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
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