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#### Heath Smith

• T4
• Posts: 391
##### Re: The flight plan, magnetic course, headwinds.
« Reply #375 on: February 20, 2012, 03:33:05 PM »

Here is the flight plan from Howland to Lae and then from Lae to Howland with two variations, one with a true course of 77.0 degrees, and one with a true course of 79 degrees.

Regardless of the variation values that he has written in the margins that do not match his true course and magnetic course values, I believe the magnetic variations listed are correct for the magnetic course and the true course he has given.

If you compare the strip chart magnetic course values, they are exactly as given in the table with a 77.0 true course which is simply his true course from Howland to Lae 257 minus 180 degrees which is not correct.

If you plug in a true course of 79 degrees (the correct true course), applying the magnetic variations from the Howland to Lae plan you see a different set of values. For example, the first leg from Lae to Howland would have a magnetic course heading of 75 not 73 as listed on the strip chart (73 MC degrees --------> that way).
« Last Edit: February 20, 2012, 03:37:44 PM by Heath Smith »
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#### C.W. Herndon

• T5
• Posts: 634
##### Re: The flight plan, magnetic course, headwinds.
« Reply #376 on: February 20, 2012, 09:55:17 PM »

Heath, I have taken Mr. Williams' strip map and annotated each section of the route in each direction. As we discussed before all numbers are rounded to the closest whole number.
I have entered above the Howland to Lae route the variation that he used for the indicated segment. I have done the same below the Lae to Howland route. I have drawn a circle at the start and end of each naviation segment that he used. I have entered the true course for each segment in each direction. This was calculated by adding the variation to the MC computed by Mr. Williams. I cautioned you about the difference between MC and MH.
Mr. Williams used a segmented route for a reason that is not entirely clear as discussed by Mr. LaPook above. 79 deg was the TC for only the first segment of the route from Lae to Howland. It changed from segment to segment until it was 77 deg for the final segment going in to Howland. The same was true of the route from Howland to Lae but in reverse order. I don't know why he chose to use a 6 deg E variation for the 2 segments nearest to Lae but the numbers in the bottom margin indicate that is what he did.

I hope this helps.
Woody (former 3316R)
"the watcher"

« Last Edit: February 20, 2012, 10:00:01 PM by Clarence W. Herndon »
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#### Gary LaPook

• T5
• Posts: 1624
##### Re: The flight plan, magnetic course, headwinds.
« Reply #377 on: February 20, 2012, 10:11:38 PM »

Here is the flight plan from Howland to Lae and then from Lae to Howland with two variations, one with a true course of 77.0 degrees, and one with a true course of 79 degrees.

Regardless of the variation values that he has written in the margins that do not match his true course and magnetic course values, I believe the magnetic variations listed are correct for the magnetic course and the true course he has given.

If you compare the strip chart magnetic course values, they are exactly as given in the table with a 77.0 true course which is simply his true course from Howland to Lae 257 minus 180 degrees which is not correct.

If you plug in a true course of 79 degrees (the correct true course), applying the magnetic variations from the Howland to Lae plan you see a different set of values. For example, the first leg from Lae to Howland would have a magnetic course heading of 75 not 73 as listed on the strip chart (73 MC degrees --------> that way).
I have attached three marked up Williams documents that should make clear how the courses are calculated. I only illustrated the first and last segments. Segment 1 is the first segment for the Howland to Lae direction but the last segment for the reverse direction. Segment 15 is the last segment for the Howland to Lae direction but the first segment for the reverse direction and this is the one that you seem to be confused about.

Williams' table of magnetic courses lists the rhumb lines connecting each pair of points he calculated along the great circle. His table doesn't show the rhumb line directly between Lae and Howland which 258.1° for the Howland to Lae direction and 078.1° for the Lae to Howland direction. Applying the 6° variation to the beginning of the rhumb line near Lae, the magnetic rhumb line course is 072.1° directly from Lae to Howland becoming 069.1° in the vicinity of Howland where the variation is 9° east.

gl
« Last Edit: February 20, 2012, 10:38:09 PM by Gary LaPook »
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#### Heath Smith

• T4
• Posts: 391
##### Re: The flight plan, magnetic course, headwinds.
« Reply #378 on: February 21, 2012, 04:19:19 AM »

