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## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: Distance Offshore/Introduction
From: Dan Hogan
Date: 1996 Nov 29, 15:18 EST

```Here are some I carry in my NAV Notebook:
The following are a collection of piloting formulas and hints I have picked
up over the years. I carry them in my Navigation Notebook. The "Distance Off
Two Landmarks or Seamarks," was first shown to me by a friend that flew a
TBM Avenger in WWII. He said 99% of his navigation to get back to the
==========================================================================|
| First   | Second    |  Dist. Off    |     Dist. off       |
| Bearing | Bearing   | Sec'd Bearing |       Abeam         |
====================================================|=====================|
Bow & Bearing |  45     |   90      | Dist. Run     | Dist. Run           |
--------------------------------------------------------------------------|
Double Angle  |  ...    | 2 * First | Dist. Run     |                     |
--------------------------------------------------------------------------|
Seven Eights  |  30     |   60      | Dist. Run     | 7/8(.875) * Dist Run|
--------------------------------------------------------------------------|
Seven Tenths  |  22.5   |   45      | Dist. Run     | 7/10(0.7) * Dist Run|
--------------------------------------------------------------------------|
Prediction    |  26.5   |   45      | 1.4 * Dist Run|  Dist. Run          |
==========================================================================|
TIME/SPEED/DISTANCE ( In Hours, Knots , Nautical Miles)
Distance = Speed * Time * ((60, for minutes) or (3600, for seconds))
THE RULE of 60
Distance Abeam * 60 = Bearing on the Bow * Range
TIME at 1 Mile = 60 / Speed
SPEED = (SQRT Bow Wave Length) * 1.33
DISTANCE at 6 Minutes = 1/10 (0.1) * Speed
DISTANCE TO HORIZON = 1.17 * SQRT of HE
BREAKERS AT HORIZION = 3 Miles Off
WINDOWS VISIBLE = 2 Miles Off
COUNT TREES = 1 mile Off
ECHO
Distance Off = 1/2 Time in seconds * .18
SOUND
DISTANCE OFF = Time in Seconds * .18
*************************
FORMULAS FOR CALCULATORS
D = distance
R = distance run
A = First Bearing
B = Second Bearing
Distance Off at Fiirst Bearing & Run Abeam
D = (R x sin A) / Cos A
Distance Off Second Bearing Form Second Bearing on Bow & Run
D = (R x sin A) / (sin A [abs. diff.] B)
Distance Off Abeam with Second Bearing on Bow and Run Betweeen
D1 = (R x sin 2B) / sin C
D2 = D1 x sin A (D2 = distance off abeam)
Distance Run to a Given Bearing & Distance Off When on That Bearing
D1 = (R1 x sin B) / sin C
D2 = D1 x sin A (D2 equals distance off abeam)
*************************************
Sailing to Weather
D = (200 / sine of the angle between tacks) * sine attack angle
D = percentage of the distance to the mark.
attack angle = the angle off the wind when sailing.
*************************************
Distance Off Two Landmarks or Seamarks
s / SIN LS : a /sin LA : b / sin LB
s  = distance between marks
LS = angle diff between a & b
a  = distance from ship to b
LA = angle diff between bearing of a from ship & bearing of b from a
b  = distance from ship to a
LB = angle diff between bearing from b to a & Bearing b from ship
************************************
Tacking Downwind
Total distance sailed =
2 * base distance * sin of the divergence angle/sin (divergence angle * 2)
Chart:
_____________________________________________________
Divergence   |  Speed	 |  Distance	 |   Time
angle       |	         |   to sail	 |   Hrs.
-------------|-----------|---------------|-----------
|           |               |
-------------|-----------|---------------|-----------
Dan Hogan
West Covina, CA
dhhogan@XXX.XXX

```
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