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    Re: Evaluation of H.O. 218
    From: Gary LaPook
    Date: 2011 Mar 14, 12:28 -0700

    H.O. 218 already has dealt with refraction by adding it in to its computed altitudes, This was done to help flight navigators since they would not have to then apply a refraction correction to their sextant altitudes. Bubble sextants normally do not have an index error and since a flight navigator doesn't have to apply any dip or semi-diameter corrections, by applying the refraction correction (with reversed sign) to the computed altitude the flight navigator could compare his sextant altitude directly with the values printed in H.O. 218 to determine his intercepts. This obviously saves time (and in a plane traveling at several hundred knots this is very important) and also prevents errors. Look at whatever form you use to correct sextant altitudes to arrive at observed altitude and then erase all the lines except "Hs" and "Ho"! When using H.O. 218 and a bubble sextant, Ho = Hs.

    If you are using a marine sextant,  the way you should use H.O. 218 is to simply not apply the refraction correction to your sextant altitude except when the altitude is less that 13° in which case you subtract just the one minute correction as shown in table IV of H.O. 218 from Hs to compute Ho. (Of course you also need to apply the other corrections, I.C., and dip.) This one minute correction only applies to low altitudes and is not applied to higher altitudes. But then, if you are shooting the sun or the moon, you will have to apply the semi-diameter correction.

    If you are using the sextant altitude correction tables in the Nautical Almanac (which combine the refraction and semi-diameter corrections) for your sun and moon shots, and you like them (I don't), then another way to use H.O. 218 is to subtract the "Stars and Planets" refraction correction from the tabulated values in H.O. 218. For low altitudes, requiring the additional one minute correction, subtract that one minute from Hs or add it to the tabulated values in H.O. 218 before subtracting the refraction correction. Run a few trials with made up sextant altitudes and you will see that you end up with the same intercepts as when using H.O. 249 and other computation methods (rounded to one minute accuracy.)

    --- On Sun, 3/13/11, Gary LaPook <glapook@pacbell.net> wrote:

    From: Gary LaPook <glapook@pacbell.net>
    Subject: [NavList] Evaluation of H.O. 218
    To: NavList@fer3.com
    Date: Sunday, March 13, 2011, 11:20 PM

    Hewitt wrote:

    Hi Paul -

    �I believe Gary has personal experience with HO 218. I have volumes D (15̊ - 19̊ N&S) and F
    (25̊ - 29̊ N&S).

    The nice thing is they're compact - 6.5"X10"X.75". They're obvious shortcoming is each covers
    only 5̊ of Latitude. Initial entry is for declination (whole number), with the pages for each
    declination thumb-tabbed. The print is large and crisp. They're well made - thick cream-toned
    paper, cloth bindings - so just as books-qua-books, they're lovely. A pleasure to handle.

    The star treatment is really slick, though limited to 22 stars. I tried one for 2010 against my
    StarPilot and did get a 5NM difference. But I was extrapolating the correction table which ends
    for the year 2000.


    I have the entire set. A comparison with H.O. 249 shows that it provides the same level of
    accuracy in very compact volumes. The computed altitudes include the refraction correction for a
    5,000 foot flight altitude but, since the minimum computed altitude tabulated is 10̊, this doesn�t
    cause a problem because for observed altitudes much greater than 10̊ the refraction is the same
    at 5,000 feet as it is at sea level (to a one minute of arc accuracy.) Even at 10̊ the difference is
    only one minute. An auxiliary correction table is included in the tables to allow for observations
    taken at different flight altitudes. I have attached a copy of this table.

    So that you can compare for yourselves, I have attached an excerpt from H.O. 218 for latitudes
    30̊-34̊ and for declination 19̊ and also the pages from H.O. 249 that covers the same

    I have highlighted examples for latitude 30̊, declination 19̊, both same and contrary names, and
    hour angles of 15̊, 55̊ and 65̊. For the all the examples except hour angle of 65̊ and
    declination 19̊ contrary name, the computed altitudes have the difference expected between the tables that are equal to the refraction correction in the Nautical Almanac.  For
    that exceptional case, which has a computed altitude of about 10̊, you find what appears to be a
    4 minute difference when a 5 minute difference is expected, but, in fact, after the proper refraction corrections are applied, the two
    computed altitudes are the same. H.O. 249 gives the computed altitude as 10̊ 34' and H.O. 218
    gives 10̊ 38' which includes the refraction correction at 5,000 feet. When refraction correction is
    applied to Hc it is added instead of being subtracted from observed altitude. The auxiliary
    correction table shows an additional refraction correction for sea level observations of 10̊ to be a
    minus 1' to be applied to observed altitude. So to apply this additional correction to the tabulated
    Hc in H.O. 218 we add this one minute making it 10̊ 39'. To directly compare the Hc in H.O.
    249 to this we must also add the refraction correction from the nautical almanac, 5.3' rounded to
    5', to the tabulated Hc of 10̊ 34' which ends up with the same Hc of 10̊ 39'.

    I have also attached the refraction correction table from the Air Almanac so you can compare the
    corrections for sea level and 5,000 feet.

    I did a more thorough comparison using H.O. 214 to look for the effect of rounding in both H.O. 218 and 249. Using all of the combinations for latitude 34 and declination of 19, I added the refraction correction from the Nautical Almanac to the values from H.O. 214 (which which are tabulated to one-tenth of a minute of arc) and found for all cases with Hc greater than 13 that they then totaled to the Hcs tabulated in H.O. 218 as expected. For Hcs of 10 to 13 adding the additional one minute of arc as required in the auxiliary table produced the correct value.

    So it appears that H.O. 218, when the refraction correction is applied properly, produces the same computed altitudes as H.O. 249 which are also correct as rounded from H.O. 214.

    I will evaluate the selected stars section of H.O. 218 is a separate post.


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