Navigational Confirmation of CQD Position

[Parks Stephenson]

I'm curious about the speculation about Boxhall being confused by the time change, or lack thereof. I would give Titanic's de facto navigation officer a bit more credit than that, especially since he worked his calculations in the same room where the Magneta system master clock was located.

Parks

 

[David G. Brown]

Titanic's 23 minute clock setback has been one of my areas of study for about three months now. From what I can see, it had nothing to do with the navigation and/or Boxhall's final CQD position. Even if Titanic did get under way again, it was stopped again prior to the clock setback. Thus, all of Boxhall's navigation was done in April 14th hours. There would have been no confusion on his part.

--David G. Brown

 

[Paul Rogers]

Apologies for jumping in; I just wanted to make a quick point.

John said: "Dave Gittins' approach to this error is quite lucid and amazingly credible in my mind. (And Boxhall, as we know from other discussions here, was likely ill and possibly fairly exhausted at the time, so a minor mistake such as Dave proposes isn't at all out of the question, "crack navigator" or not.)"

I couldn't agree more. I would find it more surprising if an error hadn't been made, what with Boxall allegedly unwell and certainly under enormous pressure.

I work as a trainer for a UK Financial Adviser company, my main role being to train new staff on the UK tax system. At the end of their training, everyone sits a three hour exam which is mainly calculation-focused. Once a year, everyone in the company (including me) sits a similar three hour exam, to guard against "knowledge fade." The calculations are quite in depth, but still relatively easy if one understands and applies the theories being tested.

Despite having trained out these topics week-in, week-out, on my last paper I still managed to drop 4 marks in one question, whilst completely misreading another. (Thankfully, I spotted the latter error whilst doing a final check before handing in the paper. Otherwise it would have been very embarrasing!) Other colleagues suffered similarly - most certainly not from any lack of knowledge but just because mistakes happen.

This is why I think Dave Gittins' theory is so believable, even without any personal knowledge of navigation.

Paul.

 

[Erik Wood]

I have not read Dave Gittins theory but from what I have heard of it described by John it sounds like a more then reasonable theory. I will have to try and find his website and look for it.

 

[Markus Philipp]

Hi all,

I think it is worth to study Dave Gittins theory. Personally I am quite convinced that this is the "correct" explanation for Boxhall's error.

Boxhall used 22 knots for his calculations. This speed estimation comes close to reality.

1. From Saturday noon to Sunday noon Titanic made 546 miles. The clock was retarded by 44 minutes in the previous night (Pitman's memorandum).
Speed: 546 miles / 24.7 hours = 22.1 knots.

2. At Sunday noon Titanic was 126 miles before the corner. The position of the wreckage is 133 miles behind the corner.

Speed: 259 miles / 11 hrs 46 mins = 22.0 knots. (Boxhall used 11.46 as time for impact)

Even if we assume an easterly current of 1 knot Titanic's position would have been 2 miles west of the wreck position.

Speed in this case: 261 miles / 11 hrs 46 mins = 22.18 knots.

Thus Boxhall was perfectly justified to use 22 knots in his calculation.

Now, what went wrong with his calculation?

Lightollers star position was taken at 7.30 p.m.
Time from 7.30 p.m. to 11.46 p.m.: 4 hrs 16 mins

Titanic travelled 22 knots * 4 hrs 16 mins = 93.9 miles.
Course was south, 86° west. 93.9 miles have to be split in southerly and westerly component. Boxhall used traversion tables for this, and he found:

93.9 miles * sin 86° = 93.6 miles west

93.9 miles * cos 86° = 6.55 miles south

No error occurred up to now. To find the final longitude Boxhall now had to convert 93.6 miles into increase of longitude at latitude 42°. Mathematically spoken, he had to figure

93.6 miles / cos 42° = 126' = 2°6' degree of longitude.

Unfortunately he slipped into the wrong column and used sine instead of cosine:

93.6 miles / sin 42° = 140' = 2°20' degree of longitude, which is 14 minutes of degree more.

He found 50°14' west. He would have found 50°00' west, with correct calculation. This is just 2 miles besides the wreckage position.

