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In my last post I provided links to the illustrations for my example
of in flight celnav. I found that those links are messy to use so
please follow this link to another copy of my post which will make it
easieer to get to the illustrations:

http://www.geocities.com/chief_of_smoke/FlightCelnav.html

gl

On Aug 6, 1:52 am, glap...@pacbell.net wrote:
> Gary LaPook writes:
>
> Now that we have discussed the technique of flight navigation we can
> now look at an example of how it is actually done. I will use the
> Polhemus computer to illustrate this process which will also show how
> handy this device is but it can also be done on a plotting sheet
> though not so conveniently.
>
> We are ferrying a 1978 Cessna Skyhawk (Cessna 172) from Casa Blanca
> Morocco to Porto Santo Island in the Madeira Islands on October 4,
> 2008 (1.jpg and 2. jpg.)
> http://www.geocities.com/glap...@pacbell.net/1.jpg
> http://www.geocities.com/glap...@pacbell.net/2.jpg
>
> The coordinates of the departure airport are 33� 33' north, 7� 40'
> west. The destination airport is at 33� 04' north, 16� 21 west. Using
> the 35� latitude disk we label the graticle and we then plot the
> locations of both airports and draw a course line between them (3.jpg
> and 4.jpg.) Now, by rotating the disk so that the destination is
> directly above the departure, we can read  out the distance by
> counting the grid lines, departure is at  minus 215 (visually
> interpolating between 210 and 220) and destination is at plus 219 for
> a total distance of 434 NM (5.jpg.) We can also read out the true
> course at the "true Index" which is 266.5�, which we will round to
> 266� (6.jpg.)
>
> http://www.geocities.com/glap...@pacbell.net/3.jpg
> http://www.geocities.com/glap...@pacbell.net/4.jpg
> http://www.geocities.com/glap...@pacbell.net/5.jpg
> http://www.geocities.com/glap...@pacbell.net/6.jpg
>
> Looking at the aircraft flight manual climb schedule (7.jpg), we see
> that we will climb at an airspeed of about 70 knots and that it will
> take 21 minutes to climb to our planned cruising altitude of 10,000
> feet (Flight Level 100, FL100) using 3.7 gallons of fuel in the climb
> and covering 27 NM. Since we also used 1.1 gallons taxiing we will
> have used up 4.8 gallons by the time we level off FL100. We adjust our
> throttle to make 2500 rpm. Since the air temperature is about standard
> (15 � C at sea level and cooling off about  2� C per thousand feet)
> this power setting will produce 61% power which will give us a true
> airspeed of 114 knots and a fuel flow rate of 6.8 gallons per hour
> (8.jpg.) Since we will cover 27 NM in the climb we will have an
> additional 407 NM to cover in cruise after we reach the top of climb
> (TOC). Winds are forecast "light and variable" so using our true
> airspeed of 114 knots we compute that it will take an additional 3+34
> for the enroute phase of the flight for a total flight time of 3+55.
> We will burn 24.3 gallons in cruise plus the climb and taxi fuel means
> we will burn a total of  29.1 gallons out of our total fuel on board
> of 50 gallons leaving us a comfortable 20.9 gallons fuel reserve.
>
> http://www.geocities.com/glap...@pacbell.net/7.jpg
> http://www.geocities.com/glap...@pacbell.net/8.jpg
>
> We take off at 1745Z and climb on course with our true heading of 266�
> and level off 21 minutes later at FL100 at 1806Z and set the power and
> auto pilot. Our ETA is 2140Z, 3+55 after takeoff. We plan on taking a
> celestial fix at 1920Z to allow for an enroute leg longer than one
> hour so as to allow for the determination of an accurate wind vector.
