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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 = 1.17 * 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 WA6PBY
"Gacha" Catalina 27
San Pedro, CA
dhhogan@concentric.net
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