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    Re: Celestial up in the air
    From: Gary LaPook
    Date: 2008 Jul 28, 05:24 -0700

    One more thing to discuss before giving an example of in flight celnav
    is corrections to sights taken in flight. We discussed this back on
    December 14, 2007 in the thread "additional corrections... (just
    search "additional corrections") which include an excerpt from AFPAM
    11-216. You should download the entire manual here:
    http://www.e-publishing.af.mil/shared/media/epubs/AFPAM11-216.pdf
    
    Review chapters 10 through 13.
    
    I want to add to the manual on this.
    
    Coriolis can be handled in a number of ways. You can move the A.P. to
    the right (northern hemisphere) 90� to the course (track) prior to
    plotting the LOPs by the amount of coriolis correction shown in the
    table in the Air Almanac and in H.O. 249 (previously posted). Or you
    can move the final fix the same way. Or, the most complicated way, is
    to make a correction to each Hc by multiplying the coriolis correction
    by the sine of the relative Zn, the Polhemus makes this relatively
    painless.
    
    Rhumb line correction is avoided by steering by directional gyro
    during the two minute shooting period and this is what is normally
    done anyway.
    
    Wander correction is small at low airspeeds and it can be avoided by
    making sure the heading is the same at the end of the shot as it was
    at the beginning of the shot. It doesn't matter how the heading
    changes during the shot (within reason) as the errors will average
    out.
    
    Ground speed correction can also be avoided by making sure the
    airspeed is the same at the end as at the beginning, any changes in
    between will also average out.
    
    Auto pilots do a good job of maintaining airspeed and heading for the
    two minute shooting period so eliminating the need for the above
    corrections.
    
    The AFPAM states you must figure the refraction correction based on
    the actual Hs as opposed to using the refraction correction based upon
    the Hc but this is a needless refinement and keeps you from completing
    the pre computation prior to the shot. Look at the refraction table in
    H.O. 249 (previously posted) and you will see for altitudes exceeding
    10� that the brackets are at least two degrees wide. So only in the
    rare cases where the altitude is almost exactly at the break point
    could you come up with a different refraction correction using Hc
    rather than Hs and even then it could only be a difference of one
    minute of altitude. For example the break point between a 5'
    correction and a 4' refraction correction is 12� so if Hs were 11� 50'
    and Hc were 12� 15' then using Hc would get you a 4' correction and
    using Hs would get you a 5' correction. This is actually only 1/2 of a
    minute error because the corrections are rounded to the nearest full
    minute.
    
    
    The parallax in altitude correction for the moon is printed on each
    page of the Air Almanac based upon the horizontal parallax (H.P.) for
    the moon on that particular day. This parallax varies with the
    distance to the moon and moves in lock step with the S.D. since they
    are both related to the distance to the moon. The H.P varies from 54'
    to 61' during the year. For example, using the page from the Air
    Almanac found on page 206, a day when the H.P is 60', and an altitude
    of 36� we find the parallax in altitude correction to be 48' and this
    would be the correction to use with a bubble sextant. If using a
    marine sextant and shooting the lower limb we would add the S.D. of
    16' to produce a total correction (but not including refraction yet)
    of 64'. Subtract the refraction correction of 1' gives the total
    correction of 63'. Using the correction table in the Nautical almanac
    for the identical parameters you get 63.5'. The Nautical Almanac moon
    correction table includes a procedure for using it with a bubble
    sextant and what this does is just backs out the S.D. correction which
    is included in the correction table and not needed for a bubble
    observation. Using this procedure produces a correction for a bubble
    observation of 47.2' which compares with the 48' from the Air Almanac.
    
    Remember to reverse the signs of these corrections and apply them to
    Hc to produce Hp (pre computed altitude) which you then compare
    directly with Hs to compute intercept.
    
    gl
    
    
    
