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Old 06-19-2019, 12:19 PM   #7
Silent Hunter
Join Date: Dec 2004
Location: AN9771
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And while I'm at it:

Calculating turn radius for (submerged) dead-reckoning:

1: Line up the Odometer distance moved during the turn on the distance scale (light yellow disk inside scale), with turn degrees in seconds on the time disk. (360 degrees is 6 minutes)
2: Locate the 'Magic value' 180/pi on time-disk at 9m33s.
3: Read turn radius on the distance disk across the 'magic value' (180/pi) at 9m33s.


Odometer distance: 250m
Turn angle: 43 degrees

Align 250(.0)meters to 43s (or 7m10s).
Read radius as 333(.1) meters against magic value 9m33s

Calculate chord distance (to locate end of turn with shortcut line)

(Or in laymen's terms: The straight line across pizza-slice crust corners)

Note: This calculation assumes a inside turn, i.e. the shortest corner. If taking an outside turn (the turn is larger than 180 degrees) then use the complement of it instead: 360 - turn angle. Example: turn =215 degrees; use 145 as turn angle and 72.5 degrees as halve of the turn in step 2.

1: Align calculated turn radius to 90 degrees (index on the dark brown disk).
2: Locate the halve turn angle on the brown disk angle scale
3: Read the semi-chord length opposite to the halve turn angle.
4: Turn the semi-chord length mark to 30 degrees (that is a 'magic number' for 0.5) on the brown sine-angle disk.
5: Read the actual chord-length opposite to 90 degrees.

[EDIT] Example:
Turn radius 333(.1) meter against 90 degrees
Halve turn angle is 21.5 degrees
Semi-chord length is opposite to 21.5 degrees at 122(.1) meter .
Turn 122(.1) meter to 30 degrees
Full chord length is 244(.2) meters opposite to 90 degrees.

P.S. I don't see why people actually bother with calculating this chord-length. But it's is provided anyway to complete the toolset.

I think it is much easier to draw a line perpendicular to own course at the start of the turn towards the center of the turn. Make it's length the turn radius. Then draw another line (or circle) from there to the angle of the end of the turn (length as radius). And start the new own-course track from that endpoint.

Last edited by Pisces; 06-19-2019 at 12:35 PM.
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