When we look at the traverse table which he used to divide by sine or cosine we can easily understand how to slip into the wrong column. The same table could be used for different calculations. The same key word "Departure" appears in bold letters in one column and in cursive letters in the other one. Depending of the type of calculation he had to use the bold or the cursive key words to find the right column.

Diff. Long. . . Departure
Distance . . . Diff. Latitude . . . Departure

121 . . . . . . 89.9 . . . . . . . 81.0
123 . . . . . . 91.4 . . . . . . . 82.3
124 . . . . . . 92.1 . . . . . . . 83.0
125 . . . . . . 92.9 . . . . . . . 83.6
126 . . . . . . 93.6 . . . . . . . 84.3 correct result here: 126
...
140 . . . . . .104.0 . . . . . . . 93.7 wrong result here: 140

Instead of 93.6 in the second column he looked up 93.7 in the third column. Thus he found 140' instead of 126' minutes of degree longitude.

This is why I think Dave Gittins' theory is so believable.

Markus

 

[Dave Gittins]

Nice work, Markus!

After I created that web page, I learned that in 1912 officers were taught to convert miles of departure to minutes of longitude by a calculation much like you suggest. I regret that I didn't copy the details. The Board of Trade expected a lot of navigation to be done by trigonometry and logarithms.

I can't recall the exact method, but it would have been as you suggest, except that the division was done by means of the logarithms of trigonometrical functions supplied by the books of nautical tables. I don't know if they made a correction for the fact that the earth is not perfectly spherical.

Like my idea, your method produces a small error at latitudes of about 45°. If you rework if for 20°, you'll see that the result of using the wrong trigonometrical function is obviously silly.

Another quite simple possible cause of the error is that Boxhall worked from a dead reckoning position for 8-00 p.m. instead of the stellar position. He thought this unlikely, because he was working from his own notes, but you never know. The poor devil was tired and possibly unwell.

 

[Markus Philipp]

Hi Dave,

your page and my idea that Boxhall switched sine and cosine rose independant from one another. At school I have learned to use logarithm tables. From this I got the idea that the same column might be used for some angle phi or (90° - phi). I played with 42 and 48 degree and found that the error would match the distance between CQD and wreckage. But I did not know what kind of tables the navigators really used. So it was just a weak idea. Later on I found your page, and you presented the tables which navigators use, and this is all the way a perfect confirmation of my idea.

You said: "another quite simple possible cause of the error is that Boxhall worked from a dead reckoning position for 8-00 p.m. instead of the stellar position. He thought this unlikely, because he was working from his own notes, but you never know. The poor devil was tired and possibly unwell".

Maybe. But where did he get the dead reckoning position at 8 pm from?
There is an interesting arguement between Lowe and Senator Smith in the US enquiry. Lowe explained that Titanic was 162 miles (sic) before the corner at noon. I think this is a typo, because 162 miles by 6 hrs makes 27 knots, which is quite unlikely. It must be 126 knots.
And one can find from Lowe's testimony that 126 miles is the correct value. Lowe said that he estimated the position at 8 pm. He used a speed of 21 knots for that. He even made a calculation on a chit of paper and figured 20.95 knots! From his tales one can hear that he must have divided something by six hours (noon to 6 pm) and found 20.95 knots. What did he figure then?
20.95 knots * 6 hrs = 125.7 miles. There we are with 126 miles (and not 162!) before the corner.
Lowe found 21 knots because he put the time of the turn at the corner to 6 pm: 126 miles / 6 hrs = 21 knots. But he should have calculated: 126 miles / 5 hrs 50 mins = 21.6 knots, or 126 miles / 5 hrs 45 mins = 21.9 knots!
Thus he used 21 instead of 22 knots. In eight hours he will loose 8 miles then. That means, Lowe's dead reckoning position at 8 pm is eight miles east of the correct position at 8 pm.

But Boxhall's CQD is 12 miles west of the wreck position.
I have read somewhere in the enquiry that Lightollers star position was plotted into the chart at 10 pm.
Boxhall in the US enquiry said that Lightollers observations were beautiful. There were three couple of stars for longitude and latitude, and they all agreed.
So I am inclined to believe that Boxhall really used Lightollers star position as base for his calculations. Otherwise there is no need for Lightoller to take precise stellar observations.

