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    Re: Raw data for bubble
    From: Gary LaPook
    Date: 2007 Mar 11, 19:39 -0700

    Gary LaPook adds;
    A typo that needs to be corrected in my last post in the second to
    last paragraph, you combine the MOB corection with the MOO correction
    to figure total "motions" corrections for the 4 minute period.
    "You look at the MOB table and take out the correction for 4 minutes
    (this is the reason for the 4 minute table) without any interpolation,
    and add to it the 4 minute correction from the MOO table."
    Also, there no reason to get fancy and shoot the moon or the planets
    at night since there are plenty of stars on good azimuths and planets
    do not improve the accuracy of the fix and the moon may decrease the
    accuracy. Working those types of sights takes much more work and time
    than working three stars using vol. 1 of H. O. 249. You might use the
    moon or possibly a planet during the day to obtain a two body fix with
    the sun.
    On Mar 11, 3:16 pm, glap...@PACBELL.NET wrote:
    > Gary LaPook wrote:
    > Congratulations, you guys have managed to reinvent the wheel!
    > Every volume of H.O. 249 contains two tables for correction for the
    > motion of the body (MOB) as well as tables for correction for motion
    > of the observer. The  MOB tables show the change in altitude both for
    > a one minute interval and for a four minute interval as well as an
    > interpolation table for other time intervals based on the observer's
    > latitude and the azimuth of the body. I will try to post them
    > tomorrow.
    > Your formula will also compute this rate. The basis for the formula is
    > that the earth turns 15 minutes of arc in one minute of time which is
    > equal to 15 NM at the equator and at a  slower rate at other latitudes
    > based on the cosine of the latitude, e.g. at 40� lat the earth is
    > turning only 11.5 NM per minute. This, then, is the rate of altitude
    > change per minute, the slope, for a body on azimuth 90� or 270�. Then
    > by multiplying by the sine of the azimuth you find how much of this
    > maximum change will affect the altitude of a body on a different
    > azimuth.
    > There is also a table for the motion of the observer (MOO) which is
    > used to adjust the Hc to allow for the motion of the observer between
    > shots and is the equivalent to advancing the LOP to obtain a running
    > fix. All fixes in the air are "running" since the plane moves a
    > significant distance between the first an last shot, about 60 NM at
    > 450 knots. Even though a boat is moving between shots its small amount
    > of movement can be disregarded.
    > The reason that these tables are provided in H.O 249 has to do with
    > the very different way that celestial is done in the air compared to
    > on the surface.
    >  First, since a bubble sextant is used you can shoot stars anytime you
    > want to during the night and are not restricted to the limited time
    > around twilight. On a boat you wait until twilight and shoot the stars
    > and record the times of the observation, which are random, for your
    > computations. In the air, you decide what time you want a fix and then
    > schedule the times you want to take the sights and then take the
    > sights at the pre planned times.
    > Second, you must come up with a fix rapidly. On a boat you can take
    > the sights and only then go below to start the computations and you
    > could wait until the next day, if you wanted to, to compute the fix.
    > Since a plane is moving so quickly, a ten minute delay in plotting the
    > fix will mean the plane could be 100 NM  from the fix by the time it
    > is plotted so procedures are used to minimize the time between taking
    > the shots and finishing the plot. This includes doing all the
    > computations before taking any sights and this is what these MOB and
    > MOO tables are used for.
    > Third, the level of accuracy achievable and the level of accuracy
    > needed are much less than for marine navigation so is is perfectly
    > acceptable to do the calculations to a lower order of precision, more
    > quickly, and the fixes obtained will be within the achievable level of
    > accuracy. As we say in the artillery, "it is a waste of time to polish
    > the cannon ball."