> We will cover 140 NM during the 1+14 minute cruise from TOC at 1806Z
> to 1720Z fix time. Since we covered  27 NM in the climb we will be 167
> NM from departure at the planned fix time. Since the departure was at
> minus 215 on the Polhemus grid we simply subtract 167 from 215 and
> place a mark on our course line at the minus 48 grid line, visually
> interpolating between 40 and 50. Rotating the grid to north up we can
> read out our 1920Z DR of 33 � 27' north, 11� 00' west (9.jpg.)
>
> http://www.geocities.com/glap...@pacbell.net/9.jpg
>
> About a half hour before the fix time we start planning our fix. We
> will be using H.O 249 Volume 1, Selected Stars, since it is the most
> convenient. First we look in the Air Almanac for 1920Z, October 4,
> 2008 and take out the GHA of Aries without interpolation, 303�
> 51' (10.pdf.) We select an AP of 33� 00' north and 10� 51' west so
> that the LHA Aries will be 293� exactly. We use only one AP since we
> are using H.O. 249 vol. 1 and we are accounting for MOO
> mathematically, not advancing the earlier LOPs to the fix time. We
> then look at the 33� north page of H.O 249, vol. 1 and looking at the
> LHA Aries we see that the selected stars are Alpheratz, Enif, Altair,
> Antares, Arcturus, Alkaid and Kochab. Because the visibility is
> limited in a Cessna 172 by its high wing we must choose, not the three
> recommended stars, but Kochab, Arctures and Antares (11.pdf.) We will
> shoot Kochab first since it is nearly on the wing tip and so advancing
> its LOP the most to the fix time will have little effect on its
> accuracy. We plan our shooting schedule, Kochab at 1912Z (eight
> minutes before fix time), Arcturus at 1916Z (four minutes early) and
> Antares at 1920Z. We enter this data our the Celestial Precomputation
> form (12.jpg, if using the Polhemus computer or the 1 minute
> adjustment tables from H.O 249 or 13.jpg if using the 4 minute
> adjustment tables from H.O. 249.) We only compute LHA for the the fix
> time shot but we use the same LHA, 293� to take out the Hcs for all
> three bodies and enter this data on the form in the row labeled "HA HO
> 249" and enter the Zns in the same columns and also on the left side
> of the form for computation of the motion adjustments. We also take
> out the "Precession and Nutation" correction for 2008 for LHA Aries of
> 293� and for a latitude of 33� north, either visually interpolating or
> simply taking the nearest tabulated value since they are all small,
> we'll use .6 NM at 241� and enter it on the appropriate form (14.pdf.)
> We will use this to adjust the fix position. We plot the AP on the
> Polhemus grid at 33� 00' north, 10� 51' west, visually interpolating
> (15.jpg.)
>
> http://www.geocities.com/glap...@pacbell.net/10.pdf
> http://www.geocities.com/glap...@pacbell.net/11.pdf
> http://www.geocities.com/glap...@pacbell.net/12.jpg
> http://www.geocities.com/glap...@pacbell.net/13.jpg
> http://www.geocities.com/glap...@pacbell.net/14.jpg
> http://www.geocities.com/glap...@pacbell.net/15.jpg
>
> Now set the front of the Polhemus "SET TRACK" pointer to 266, the "SET
> GS" (ground speed) to 114 and the "SET LAT" to 33 and then tighten the
> nut to keep the settings from changing (16.jpg.) (We could also do the
> same adjustments using the MOB and MOO tables from H.O 249.) Looking
> around the outside edge for the Zns of each body we find the relative
> Zns (ZN-TR) and enter them on the form, 75� for Kochab, 15� for
> Arcturus and 44� for Antares. Using each body's Zn look in the
> "CORRECTION FOR MOTION OF THE BODY" window and take out the MOB one
> minute correction and enter it in the appropriate blank (17.jpg or
> 18.pdf or 19.pdf.) Since all three Zns are to the west they are all
> found on the black scale so the signs are all plus. Next, using the
> relative Zns  (ZN-TR) look in the "CORRECTION FOR MOTION OF THE
> OBSERVER" window and take out the one minute corrections for MOO
> (20.jpg or 21.pdf or 22.pdf.) Since all of the relative Zns are ahead
> of the plane they are all found on the white scale making all of their
> signs negative. We sum the MOB and MOO adjustments to the "ONE MINUTE
> ADJ." line keeping track of the signs. Since we are planning the first
> shot 8 minutes early, the second shot 4 minutes early and the last
> shot on time, we multiply the one minute adjustments by the delta time
> to produce the total motions adjustments. (We get identical values if
> we use the one minute MOB and MOO tables.  If we are using the 4
> minute adjustment tables we multiply by 2 and 1 adjustment periods
> respectively and get the same values.) We look at the refraction table
> (23.pdf) in the 10,000 foot altitude column and take out the
> refraction for each body and enter it on the form with a plus sign and
> carry them to the "MISCEL" line. Add the total motion adjustment to
> the MISCEL line to arrive at "TOTAL ADJ." and carry to the right side
> of the form into the appropriate columns. Combine the "HA" from H.O.
