Saturday, July 10, 2021

HP 48G: Scientific Applications

HP 48G:   Scientific Applications



Calculators Featured:  HP 48G, HP 48G+, HP 48GX


Theoretic Freezing Level


The program FRZLVL calculates the theoretical freezing level in feet above sea level given the outside temperature at a given altitude.  The results are displayed in feet (the feet unit is attached).  


HP 48G Program: FRZLVL


<< "FREEZING LEVEL"

{ { "ALT:" "DEFAULT FT" }

{ "TEMP:" "DEFAULT °C" } }

{ }  { }  { }  

IF INFORM

THEN OBJ→ DROP DUP TYPE

IF 13 == THEN '1_°C' CONVERT

ELSE '1_°C' →UNIT 

END SWAP DUP TYPE 

IF 13 == THEN '1_ft' CONVERT

ELSE '1_ft' →UNIT

END SWAP '1000_ft/°C' 

* DUP2 2 / +

"DRY" →TAG 3 ROLLD

1.5 / + "WET" →TAG END >>


Instructions


1.  Run FRZLVL

2.  ALT:  Enter altitude.  You can attach units if you want, the default is altitude is in feet.

3.  TEMP:  Enter outside air temperature.  You can attach units if you want, the default unit is degrees Celsius (°C).

4.  Results: freezing dry level in feet and freezing wet level in feet.  


Example


Altitude:  1,750 ft

Temperature:  -2°C  (28.4°F)


Results:

DRY:  750_ft

WET:  416.666666667_ft


Source:

Hewlett Packard  "Predicting Freezing Levels" HP 65 Aviation Pac 1.  Hewlett Packard.  1974


Lens Calculations 





Variables


Please note the inequality restrictions.  


R = radius of curvature

D = diameter of the lens, D ≤ 2*R

S = sag S ≤ R

θ =  tangent angle between lens axis and reflection 


HP 48G Program: LENSANG


<< 'R=(D^2+4*S^2)/(8*S)' STEQ

{ { "R/D" << 'D' STO 'R' STO EQ  'S' 0 ROOT 'S' →TAG >> } 

{ "R/S" << 'S' STO 'R' STO EQ 'D' 0 ROOT 'D' →TAG >> }

{ "D/S" << 'S' STO 'D' STO EQ 'R' 0 ROOT 'R' →TAG >> } 

{ "→θ" << 'D' RCL 'R' RCL 'S' RCL - 2 * / ATAN 'θ' DUP2 STO →TAG >> } }

TMENU >> 


Instructions


1.  Run LENSANG.  A temporary custom menu appears.  

2.  Enter two known amounts and press the appropriate key to store the variables:


If R and D are known:  R [ ENTER ] D [ F1 ] 

If R and S are known:  R [ ENTER ] S [ F2 ]

If D and S are known:  D [ ENTER ] S [ F3 ]


The third variable between R, D, and S is calculated and displayed as a result.


3.  Press [ F4 ] to calculate the angle, θ.  


Results are stored in the variables R, S, D, and θ.


Examples


Known:  R = 5.8, D = 7.6

LENSANG  5.8 [ ENTER ] 7.6  [ F1 ] (R/D)

Result:  S: 1.41821953996

[ F4 ] (θ).  Result:  θ:  40.9327245742


Known:  D = 11, S = 9

LENSANG 11 [ ENTER ] 9 [ F3 ] (D/S)

Result:  R: 6.18055555556

[ F4 ] (θ).  Result:  θ:  -62.8591312297


Source:


Tuchscherer, L.D.  "Lens Calculations - SAG, ANGLE, MIN/MAX" HP 67 Optics  Hewlett Packard.  1978.


Period of a Pendulum


The program PENDULUM calculates the period of a pendulum given two parameters:


ANGLE: the angle that the pendulum swings out.  The angle must be entered in radians.


LENGTH:  The length of the pendulum in meters. 


Unlike most calculations, the program uses an Legendre elliptic integral of the first kind to increase accuracy.  


T = 4 * √(L / g) * ∫( dx / √(1 - k^2 * sin^ x), x, 0, π/2) where k = sin(α/2)


g = Earth's gravitational constant = 9.80665 m/s^2


This program does not use units.  


HP 48G Program: PENDULUM


<< RAD 

"PENDULUM"

{ { "ANGLE:" "IN RADIANS" }

{ "LENGTH:" "IN METRES" } }

{ } { } { } 

IF INFORM

THEN OBJ→ DROP

9.80665 / √ 4 *

SWAP 2 / SIN SQ 0 θ π 2 /

→NUM 3 ROLL 'X' 

SIN SQ * 1 SWAP - √

INV 'X' ∫ →NUM *  

"PERIOD" →TAG END >>


Example


ANGLE:  π/6   (enter this as 'π/6')

LENGTH: 1.5  (m)

Result:  

PERIOD:  2.50011881685 (s)


Source:

Steers, Hugh.  "The Pit & Pendulum"  Datafile.  ISSN 1352-8254.  Handheld and Portable Computer Club.   V29 N1.  January - March 2010


Eddie


All original content copyright, © 2011-2021.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 


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