Antonio, foeth, George and Iankw
...let’s review the record.
We have before us the question of Bismarck’s speed as observed on film and the light this sheds on the issue of the Winklareth Theory.
George and I have been around and around about fluid dynamics and the issue of whether or not the oceanic current is of any consequence in this case. Happily, as George posted, foeth will help us out. And so he has.
As far as the current is concerned...it is not important, as all things are relevant to each other... foeth
foeth wrote:I’d start by ignoring both wind speed and currents... foeth
foeth wrote:I think you don’t need fluid dynamics but uncertainty analysis... foeth
foeth wrote:Apparently somebody thought it would be a good idea to calculate it (the water column) using FEM (Finite Elements Modeling), but why ? (All quotes Thursday, 2-25-05/ 9:17am) foeth
Why indeed ? These are all very good points and underscore precisely topics I have previously addressed.
We must recognize that we are not modeling a scenario but are making educated judgements by observing events captured on film. Fluid dynamics is not a viable solution as it does not address the issue at hand. As foeth pointed out, we are actually looking at an analysis of error in defining the characteristics of the film under study.
This is exactly what Antonio and I have done, independently of each other, and we have derived sufficiently similar results as to provide a confident validation to the numbers. The amazing thing about George and I going on about this as though we were in some sort of great disagreement is that we agree, when our respective posts are evaluated, that Bismarck was traveling between 29.5 and 30.0 knots. Therefore, I agree that it’s silly to waste so much time on needless recriminations and I apologize to the Board on behalf of the both of us for not pointing this out earlier.
Insofar as we now have a consensus that the oceanic currents and fluid dynamics play no role in this exercise we can now move to the issue of determining the speed of Bismarck and what effects this has on the Winklareth Theory.
First, allow me to make some comments about the following statement:
foeth wrote:The speed can be given as 30 knots +/- 3.6 knots. ANY speed in this range is CORRECT. Even if (the) estimate in time is perfect and the error in position is only 5m (2%) you’re off by 1.2 knots. (Thursday, 2-25-05/ 9:40am) foeth
I believe there are some practical impediments to assigning a speed of 30 +/- 3.6 knots to Bismarck which compel us to review this estimate. First, the highest speed I have seen anywhere for Bismarck and upon which I can rely is 30.8 knots. Second, the lower end of the stated value – 26.4 knots – is not consistent with other testimony which places Bismarck as steaming at least 28 knots during the Denmarck Strait action. If we consider these facts as reasonable then I would submit foeth’s estimate must contract to 28.0 to 30.8 knots (or an even 31.0 knots for sake of simplicity). Thus practicality would suggest we are presented with a speed of 29.5 +/- 1.5 knots.
On this basis foeth pardon me in assigning to you this estimate of 29.5 +/- 1.5 knots.
Reviewing what George has written,
George Elder wrote:I am content that (Bismarck) must have been traveling at least 29 knots...(but) I am not yet prepared to say she was going at 30 to 31 knots... (Thursday, 2-25-05/ 6:42pm) George
Here, having posted his opinion that Bismarck must have been traveling between 29 and 30 knots, I will assign George his estimate of 29.5 +/- 0.5 knots.
I have previously posted that my own estimate yielding a speed of 30.0 +/- 0.5 knots.
Now, in response to foeth’s calculations which he covered in detail,
foeth wrote:...I introduced a 0.5 s(econd) error. I cannot assume that the speed of the camera runs true or that the number (Antonio’s film counter – Randy’s emphasis) is read accurately enough, the point in time of the watercolumn is correct, etc. The error in distance is about 5%. (Thursday, 2-25-05/ 9:40am) foeth
I would point out that I did
assume the camera to be functioning correctly throughout the sequence. This is as much a judgment call as foeth has made and likely as correct or incorrect as his judgment may be. However, the time interval is sufficiently abbreviated as to preclude the introduction of any significant error, in my opinion.