Gary and Clarence,

Maybe I am confused about what Google Earth is producing when I draw a line from Lae to Howland and Howland to Lae. Google Earth reports 257.69 degrees from Howland to Lae. I am assuming this is the true course which Williams stated as 257°3' which is 257.05 in decimal that are very close (257.69 - 257.05 = 0.65 degrees). I used 257 in the spreadsheet to keep it simple. Likewise if you draw a course from Lae to Howland, this is 79.65 degrees. For simplicity I used 79 in the spread sheet. I was not attempting to use the true course from the first segment on the Lae to Howland flight but I can see how you thought that was the case. Are you saying that the true course from Lae to Howland is not 79.65 degrees? If this is not the case, I would like to know how to obtain the correct value. From the great circle calculators I have found, they all seem to agree with this value.

I did see what Williams had given for the magnetic variations outside of Lae on the strip chart at 6° and assumed that those value are incorrect as it does not jive with the true course and magnetic course. I also assume that you can just subtract the true course from the magnetic course to the variation that he used in his calculations, not what is given at the top of the strip chart. This was the case for the first 5 or 6 segments in the plan from Howland to Lae then the numbers started to deviate. Is this suggesting that the true course was changing? If you look at the spreadsheet (pdf) you can see that I applied the same magnetic variations in all cases.

I will need to study this more because what you suggested Clarence is that they did not fly on a straight line, and the true course varied with time. My assumption is that the true course never changes, only the magnetic variation is changing. Is this correct that you are saying that the true course did indeed vary as they went along?

Gary, I do not understand where you are obtaining the 258.1° and 078.1° for the rhumb line. Can you tell me how you obtained these value from the Williams flight plan or strip chart? These seem to be the TC values given by Williams with 1 added to one value and subtracted from the other (257°3' + 1, 79°3' - 1).

Thanks.

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#### JNev

• T5
• Posts: 778
• It's a GOOD thing to be in the cornfield...
##### Re: The flight plan, magnetic course, headwinds.
« Reply #379 on: February 21, 2012, 05:27:16 AM »

Gary probably knows more about how Google Earth calculates routes than I do, but I suspect it uses a farily intense algorithm that mortal navigators do not use when computing a great circle.  Even though the route is close to the equator, it is not ON the equator but crosses.  I wonder if the differences you are seeing are due to that - and that the world isn't perfectly round (does Google Earth impose a factor for that - dont' know).

I suspect you would be better off doing the calculations long-hand and not try to match Google Earth.

The net result should be the same, however.

I'm still amazed at the fascination with this - but who knows?  It does illustrate that errors can be made, and islands missed by mere miles, despite the best of effort.

LTM -
- Jeff Neville

Former Member 3074R

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#### C.W. Herndon

• T5
• Posts: 634
##### Re: The flight plan, magnetic course, headwinds.
« Reply #380 on: February 21, 2012, 09:47:24 AM »

Heath, I agree with Jeff that Gary knows much more about naviation than anyone else on the Forum. I don't know how Google Earth works but I assume it is based on GPS co-ordinates which are much more accurate than the information available in 1937. I also don't know if this is straight line distance or great circle. In this case it would probably not make much difference in the distance or TC only in the accuracy. Trying to compare the results from the Williams chart to a GPS based system is nearly the same as trying to compare apples to oranges. GPS can give locations to within a few feet if you have the right equipment.

I think part of the problem is that you are trying to learn in a few days time what navigators spend many months of intensive training learning and many years of experience prefecting.

Mr. Williams, I am sure, used the latest charts and other information available to him when he plotted the routes on his strip maps.

To answer your question about the routes not being a straight line--yes and no. He was trying to approximate the great circle route between the two points which is not a straight line on a paper map. He did this by breaking the route into smaller segments. The TC for each segment is a straight line and yes the TC changes by a small amount from segment to segment. In 1937 they did not have the equipment that would follow a true great circle route.

When I had to retire from flying in 1997 my aircraft had some of the most modern navigation equipment available and it would not track a true great circle route.

I don't know where you obtained your mag var numbers but in order to approximate the map the Mr. Williams drew you must use the numbers he used. I'm sure these came from the most current information he had at the time. You must also use the MC numbers that he used for each segment since these where calculated from the TC that came from his larger charts.

I present this information from a pilot's viewpoint and not from a navigator's.

