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» Online Classroom   »   » Public Discussion of Cel Nav   » Hawaii by Sextant - Fit slope method

   
Author Topic: Hawaii by Sextant - Fit slope method
climber


 - posted March 27, 2016 11:14 AM      Profile for climber           Edit/Delete Post 
I'm going to start over as I have somewhat lost track of my questions. Thanks for clearing me up on the automatic advancement of LOPs vs the Fit-Slope Method.

Now I need to understand the Fit-Slope Method beginning on page 100.

In the first paragraph on page 100 it is stated ".... But we want to stress that a great virtue of this method is that it does not take a computer to solve underway." However, in the second paragraph from the bottom on page 100 it is stated " It is best at this point to compute the Hc rather than to try to use tables".

This my primary point of confusion - can the Fit-slope Method be performed manually, without a computer? If so, how?

Here is how I tried it.

I hand-calculated the Hcs for the first and last sun sights in Problem 1 (page 11). The graphs arew presented on page 101. However, these two sights were taken 6' 8" apart and the distance travel was only about 0.7 mm which makes the two DR positions essentially the same when doing a manual calculation. Therefore I calculated the Hc for the first and last sight using the 0844 DR position. Using this line slope I picked the second sun sight as the best, which was also the one picked in the book.

What I would like to know is, can the Fit-Slope Method be used in this manner without a computer? Was I just lucky in this case?

this is an important point and, before I start using a canned program I'd like to understand the method manually first.

Thank you.

From: apalachicola
climber


 - posted March 27, 2016 11:21 AM      Profile for climber           Edit/Delete Post 
This question concerns the plots in Figure A3.

If I performed sight reductions on all 7 sights for problem 1 (data presented on page 11) I could plot all 7 LOPs on a universal plotting sheet. I could then advance all the LOPs to 0847 manually, just as if we're doing a fix. That would be a lot of lines but if I did that would I end up with Figure A3?

When doing this manually I would use one DR position for each set. I understand I would lose some accuracy but would this manual method be a good approximation of the computer-generated plot?

This was one of my questions previously. Perhaps I understand it better after a few hours of thought.

Thank you.

From: apalachicola
David Burch


 - posted March 27, 2016 11:55 AM      Profile for David Burch           Edit/Delete Post 
First, does this 6' 8" mean 6 minutes and 8 seconds? If so, may I encourage you to not use that type of abbreviation in navigation.

Next, I do not follow the distinction between calculating and computing. these are the same. ie if you calculated Hc then that is the full procedure. no other computers or software needed.

to address the first part,

The fit slope method can be done without a computer or calculator, as noted, but also as noted it is best done with a calculator... by far. ie you have a precise lat, a precise dec and a precise LHA for the times at each end of the sight session and you compute the Hc values using these .

If you want to use this without any electronics, then you must do a sight reduction from a specific DR position. You can do that with either Pub 214 or What is called the S-Tables, designed by Mike Pepperday. The latter i think are still available online. Also as noted, this can be done with Pub 229, but it is tedious. You can learn about that from the instructions to Pub 229.

Please note also that we should keep this in perspective:

You would never be doing such things in an emergency with limited equipment. we are after all, just trying to squeeze the accuracy of a sight from a very easy to get ±3 or 4 miles, down to a confident ±1 mile or maybe ±0.5 mi.

You would almost certainly have a calculator available in these circumstances and most likely know the right equations or have them written down so you can solve for Hc.

Pursuing this by pure table sight reduction is frankly a bit incongruous.

With that said, there can indeed be other virtues to doing sight reduction from a DR position rather than an AP. We do it that way all the time when computing the sights, which in turn allows for a plotting procedure that is very convenient and informative.

As noted there are three or four solutions by tables alone. I will put this on the list to write an article about the options for doing this, but if the only motivation is doing the fit slope method without a calculator, I see that hard to justify.

We will try to look over your specific example as soon as possible.

From: Starpath, Seattle, WA
climber


 - posted March 27, 2016 12:26 PM      Profile for climber           Edit/Delete Post 
I didn't expect any quick answers, especially on a weekend. Thanks.

This question pertains to Problem 3b in the Hawaii book.

Using the 1400 fix I can calculate the local time of civil twilight (at that Lat and Lon) using the almanac table and the Arc to Time conversion table.. However, that time is about 7 hours from that fix. In those 7 hours I will have traveled some distance west.

Is the proper method to plot the DR position using the time interval between the fix and the civil twilight time calculated from that fix and then recalculate the time of civil twilight using the new DR longitude? This makes it an iterative process. How many iterations would be necessary? Some level of accuracy is necessary so as to accurately predict the star and planet positions so they would be easy to find with the sextant.

