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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
    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
        West Covina, CA
        dhhogan@XXX.XXX
    
    

       
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