    On Jul 25, 7:48 pm, Gary LaPook  wrote:
    > We can also use the Polhemus computer to calculate the MOO adjustment.
    > We do this by setting the ground speed  in the setting window and read
    > out the MOO in the "ZN-TR" window adjacent  to the relative Zn. (See
    > Pol1.jpg) (Zn-TR is another way of saying "relative Zn" since you
    > calculate relative Zn by subtracting Track from Zn.) Looking at the top
    > of the TR-ZN window where the relative Zn of 000� is adjacent to "5" in
    > the MOO window showing that the aircraft moves 5NM per minute which
    > causes the altitude to also change 5' every minute when the body is
    > directly ahead of or directly behind the aircraft. This MOO is
    > equivalent to the MOO table at page 6 of the original PDF which
    > tabulates the MOO adjustment per minute. Multiplying this 5' times the
    > same eight minute period gives the same 40' adjustment we got from the
    > MOO table on page 4 of the PDF. You will also find that the adjustment
    > is 2.5' adjacent to the relative Zn of 60� which multiplied by eight
    > minutes gives the 20' adjustment we found in the table on page 4.
    >
    > The Polhemus makes it easy to figure the relative Zn. You place the "SET
    > TRACK" pointer on the track of the aircraft ,130�  as shown in the
    > attached image. (see Pol2.jpg) Look at the next image (Pol3.jpg) for the
    > second case, a track of 70� and you find the relative Zn, 60� on the
    > inner scale.
    >
    > The Polhemus also makes it easy to figure the sign to use for the
    > adjustment, if the relative Zn is on the white scale, meaning the body
    > is ahead, then the sign is minus and if found on the black scale (the
    > body is behind) then the sign is plus when these adjustments are made to
    > Hc, the normal method. This same pattern is revealed in the two MOO
    > tables, the top of the tables show the body ahead and the bottom has the
    > body behind.
    >
    > gl
    >
    > glap...@pacbell.net wrote:
    > > Now let's talk about the "motion of the observer" (MOO) adjustment.
    > > Every fix in the air is a running fix because the aircraft moves a
    > > considerable distance between the first and last sight. Assuming the
    > > normal eight minute spacing between the first and last shot, a slow
    > > airplane, say 100 knots, will have traveled 14 NM while a 450 knot
    > > plane will have traveled 60 NM. In marine practice the navigator will
    > > advance the earlier LOPs to cross them with the last shot. The MOO
    > > adjustment accomplishes the same thing.
    >
    > > As an example of how this works consider a sun shot taken at 1000Z
    > > resulting in an observed altitude, Ho, of 35� 55'. After doing the
    > > normal sight reduction you end up with an Hc of 35� 45' at the chosen
    > > A.P and a Zn of 130�. This results in an intercept of 10 NM toward the
    > > body, 130�. To plot this LOP you draw the azimuth line from the A.P
    > > and measure off the 10 NM intercept toward the sun and plot the LOP
    > > perpendicular to the Zn.
    >
    > > Then, two hours later at 1200Z you take another altitude of the sun
    > > and to obtain a 1200Z running fix you must advance the 1000Z sun line
    > > to cross the 1200Z line. There are three ways to advance the LOP.
    > > First, you can pick any spot on the LOP and lay off a line in the
    > > direction of travel of the vessel, measure off the distance traveled
    > > along that line, make a mark there and then draw a line through that
    > > mark that is parallel  to the existing LOP and label the advanced LOP
    > > "1000-1200Z SUN." A second way is to advance each end of the LOP and
    > > then just draw a line through these two points, this avoids having to
    > > measure the azimuth when laying down the advanced line. The third way
    > > is to advance the original A.P and then from the ADVANCED A.P. plot
    > > the LOP using the ORIGINAL intercept and Zn. Any of these methods will
    > > produce the same advanced LOP.
    >
    > > Now let's consider a simple case. Suppose the vessel's course is the
    > > same as the Zn, in this case, 130� and the vessel's speed is 20 knots
    > > meaning it has traveled 40 NM in the two hour period. In this simple
    > > case we can just extend the Zn line an additional 40 NM and then plot
    > > the advanced LOP at that point. So,  the LOP is now 50 NM from the
    > > original A.P., the original 10 NM intercept plus the additional 40 NM
    > > that the vessel has traveled on the same course as the azimuth. Since
    > > we have no interest in actually plotting the 1000Z LOP, as we are just
    > > planning on having the 1200Z running fix, we can skip drawing the
    > > earlier LOP and just plot the advanced LOP by adding the distance
    > > traveled to the original intercept to get a total intercept now of 50
    > > NM and using that adjusted intercept to plot the advanced LOP using
    > > the ORIGINAL A.P. This method also creates the exact same advanced LOP
    > > as the other three methods. This last described procedure is how the
    > > MOO table is used.
    >
    > > Look now at the MOO table, page 4 of the PDF in my original post.
    > > Assume now we are in 300 knot airplane and the first sight is taken at
    > > 1152Z, eight minutes prior to the planned fix time. At the top of the
    > > column marked "300" knots ground speed you find the number "20"