> 249 with the total adj. to arrive at Hc.
>
> http://www.geocities.com/glap...@pacbell.net/16.jpg
> http://www.geocities.com/glap...@pacbell.net/17.jpg
> http://www.geocities.com/glap...@pacbell.net/18.pdf
> http://www.geocities.com/glap...@pacbell.net/19.pdf
> http://www.geocities.com/glap...@pacbell.net/20.jpg
> http://www.geocities.com/glap...@pacbell.net/21.pdf
> http://www.geocities.com/glap...@pacbell.net/22.pdf
> http://www.geocities.com/glap...@pacbell.net/23.pdf
>
> The last bit of information we take from the Polhemus is the Coriolis
> correction which is found in the "CORIOLIS & WANDER CORR." window.
> Look at the latitude, 33�, and take out the coriolis correction of 1.7
> NM (20.jpg), ( 2 NM if taken from the H.O. 249 table 23.pdf.) We will
> use this to move the plotted fix 1.7 NM in direction 356� , 90� to the
> right of the track to account for coriolis. (Alternatively we could
> make the same adjustment to to the AP prior to plotting the LOPs,
> dealers choice. We could also use the Polhemus to derive a coriolis
> correction to be applied to each Hc mathematically but that is a
> needless complication especially at low air speeds.)
>
> http://www.geocities.com/glap...@pacbell.net/20.jpg
> http://www.geocities.com/glap...@pacbell.net/23.pdf
>
> We are now done with the precomputations and can relax until time to
> shoot Kochab. About 1908Z we get the sextant ready, illumination on,
> bubble formed, averager set and altitude set to about 37�. We also
> make sure that the directional gyro is set and that the autopilot is
> set to heading mode. We look out the window, locate Kochab and bring
> it into the center of the bubble. At 1911Z we trigger the averager and
> continually adjust the altitude knob to keep Kochab centered in the
> bubble. Two minutes later the shutter on the sextant automatically
> closes ending the two minute shooting period and the average time of
> the shot is 1912Z. (If using an A-10A and some other sextants you must
> keep track of the progress of the shot and stop at the two minute
> mark.) The sextant altitude of Kochab is 37� 35'. We enter this in the
> form, compare it to the already adjusted and corrected Hc and
> determine that the intercept is 7 NM toward Kochab, Zn 341�. (No need
> to correct Hs for refraction as this was already taken of by applying
> the refraction correction with reversed sign to adjust Hc.)