Woody (former 3316R)
"the watcher"

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#### Heath Smith

• T4
• Posts: 391
##### Re: The flight plan, magnetic course, headwinds.
« Reply #381 on: February 21, 2012, 04:36:02 PM »

Clarence,

I re-worked the data and used the magnetic variation data on the strip chart as you suggested. Executing the flight plan as given from Lae to Howland, at the end of the line, this would be a point about 19SM North of Howland. This still seems like a pretty crude flight plan if this is correct. Using the NOAA NGDC model data would only put you 3SM closer to Howland.

I am not sure if you use Google Earth but I have attached the executed flight plan both from Howland to Lae and Lae to Howland inside of a .kml file.

Thanks.
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#### Gary LaPook

• T5
• Posts: 1624
##### Re: The flight plan, magnetic course, headwinds.
« Reply #382 on: February 21, 2012, 06:21:43 PM »

Gary and Clarence,

Maybe I am confused about what Google Earth is producing when I draw a line from Lae to Howland and Howland to Lae. Google Earth reports 257.69 degrees from Howland to Lae. I am assuming this is the true course which Williams stated as 257°3' which is 257.05 in decimal that are very close (257.69 - 257.05 = 0.65 degrees). I used 257 in the spreadsheet to keep it simple. Likewise if you draw a course from Lae to Howland, this is 79.65 degrees. For simplicity I used 79 in the spread sheet. I was not attempting to use the true course from the first segment on the Lae to Howland flight but I can see how you thought that was the case. Are you saying that the true course from Lae to Howland is not 79.65 degrees? If this is not the case, I would like to know how to obtain the correct value. From the great circle calculators I have found, they all seem to agree with this value.

I see you have a basic misunderstanding. Plotted on a standard chart, a Mercator projection, the strait line between points, a true course that does not change direction, is called a "rhumb line" and it crosses all intermediate meridians at the same angle so the course stays constant. A "great circle" changes direction as in goes along and as plotted on a chart is curved that is convex toward the nearest pole. That is why the great circle course from Lae starts out at 079.4° and finishes, after changing direction by about two degrees, at 077.6°. On a globe, however, a great circle appears as a straight line and this is what Google Earth displays, it is the shortest distance between two points located on the surface of a globe. The rhumb line will also take you to the same destination just as precisely as the great circle but the rhumb line is longer, sometimes just slightly, as in the Howland case, but at other times, greatly longer. See attached illustration.
Quote

I did see what Williams had given for the magnetic variations outside of Lae on the strip chart at 6° and assumed that those value are incorrect as it does not jive with the true course and magnetic course. I also assume that you can just subtract the true course from the magnetic course to the variation that he used in his calculations, not what is given at the top of the strip chart. This was the case for the first 5 or 6 segments in the plan from Howland to Lae then the numbers started to deviate. Is this suggesting that the true course was changing? If you look at the spreadsheet (pdf) you can see that I applied the same magnetic variations in all cases.

I will need to study this more because what you suggested Clarence is that they did not fly on a straight line, and the true course varied with time. My assumption is that the true course never changes, only the magnetic variation is changing. Is this correct that you are saying that the true course did indeed vary as they went along?

Gary, I do not understand where you are obtaining the 258.1° and 078.1° for the rhumb line. Can you tell me how you obtained these value from the Williams flight plan or strip chart? These seem to be the TC values given by Williams with 1 added to one value and subtracted from the other (257°3' + 1, 79°3' - 1).

Thanks.
As I said in my prior post, Williams did not compute the rhumb line from Lae to Howland, the 078.1° is what I computed. You can see that the initial great circle is 1.3 degrees to the south of that and the final great circle course is half a degree to the north of that which is why it is curved to the south of the rhumb line, convex to the south pole.

Do the experiment with Google Earth that I recommended in this post and I think you will have a better understanding of the great circle.

gl
« Last Edit: February 21, 2012, 08:05:14 PM by Gary LaPook »
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#### Gary LaPook

• T5
• Posts: 1624
##### Re: The flight plan, magnetic course, headwinds.
« Reply #383 on: February 21, 2012, 06:29:48 PM »

Clarence,

I re-worked the data and used the magnetic variation data on the strip chart as you suggested. Executing the flight plan as given from Lae to Howland, at the end of the line, this would be a point about 19SM North of Howland. This still seems like a pretty crude flight plan if this is correct. Using the NOAA NGDC model data would only put you 3SM closer to Howland.

I am not sure if you use Google Earth but I have attached the executed flight plan both from Howland to Lae and Lae to Howland inside of a .kml file.

