Advanced search  
Pages: [1]   Go Down

Author Topic: Visualizing the 337-157 LOP  (Read 24685 times)

Martin X. Moleski, SJ

  • Administrator
  • *
  • Posts: 2909
Visualizing the 337-157 LOP
« on: September 11, 2010, 07:05:15 AM »

NB: This is a corrected version of this post.  Other claims I made about how celestial navigation works have proven to be false. 

"I was so wrong, for so long,
But I've seen the light, darlin, I'll make it right
I was wrong."


"337-157" defines a straight line on a compass.  It runs from the north-northwest (NNW, 337 degrees) to the south-southeast (SSE, 157 degrees).  It is 180 degrees from 357 to 157 and vice-versa.  The line shown at 67 degrees was the azimuth ("compass heading," more or less) of the sun as seen at dawn from a latitude close to the equator all around the earth on 2 July 1937.  337-157 is at right angles to 247-67.



The terminator is the line between night and day.   It makes a Great Circle around the globe.  On the morning of 2 July 1937, the line between night and day was in the vicinity of Howland Island was a slanted line running roughly 337°-157°.



At the summer solstice, the terminator touches the arctic circles around the North and South poles.  At dawn all around the globe, it is about 23.5 degrees west of north (NNW, 336.5 degrees on the compass) and 23.5° east of south (SSE, 156.5 degrees on the compass).


Between the two solstices (~182 days), the line made by the terminator at dawn moves to N-S at the equinox, then to abut 23.5 degrees east of north (NNE, 23.5 degrees on the compass) and 23.5 degrees west of south (SSW, 203.5 degrees on the compass).  So the swing of the LOP that approximates to the slant of the great circle picked out by the terminator is 47 degrees in 182 days (an average of 0.25 degrees of change each day). 





As the earth rotates eastward across the terminator on any one day, every observer at the same latitude will derive essentially the same LOP from the dawn sighting.  In fact, the sun's position changes an average of about 0.01 per hour as the terminator between night and day sweeps across the earth, but that is a pretty negligible amount; few aircraft are equipped to navigate in hundredths of a degree. 

Airplanes approximate the Great Circle routes by flying a series of "rhumb lines" plotted on 2-dimensional charts which approximate the smoothly varying curve of the 3-dimensional Great Circle that represents the shortest distance between two points on the face of the earth.

Note: the "dawn sighting" does not have to be taken right at the crack of dawn.  For all practical purposes in air navigation, any observation taken during the first hour of daylight on 2 July 1937 in the vicinity of Howland Island would have the same azimuth  for the sun (67°) and produce the corresponding Line of Position (LOP) on the navigator's charts: 337°-157°.
LTM,

           Marty
           TIGHAR #2359A
 
« Last Edit: January 05, 2012, 08:57:56 AM by Martin X. Moleski, SJ »
Logged

Martin X. Moleski, SJ

  • Administrator
  • *
  • Posts: 2909
Re: Visualizing the 337-157 LOP
« Reply #1 on: September 13, 2010, 09:52:44 AM »

So, as I think I have understood, establishing a 'point' at at given latitude would then depend solely on 'time or sunrise' at that 'point'.

It's not a point.  It's a line.  And it's not a nice neat line.  It's fuzzy because of the limits of the instruments and the limits of the human observer's eyes and hands.

Quote
Had the LOP been established in earlier, planned fashion ...

You are smuggling in the assumption that taking LOPs was an emergency measure.  As I said in the other board, it was not. 

Quote
... they would have likely used the classic off-set and known to fly north (or south); for reasons stated by Ric on June 26, 2010 they likely did not use the offset method and were highly dependent on the RDF approach - until too late.

They bet their lives on having two-way communication and RDF to bring them in.

They lost the bet.

There is no certitude that Fred (or any navigator) could have gotten them within visual range of Howland using the offset method.  That's pure speculation.  Maybe you're right; maybe not.  We don't know enough about the conditions of the flight to say.
LTM,

           Marty
           TIGHAR #2359A
 
Logged

Martin X. Moleski, SJ

  • Administrator
  • *
  • Posts: 2909
Re: Visualizing the 337-157 LOP
« Reply #2 on: September 13, 2010, 09:54:45 AM »

- she had defied FN's judgment before (approaching Africa) and could have done so again. 