>
> We complete the same steps with Arcturus and Antares and get an Hs of
> 19� 51' for Arcturus and an Hs of 16� 20' for Antares producing
> intercepts of  9 NM away and 11 NM away respectively. Using the
> Polhemus we plot the three LOPs. First we set the Zn of Kochab, 341�,
> at the TRUE INDEX and then measure up 7 NM from the A.P. and draw the
> Kochab LOP parallel to the right-left grid lines on the Polhemus base
> (24.jpg and 25.jpg.) We do the same for the Arcturus and Antares LOPs
> remembering to measure down since these are AWAY intercepts (26.jpg
> through 29.jpg.)  We move the fix from the center of the cocked hat
> 1.7 (or 2) NM in direction 356� for coriolis and then .6 NM in
> direction 241� for precession and nutation. We do this with visual
> interpolation since these are small values (30.jpg.) If larger, we
> would set the respective Zns under the TRUE INDEX and measure up the
> appropriate amount for each of these corrections. The fix is 33� 13'
> north, 10� 41' west.
>
> http://www.geocities.com/glap...@pacbell.net/24.jpg
> http://www.geocities.com/glap...@pacbell.net/25.jpg
> http://www.geocities.com/glap...@pacbell.net/26.jpg
> http://www.geocities.com/glap...@pacbell.net/27.jpg
> http://www.geocities.com/glap...@pacbell.net/27.jpg
> http://www.geocities.com/glap...@pacbell.net/28.jpg
> http://www.geocities.com/glap...@pacbell.net/29.jpg
> http://www.geocities.com/glap...@pacbell.net/30.jpg
>
> Showing the convenience of the Polhemus even more, we find the wind
> encountered in flight and the new course and distance to the
> destination. Since our DR in this case is also our "no wind position"
> or "air position" where we would be if there were no wind. Any
> difference between the DR and the fix must be caused by the wind. We
> now rotate the disk to place the fix directly below the DR and read
> out the distance between the DR and the fix which shows how far the
> wind pushed the plane, in this case 21 NM (31.jpg)in the 1+14 the
> plane flew in cruise so we divide this 21 NM by this amount of time
> and find the wind speed of  17 knots. The direction of true wind is
> also now aligned with the "TRUE INDEX" which shows 311� (32.jpg.)
>
> http://www.geocities.com/glap...@pacbell.net/31.jpg
> http://www.geocities.com/glap...@pacbell.net/32.jpg
>
> Now we can rotate the disk to place the destination directly above the
> fix and find the distance and true course to the destination of  282
> NM (33.jpg), course 270� (34.jpg.) Using this new course and the
> measured winds on our E-6B or MB-2A we calculate a new wind correction
> angle, new heading, new ground speed, new ETA and new fuel required.
> Wind correction angle will be  6� RIGHT making the new heading of
> 276� . The new ground speed will be 101 knots for the remaining
> distance of 282 NM  which means it will take an additional 2+48 to
> arrive, making the new ETA of 2208Z. This means that  we will arrive
> 28 minutes later than planned, using  an extra 3.2 gallons reducing
> our fuel reserve to 17.7 gallons which is still a comfortable safety
> margin, more than two hours of extra fuel.
>
> http://www.geocities.com/glap...@pacbell.net/33.jpg
> http://www.geocities.com/glap...@pacbell.net/34.jpg
>
> Although this is a fairly short flight it is still very useful to get
> the celestial fix so that we can be sure we are not running into a
> strong headwind or getting blown far off course.
>
> Celnav is done the same way in faster aircraft. Since most jets are
> flight planned at about .7 mach, about 450 knots, this just makes the
> adjustment for MOO and coriolis larger but the same methods are used.
> Using the Polhemus it takes only 40 seconds to plot the three LOPs,
> about 13 seconds each, and just 30 seconds total to measure the wind
> drift and direction and the course and distance to destination. Then
> 25 seconds on the MB-2A gives you wind correction angle and ground
> speed and another 30 seconds gives you time to destination and fuel
> required. So by doing precomputations and by using the Polhemus you
> can have the fix and the new heading, ETA and fuel required only two
> minutes after finishing the last shot. Try that with other computation
> and plotting method!
>
> gl
>
> 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 
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
>
> > ...
>
> > read more �
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