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#### Gary LaPook

• T5
• Posts: 1624
##### Re: The flight plan, magnetic course, headwinds.
« Reply #450 on: March 14, 2012, 05:24:32 AM »

I don't know where he came up with an eight degree wind correction angle. The plane was cruising at 150 mph and the inbound course to Howland is 078° true and with a wind from ENE at 24 mph the wind correction angle was only 1.6 ° left so the true heading of the plane would have been 076.4° (call it 076°.) With the wind out of the ESE then the wind correction angle would have been 5.2° (call it just 5°) right and the true heading would have been 083°. Neither of these winds would have caused Noonan to use an 8° wind correction angle.

gl

Unless he made a mistake, or calculated the winds incorrectly.
Oh, you mean Williams made the mistake.

gl
« Last Edit: March 14, 2012, 05:26:26 AM by Gary LaPook »
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#### Erik

• T3
• Posts: 185
##### Re: The flight plan, magnetic course, headwinds.
« Reply #451 on: March 14, 2012, 05:27:45 AM »

I don't know where he came up with an eight degree wind correction angle. The plane was cruising at 150 mph and the inbound course to Howland is 078° true and with a wind from ENE at 24 mph the wind correction angle was only 1.6 ° left so the true heading of the plane would have been 076.4° (call it 076°.) With the wind out of the ESE then the wind correction angle would have been 5.2° (call it just 5°) right and the true heading would have been 083°. Neither of these winds would have caused Noonan to use an 8° wind correction angle.

gl

Unless he made a mistake, or calculated the winds incorrectly.
Oh, you mean Williams made the mistake.

gl

Or even AE.  Afterall, she had the controls.
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#### Heath Smith

• T4
• Posts: 391
##### Re: The flight plan, magnetic course, headwinds.
« Reply #452 on: March 14, 2012, 05:30:25 AM »

Given just the assumed error, one can easily see that they could end up 15NM+ off target. Given that the winds were from the ENE, it would also be reasonable that they were compensating for those winds and accidentally under or over compensated for those winds. A couple of 15NM errors and you are out of visual range which is what must have happened. If they were accurately tracking speed, this would place them at certain positions North or South of Howland.
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#### Gary LaPook

• T5
• Posts: 1624
##### Re: The flight plan, magnetic course, headwinds.
« Reply #453 on: March 14, 2012, 10:56:36 AM »

Given just the assumed error, one can easily see that they could end up 15NM+ off target. Given that the winds were from the ENE, it would also be reasonable that they were compensating for those winds and accidentally under or over compensated for those winds. A couple of 15NM errors and you are out of visual range which is what must have happened. If they were accurately tracking speed, this would place them at certain positions North or South of Howland.
Yep, that is why you would not just use dead reckoning for this flight but would need a navigator to keep the plane on course. Every time you get a new fix it cures any existing error that has crept in the D.R. position since the last fix and replaces it with a fixed uncertainty of a 10 NM circle surrounding the plotted new fix. And when using the sun line landfall approach, any accumulated uncertainty in the D.R. collapses into a line 14 NM thick (7 NM uncertainty on each side of the plotted LOP) with the line being as long as twice the reasonable maximum uncertainty in the DR at that point.

gl
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#### Heath Smith

• T4
• Posts: 391
##### Re: The flight plan, magnetic course, headwinds.
« Reply #454 on: March 14, 2012, 05:42:39 PM »

Quote
And when using the sun line landfall approach, any accumulated uncertainty in the D.R. collapses into a line 14 NM thick (7 NM uncertainty on each side of the plotted LOP) with the line being as long as twice the reasonable maximum uncertainty in the DR at that point.

I understand what you are saying but I do not understand how the accumulated uncertainty collapses. For example, lets say they were 400NM out when they obtained their last fix, how does 40NM collapse to 14NM along the line? I would suspect a total possible DR error with a radius of 54NM and I do not see how this is reduced to a 14NM strip.
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#### John Ousterhout

• T4
• Posts: 487
##### Re: The flight plan, magnetic course, headwinds.
« Reply #455 on: March 14, 2012, 06:24:03 PM »