Ric has debunked that claim dozens of times in the years I've been reading the Forum.
LTM,

           Marty
           TIGHAR #2359A
 
Logged

Martin X. Moleski, SJ

  • Administrator
  • *
  • Posts: 2909
Re: Visualizing the 337-157 LOP
« Reply #3 on: September 13, 2010, 07:03:36 PM »


"It's not a point.  It's a line.  And it's not a nice neat line.  It's fuzzy..."

No, at ONE given latitude, a LOP CAN describe a POINT (where it crosses the latitudenal line) - that was the 'point' in my statement.  

If you know your latitude, then yes, of course, that becomes a second LOP that crosses the dawn LOP and then,
of course, you have a fuzzy point instead of a fuzzy line.

But you can't get your latitude from the observation of the sun at dawn.  All you get from that one observation is one fuzzy LOP.  No fix.  No point.


Quote
"You are smuggling in the assumption that taking LOPs was an emergency measure..."

No, I pulled that right out of Ric's own basket; it was derived from Ric's statement, which I quoted; he noted PAA's reliance on RDF techniques and the lack of use of LOP-offset navigation as the norm at the time, not I.  

Ric says that Pan Am didn't use the offset-method, as ships did, deliberately steering north or south of one's goal so as not to have much ambiguity about which way to turn when reaching the advanced LOP drawn on the chart through one's objective.

But saying that they didn't use the offset method is not the same thing as saying that the navigators drew no LOPs on their charts during the flight.

Quote
Nor was it an 'assumption', but a fair wonderment: to me, a question was suggested on why I should think that FN was constantly shooting the stars and sun to get lines of position through-out the flight with a notion of knowing where he was at all times - I don't think it happened that neatly by what I've read here.  I merely wondered 'aloud' whether the AE-FN flight might have proceeded in the same fashion as the PAA flights, per Ric's own noting that 'LOP - offset' navigation was NOT being widely used by 1937.  Nothing was smuggled - merely brought forth from a TIGHAR posting, and wondered about.  I belive the 'LOP-offset' was a last-minute attempt to locate the island (without the offset being planned in advance, as I think Ric believed when he wrote what he did).  

I think I've read everything Ric has written on the Forum--more than once.

I don't think he ever intended to say that Fred didn't try to get mid-course fixes, as best he could, nor that Fred suddenly would latch onto the offset method when within 100 miles of LOP through their destination.  On the contrary, Ric has said, even in this version of the forum, that the fact that the last transmission said "we are flying north and south" is evidence that Fred did not attempt an offset at the last minute.

Quote
... given FN's capabilities, had he planned the whole flight with LOP-offset as a ready, firm back-up to the RDF 'capability', it is highly likely that he would have found Howland that way (weather / visibility permitting, etc. - all fair variables to 'assume', or at least ponder).

SAC's standard for passing navigator tests was +/- 5 miles in the 1950s and 1960s (from a post by a SAC navigator).

Planning to fly an offset requires more fuel and only removes one issue from the equations governing navigation.

If the flight had ended in the dark or close to dawn (as originally intended), and if Fred could have gotten some fixes when they were right near the island from several  celestial objects, he might have been able to get them within visual range.  But when I construct error bars for him, I don't think I could expect him to get closer than +/- 10 miles under the best conditions for taking sights and finding his position.  Apart from the limits of his instrument, his eyes, the steadiness of his hands, the rapidity of his fingers in marking the sight, there is the issue of the accuracy of the altimeter, over which he had no control.  On approach to an airport, pilots usually get the local barometric reading, if they can, and tweak the setting on their altimeter.  My own wild guess is that they couldn't be sure that they were within a hundred feet in reality of the reading on the altimeter.  And that uncertainty, along with all the others, makes all the LOPs and fixes fuzzier and fuzzier.

Quote
"Ric has debunked that claim dozens of times in the years I've been reading the Forum. (about AE 'disobeying' FN)"

I'm familiar with that.  FN said go straight and she turned left, in effect, and later was contrite and supposedly listened afterward.  It can be 'debunked' all one wishes, but we have no way of knowing -
a) how well AE performed over the open Pacific under the conditions of that flight,
b) how strong her own instincts may have been to 'return' vs. other instructions from FN,  
c) how reliant FN may have been on dead-reckoning for hours on end, or
d) how well FN was able to perform due to many possible variables.

