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Gary LaPook wrote:


I have reposted this from the "Raw Data for Bubble" thread, since it
might have broader interest.

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 of 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." This is why H. O. 249 only gives the Hc to the
minute, not the tenth of a minute as in H.O 229.




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 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. 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.




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.






The reason using the moon may reduce the accuracy of a fix is the
difficulty of trying to estimate the center a non full moon
and place it in the center of the bubble. Even if the moon looks full
it may not be exactly so a possible error. You also have trouble
trying to put the limb of the moon in the center of the bubble.

Regarding the computations, you work a moon sight like you would a the
sun or
planet using H.O 249 vol. 2 or 3. The only extra step is the parallax
in altitude correction but this is simple since there is a table on
each daily page of the Air Almanac listing this correction for the
moon on that day. You would add it to Hs if using marine practice or
subtract it from Hc to compute Hp using aernautical practice.

Another point, for those learning celestial, I think it is usefull to
use the sextant correction tables from the Air Almanac rather than
those in the Nautical Almanac. In the N.A many of the corrections are
combined into one, e.g. refraction, semi-diameter and parallax in
altitude are all combined in the moon correction table. A learner will
not see the pattern or where the various items of the correction comes
from. Using the A. A. you have separate corrections for refraction
(for all bodies), dip (if using the natural horizon), semi-diameter
(if using the moon or the sun), and parallax in altitude (if shooting
the moon.) This can give you a better grasp on what is going on rather
than rote memorization of the process using the N. A. correction
tables.


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