Thanks.
There is a limit at to how precisely you can compute these things and you cannot fly them anywhere close to the level that you can compute them.  Considering the accuracy of the starting and finishing points, only to the nearest one nautical mile (and we know the Howland coordinates used by Williams were off by about five NM) it is silly to try to compute these things to the level that you are trying to do. Just because your calculator displays ten decimal points does not justify using them all. Same with the numbers spit out by Google Earth. On a 2500 SM flight, doing the computations to a precision of whole degrees (as Williams tabulates) allows approximately a 40 SM error at the end and to this you have to add in the uncertainty due to the accuracy of the variation data he used. ("Rule of 60," one degree error puts you off course one mile for every 60 miles flown. This is the rule of thumb used by pilots and navigators. A more precise value is one mile off course for every 57.298688 miles flown, but "one-in sixty" is close enough.)

gl
« Last Edit: February 21, 2012, 06:55:43 PM by Gary LaPook »
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#### Heath Smith

• T4
• Posts: 391
##### Re: The flight plan, magnetic course, headwinds.
« Reply #384 on: February 21, 2012, 06:53:45 PM »

Quote
On a 2500 SM flight, doing the computations to a precision of whole degrees (as williams allows approximately a 40 SM error at the end and to this you have to add in the uncertainty due to the accuracy of the variation data he used.

There is nothing of any great precision involved. Whole degrees and whole miles were used for the Google Earth course line. It is simply an execute of the flight plan assuming without error. I am not sure why you are fixated with precision?  If you want to create an area of uncertainty at the end, that is a different topic. There is nothing used here that contains any precision and nothing was "spit out" by Google Earth.

Are you referring to the contents of the KML file? That is really irrelevant, that is just data formatting. If you calculate an angle at 45 degrees and it is stored as 45.000000000000001, it is still just 45 degrees.

« Last Edit: February 21, 2012, 07:05:29 PM by Heath Smith »
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#### Heath Smith

• T4
• Posts: 391
##### Re: The flight plan, magnetic course, headwinds.
« Reply #385 on: February 21, 2012, 07:01:11 PM »

Quote
I see you have a basic misunderstanding. Plotted on a standard chart, a Mercator projection, the strait line between points, a true course that does not change direction, is called a "rhumb line" and it crosses all intermediate meridians at the same angle so the course stays constant.

Yes, that was the incorrect assumption that I had made, I assumed that the course stayed constant and that is why I ignored the magnetic variation on the chart and instead calculated the magnetic variation. I do see the difference now. It seems for simplicity's sake, the rumb line would have advantages for navigation.

Thanks for pointing out the differences.

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#### Tom Swearengen

• T5
• Posts: 818
• earhart monument, Hawaii
##### Re: The flight plan, magnetic course, headwinds.
« Reply #386 on: February 21, 2012, 07:49:55 PM »

See Gary----I was trying to get the same understanding that Heath and others now have.
Man---I wish I had paid more attention in High School math class, instead of studying girls.
Thanks for taking back to the future Gary!!
Tom Swearengen TIGHAR # 3297

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#### John Ousterhout

• T4
• Posts: 487
##### Re: The flight plan, magnetic course, headwinds.
« Reply #387 on: February 21, 2012, 09:00:57 PM »

At this point I found it rather sobering to re-read Fred's memo written for Pan-Am, found at http://tighar.org/Projects/Earhart/Archives/Documents/Reports/NoonanPanAm.pdf
It's also on the disc that accompanies each copy of Finding Amelia.
Cheers,
JohnO

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#### Heath Smith

• T4
• Posts: 391
##### Re: The flight plan, magnetic course, headwinds.
« Reply #388 on: February 22, 2012, 04:34:58 AM »

Quote
You may be putting wholes into the Google Earth application, but I'll guarantee you it doesn't calculate by wholes as it tracks the globe, even if it 'answers' with wholes.  Plus, have you compared the island's and Lae's positions (lat - long) on Google compared to the charts of 1937?  Could be some slight differences; forgive that if you have / if there are not, just a thought.

The reason I believe Gary makes a big deal about precision is there is no way to work that on the charts on table top or especially in a moving plane, and there is no way that human (or autoflight) can track headings with an airplane anywhere close to what you can get out of a calculator.  It's a matter of what's practical.

Jeff,

Whole degrees and who miles were used to plot the points given to Google Earth. GE did not compute anything as it only displays the data given to it in this case. I calculated the points using a different method.

