HP Prime and TI-84+: Saturation Vapor Pressure, Dew Point, Density
Altitude (US Units)
The Program AIRUS
uses US units as the inputs and outputs:
Input:
T = Temperature
in Fahrenheit (°F)
B = Air
Pressure in inHg (inches of Mercury)
H = Relative
Humidity (%)
You can find
these measurements on various weather websites.
Such websites are Accuweather (www.accuweather.com)
and Weather Underground (www.wunderunderground.com).
Output:
S = Saturated
Water Vapor (psi)
A = Approximate
Actual Density Altitude (DSI) (feet)*
X = Dew Point (°F)
*This is an
approximation of density altitude, is an equivalent elevation where the standard
atmosphere is met. (per ICAO, 29.921
inHg, 59°F, 0% humidity).
Let me stress, the density altitude is an approximation.
A list
consisting of temperature, air pressure, relative humidity, saturated water
vapor, approximate DSI, and dew point is also returned to the home screen.
Equations Used:
Convert
Temperature from Fahrenheit to Celsius:
C = (T-32)*5/9
Saturation
Vapor Pressure (psi):
S=(610.78*10^((7.5*C)/(C+237.3)))/
6894.757292318
Dew Point (°C):
W=237.3*V/(1-V)
where:
V=(LN(H/100)+((17.27*C)/(237.3+C)))/17.27
Convert from
Celsius to Fahrenheit:
X = W*9/5 + 32
Density
Altitude (feet):
A=145442.1563*(1-((17.326*B)/(1.8*Z))^.235)
where:
Z=(C+273.15)/(1-.378*Y/(33.8639*B))
Y=6.1078*10^((7.5*W)/(237.3+W))
HP Prime: AIRUS
EXPORT AIRUS()
BEGIN
// 2015-02-28 EWS
// U.S. Units
LOCAL t,b,h;
LOCAL c,s,d,p,a,v,w;
LOCAL x,y,z;
// Data
INPUT({t,b,h},
"Weather
Data",
{"t
:","b :","h :"},
{"Temperature
(°F)",
"Pressure
(inHg)",
"% Relative
Humidity"});
// t to Celcius
c:=(t-32)*5/9;
// Saturation Vapor
Pressure (Pa)
// wikipedia
s:=610.78*ALOG((7.5*c)/(c+237.3));
// to psi
s:=s/6894.757292318;
// Dew Point (°F)
// ag.arizona.edu
v:=(LN(h/100)+((17.27*c)/(237.3+c)))/17.27;
w:=237.3*v/(1-v);
// w to °F
x:=w*9/5+32;
// Density Altitude
// www.srh.noaa.gov
y:=6.1078*ALOG((7.5*w)/(237.3+w));
z:=(c+273.15)/(1-.378*y/(33.8639*b));
a:=145442.1563*(1-((17.326*b)/
(z*1.8))^.235);
// Output
PRINT();
PRINT("Input:");
PRINT(t+"°F,
"+b+"inHg, "+h+"%");
PRINT("Output:");
PRINT("Sat.
Water Vapor (psi): "+s);
PRINT("Approx.
DSA (ft): "+a);
PRINT("Dew
Point (°F): "+x);
RETURN
{t,b,h,s,a,x};
END;
TI-84+ AIRUS:
Disp “T: TEMP °F”
Disp “B: PRESSURE
(INHG)”
Disp “H: REL.
HUMIDITY”
Prompt T,B,H
(T-32)*5/9→C
610.78*10^((7.5C)/(C+237.3))→S
S/6894.757292318→S
(ln(H/100)+((17.27C)/(237.3+C)))/17.27→V
237.3V/(1-V)→W
9W/5+32→X
6.1078*10^((7.5W)/(237.3+W))→Y
(C+273.15)/(1-.378Y/(33.8639B))→Z
145442.1563*(1-((17.326B)/(1.8Z))^.235)→A
Disp “SAT. WATER
VAPOR (°F)”
Pause S
Disp “APPROX DSA
(FT)”
Pause A
Disp “DEW POINT (°F)”
Pause X
Disp {T,B,H,S,A,X}
Example:
Input:
T = 68°F
B = 29.94 inHg
(inches of Mercury)
H = 70%
Output:
S = 0.339111794
psi
A = 790.3879774
feet
W = 57.85583006
°F
Sources:
“Density
Altitude” National Weather Resource: Southern Region Headquarters URL: http://www.srh.noaa.gov/images/epz/wxcalc/densityAltitude.pdf Retrieved February 28, 2015
“Density of Air”
and “Density Altitude” Wikipedia.
URL: http://en.wikipedia.org/wiki/Density_of_air
, http://en.wikipedia.org/wiki/Density_altitude
Retrieved February 26, 2015
“Dewpoint
Formulas” University of Arizona. URL: http://ag.arizona.edu/azmet/dewpoint.html Retrieved February 28, 2015
Glover, Thomas
J. “Pocket Ref” 4th Editiion. Sequoia Publishing, Inc.: Littleton, CO. 2012
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This blog is property
of Edward Shore - 2015
