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Old 06-11-2020, 04:07 AM   #1
DMW
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Default Thinking out loud - improved speed calculations

Hello,

Just some thoughts about errors in speed calculations for the method of timing the boat travelling a distance equal to its own length

Errors:
1. Own boat speed
1a. Solution, stop the boat or travel on a direct bearing to target. (Yes you can subtract your own speed but that requires accurate knowledge of target course and maybe some trigonometry)

2. Timer has 1 second resolution
I have two solutions to this.

2a. Once "stopped" we can round the same way we round in some programming languages. Add "0.5" seconds by tapping the T button twice in quick interval (of about 0.5 seconds), one can practice using timer app on phone. This should add 0.5 of a second, so
3.0 sec (acutal) -> 3.5sec (with addition) -> 3sec (displayed) - still correct
3.6sec (actual) -> 4.1secc (with addition) -> 4sec (displayed) - correctly rounded
etc.

2b. Other method: (use with 2a.) Once you have the first time, the clock still has the decimal stored within it, so to utilise this just do the same measurement again but do not clear the timer between the two measurements. This will result in approx twice the time and have to use 2x boat length but: Averages some human error, uses decimal from the first reading. E.g. first reading is 29.6 seconds, displays 29 sec. Second reading is 29.5 seconds, would display 29 if reset clock but the total is 59.1 displays 59. Results in 0.1s error rather than 1.1 second error.
Also if one uses the rounding method from point 1a. this reduces the maximum error from 2sec to 0.5sec.

3. Beam error
3a. So the idea of this error is that looking for the back of the ship due to the angle and that the ship has width, the exact back of the ship may be hidden. For a heavy tanker type 26 length = 147, beam = 23, beam error at 45 degrees is 23/4=5.75m and so added length error is 4%
3b. This is not likely the case because the back of the ship is rounded not flat, and so this likely isn't any significant error IRL, without a proper ship profile cant be truly sure about this one but I tend to ignore it. The front is generally quite pointy so less problematic.

4. TDC Parallax error
4a. This one annoys me the most, due to the position and 3D rendering of the TDC this can lead to noticeable parallax error on the dials.
4b. What is interesting is that speed has pretty much the most significant impact on torpedo angle, but yet the Germans didn't put in a decimal indicator dial like they did for AoB which means its least accurate to input. I wonder if this is because IRL the speed measurements were inaccurate and so there is less point in having an accurate dial for this.

4c. To demo the TDC parallax these images are with a fresh boat nothing touches, so are all technically at 0 but appear to be non-zero.

https://ibb.co/sy260q9

4d. As mentioned the target speed is most important, but due to the gauge position it suffers parallax.
Using this video:


I set up for a 6knot target
first issue is because of parallax it is hard to input proper bearing using TDC (maybe i should have used the A.P.)
tan-1(6/30)=11.3°

https://ibb.co/YQ7CFBq

I think that is about 11° in the picture, it appears to increment by 1 so I counted 11 from 0.
You can see that the speed appears to be somewhere about 5.8 knots rather than 6 leading to a 3% error

4e. I wonder if we can have an option to move you view around the TDC allowing one to align themselves with dials to remove parallax error



Just some thoughts out loud

Happy hunting!
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Old 06-11-2020, 05:02 AM   #2
DMW
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Note: I just repeated the speed experiment and got pretty much 0 error, my bearing wasn't on 11.3° so maybe this isnt such an issue as I thought
I was going to repeat because using % as an error before non-linear equations isn't really fair.

https://ibb.co/9vtJRm6

I also did a quick test in the tutorial

Speed measured using map = 6.08 knots
Speed calculation with 1 boat length = 6.17 knots, error 0.09
Speed calculation with 2 boat lengths and rounding = 6.014 knots, error 0.066

Maybe no significant gains here either!

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Old 06-11-2020, 06:37 PM   #3
derstosstrupp
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Very good post! I’m glad to see my video is getting used!
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