What is interesting about following the flight plan is that it does not matter what position was known for Lae back in 1937 because you are following a set of instructions (flight plan) from the real point in space. The whole point to the exercise was to follow and plot the course that Williams created just to see where it ends up. I believe the answer is 19SM North of Howland. This of course does not take in to any of the errors that Gary mentioned (Rule of 60 for example). This was not any sort of attempt to create an X marks the spot, suggesting that this is where they ended up.

The real source of errors like human errors both in starring at compasses for many hours, celestial navigation errors, changing head winds, etc, would far exceed the errors in Williams plan. As John pointed out with the Noonan Pan Am document, Noonan was well aware of these errors inherent in the system.

When I think about all the potential errors I think of something like a cone of uncertainty much like is used in hurricane forecasting. I have not yet attempted to do anything like that and as Gary suggested simple rules like the Rule of 60 captures the majority of the potential sources of error and makes for a nice simple computation. I guess that I cannot see any reason to expend a lot of effort in modeling potential errors unless you wanted to perform real experiments with say humans starring at a compass all day and track and average their responses. This would be a whole lot of work for little if any value.

I believe I now see why Gary pushes the point about the rumb line for simplicity. If you find that you are not on course for whatever reason, computing your way back to the rumb line flight line would be much easier than attempting to find your way back to the great circle flight line because in the case of the GC plan, you have to consider all of the headings and distances for all of the previous segments that you have completed up to the point where you want to perform new calculations. With the rumb line you do not need to worry about any of that and you can proceed to your calculations. For that reason alone I can see why the rumb line is the way to go. Perhaps I have that incorrect but that is the way I see it at this point. Perhaps Gary will correct me if that is not the case.

As for the precision stuff, I am of a completely different mind set. When you write software for a living, you cannot possibly consider and re-consider the practical precision for each calculation that you perform. You would go mad if you attempted to do so. For example, the following constant is used for Pi:

const double PI = 3.14159265359;

This is pretty unisveral in software development. You run your calculations using this value and you do not consider the precision of the particular task in the real world that is being performed, you use the theoretical value. As we know Pi has an infinite fractional value so you just pick a value that works for anything practical and run with it. At the output stage, yes, you can trim the data back to a reasonable precision however that is more work and of little value unless there is a need to do so. Like the KML file that I posted, that is generated by code for data representation, it is not meant to be read by anyone. If you peek under the hood you see this huge fractional value but there is a nothing of value gained by expending the effort to round to the nearest 10th for example as no one is supposed to view the data with an editor. In fact most of the values you using for floating point are internally stored as described and you are not concerned until a human has to read the value on a print out or summary report.

At least for myself, I believe I have learned quite a bit about the Williams flight plan and I find it interesting to walk through the mechanics of the calculations. There is probably no value in the final end point at Howland as I tend to believe now that FN did not use that plan due to the above mentioned reasons. The GC flight plan works great on maps and when you are going to simply follow a step by step instruction but if you need to make corrections as you go, this is not very practical. The problem with step by step instructions is they do not work over large areas when you know that you will be required to make corrections along the way.
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#### Gary LaPook

• T5
• Posts: 1624
##### Re: The flight plan, magnetic course, headwinds.
« Reply #389 on: February 22, 2012, 11:00:00 AM »

As for the precision stuff, I am of a completely different mind set. When you write software for a living, you cannot possibly consider and re-consider the practical precision for each calculation that you perform. You would go mad if you attempted to do so. For example, the following constant is used for Pi:

const double PI = 3.14159265359;

This is pretty unisveral in software development. You run your calculations using this value and you do not consider the precision of the particular task in the real world that is being performed, you use the theoretical value.
We all do that when dealing with programming a computer. When I wrote programs to do navigational calculations I often ran into a "division by zero" type of error message caused by a trig function for that angle being zero. This occurred because the human entering the data uses whole numbers. For example if you enter the latitude of two places that are at the same latitude, the direction is 90 degrees and the sine of 90 is zero so using this value is a subsequent calculation produces that error message. The easy solution was to write a loop that tested for this situation and if it occurred have the computer add 0.00000001 to the latitude of the second location so that it wasn't exactly 90 degrees and this kludge has no real effect on the results and made the computer happy.

gl
« Last Edit: February 22, 2012, 11:39:26 AM by Gary LaPook »
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