If you're in the clouds, you can't get fixes.  Ric's argument is that AE deliberately lied about "disobeying" Fred so that they could make a safe landing at a nearby airport rather than head toward a distant airport and back out over open water as darkness fell.  It makes sense to me. It's not a knockdown argument, of course, and YMMV.
LTM,

           Marty
           TIGHAR #2359A
 
« Last Edit: September 15, 2010, 09:39:18 PM by moleski »
Logged

Martin X. Moleski, SJ

  • Administrator
  • *
  • Posts: 2909
Re: Visualizing the 337-157 LOP
« Reply #4 on: September 14, 2010, 03:45:48 AM »

Highlights from an earlier incarnation of the Forum:

http://tighar.org/Projects/Earhart/forum/Highlights61_80/highlights69.html

Subject:     RE: 10 miles or 100
Date:    1/3/00
From:    Alan Caldwell

I think I told you I was trying to work the celestial backwards to pin down possible tracks or areas where the Electra could have been for Noonan to get a sun shot azimuth of 67 degrees. I have been working with the Dept. of Aerospace Engineering & Center for Space Research Engineering Mechanics at the University of Texas. I received a reply from that department this morning showing me how to make the computations. The preliminary results are general and as follows:

Using an azimuth of 67 degrees exactly and not a fraction off there was no place south of Howland inbound that Fred could have found a 67 degree azimuth. I recognize a slight deviation from exactly 67 degrees could have occurred but it would not change the general conclusion.

If they were on course due west of Howland inbound he had a 67 degree azimuth all the way.

They could also have been north of course as much as 120 nm but at about 200 miles west.


http://tighar.org/Projects/Earhart/forum/Highlights61_80/highlights69.html

Subject:     Re: 10 miles or 100
Date:    1/3/00
From:    Alan Caldwell

Ric asks:

> Does this mean that in order to get a 157/337 sunrise LOP they HAD to be
> somewhat north of course at that time?

I wish I could answer that with a definite yes or no but it DOES appear that the answer must be yes. I checked all the coordinates south of 0 degrees 48 minutes North all the way back to 179W. It is possible but less than likely that 67 degrees could be found. But there are close fractions. The easy one would be 67.2 or 66.8 and if they are rounded off or Fred's sextant was not quite that accurate then he could well have been dead on course. I'll check out 77 degrees and see how it comes out but generally speaking I found little probability they could be south of a due east course.


http://tighar.org/Projects/Earhart/forum/Highlights61_80/highlights69.html

Subject:     Re: 10 miles or 100
Date:    1/4/00
From:    Alan Caldwell

Ric asks:

> Is it possible to plot a band on a map which encompasses the locations
> where the airplane could have been and gotten a 67 degree sunrise (plus or
> minus a couple of tenths)?

Yes, but I won't have time to work on the 77 degree course thoroughly until this weekend but preliminary checks show that although a 67 degree azimuth could be obtained at 6:20a to 6:30a from 179W to 176W the sun's elevation was extremely low --- averaging only a degree and a half above the horizon with a maximum height of 3.3 at the 176W line at 6:30 and at that time They should have been somewhat west of that longitude, about 60nm or so. ( arbitrarily figuring 133k GS)

What that tells me is that they could have been on course but probably on a course somewhat due west to east or even slightly north of that track. There is a lot of room to maneuver and still find 67 degrees of azimuth but I suspect we will be able to eliminate being well south of Howland or well north. It appears to me from first glance your theory that they were pretty close to track and hit Howland fairly close is supportable. I think it also makes it more likely they missed Howland simply because they couldn't see it visually and not because of any gross navigation error.

Alan
#2329

From Randy Jacobson

This is kinda silly. FJN doesn't actually measure the 67 degree azimuth to the sun. He assumes a position on the globe, the books tell him when the sunrise is going to be and the azimuth. There will be a good range of latitudes that will give him that azimuth +or- a few tenths of a degree. He then compares the book time of sunrise to what he observes, and that gives him a correction towards/away from the sun along a 67/247 line. What's important is where Noonan THINKS he is, not where he really is, that determines the 67 degree line.


http://tighar.org/Projects/Earhart/forum/Highlights61_80/highlights70.html

Subject:      Re: 10 miles or 100?
Date    1/11/00
From:    Alan Caldwell

> Is there a way that Randy's solution (and others for that matter)
> could be reproduced visually with step-by-step explanations, and then
> distributed in the next TIGHAR Tracks? This whole issue is VERY confusing
> to most of us and I think a "show-and-tell" approach would better educate
> all of us.

