HP 48G Collection
Contents:
Intensity of Spherical Light Source
Speed of Light in Dry Air
Pressure of Air
Earth's Gravity at a Specific Latitude
Light of Sight: Altitude
Intensity of the Spherical Light Source
INTSP:
<< '1_cm' * '1_m' CONVERT SQ 4 * π * →NUM SWAP '1_W' * SWAP / >>
I = P/(4π(r/100)^2)
Input:
2: power in Watts (W)
1: spherical radius in centimeters (cm) No need to enter units.
Output:
1: intensity (W/m^2) with unit object attached
Example:
Input:
2: 1368 (W) 1: 5 (cm)
Output:
1: ≈ 43544.7924_W/m^2
Speed of Sound in Dry Air
CAIR:
<< '1_°C' * '1_K' CONVERT 1.4 * 'R' CONST * '.289647_kg/mol' / UBASE √ >>
c_air = √(φR(T°C+273.15)/M_air)
φ = 1.4, ideal adiabatic of air
M_air = 0.289647 kg/mol, mole of air molecule
R ≈ 8.314462 J/(mol K), ideal gas constant
Input:
1: temperature in degrees Celsius (°C) No need to enter units
Output:
1: speed of sound in air (m/s) with unit object attached
Example:
Input:
1: 18 (°C)
Output:
1: ≈ 342.0631_m/s
Pressure of Air
ρAIR (ρ character: [ α ] [ |→ ] [ R ]):
<< '1_°C' * '1_K' CONVERT 287.05007 '1_J' * '1_kg' / '1_K'
* INV 'StdP' CONST '1_Pa' CONVERT * UBASE >>
ρ = P/(R*(T°C+273.15))
P = 101325 Pa, Standard temperature of pressure
R = 287.05007 J/(kg K)
Input:
1: temperature in degrees Celsius (°C) No need to enter units
Output:
1: air pressure_J/(kg K) with unit object attached
Example:
Input:
1: 18 (°C)
Output:
1: ≈ 1.2124_kg/m^3
Earth's Gravity at a Specific Latitude
The true earth gravity force depends on several factors, such as latitude and altitude. This estimation takes the latitude (north/south) into account.
The constant 9.80665 m/s^2 is an accepted average, the true force varies.
gLAT:
<< RAD HMS→ 90 / π * →NUM COS .026 * 9.806 SWAP - '1_m/s^2' * >>
g_Earth = g_45-(g_poles + g_equ) / 2 * cos(lat * π / 90 radians)
Simplified: g_Earth = 9.806 – 0.026 * cos(lat * π / 90)
g_45 ≈ 9.806 m/s^2
g_poles ≈ 9.832 m/s^2
g_equ ≈ 9.78 m/s^2 Take the cosine of (latitude * π / 90) radians
Input:
1: latitude in D.MMSS (degrees, minutes, seconds) No need to enter units
Output:
1: Earth's gravity at latitude_m/s^2 with unit object attached
Example:
Input:
1: 20.2214
(20°22'14")
Output:
1: ≈ 9.7863_m/s^2
Source: Grainger Engineering Office of Marketing and Communications. (answer written by Rebecca H.) (2016, November 21). “How gravitational force varies at different locations on Earth.” Illinois. https://van.physics.illinois.edu/ask/listing/64061. Retrieved March 10, 2026.
Light of Sight: Altitude
The program calculates altitude required for an airplane to receive a signal from an airplane.
Program LOSALT:
<< '1_nmi' * 3 ROLLD '1_ft' * '1_nmi' CONVERT '3440_nmi' + SQ 3 ROLLD '1_ft' * '1_nmi' CONVERT '3440_nmi' + SQ DUP 4 ROLL SWAP - √ 3 ROLL SWAP - SQ + √ '3440_nmi' - '1_ft' CONVERT >>
Inputs:
3: height of the antenna in feet
2: average height of the terrain between the airplane and antenna
1: horizontal distance from airplane to antenna in nautical miles
Enter numbers only, no need to attach units.
Output:
1: required height in feet, _ft unit object attached
Example:
height of antenna: 426 ft
average terrain height: 846 ft
horizontal distance: 57 nautical mi
required altitude: ≈1519.7282 ft
Note: An average Earth radius is 3440 nautical miles is used. Results will vary since Earth is a spheroid.
Formulas Used:
R_ter: terrain height, Rt = radius_Earth + R_ter
R_atn: antenna height, Ra = radius_Earth + R_atn
D: distance to antenna
R_alt: altitude 1 nmi ≈ 6076.1155 ft R_alt = √(Ra^2 + (D - √(Ra^2 - Rt^2))^2) – radius_Earth
This is a partial adaption of the line of sight distance program of the HP 67.
Source: Hewlett Packard. "Line of Sight Distance" HP-67/HP-97 User's Library Solutions: Avigation. Corvallis, OR. Rev. E. April 1979. pp. 18-22
Eddie
All original content copyright, © 2011-2026. 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.
