HP Prime and TI-84+: Saturation Vapor Pressure, Dew Point, Density Altitude (US Units)

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”  4^th Editiion.  Sequoia Publishing, Inc.:  Littleton, CO.  2012  Print

  

This blog is property of Edward Shore - 2015