# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Flight Navigation**

**From:**Gary LaPook

**Date:**2007 Mar 12, 01:07 -0700

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. --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to NavList@googlegroups.com To unsubscribe, send email to NavList-unsubscribe@googlegroups.com -~----------~----~----~----~------~----~------~--~---