I don't have any problem with predicting star and planet positions if I am not moving (e. g., sitting on a beach waiting for sunset) but predicting from a moving platform is new to me.

From: apalachicola
Capt Steve Miller


 - posted March 27, 2016 03:46 PM      Profile for Capt Steve Miller           Edit/Delete Post 
Re the Figure A3 plot - you would end up with a UPS plot that is nearly identical depending on the accuracy of your plot. I would advance the Venus sights to the Sun sights as they were 3h 30+m apart while doing a UPS manual plot.
From: Starpath
Capt Steve Miller


 - posted March 27, 2016 03:50 PM      Profile for Capt Steve Miller           Edit/Delete Post 
Re the 3b problem:
We use a time midway between Civil and Nautical Twilight as the time for precomputing the Stars available. It is usual to do an iteration to zero in on the DR of the initial determination of our twilight time. Generally only one iteration is needed.

From: Starpath
climber


 - posted March 28, 2016 01:25 PM      Profile for climber           Edit/Delete Post 
Thanks. These replies help a lot.

I guess the only question I have left, at this time, still pertains to the Fit-Slope Method. I think that if I use one DR position to manually calculate the Hcs for the first and last sight and pick the best sight using the slope of that line I should be reasonably close. This assumes that the sights are only a mile or two apart.

However, if the first and last sights are 5 miles apart, or more, it would be worthwhile plotting two DR positions. This is a judgement call - cost/benefit assessment. My objective would not be to necessarily pick the best sight. It would be to eliminate any obviously bad sights.

Does that sound reasonable?

I understand the limits of accuracy we are dealing with. Adding more decimal places by using a calculator does not necessarily increase acccuracy - there are a number of sources of error to be considered. I'm just trying to do the best possible given the equipment. Using a calculator speeds things up but I still want to know the underlying principles.

I am using Pub. 229. I'll check out the S-tables.

Thanks for your patience. If sometimes takes me a few tries to get the problem statement correct.

From: apalachicola
David Burch


 - posted March 28, 2016 02:46 PM      Profile for David Burch           Edit/Delete Post 
I do not want to interrupt your conversation with Steve, but i only add that you must use two different DR positions for the fit slope method. One corresponding to just before the sights time and one just after the sights time.

Please review earlier notes.

This is the key to how the method works. And again, this is a method looking for corrections less than 1' or so at times, so you cannot make more approximations than already made in the method itself.

From: Starpath, Seattle, WA
climber


 - posted March 28, 2016 04:23 PM      Profile for climber           Edit/Delete Post 
I appreciate the comment. I think I understand your point and I agree. If I am using a calculator I would certainly use two DR points.

My issue is that, for example, in problem 1 in the Hawaii book, the first and last sights are only 0.7 nm apart. When using manual plotting this is pretty much insignificant. Therefore the calculations for the Hcs, , when using the same DR position, results in the change of the Hc between the first and last sight being due entirely to the time interval. Graphing the four Ha values from the sights using the same DR position is based on the same time interval. Therefore the slope of the manual sights (the Has) should be the same as the slope of the two Hc points since the changes in the sights will be entirely due to the passage of time.

I realize that this is not strictly true but over a distance of 0.7 nm, when doing manual plotting, it should be a pretty close approximation. If the distance traveled is 5 or 10 miles then I would plot the DR track and use two DR positions. This would be feasible using manual plotting.

Returning to Problem 1, therefore, , if the slope of the Hc points is moved to the actual sights and one of those lies off the line then that is obviously a bad sight. If I select one on the sights from a group that fits the Hc line I should be close.

I do see a couple of issues with this, and I am sure there are more that I don't see. For example, what if there are two groups of points, each with an equal number of sights, where both groups have the same slope as the Hc line but each the two groups do not lie on same line? That is, there are three points on each line but the lines are separated by 10' (for an example)? I would pick the group with values that lie closest to the Hc line - I.e., those with the smallest a-values.

I may be way off base here. I'm just trying to do this without an electronic device. I went through engineering school with a slide rule (showing my age here) and I still don't trust computers or calculators without first verifying the programming. Plus, electronics WILL fail so I'd like to understand the method.

The more the merrier in this. I am learning a lot from this and, again, I appreciate your patience and help.

I know that what I'm talking about probably isn't kosher. I'm trying to find a manual means of accomplishing what is done in the book via electronics.

From: apalachicola


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