Cheers
Markus

 

[Erik Wood]

Very interesting calculations.

 

[Paul Lee]

There a debate going on here about this:

https://www.encyclopedia-titanica.org/discus/messages/5664/86164.html?1083784756

Best wishes

Paul

 

[Jim Currie]

On day 11 of the BOT Enquiry,a great deal of examination into the content of 'the ice warning message from 'Caronia' took place. Mr.Lightholler was on the stand. He stated it was the only message he saw and that he first knew about it at about 1 pm on the 14th. He further discussed it with Mr. Wilde when he relieved him at 6m that evening.
That particular message warned that the eastern extremity of the ice was 49 degrees west longitude.
When he went on watch at 6:00pm that night, Lightholler made a quick mental calculation and reckoned that the ship would be at the ice about 9:30pm - half an hour before the end of his watch. However,as a check, he ordered Moody to make a proper calculation. Contrary to Lightholler's timing - Moody calculated that Titanic would reach the ice an hour and a half later than Lightholler thought - at 11:00pm.
You might think that since one calculation was mental and the other was 'on paper' the latter would be the more accurate. It certainly would have been more believable had there been a few minutes of longitude or time different. However an hour and a half or 33 miles is not insignificant.
Lightholler was a very experienced Extra Master. He would, without doubt, know that a ship on a course of 266T travelling at 21.5 or 22.0 knots in latitude 42N would increase its westerly longitude by approximately 29 - 30 minutes every hour. So how come the huge discrepancy? Lightholler dismissed it by saying Moody had probably a different source of information but I do not think so and I don't think he did either!

Is this what happened?


Both men came on watch at 6:00pm.- 3.5 hours until 9:30 pm at say 22 knots is 77 miles which converted to longitude in latitude 42.00N is about 104 minutes or 1 degree 44 minutes of longitude However, 144 minutes is 2 degrees 24 minutes - a difference from Lightholler of 40 minutes of longitude which, converted to miles is 30 miles - just under and hour and a half at Titanic's speed. This would account for Moody's estimated time of arrival at the ice being 11pm instead of Lightholler's 9-30pm.

Lightholler's navigation was again tested at
Q13554 to Q13556 of the Enquiry when he mentally calculated back from Boxhall's 50-14W. CQD to the time of passing 49W. He once again, reckoned his second bit of mental maths agreed closely with his (Lighthollers) original estimate of 9-30pm for Titanic being at the eastern edge of the ice

It follows that if Lightholler's back-calculating to 49 W fitted with Boxhall's CQD Longitude - both men were reading from the same 'hymn sheet'.

In an attempt to work out how Lightholler worked back his estimated time of passing the 49th. meridian I have used two timings - 14th. time and 14th + 23 minute clock change. I term them Run A and Run B.


CQD Longitude = 50. 14 W
Time of Impact= 1140 pm

Lightholler's passing the 49 W time:0930pm(14th).

Run A- 9:30 to 1140
2hrs 10'@22.0 = 47.7 miles D.long 1. 04 E
Run B- 9:30 to 12:03 am (23' set-back).
2hrs 33'@22.0 = 56.1 miles-D.long 1. 16 E
These give:
DR Longitude @ 9:30 pm - Run A = 49. 10 W

DR longitude " " " - Run B = 48. 58 W

Applying a further Run back from 9:30 pm until 6m:

Run: 3hr.30min.@ 22.0 = 77 miles- D.Long 1. 44 E
Gives DR LOngitude @ 6m for:
Run A = 47. 26 W
Run B = 47. 12 W

Then back yet another 10 minutes to the Turn gives:

DR Longitude @ 5:50pm for Run A= 47. 21 W
for Run B= 47. 08 W

However Longitude of the wreck is 49 58 W

Turn 5:50pm to impact 11:40pm is 5hr 50 min.
@ 22 knots this makes a D.Long of 2 52 E

This gives a DR Longitude @ 5:50 of 47 06 W
This last DR is 128 miles from the wreck site and 5 miles x 240T from The Corner. The distance from The Corner to the wreck site is 133 miles.

