Vector Arithmetic

HP-29C / GO-25, 2019.07.30

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*Theory*

Grizzled bush pilot Apeneck Sweeney's converted Swordfish aircraft has a true air speed of 150 knots and an
estimated heading of 45°. The Swordfish is also being buffeted by a headwind of 40 knots from a bearing
of 25°. What is the actual ground speed and course of the Swordfish?

The course and ground speed are equal to the sum of the instrument vector (150 knots, 45°) and the wind vector (-40 knots, -25°), but since the wind vector opposes the instrument vector the result is a vector subtraction. (North becomes the x-coordinate so that the problem corresponds with navigational convention.)

The vectors are converted to rectangular coordinates and summed using the
g and
D
keys. Using the **RCL**
key the result of the vector arithmetic is recalled from storage registers **R₇** (Σx) and **R₄** (Σy)
and placed in the **X** and **Y** registers. The new summed rectangular coordinates are then converted
back to polar coordinates to give the vector of the actual ground speed and course, (113.24 knots, 51.94°).

*Instructions*

To run, enter:

e **00**

,

01 15 74 ; NOP 02 14 11 02 ; FIX 2 03 15 32 ; DEG 04 14 33 ; CLEAR REG 05 04 ; 4 06 05 ; 5 07 31 ; ENTER 08 01 ; 1 09 05 ; 5 10 00 ; 0 11 14 09 ; ->R 12 25 ; Σ+ 13 02 ; 2 14 05 ; 5 15 31 ; ENTER 16 04 ; 4 17 00 ; 0 18 14 09 ; ->R 19 14 25 ; Σ- 20 24 04 ; RCL 4 21 15 74 ; NOP 22 24 07 ; RCL 7 23 15 09 ; →P 24 14 74 ; PAUSE 25 21 ; Swap xy 26 14 74 ; PAUSE 27 15 74 ; NOP 28 13 00 ; GTO 00