    > So here is an example of how it is done. First, you decide what time
    > you want a fix, which is usually on the hour. The Air Almanac gives
    > the data for every ten minutes  (I will post a page from it also) so
    > by choosing one of the listed times (usually on the hour) you don't
    > need to do any interpolation of the data. You assume a longitude so
    > that LHA Aries is a whole number and then go to H.O.249 Volume 1 for
    > selected stars and choose which stars you want to shoot which are well
    > spaced in azimuth. Since you are usually above the clouds you can
    > shoot in any direction. You take the values of altitude and azimuth
    > from H.O.249 without any interpolation. These would be the Hc's if all
    > the shots were taken at the planned fix time, which is not possible.
    > You usually plan to space the shots by four minutes since each shot
    > takes two minutes for the use of the averager and this allows two
    > minutes then between shooting to write down the measured altitude
    > (maybe actually plot the LOP) and reset the sextant to get ready for
    > the next star. A common shooting schedule would be to start the first
    > shot at 51 after the hour. You set up the sextant, using the expected
    > altitude and azimuth, and start tracking the body and then you check
    > your watch and trigger the averager at 51:00. You usually shoot the
    > first star near the wing tip since advancing its LOP to the fix time
    > will have little effect on its accuracy. You continue shooting until
    > the shutter closes on the sextant, blocking the view, which tells you
    > that two minutes have elapsed, you have, therefore, shot until 53 so
    > that the mid time is 52 , which is 8 minutes before the fix time.
    > You use the next two minutes to reset the sextant and start tracking
    > the second star and start the averager at 55:00 so the mid time of the
    > second shot is 56:00, 4 minutes prior to fix time. You start the last
    > shot at 59 and continue shooting until 01 after the hour, so the mid
    > time of the third star is on the hour.
    > In order to be able to plot the fix as quickly as possible after
    > shooting the last star you pre compute the expected altitudes so you
    > can compare them immediately with the SEXTANT altitudes (Hs) to
    > determine the intercepts. So, using the MOO and MOB tables you adjust
    > the Hc from H.O 249 to allow for the two shots taken 4 and 8 minutes
    > before fix time. No correction is need for the shot centered on 00.
    > You look at the MOO table and take out the correction for 4 minutes
    > (this is the reason for the 4 minute table) without any interpolation,
    > and add to it the 4 minute correction from the MOO table. This will be
    > the correction for these "motions" for the star shot at 56. You do the
    > same for the first star but you multiply the sum by 2 for the total
    > "motions" for the 52 shot. You add these motions to the Hcs obtained
    > from  H.O. 249. You also ADD the refraction correction (that' right,
    > ADD) and add the index error (if any) so as to arrive at Hp, pre
    > computed altitude. Since you have allowed for index error and
    > refraction (no need for dip when using the bubble sextant) in
    > computing the Hp you do not have to apply them to the Hs so you can
    > compare Hs directly with Hp to determine intercept. It is obvious that
    > the this procedure allows for the determination of intercept much more
    > rapidly after the shot than in marine practice.
    > As part of the pre computation process you have plotted the A.P. on
    > the chart  (only one is needed with H.O. 249 vol. 1 ) after applying
    > the correction for coriolis, precession and nutation, and the azimuths
    > so you can quickly plot the LOPs on the chart (or plotting board). You
    > have completed the fix in one or two minutes after the last shot
    > depending if you had time to plot the first LOPs between shots. So you
    > have a fix at 02 or 03 after the hour and can compute the winds
    > encountered over the last hour and compute a new heading to
    > destination. So by 06 you can give the pilot a new heading and a new
    > ETA.
    > If anybody is interested I can post an example of how this is done.
    > On Mar 10, 5:29 pm, "Peter Fogg"  wrote:
    > > Bill asked:
    > > > Does this look like the method you use to calculate slope?
    > > > Delta H (rate of change in arc minutes) per minute of time  (divide by 60
    > > > for degrees)
    > > > Delta H = 15 * cosine latitude * sine azimuth (or its supplement)
    > > I used a graphical method to indicate slope which gave +32 minutes of
    > > arc over 5 minutes.
    > > This formula gives 32.02; so looks good.
    > > Thanks Bill
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