The Lighhollers of-the-cuff DR worked-back longitude in Run B above points to him having allowed for the clocks being set back 23 minutes when calculated the distance run from crossing the 49th. meridian until impact. This would be natural since he was in bed when the impact came and would naturally expect the first part of the set-back being carried out. I also suggest that's what Boxhall did as well. How else could Lightholler have suggested that Boxhall's CQD was correct? However, it does not prove that the clocks were actually set back - the position of the wreck points to it not having been done so. To cover 128 miles in 6 hours 13 minutes,(5:50 to 12:03am next morning), Titanic would average 20.6 knots. There has never been any suggestion that she was travelling at less than 21.5 knots. I have a sneaking suspicion that Boxhall and Lightholler both knew she was averaging more than 22.0 knots!

 

[Samuel Halpern]

Still having fun Jim?

A few points with regard to what you wrote above.

>>Both men came on watch at 6:00pm.<<

Lightoller came on at 6:00pm but Moody went off duty at the time. He didn't come back on until the end of the 2nd dog watch at 8:00pm, the same time Boxhall came back on. Lightoller's watch was from 6 to 10 as you know.

>>He once again, reckoned his second bit of mental maths agreed closely with his (Lighthollers) original estimate of 9-30pm for Titanic being at the eastern edge of the ice<<

Not really. What Lightoller said was, "It works out somewhere about half-past 9." He never did the mental math. If he did he would have seen that 49° 00' W to 50° 14' W is 74 minutes of arc, or about 55 miles at their lat. At 22 knots, it takes just over 2.5 hours to run that distance. But 2.5 hours back from 11:40 is 9:10, not 9:30. Even if you assume 21.5 knots, which is what Lightoller also said he thought the ship was making, it pushes the time back even more.

 

[Jim Currie]

Exactly! that's the point Sam.

We don't know if he actually did the maths in his head when referring back but I can't see why he would confirm anything to to his inquisitors if he didn't have a go. There were quite a few present at the time who were very capable of doing the same mental exercise.
I did the actual work and agree with your findings. However, how could Lightholler use the
expression 'exactly' so often in such company and not be sure of a contradiction? As I pointed-out; it would be very easy for him to make such a mental calculation.

As far as Moody is concerned; Lightholler must have been lying when at Q13551:

"I do not know what time it was that Moody told you you would reach the ice at 11?". Lightholler replied "It was some time shortly after that I came on deck". I cannot remember the exact time". He would come on deck at 6 pm so was Moody there as well? I don't think so.
-
Moody would need a reference DR to work from there was no fix since the sights had still to be worked-up. I am aware of the difference between the DR used for the 'fix' that seemed to place the ship 20 miles ahead. If they ran that particular DR up to 8:00pm watch change it would still have that difference in it. However, even that's less than an hour steaming so does not account for Moody's hour and a half or 30 mile difference between his and Lightholler' ETA at the easternmost edge of the ice. That's why I became suspicious. I could well imagine that to check his (Lightholler's)mental ETA would be the first order given to Moody. Since Boxhall would more than likely be working the sights, Moody would get that lesser task. Is it possible that Moody was on the bridge at evening meal time as a bridge relief?

 

[Jim Currie]

Sam,

As for Lightholler's work-back:

He knew the time of impact was 11:40 pm
He previously estimated the time of being at the ice to be 0930. That's 2 hour's 10 minutes steaming between these times. At 21.5 or 22 knots this gives a distance of 46.6 and 47.7 miles respectively which on a course of 266T in latitude 42 gives D. Longs of 1 degree 03' and 1 degree 04' eastward. Subtracting these from Boxhall's CQD longitude of 50.14. gives a DR positions at 9:30pm of 49 degrees 11'W. or 49 degrees 10'W. Obviously too far west. However if you run another 23 minutes back at 22 knots that's another 11.5 minutes of longitude which puts Titanic right on the money for Lightholler's DR at 9:30 pm 14th. time.

 

[Jim Currie]

Sam,

Obviously our approach to the problem is different. You worked out the problem from the perspective of difference of longitude and ignored time. I approached it from the time factor in the first instance as I believe, Lighholler would have done. As I said before; he was supremely confident that Titanic would arrive at 49 W at 9:30 on the evening of the 14th. He also knew the popular time of impact was 11:30. Perhaps he knew Boxhall had made a mistake and, as he did with the other junior navigating officer -put up a smoke screen to protect him.