Dennis, you have hit on the very problem that caused me to post my first few notes.

It quickly became obvious from the postings that only a very few people on the forum understood, even vaguely, what an LOP was. Postings showed they didn't understand how Noonan could get on the LOP or know he was on it. Consequently I tried to craft an explanation of that one issue without confusing everyone more with a lengthy course on celestial navigation. An attendant problem was how to do that knowing there were a couple of people who DID know something about celestial procedures. I decided to totally ignore the dead reckoning (DR) portion (which I announced) and to do that I had to sort of fudge. I stated in one of my first notes that I was only dealing with the LOP issue and that what I was writing was technically NOT accurate and that this was not the way it was really done. I did that solely to eliminate all the work going into shooting and plotting the fix to show ONLY what an LOP was and why Noonan could know when he was on it whether he was ON course, or north or south of it.

While working on this it dawned on me that the 67 degree azimuth might be significant information so I contacted a number of professionals in this regard. After giving the background I posited that the 67 degree sun azimuth might tell us something as to where in general Noonan might have been during a very small time and position envelope. I contacted the US Naval observatory, the British outfit that publishes their air almanac, the aerospace mechanics and engineering department at the University of Texas, a Canadian government observatory and several other professional astronomers. All believed it was a reasonable and possible experiment and mathematically workable -- my detractors to the contrary.

One forum member who is quite knowledgeable of celestial procedures instead of seeing the possibility got side tracked by his accurate knowledge that a sun azimuth is not actually shot but rather only the altitude. This is true to a certain extent. The azimuth is instead plotted using the sun shot and the almanac tables. It also is shot using an azimuth circle which was a standard technique long before this particular flight. It is also true that when shooting the particular body the azimuth will tell the navigator valuable information.

The azimuth of the sun, contrary to what has been suggested, does NOT remain the same all day. It changes with the observer's time and position. If you will look at the sun data for Howland's position for the morning of July 2, 1937 you will see that the azimuth varies throughout the day. If you pick a position dead on the island and look in the table for a particular time, say 07:00a you will find a certain azimuth. If instead you pick a place 60nm dead north and check the table you will NOT find the same azimuth. It varies from north to south.

If you will picture yourself that morning 180nm west of Howland on a true course of 77 degrees and you look at the sun and note its direction, then picture yourself three or four hundred miles either north or south of that course and it should be obvious that the sun MUST be at a slightly different angle.

The bottom line is that there may be enough information to GENERALLY place Noonan between sunrise and 8:45 local.

While going through this exercise it also dawned on me that everyone has pretty much made the loss a navigation issue. Noonan has been restricted to only a sun line. He has not been allowed to shoot the moon or planets all of which was available to him that morning. I have also checked and found the data WAS available in the charts of the day. There were even SOME air almanacs but what they contained for the relevant period I haven't determined. I have found that the British air almanac was available but only for the last quarter.

We have not allowed Noonan to use an azimuth circle that was standard for the day nor have we even given him the reasonable possibility of checking his drift and ground speed. ALL normal navigation techniques that ANY navigator would have used let alone a MASTER navigator with years of nautical and Pan Am experience. In our rush to explain why they missed Howland we have stripped Noonan of all his great experience and expertise and the tools of his trade. We have created an impossible task for Noonan in addition by exploiting all the known celestial errors and variables and somehow implying Noonan would either not have known of them or could not take them into consideration. Some have even made him incapacitated from drink.

And yet the possibility that our duo simply could not visually spot a tiny island among all the cloud shadows seems too far out to accept. Interesting.


http://tighar.org/Projects/Earhart/forum/Highlights101_120/highlights112.html

Subject:    Erroneous Howland Position?
Date:    10/30/00
From:    Randy Jacobson

Noonan’s 10 mile navigational uncertainty was based upon nighttime celestial navigation, shooting LOP’s from at least 2 or more targets. For the sunrise LOP, his precision of navigation would be that he could navigate the plane to within 10 miles of the LOP determination, but he would not be able to determine his position along the LOP at all.


http://tighar.org/Projects/Earhart/forum/Highlights121_140/highlights127.html

Subject:    Re: Professionals
Date:    2/19/01
From:    Randy Jacobson

I've not piped up to date, but let's get something very clear here: FN did not navigate anywhere near 50 to 100 miles off his target. The Oakland to Honolulu maps indicate the plane was that far off the perfect rhumb line between the two points if and only if there was no winds aloft. Without real-time, constant navigational control, no navigator, repeat, NO navigator or pilot could or even would try and maintain that level of navigational precision to stay on a rhumb line over water. It simply wasn't possible then. And there is no reason for anyone to do so...just monitor where the plane is going, and make corrections when necessary to ensure you do come to your target position.

