(45) Air Navigation with a Pocket Electronic Calculator

[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