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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
carrier was dead reckoning.

==========================================================================|
              | 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 = 1.144 * 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
    dhhogan@earthlink.net  dhhogan@delphi.com

==========

Date: Thu, 15 Jun 1995 22:26:39 -0400
From: sgrant@BIONET.BIO.DFO.CA (Steve Grant)
Subject: Navigation Formulae
To: navigation@ronin.com

Another useful 'trick' for estimating distance off is to hold up a pencil
(or your finger) at arm's length aligned with the edge of an object whose
length you know, say an Island, with one eye closed. Then switch eyes (i.e.
close the open one and open the other); the pencil will appear to jump. The
"Formula" is: "dist = 10 x length of object". e.g. if you are looking at an
island that is 1 mile across, from the direction you are looking at it, and
the pencil jumps exactly from one edge to the other you are about 10 miles
away. The main assumption here is that the angle subtended between your
finger at arm's length and your eyes is about one tenth of a radian i.e.
5.7 deg.  The above equation should really be "dist = (57.3/A) x length of
object" where A is the angle in deg. that the pencil (or finger) moves.
Most people have an "A" of 6-7 deg. You sould 'calibrate' yourself and get
more accurate results! But remember, if it takes two "blinks" to get from
one side of the island to the other the distance is 'half' - not double
because you are 'dividing' be 'A'! Enjoy! You will find this and dozens of
other practical by-eye navigation techniques in "The Practical Pilot -
Coastal Navigation by Eye, by Leonard Eyges, International Marine
Publishing Co., Camden, ME.
STG

Steve Grant             sgrant@bionet.bio.dfo.ca
Canadian Hydrographic Service,  Bedford Institute of Oceanography
P.O. Box 1006,           Dartmouth, NS, Canada, B2A-4A2
23 Garden Court Terrace, Dartmouth, NS, Canada, B3A-3S6
(H) 902-463-5019        (W) 902-426-5409
==========

From: Dan Pfeiffer 
Subject: Re: Navigation Formulae
To: navigation@ronin.com
Date: Fri, 16 Jun 95 8:33:36 EDT

>
> Another useful 'trick' for estimating distance off is to hold up a pencil
> (or your finger) at arm's length aligned with the edge of an object whose
> length you know, say an Island, with one eye closed. Then switch eyes (i.e.
.....snip....
> because you are 'dividing' be 'A'! Enjoy! You will find this and dozens of
> other practical by-eye navigation techniques in "The Practical Pilot -
> Coastal Navigation by Eye, by Leonard Eyges, International Marine
> Publishing Co., Camden, ME.
> STG
>
Another great source for all sorts of tricks like this and lots
of other facinating stuff is a book called "Emergency Navigation".
I don't have the author's name (lent mine ...) but I recently
saw it in a book store at Fisherman's Warf S.F. while visiting
with AWS last month.  So the book is available.  And I think it's
in the West Marine catalog.  Maybe someone knows the author.
The book is all about how to navigate with next to no instrumentation
(e.g. just your fingers) and how to fabricate simple instruments
from items you might have abord.

-DHP
pfeiffer@humboldt.kent.edu

   

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