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Re: Celestial up in the air
From: Gary LaPook
Date: 2008 Jul 25, 03:10 -0700

```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

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 will see that the altitude changes at
> the predicted rate, 30' per degree of LHA change. Also look at Capella
> for LHA 18 to 32 on page 13 to see that this also works for selected stars.
>
> But what happens if the azimuth is not straight east or west? In this
> case the change of altitude is related to the cosine of the difference
> in the azimuth from east or west (which just happens to be the same as
> the sine of the azimuth) times the rate of change for the straight east
> and west cases. Using, for example, cases where the azimuth is 30� (sin
> is .5), which is 60� (cos is .5) from east, the change in altitude
> should be at half the rate of the east case since the cosine of 60� is
> .5. Look at page 8 for 0� latitude LHA 6 to 7 and declinations of 11 to
> 12 (producing azimuths of 30�) show changes of altitude at a rate of 30'
> per degree of LHA change, just as expected, one half the rate for the
> straight east case. Look at page 9 for the 60� latitude, LHA 25 to 28
> and declination zero for 150� azimuth gives a rate of 15' per degree of
> LHA change (one half of one half of 60')  and look at page 11, Capella
> LHA 115 to 117 and page 13, Betelgeuse LHA 64 to 65 for examples for
> selected stars.
>
> These changes are the basis for the "Motion of the Body" (MOB)
> adjustment tables attached as pages 5 and 7. Review these tables and you
> will see they produce the same resulting changes in altitude as shown in
> the previous discussion. Another way to look at this is that you are
> interpolating for minutes of LHA (LHA not being whole degrees) as
> discussed in the previous thread regarding such interpolations using
> minutes of time rather than minutes of LHA as the entering arguments.
>
> Now we come to, what might be confusing, the sign to apply to these
> adjustment. Consider the first example, on the equator looking straight
> west. Since the altitude is decreasing as time goes by, if the sight is
> taken before fix time (the time used for the computation) then the
> measured altitude, Hs, should be higher than that computed for the fix
> time by the amount shown in the "MOB" table or 15' higher for each
> minute the sight is earlier or one degree if the shot is four minutes
> before fix time. This adjustment would be added to the Hc for the fix
> time to compute the Hc for the earlier sight so the sign would be "+" so
> as to arrive at the same intercept. So for any body observed to the west
> the sign will be "+" and, by the same logic, the sign will be "-" for
> any body observed to the east. If a shot were taken after the fix time
> (which is not normally done) you would reverse the signs of these
>
>  The MOB table and also the MOO tables have a confusing table specifying
> what sign to use. You would use the listed sign if the sight were
> earlier than the fix time and the adjustment was to be applied to the
> observed altitude. Since normal practice is to make the adjustment to
> Hc, not to Ho, you must reverse the listed signs. If the shot were taken
> after the fix time you would reverse the already reversed signs and used
> the listed signs (whew).  But for normal flight navigation cases just
> remember to reverse the listed signs as you make the adjustments to Hc.
>
> The next installment will discuss the "motion of the observer" adjustment.
>
> gl
>
> Gary J. LaPook wrote:
> > I was alaready thinking about doing that and will try to get it done
> > in the next couple of days.
>
> > gl
>
> > jean-philippe planas wrote:
>
> >> Gary,
>
> >> I also enjoyed your very clear article.
> >> However, could it be possible that you provide the list with a
> >> practical exercice (example) with figures taken from a real LOP
> >> computation involving 3 bodies shooting in the air to illustrate the
> >> process?
> >> JPP
>
> >> --- On Sun, 7/13/08, Frank Reed  wrote:
>
> >>     From: Frank Reed
> >>     Subject: [NavList 5822] Re: Celestial up in the air
> >>     To: "NavList"
> >>     Date: Sunday, July 13, 2008, 3:12 PM
>
> >>Gary,
>
> >>I very much enjoyed your article and learned quite a bit from it. Well-
> >>written and clear!
>
> >>-FER
>
>
>
>  HO 249 extracts .pdf
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