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    Re: Celestial up in the air
    From: Gary LaPook
    Date: 2008 Jul 28, 05:30 -0700

     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. (Page 206 of
    AFPAM 11-216.)
    Additionally, formulas for these correction are found on pages 393 and
    394 of the same manual.
    On Jul 28, 5:24 am, glap...@pacbell.net wrote:
    > 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 
    > 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
    > ...
    > read more �
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