As far as D. Long is concerned; we need to match 49.00W. with 50.14W as you rightly say...
1 degree and 14 minutes of longitude -74 minutes. At 21.5 knots that would take 2.55 hours - correct as you say again but that would place the ship at the impact point at 0930 + 2hrs,33 minutes = midnight + 3minutes but we know it happened 23 minutes earlier at 11:40pm.

I think the main thing that would concern Lightholler was his 9:30 v ice calculation.

 

[David G. Brown]

Lightoller's prediction of ice is most curious because it was apparently not one prediction, but two. On his testimony during the British inquiry has been under discussion so far. At that time he alleged that Sixth Officer Moody predicted they would be up to the ice after 11 p.m. while he claimed to have thought it would be closer to half-past nine. (BOT questions 13486 through 13556.)

However, this was not Lightoller's first story. During the U.S. Senate inquiry he said something quite different. In that version only First Officer Murdoch is mentioned and Moody is nowhere to be found. "When I ended the watch we (Murdoch & Lightoller) roughly judged that we should be getting toward the vicinity of the ice...somewhere about 11 o'clock," Lightoller said. "I remarked on the general condition of the weather, and so on, etc., and then I just mentioned as I had done previously, 'We will be up around the ice somewhere about 11 o'clock, I suppose.'"

Which version was correct? Lightoller was never asked to resolve the matter so it will probably remain a mystery. We can only speculate on why he claimed to have predicted the ship would reach ice at two different times: 9:30 p.m. or after 11 p.m.

The most substantive clue lies in the longitudes quoted by Lightoller for ice reports. He said it was reported between 49º and 51º West. Assuming a 22 knot speed and an 11:40 p.m. time for 50º14' West longitude (both per Boxhall), it is possible to work backwards to approximate what Lightoller might have been thinking.

11:40 p.m. 50º14' West
11:30 p.m. 50º09' West
11:00 p.m. 49º55' West
10:00 p.m. 49º21' West
9:30 p.m. 49º06' West

If Moody used a mid-longitude of the ice reports, he would have estimated the time for when the ship passed 50º West. The table above shows that should have occurred a few minutes past 11 p.m. as Lightoller claimed during his U.S. testimony. However, there is a problem with this. Lightoller indicated he used the nearest longitude to the ship, 49º West, for his prediction. That crossing should have taken place just before 9:30 p.m. which was, conveniently enough, the second officer's second "prediction."

Neither Moody nor Murdoch survived to corroborate either of Lightoller's claimed predictions. Even worse, Moody's death prevented him from confirming his prediction, if it were made at all. Lacking any proof one way or the other, Lightoller's conflicting statements must be considered as suspect when it comes to the truth.

Lightoller's earlier American testimony indicates no special attention was paid to ice between 49º and 50º West longitude. In view of the disaster, this was hardly prudent navigation given the reports of other ships. It raises the spectre of criminal liability on the part of the navigating officers for having ignored ice warnings they had on hand.

Later, in London, Lightoller produced a more prudent story of being on the alert for ice right from the moment the ship crossed the 49th meridian. This story supports the "everything was against us" view of the disaster that Lightoller espoused.

It is possible that the "after 11 p.m." prediction was, as he said in America, Lightoller's work while on the bridge of Titanic. Unfortunately, Moody's alleged 9:30 p.m. prediction makes no such sense. Remember, Moody's must be created using an 11:40 p.m. time for longitude 50º14' West — the incorrect CQD longitude created by Boxhall. No matter how you compute the navigation, that longitude is too far west for the ship's accident which took place closer to 50º00' West.

The only way to make sense out of the alleged Moody prediction is to assume it was really a post-prediction by Lightoller based on the erroneous CQD longitude. By doing so, the second officer gave his performance on the doomed ship's bridge a more prudent appearance for the benefit of the London inquiry. Lightoller made it seem he was looking for ice two hours and more before the accident —- quite a different story from his "somewhere about 11 p.m." U.S. testimony.

-- David G. Brown