From: Doug Brutlag

... I own and have used a (similar) model of the A-5 Pioneer sextant that Fred used on the ill-fated trip. I also own several other models of hand held aviation sextants. I will not claim to be an expert but I can say from experience using them and having face to face discussions with retired navigators who depended on them in their careers, the typical average accuracy for decent navigator was 10-15 miles and on occasion 20 was considered the limit of acceptable (barely). Fred mentions in a letter to PVH Weems an accuracy of 10 miles (approximately). Call it the average --- some did better, some did worse.
LTM,

           Marty
           TIGHAR #2359A
 
« Last Edit: September 14, 2010, 04:17:14 AM by moleski »
Logged

Martin X. Moleski, SJ

  • Administrator
  • *
  • Posts: 2909
Re: Visualizing the 337-157 LOP
« Reply #5 on: September 15, 2010, 12:09:05 PM »

Thanks for bringing the old posts forward, Marty - very educational and helpful in overall understanding of how we got to where we are in the search.

My pleasure.

I've revised the initial post in this thread with all-new drawings.

I was wrong about how celestial navigation works.  I think the new drawings are more accurate.  It is not the case that there is a 337-157 LOP that can be derived from the dawn terminator all year long.  But when the terminator between night and day is slanted at 337-157, everyone on the same latitude that morning sees the sun at 67 degrees and would know that they are on a LOP of 337-157 at that moment.
LTM,

           Marty
           TIGHAR #2359A
 
« Last Edit: September 15, 2010, 09:16:29 PM by moleski »
Logged

Mike Piner

  • T1
  • *
  • Posts: 44
Re: Visualizing the 337-157 LOP
« Reply #6 on: September 15, 2010, 03:16:04 PM »

Most posts have not mentioned that the sun did not come up that morning in relation to the heading of the electra as dead ahead,  but about 13 degrees to the left. (as I compute it).  I wonder did that affect where they were looking for Howland Island, in all the excitement of finally being there. Turning on the LOP then would not have been a problem , as the heading would still be 157 degrees.
Logged

Kevin Weeks

  • TIGHAR member
  • *
  • Posts: 191
Re: Visualizing the 337-157 LOP
« Reply #7 on: September 17, 2010, 05:58:35 AM »

marty, do you know the difference in the LOP given a change in latitude??

Most posts have not mentioned that the sun did not come up that morning in relation to the heading of the electra as dead ahead,  but about 13 degrees to the left. (as I compute it).  I wonder did that affect where they were looking for

Howland Island, in all the excitement of finally being there. Turning on the LOP then would not have been a problem , as the heading would still be 157 degrees.

we cannot assume what the heading of the electra was. the heading of the electra would not have been the exact straight line course between the origin and destination. FN would have used an estimation of wind direction and speed to set the course and account for drift. Depending on his estimation of drift would have changed his course. We assume he estimated his drift incorrectly to come up for enough away from howland not to see it. there is no way to tell what course they actually flew on.



Logged

Martin X. Moleski, SJ

  • Administrator
  • *
  • Posts: 2909
Re: Visualizing the 337-157 LOP
« Reply #8 on: September 17, 2010, 06:41:49 AM »

marty, do you know the difference in the LOP given a change in latitude??

Only for one day and three locations: 11 September 2010.  Playing with the Sun Position Calculator gave me some numbers for Howland, Niku, and a place just south of Buffalo.  This is what showed me that my two-dimensional drawings were wrong.

Quote
we cannot assume what the heading of the electra was. the heading of the electra would not have been the exact straight line course between the origin and destination. FN would have used an estimation of wind direction and speed to set the course and account for drift. Depending on his estimation of drift would have changed his course. We assume he estimated his drift incorrectly to come up for enough away from howland not to see it. there is no way to tell what course they actually flew on.

I think you're right.  We have to deal with a cloud of possible positions and headings based on probabilities that are not strictly calculable.