    > > showing that the plane will travel 20 NM (and so the altitude of the
    > > body should change by 20 minutes of arc) in a 4 minute period. Also
    > > notice that the top row of values are marked for a relative Zn of 000�
    > > meaning the body is directly ahead, as in our example. The plane will
    > > obviously travel 40M in the normal 8 minute period from the first to
    > > the last shot of a three star fix. The sign convention is the same as
    > > that for the MOB table so simply draw a horizontal line across the
    > > center of the table and place a big minus symbol for the top half and
    > > a big plus mark for the bottom of the table. If the body is in front
    > > of you the sign is minus and the sign is plus if the body is behind
    > > you. With these markings we can take out of the table a minus 20'
    > > value for our example and double it to have a total MOO adjustment of
    > > minus 40' to apply to the Hc.
    >
    > >  Let's do the math. Hc of 35� 45' minus 40' gives us an adjusted Hc of
    > > 35� 05'. Since the Ho is 35� 55' we compute an intercept of 50 NM
    > > TOWARD and plot the LOP using the ORIGINAL A.P. and Zn  and this new
    > > adjusted intercept. You can see that this method produces the same
    > > advanced LOP as the previous methods.
    >
    > > In the more normal case the course will not be the same as the Zn so
    > > the change in altitude will be less since the maximum change occurs
    > > when the body is straight ahead or directly behind the aircraft.  The
    > > change in altitude due to MOO is computed by the cosine of the
    > > difference between the Zn and the course ( "track" in the air), the
    > > relative Zn multiplied by the maximum change possible, the zero degree
    > > relative Zn case. So, in our example, if the track of the the plane
    > > (course) were 070� then the relative Zn would be 60� (130-70=60) and
    > > we would look in the table for that relative Zn in the 300 knot column
    > > and take out a value of 10' which we would expect since the cosine of
    > > 60� is .5 so the MOO should be one half of the maximum possible for a
    > > 300 knot ground speed.
    >
    > > In practice, the MOO and the MOB adjustments are totaled and then
    > > multiplied by the adjustment periods covered, (4 minutes on pages 4
    > > and 5 and one minute on pages 6 and 7) to arrive at the total
    > > "motions" adjustments.
    >
    > > gl
    >
    > > On Jul 23, 2:58 am, "Gary J. LaPook"  wrote:
    >
    > >> Before I can give an example of how celnav is done in flight I must
    > >> explain how some things are done differently in flight.
    >
    > >> The first thing to discuss is the "motion of the body" adjustment. The
    > >> marine practice is to take the sight, consult the almanac for the GHA of
    > >> the body (or Aries) for the even hour before the sight and then add an
    > >> increment for the minutes and seconds after the hour. The navigator
    > >> then  chooses an assumed longitude to make the the LHA used in the
    > >> computation a whole number of degrees.
    >
    > >> It is done differently in flight. The flight navigator plans a fix time
    > >> on the hour or at even ten minute intervals after the hour (the Air
    > >> Almanac publishes data for every ten minutes) and takes out the GHA
    > >> without any interpolation. He then chooses an assumed longitude to make
    > >> a whole number of degrees of LHA and computes his Hc based upon this.
    > >> Since two out of the three sights will be taken earlier than the fix
    > >> time it is necessary to make adjustments to allow for this and this is
    > >> what the "motion of the body" adjustment is all about and this is how it
    > >> works. Think this one through. Imagine your  latitude is on the equator
    > >> and you are shooting a star directly west of your position, azimuth
    > >> 270�. Since the earth turn 15' per minute of time, (15 nautical miles)
    > >> the altitude of that star will get lower at the same rate, 15' per
    > >> minute and 60' in four minutes. Attached are pages from H.O. 249 to
    > >> illustrate this. Look at the first column on page 8 of the PDF file
    > >> which is the 0� page of H.O. 249 volume 2 and you will see that the
    > >> altitude decreases exactly one degree (60') for each one degree increase
    > >> of LHA which takes four minutes of clock time. This also works with H.O.
    > >> 249 volume 1, see page 11 and look at Procyon at LHA Aries of 45 to 48.
    >
    > >> What happens at a different latitude? The earth still turns at the same
    > >> rate but the minutes of longitude become smaller as you move away from
    > >> the equator based on the cosine of the latitude. For example, at a
    > >> latitude of 60�  a degree of longitude is only half  as long as it is at
    > >> the equator since the cosine of 60� in .5 (30 nautical miles) and the
    > >> change of altitude for a sight on an azimuth of 270� should also be one
    > >> half or 30' per degree of LHA change. Look at the all columns on page 10
    > >> of the PDF file, which is the 60� page, at LHA 85� to 90� which results
    > >> in a 90� (270�) azimuth and you
    >
    > ...
    >
    > read more �
    >
    >  Pol1 .JPG
    > 188KViewDownload
    >
    >  Pol2.JPG
    > 188KViewDownload
    >
    >  Pol3.JPG
    > 188KViewDownload
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