Heath,
I'll take a stab at an explaination, and hope Gary corrects my understanding.
Think of the LOP as establishing a 1-dimensional fix.  You'll know pretty accurately when you arrive at the line, but not as accurately where along that line you are.  You know you're on the line with an accuracy of 14nm, but you don't know your position along that line to the same degree of accuracy.  If you had a DR uncertainty of +/- 50 miles before you arrived at the line, for example, and your approach to the line was perpendicular to it, then you'll know your position relative to the line +/- 7nm, but still have the +/- 50 mile uncertainty along the line.  That's why it makes sense to intentionally DR to a target on the line about 50 miles up the line from your destination, then turn and follow the line.  If your ded-reconing was off to the maximum normal deviation along the line away from your destination, then you'll have to fly down the line 100 miles to your destination.  If your DR'g is right-on, you'll only fly 50 miles to your destination.  If your DR was off the maximum the other direction, you'll arrive right over your destination as you reach your LOP.
Cheers,
JohnO

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#### Gary LaPook

• T5
• Posts: 1624
##### Re: The flight plan, magnetic course, headwinds.
« Reply #456 on: March 14, 2012, 11:41:11 PM »

Quote
And when using the sun line landfall approach, any accumulated uncertainty in the D.R. collapses into a line 14 NM thick (7 NM uncertainty on each side of the plotted LOP) with the line being as long as twice the reasonable maximum uncertainty in the DR at that point.

I understand what you are saying but I do not understand how the accumulated uncertainty collapses. For example, lets say they were 400NM out when they obtained their last fix, how does 40NM collapse to 14NM along the line? I would suspect a total possible DR error with a radius of 54NM and I do not see how this is reduced to a 14NM strip.
A picture is worth a thousand words.

Diagram A shows the DR uncertainty after flying 400 NM starting from a pinpoint visual fix with basically zero uncertainty in the starting fix. The uncertainty increases one mile for every ten miles flown so after 400 NM you can draw a circle of radius 40 NM around the DR position and you can be very certain that you must be inside that circle and you are much more likely to be near the center than near the edge of the circle. (In a very rare case you might be outside of the circle but, even then, you will be very near to the circle.) Since you know that you are inside that circle you have excluded the entire rest of the world as your possible location.

Diagram B shows the same thing but starting from a celestial fix that has the standard 10 NM uncertainty. Since you might actually be near the edge of that circle in any direction, this 10 NM uncertainty must be carried forward in figuring the uncertainty of a DR position so you add the original 10 NM uncertainty to the 40 NM uncertainty resulting from dead reckoning for 400 NM, so you draw the circle of uncertainty with a 50 NM radius.

Diagram C shows a celestial LOP with the band of uncertainty on each side. These bands of uncertainty are just like the circles of uncertainty around the DR in that they exclude the entire world outside the uncertainty bands. You know that you must be somewhere within the bands, you can't be anywhere else on earth.

Diagram D shows a celestial fix consisting of two LOPs that cross, along with their respective uncertainty bands. Since you must be within the uncertainty bands along LOP "A" and, at the same time, you must be within the uncertainty bands along LOP "B," the only place you can be on earth is where these two areas overlap, the rest of the world has been eliminated. Since the uncertainty of celestial fixes is taken as 10 NM, and this represents the corner of the overlap, the uncertainty of the two LOPs cannot exceed 7 NM, (ask Pythagoras why this is true.) (The diagram shows the ideal case with the two LOPs crossing at right angles which results in a circle of uncertainty around the intersection of the LOPs. When the LOPs cross at a different angle (known as the "cut") then the area of uncertainty is actually an ellipse but for normal cuts you can just consider that they are also circles.)

Diagram E shows the uncertainty circle surrounding a DR position which eliminates everything outside the circle. Imposed on top of this circle is a celestial LOP. Since you can only be within the area of overlap between the LOP uncertainty band and the uncertainty circle around the DR position, this then eliminates everything outside the LOP uncertainty bands and thus eliminates the two half-moon slices of the circular DR uncertainty area. So with this LOP, and the knowledge of the length of the DR leg, you know that you are within the 14 NM wide LOP uncertainty band and that the length of that LOP is limited by the diameter of the DR uncertainty circle.

So that is why the DR uncertainty circle collapses into a band 14 NM thick and 100 NM long (in this illustration.)

gl
« Last Edit: March 14, 2012, 11:50:02 PM by Gary LaPook »
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#### Gary LaPook

• T5
• Posts: 1624
##### Re: The flight plan, magnetic course, headwinds.
« Reply #457 on: March 15, 2012, 02:23:32 AM »

Oh, you mean Williams made the mistake.

gl

Or even AE.  Afterall, she had the controls.
Now you have me confused. You wrote, "unless he made a mistake." The he who talked about an eight degree wind correction angle was Williams, not Noonan and not Earhart.

gl
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#### Heath Smith

• T4
• Posts: 391
##### Re: The flight plan, magnetic course, headwinds.
« Reply #458 on: March 15, 2012, 03:50:05 AM »

Gary,

I believe that I understand everything that you had posted with the exception of determining the LOP. Are you suggesting that the LOP is determined with a celestial (solar) fix? What if there is no way to obtain a fix for the LOP, are you not back to the DR radius of 50NM?

