makes it hard to uncurl your fingers from the rungs of the ladder, it might as well be "absolute zero" -- for that matter, it might as well be the end of the universe. Whatever it is, it feels so #$%!@ cold that it doesn't need numeric definition. And I thought Stanford students had a sense of humor. -- Ray MSEE '88
kenw@col.hp.com (Ken Wyatt) (01/26/91)
> From: akcs.joehorn@hpcvbbs.UUCP (Joseph K. Horn) > Subject: Re: Wind Chill Index > > 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 I am guessing that your skin temperature is 91.4
mcgrant@elaine23.stanford.edu (Michael Grant) (01/27/91)
>No, Mike, I meant -273C. It's something we earth people call humor. Maybe >someone will explain it to you. > > >-- > >>>==>PStJTT > Patrick St. Joseph Teahan Taber, KC1TD Humor? Oh, that's the stuff I had a ton of until I entered graduate school, and saw my first tuition bill. Mike