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    Re: F tables - "F-Tafel"
    From: Gary LaPook
    Date: 2013 Jan 30, 14:13 -0800
    As I said before:

    "I find it surprising that neither Bygrave nor Dennert & Pape came up with a method for dealing with the situation of the body's declination being within 20 minutes of zero since this situation exists for the sun (the most important body) for two days in the spring and two days in the fall, four days out of 365 days a year. My method was not hard to discover and provides accurate results for this situation so it's a mystery to me why similar instructions were not provided with these instruments. Without providing such a procedure navigators would need to learn and carry a complete other celestial computation method to be able to operate each day of the year."

    This confirms that the navigator would have to learn and carry the tables for a completely different method just to deal with this rare special case, the F-Tafel. So I still don't understand why nobody came up with my method to deal with the special case.



    --- On Wed, 1/30/13, Dave Walden <waldendand@yahoo.com> wrote:

    From: Dave Walden <waldendand@yahoo.com>
    Subject: [NavList 22177] F tables - "F-Tafel"
    To: garylapook@pacbell.net
    Date: Wednesday, January 30, 2013, 1:05 PM

    F-tafel, tafel zur vereinfachten berechnung von höhenstandlinien. Im auftage des Oberkommandos der Kriegsmarine herausgegeben von der Deutschen seewarte.
    Corporate Author: Deutsche Seewarte.
    Language(s): German
    Published: Hamburg, 1941.
    Edition: 3. aufl.
    Subjects: Azimuth.
    Note: In upper right corner of t.-p.: 2154.
    Physical Description: xxiii, 88 p. 30 cm.
    Original Format: Book
    Original Classification Number: VK 563 .H19 1941
    Locate a Print Version: Find in a library


    F-Tafel. Tafel zur vereinfachten Berechnung von Höhenstandlinien. Im Auftrage des Oberkommandos der Kriegsmarine herausgegeben von der Deutschen Seewarte.

    * Bookseller: Versandantiquariat Lutz Bäsler (Bad Homburg, Hess, Germany)
    * Bookseller Rating: 3-star rating
    * Quantity Available: 1

    Add to basket

    Price: £ 42.35

    29S[U].—Hamburg, Deutsche Seewarte, publication no. 2154, F-Tafel.
    Tafel zur vereinfachten Berechnung von Höhenstandlinien. 3 Auflage.
    Hamburg, August, 1941. xxiii, 88 p. 19.6 X 29.2 cm. In the third
    edition there were extensions and corrections of the introductory material,
    and of 8 of the 11 tables.
    The method and principal table of this volume are similar in many respects to those of
    H. O. 208 (Dreisonstok, see MTAC, v. 1, p. 79f). The astronomical triangle is divided
    into two right spherical triangles by a perpendicular from the zenith upon the hour circle
    of the star; U is the co-declination of the foot of the perpendicular, and V is log cos B,
    where B is the angle subtended at the zenith by U. By Napier's rules,
    tan U = cos I cot L
    sin B = sin / cos L,
    where /, L, and d are the local hour angle, latitude and declination respectively. By applying
    another of Napier's rules to the right triangle of which the star is one vertex, the altitude,
    h, may be found by
    sin h = cos B sin (d + U)
    log sin h = V + log sin (d + U).
    For the determination of azimuth, Z, two more auxiliary quantities are introduced,
    P which is the great circle distance from the star to the east- or west-point of the horizon,
    and Gr. 4 which is the declination of the intersection of the hour circle of the star with the
    prime vertical. Thus, sin t cosd ■>c osP and sin Z = cos P sec h. Also, tan Gr. S = tan L cos t.
    In Table F I, with vertical argument, latitude 0(1°)70°, and horizontal argument,
    local hour angle 0(4m)6h, three values per page, there are tabulated four quantities, U to
    the nearest O'.l, V to 5D, Gr. 5 and P, each to the nearest 0?1. In the second part of
    Table F I, the vertical argument is latitude, 70°(1°)90°, and the horizontal argument is
    local hour angle 0(4m)6h, nine values per page, three in each horizontal section.
    At ths bottom of the vertical columns in Table F I are azimuths; entering the left
    hand column with altitude as argument, and moving across the pages horizontally until one
    finds under P, the value already copied out, one can drop to the bottom of the column
    and read off the azimuth angle. Since the tabulated values of the azimuth angle go up to
    90° only, it is necessary to have another device to determine the quadrant. When the
    hour angle is greater than 6b, the azimuth is measured from the elevated pole; when the
    local hour angle is less than 6h and L and d are of opposite name, the azimuth is measured
    from the depressed pole. If the local hour angle is less than 6h and L and d are of the same
    name, the azimuth is measured from the elevated or depressed pole according as the declination
    is greater or less than the quantity Gr. a.
    In case the altitude is great, or the azimuth near 90°, the value of the azimuth may be
    poorly determined by the use of Table F I. In such a case, it will be noted that the value
    of P lies below a dotted line running across the page. One must then use instead Table
    F XI, which gives P to the nearest minute of arc and the variation in P corresponding to
    1' change in d or h.
    Table F II is a table of log sin x, x = [0(0'-1)6°(1')90°; 5D], with generous tables of
    proportional parts.
    Tables F DI and F IV represent the principal advantages this volume possesses over
    other similar tables; they permit one to determine the corrections (to the nearest 0!1) to
    the computed altitude corresponding to slight changes in time (up to 2m by 10* steps) or latitude
    (up to 30' by 1' steps) respectively. In both cases, one can interpolate very easily by a
    shift of the decimal point. Table F III is a well-designed triple-entry table occupying only
    five pages; one starts down the column at the left headed by the value nearest the assumed
    latitude, stops at the value nearest the computed azimuth and moves to the right to the
    column headed by the number of seconds change in time. Table F IV is a small doubleentry
    table on a single page; the vertical argument is azimuth 0(5°)20°(2°)90°, and the
    horizontal argument is change in latitude, l'(l')10'(10')30'. These two tables allow one to
    work either with an assumed position or with a dead reckoning position.
    Table F V is for changing time into angular measure and conversely. Table F VI gives
    the corrections for refraction, semi-diameter and parallax to be applied to the altitude
    (3°-90°) of the lower- or upper-limb of the moon; there is a supplementary table for height
    of eye. Table F VU gives the combined correction for refraction and height of eye (0-30
    meters) to be applied to the altitudes (3°-90°) of fixed stars or planets. Table F VIH yields
    the correction for refraction, semi-diameter and height of eye (0-30 meters) to be applied
    to altitudes (3°-90°) of the sun's lower limb; there are also two auxiliary tables to provide
    corrections to the altitudes to take care of the varying semi-diameter of the sun through the
    year, and for the case where the sun's upper limb was observed. The latter takes only a
    very small amount of space and would seem to be quite worthwhile. Tables F IX and F X
    provide similar corrections for use with the bubble sextant.
    The tables are well printed on a good grade of paper. In a number of cases, the rules
    needed to make decisions as to quadrants, etc. are printed on each page. As for the accuracy
    of the tabulated values, only a few rounding off errors of a unit in the last place were
    discovered in a brief examination.
    Charles H. Smiley
    Brown University
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