Vector Arithmetic

HP-29C, 2019.06.27

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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
f
g
key the result of the vector arithmetic is recalled from storage registers **R.₁** (Σx) and **R.₃** (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 ¦ **0**.

01 15 13 00 ; LBL 0 02 14 11 02 ; FIX 2 03 15 34 ; DEG 04 14 34 ; CLEAR 𝝨 05 04 ; 4 06 05 ; 5 07 31 ; ENTER 08 01 ; 1 09 05 ; 5 10 00 ; 0 11 14 44 ; ->R 12 25 ; Σ+ 13 02 ; 2 14 05 ; 5 15 31 ; ENTER 16 04 ; 4 17 00 ; 0 18 14 44 ; ->R 19 14 25 ; Σ- 20 24 25 ; RCL Σ+ 21 15 44 ; →P 22 14 74 ; PAUSE 23 21 ; Swap xy 24 14 74 ; PAUSE 25 15 12 ; RTN 26 74 ; R/S