(45) Air Navigation with a Pocket Electronic Calculator

[SlideRule]

SOME navigators may prefer other methods and other tools, but the Hewlett Packard HP-45 has some fascinating abilities. It might be called the poor man's INS computer, though it does not of course find position. Its only disadvantages are the need for a hood in sunlight and the need for concentration and freedom from distraction. It can be used on the knee for no table is required, and it replaces conversion tables and several other mathematical tables. To a large extent it can replace plotting charts, flight planning charts, Dalton computers, protractors and dividers.
It simplifies ground speed/distance/time and fuel calculations especially, with its ability simply to convert hours, minutes and seconds or degrees, minutes and seconds to and from decimals. It calculates in the decimal mode …
the rest of the article Air Navigation with a Pocket Electronic Calculator, completes the exegesis for an HP-45 with respect to allowable (> 1000 mi.) straight-line air navigation; replete with formulas, illustrations, descriptions, key-code routine(s), etc.

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SlideRule

[StephenG1CMZ]

I guessed allowable > 1000 was meant to say allowable < 1000, since its the larger distances where the straight-line approximation of a sphere is more noticeable. But the text does indeed refer to distances over 1000 miles in US and Canada...
Which leaves me wondering whether other countries were more accurate, or simply using km instead of miles.

[SlideRule]

In my first draft, I put ≤ in rather than >: went with the article for clarity.

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SlideRule

[Thomas Klemm]

The routine for the rhumb-line course is overly complicated.
We don't have to convert angles to radians if we keep the calculator in DEG mode.
Keeping the intermediate values on the stack makes the use of registers obsolete.

HP-45

λ_A D.MS→
λ_B D.MS→
-
π ×
180 ÷

L_A D.MS→
90 +
2 ÷
TAN ln

L_B D.MS→
90 +
2 ÷
TAN ln

-
→P R↓


Example

-15.2553 D.MS→
-59.3630 D.MS→
-
π ×
180 ÷

0.7710


28.0738 D.MS→
90 +
2 ÷
TAN ln

0.5119


13.0546 D.MS→
90 +
2 ÷
TAN ln

0.2306


-
→P R↓

69.9548


180 +

249.9548



HP-15C

With this calculator the hyperbolic trigonometric functions can be used:

\(
\begin{align}
\psi =\operatorname {gd} ^{-1}\phi =\operatorname {arsinh} (\tan \phi )
\end{align}
\)


λ_A →H
λ_B →H
-
→RAD

L_A →H
TAN
HYP^-1 SIN

L_B →H
TAN
HYP^-1 SIN

-
→P R↓


Example

-15.2553 →H
-59.3630 →H
-
→RAD

0.7710


28.0738 →H
TAN
HYP^-1 SIN

0.5119


13.0546 →H
TAN
HYP^-1 SIN

0.2306


-
→P R↓

69.9548


180 +

249.9548


The example calculates the course angle from Las Palmas (Spain) to Bridgetown (Barbados) on the loxodrome.

References

• Course angle and the distance between the two points on loxodrome (rhumb line).
• Calculate distance, bearing and more between Latitude/Longitude points
• Rhumb line
• Gudermannian function