In addition, I eliminated the error in timing the sequence by the simple installion of a digital chronometer in parallel with the laser reader of the DVD player. With shuttle operation this could theoretically read to 0.001 seconds but for practical purposes it would obviously be far more reliable to settle for a reading in the region of 0.050 seconds, a neglible factor for our calculations here. The same measurement applies to the water column which is, after all, nothing more than a positional reference...a football goal post, as it were.
As for the error in distance, as it happened I had chosen 5 meters, which places us at 2%, which is, of course, exactly what foeth had pointed out. Thus I arrived at 29.45 to 30.45 knots. Since this number reminds one of a statistical statement which defines a family as 3.7 people (whoever heard of 7/10ths of a person ?) I simply reduced the value to a more digestable 29.5 to 30.5 knots, or 30 +/- 0.5 knots.
Thus between Antonio, foeth, George and myself, we have arrived at a speed band of 28 to 31 knots for Bismarck and a speed band of 29.5 to 30.0 knots around which all four of us have expressed agreement. Antonio has posted his calculations. We would note that foeth has posted a value for Bismarck which he may or may not agree I have ‘corrected’ properly given the circumstances. George has expressed his agreement and a more important statement. Let’s revisit his posting, as follows:
George Elder wrote:... With regard to speed estimates...I am content that the ship must have been traveling at least 29 knots given all we know from the record. I am not yet prepared to say she was going at 30 to 31 knots, and especialy 31 knots...As I have admitted, I am not at all sure how one can accurately judge the Bismarck's speed given what we now have available. I think we should search out a method that will have an acceptable error margin, say +/- 0.5 knots at most. That is a demanding standard, and perhaps it cannot be obtained. (Thursday, 2-25-05/ 6:42pm) George
It is an interesting to read George’s comment that an error of “...+/- 0.5 knots...is a demanding standard...” when, in fact, he wrote immediately prior that, in his opinion, Bismarck was traveling “...at least 29 knots...” and was not “...prepared to say she was going (more than) 30 knots...” In other words, he supports the contention that Bismarck was steaming at 29 to 30 knots or – put another way – 29 +/-0.5 knots, the very demanding standard he deems necessary for the discussion !
Looking back on all that has been written, I can not understand what George and I are even arguing about since we are in such agreement as we are. And although we have established estimates to within +/- 0.5 knots, it is also quite unnecessary for the purposes of our problem as I can readily demonstrate. All of which leads us back to the point where we can discuss the effects of these calculations with regard to the Winklareth Theory, which is the object of this exercise.
If we agree, as obviously we do, that Bismarck was traveling between 28 and 30 knots, it can be demonstrated that there is no need to worry about whether we can define Bismarck’s speed to within +/- 0.5 knot. Although I believe we have, and have so demonstrated, the distinction is quite meaningless.
It is meaningless because even if we assume that Bismarck began the action only 2000 yards astern of Prinz Eugen (my own estimate which many believe is artificially low) and that she was traveling at our agreed upper limit of 30 knots there is simply no physical way Bismarck could have overhauled Prinz Eugen in the timeframe defined by the Winklareth Theory. On the other hand, if Bismarck was further
astern of Prinz Eugen (very likely from the evidence I am seeing) and was steaming at our agreed lower limit
of 28 knots, then the case supporting theWinklareth Theory is further undermined and, actually, is quite hopeless.
we have established:
That, for the purposes of our exercise, the effects of current and wind are negligible and the application of fluid dynamics modeling has no value in determining Bismarck’s speed,
That the methods employed by Antonio, foeth, George and myself in determining Bismarck’s speed and the variation of our respective determinations is acceptable, valid and verifiable for our exercise,
That the sea speed of Bismarck in our collective determination is 29 +/- 1 knots, a speed envelope fully sufficient to address our question, and
That considering this speed envelope as determined for Bismarck, in no case will Bismarck overhaul Prinz Eugen as postulated in the Winklareth theory.