Thanks.
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#### Gary LaPook

• T5
• Posts: 1624
##### Re: The flight plan, magnetic course, headwinds.
« Reply #459 on: March 15, 2012, 02:45:31 PM »

Gary,

I believe that I understand everything that you had posted with the exception of determining the LOP. Are you suggesting that the LOP is determined with a celestial (solar) fix? What if there is no way to obtain a fix for the LOP, are you not back to the DR radius of 50NM?

Thanks.
O.K., I see you came in late. I am not "suggesting" that Noonan observed the sun and derived the LOP, I have been saying that clearly for many years as has everybody else who has studied the navigation. See what I posted here for a more complete explanation. And see standard navigation references available here. Just where did you think the 157-337 line came from?
gl
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#### Heath Smith

• T4
• Posts: 391
##### Re: The flight plan, magnetic course, headwinds.
« Reply #460 on: March 15, 2012, 03:13:24 PM »

I assume that it was an advanced line of position pre-plotted on a chart and nothing else since they were no where near Howland at sunrise at Howland. Perhaps that was the plan before they diverted around the storm outside of Lae but it did not turn out that way. In my opinion, being on the 157/337 line at 20:13GMT suggests that they could not obtain a fix but since they were already on that line they just continued their search.

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#### Gary LaPook

• T5
• Posts: 1624
##### Re: The flight plan, magnetic course, headwinds.
« Reply #461 on: March 15, 2012, 03:47:32 PM »

I assume that it was an advanced line of position pre-plotted on a chart and nothing else since they were no where near Howland at sunrise at Howland. Perhaps that was the plan before they diverted around the storm outside of Lae but it did not turn out that way. In my opinion, being on the 157/337 line at 20:13GMT suggests that they could not obtain a fix but since they were already on that line they just continued their search.
The only way that they could identify being on the 157/337 line is that they got at least one, and probably several, observations of the sun in the vicinity of Howland.

gl
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#### Gary LaPook

• T5
• Posts: 1624
##### Re: The flight plan, magnetic course, headwinds.
« Reply #462 on: March 15, 2012, 03:55:59 PM »

I assume that it was an advanced line of position pre-plotted on a chart and nothing else since they were no where near Howland at sunrise at Howland. Perhaps that was the plan before they diverted around the storm outside of Lae but it did not turn out that way. In my opinion, being on the 157/337 line at 20:13GMT suggests that they could not obtain a fix but since they were already on that line they just continued their search.
I have pointed this out before, there was no sunrise observation, Noonan observed the sun more than a half hour after sunrise, see my fuller explanation here.

gl
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#### Heath Smith

• T4
• Posts: 391
##### Re: The flight plan, magnetic course, headwinds.
« Reply #463 on: March 15, 2012, 04:17:12 PM »

Quote
The only way that they could identify being on the 157/337 line is that they got at least one, and probably several, observations of the sun in the vicinity of Howland.

If that were true, given the error of 14NM, Howland would have been impossible to miss. Are you suggesting that passed within 14NM and failed to see Howland?

I would suggest that they were simply following a magnetic heading. The line was pre-plotted and was good as another other heading to search along. The way the established the line was to fly straight in at Howland. When they did not find it, they circled then followed the 157/337 line North and South. I would suggest that they then performed a creeping line search where the 157/337 lines comprised the long parallel lines in the search.

As I stated before, I do not believe they were any where near the 157/337 line (North or South of Howland) at the moment of sunrise at Howland.
« Last Edit: March 15, 2012, 04:23:39 PM by Heath Smith »
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#### John Ousterhout

• T4
• Posts: 487
##### Re: The flight plan, magnetic course, headwinds.
« Reply #464 on: March 15, 2012, 08:04:01 PM »

"...given the error of 14NM, Howland would have been impossible to miss..."
I'm convinced that a Lockheed could have been less than 5 miles from Howland and no one would hear or see it.  By descriptions of looking for Howland and similar islands in similar scattered cloud(y) conditions, I believe AE/FN could have easily missed recognizing it at a range of less than 5 miles.  I already know how difficult it can be to spot an unfamiliar airfield at 14 nm range from first hand experience.  Someone might navigate to within +/- 5miles of Howland and still reasonably miss spotting it, and be missed by spotters on the "ground".  5 miles is too far to spot or hear an aircraft.
Cheers,
JohnO

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