  • We know they did not land at Howland Island (a provable negative if we accept the testimony of the people near Howland as reliable).  How close could they have come to Howland and Baker and not have seen them?  One's guesses about that range will set a northern and eastern boundary for the cloud we're constructing.
  • At what altitude were they flying?
  • What was their range of vision from the cockpit that morning?
  • How far along the line that they supposed went through Howland did they fly north?
  • The Niku hypothesis is that they either arrived within visual distance of Gardner by following the 337-157 line drawn through Howland or by later refinements in celestial navigation.  Where would they have to have been to miss Howland but find Niku?
  • The Post-Loss Radio Messages suggest that AE and FN landed with enough fuel to transmit, on and off, for a few days or more.  What constraints does the evidence (if it is evidence) of post-loss transmissions place on the cloud of probable positions between Howland and Niku?  The closer they came to Howland, the less fuel they would have to transmit, and vice-versa.  If our cloud is far from Howland, that impugns Fred's navigation; if it is close to Howland, that raises questions about the evaluation of the post-loss radio messages.
  • How likely is it that AE managed to minimize fuel consumption during the 20 hours and 13 minutes that we are sure they were aloft?  What is the best-case scenario?  The worst-case scenario?  Guesses about these factors will expand or shrink the size and shape of the probability cloud between Howland and Niku as well as of the reliability of later alleged transmissions from the plane.

I'm sure there are other factors I've missed.  To the extent that one judges that TIGHAR has found good evidence for the presence of AE and FN on Niku, the argument about the right size and shape of the cloud is moot (interesting, debatable, and irrelevant).  If they ended up on Niku, it doesn't matter how close they got to Howland and Baker.  It may have been an improbable event, but strange things do happen.
LTM,

           Marty
           TIGHAR #2359A
 
Logged

Martin X. Moleski, SJ

  • Administrator
  • *
  • Posts: 2909
Re: Visualizing the 337-157 LOP
« Reply #9 on: September 17, 2010, 11:12:54 AM »

Thanks for the patience, hard work and sharing.

My pleasure.  I've learned a lot this week.  ;o)
LTM,

           Marty
           TIGHAR #2359A
 
Logged

Mike Piner

  • T1
  • *
  • Posts: 44
Re: Visualizing the 337-157 LOP
« Reply #10 on: September 17, 2010, 01:42:38 PM »

FOR ME I KNOW ONLY THAT THE KNOWN IS UNKNOWABLE, AND WE ARE LOOKING AT EXPERTS STIRRING A POT OF STEW,  I CAN'T SAY " EXCELLENT " TO ANY OF IT.  I PLOTTED ON PAPER WHAT I DIDN'T KNOW AND FORGOT THE WIND DRIFT, SO I HAVE TO GET SOME PAPER AND START AGAIN TO DO SOMETHING THAT WILL BE TOTALLY USELESS.  MAYBE THEY TURNED SOUTHEAST AND EXPERTLY NAVAGATED TO GARDNER .  But I enjoy speculating, and seeeing what you folks write.  One day we will know (some of it)when it is solved  M Piner  LTM :
Logged

Mike Piner

  • T1
  • *
  • Posts: 44
Re: Visualizing the 337-157 LOP
« Reply #11 on: September 22, 2010, 01:36:45 PM »

I read a lot of heady calculations, and it is good to try this, but the Monte Carlo work thought that they were south of Howland.  It is strange that no sunrise was declared.  Perhaps they were 200 mi late, and no sunrise, even tho 1744 GMT is the time of sunrise.  They continued on, thought she was "on you', then flying 51 more minutes, no way of knowing where they were, and Fred got a Moon- Sun fix, told AE a course, and found Gardner.  Pure speculation. 
Logged
Pages: [1]   Go Up
 

Copyright 2018 by TIGHAR, a non-profit foundation. No portion of the TIGHAR Website may be reproduced by xerographic, photographic, digital or any other means for any purpose. No portion of the TIGHAR Website may be stored in a retrieval system, copied, transmitted or transferred in any form or by any means, whether electronic, mechanical, digital, photographic, magnetic or otherwise, for any purpose without the express, written permission of TIGHAR. All rights reserved.

Contact us at: info@tighar.org • Phone: 610-467-1937 • Membership formwebmaster@tighar.org

Powered by MySQL SMF 2.0.15 | SMF © 2017, Simple Machines Powered by PHP