A Question For Those Good At Math

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A Question For Those Good At Math
« on: January 17, 2016, 10:47:19 AM »

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Slemon

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Re: A Question For Those Good At Math
« Reply #1 on: January 17, 2016, 11:09:11 AM »
Ooh, fun!

Taking the parameters given in the question literally, in a purely theoretical setting, then if we use the relationship between the segment of a circle and the known radius, it has 15.127 miles to go (from a back-of-the-envelope calculation), or nearly 80,000 feet. 150 feet really isn't all that deep.
So it's trivial to conclude that it would take 24.647 minutes, by my calculations.

More realistically, of course, a submarine couldn't travel in a perfect straight line like that because gravity acts perpendicular to the Earth's surface, and it'd take constant correction to be able to travel in a straight line.

What does this have to do with RET or FET? It seems to just be proposing a hypothetical situation which couldn't realistically occur.
We all know deep in our hearts that Jane is the last face we'll see before we're choked to death!

Re: A Question For Those Good At Math
« Reply #2 on: January 17, 2016, 11:25:56 AM »
That's interesting. I got approximately 5 minutes.

And submarines can and do travel in a straight line according to this submarine technician https://plus.google.com/+JamaalWilliams4Jesus/posts/8omik66o7Zw

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Orifiel

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Re: A Question For Those Good At Math
« Reply #3 on: January 17, 2016, 11:27:29 AM »


150ft and 32 knots?
30m and 59km/h; 16.4 m/s

Should take about 2 seconds, traveling in a straight line upwards and having no resistances whatsoever.

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Orifiel

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Re: A Question For Those Good At Math
« Reply #4 on: January 17, 2016, 11:29:23 AM »
That's interesting. I got approximately 5 minutes.

And submarines can and do travel in a straight line according to this submarine technician https://plus.google.com/+JamaalWilliams4Jesus/posts/8omik66o7Zw

Your post is not readable. It says "Page not found" and how did you get 5mins? This is literally just a plug and chug equation.
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sceptimatic

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Re: A Question For Those Good At Math
« Reply #5 on: January 17, 2016, 11:31:53 AM »


150ft and 32 knots?
30m and 59km/h; 16.4 m/s

Should take about 2 seconds, traveling in a straight line upwards and having no resistances whatsoever.
The OP is not talking about vertical. The OP is talking about horizontal at 32 knots starting at 150 feet below the surface.

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Slemon

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Re: A Question For Those Good At Math
« Reply #6 on: January 17, 2016, 11:34:58 AM »
That's interesting. I got approximately 5 minutes.

And submarines can and do travel in a straight line according to this submarine technician https://plus.google.com/+JamaalWilliams4Jesus/posts/8omik66o7Zw
What was your measure for horizontal distance travelled? I may have made a mistake, it was a hasty scrawled calculation, but I'd need to know more of your workings to compare.

Submarines can travel in an approximately straight line. The problem is 'straight' on the Earth's surface is typically 'perpendicular to the force of gravity.' That's not a constant direction. I assumed you meant straight in a fixed reference frame.

Also, that link doesn't work.
We all know deep in our hearts that Jane is the last face we'll see before we're choked to death!

Re: A Question For Those Good At Math
« Reply #7 on: January 17, 2016, 11:38:48 AM »
That's interesting. I got approximately 5 minutes.

And submarines can and do travel in a straight line according to this submarine technician https://plus.google.com/+JamaalWilliams4Jesus/posts/8omik66o7Zw

Your post is not readable. It says "Page not found" and how did you get 5mins? This is literally just a plug and chug equation.

These links should work

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Orifiel

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Re: A Question For Those Good At Math
« Reply #8 on: January 17, 2016, 11:40:25 AM »


150ft and 32 knots?
30m and 59km/h; 16.4 m/s

Should take about 2 seconds, traveling in a straight line upwards and having no resistances whatsoever.
The OP is not talking about vertical. The OP is talking about horizontal at 32 knots starting at 150 feet below the surface.

Ahh, ok, well I don't want to actually do that math right now...
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Re: A Question For Those Good At Math
« Reply #9 on: January 17, 2016, 11:42:49 AM »
The technician guy, if I remember correctly, said they would travel a long way in a straight line according to their instruments and they never adjust for the supposed curvature of water.
« Last Edit: January 17, 2016, 12:09:52 PM by JamaalW »

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Orifiel

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Re: A Question For Those Good At Math
« Reply #10 on: January 17, 2016, 11:44:17 AM »
That's interesting. I got approximately 5 minutes.

And submarines can and do travel in a straight line according to this submarine technician https://plus.google.com/+JamaalWilliams4Jesus/posts/8omik66o7Zw

Your post is not readable. It says "Page not found" and how did you get 5mins? This is literally just a plug and chug equation.

These links should work

" class="bbc_link" target="_blank" rel="noopener noreferrer">

" class="bbc_link" target="_blank" rel="noopener noreferrer">
Yeah, they do work *thumbs up*
Je parle Français and yes, I am une fille

Pumpkin god 4 lyf

Re: A Question For Those Good At Math
« Reply #11 on: January 17, 2016, 01:30:36 PM »
The technician guy, if I remember correctly, said they would travel a long way in a straight line according to their instruments and they never adjust for the supposed curvature of water.
I'm not an expert in submarines, but don't they need to do something with air tanks to rise.

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getrealzommb

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Re: A Question For Those Good At Math
« Reply #12 on: January 17, 2016, 01:47:13 PM »
It would eventually beach its self in the shallower waters. (no math required) 

As a submarine dives it  "feels" a steadily increasing pressure from the water surrounding it because the deeper it goes the greater the mass of water above it. This, in turn, squashes the submarine and compresses the gas volume in the floatation tanks. As the volume decreases, so the effective density of the submarine increases (because density (D) = mass (m) / volume (v)). 

If a submarine just propelled itself along without changing its buoyancy it would merely maintain its depth relative to the surface.  if something is the same density as the medium in which it is suspended then it will neither rise nor fall. So all that would happen is the sub would carry on relative to the surface until it run aground.

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rabinoz

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Re: A Question For Those Good At Math
« Reply #13 on: January 17, 2016, 03:16:28 PM »
That's interesting. I got approximately 5 minutes.

And submarines can and do travel in a straight line according to this submarine technician https://plus.google.com/+JamaalWilliams4Jesus/posts/8omik66o7Zw
Yes, I might take a bit of notice of that except for:
This post could not be found.
This URL may be incorrect, the post may have been deleted, or the post may not have been shared with this account

And in "submarines can and do travel in a straight line", how is a straight line defined?  Quite probably at a constant depth below the surface!, and no, I don't claim to be a submarine technician!

Next you will be telling that aircraft flying level will end up in space in a short time!  Pull the other one.
And then that aircraft gyroscopic-AIs prove the earth is flat - No they do not.

But what you really should explain very carefully is how a marine gyro-compass works on a stationary earth!
Note, I said a marine gyro-compass not an aircraft gyro-compass, there is a big difference!
Then carry on and tell us why the type of gyro-compass used on a ship could not be used in an aircraft.

Over to you, your turn to do some high level maths!
Not really, just some sound explanations for a start will do!

Re: A Question For Those Good At Math
« Reply #14 on: January 17, 2016, 04:05:42 PM »
Quick calculation gives me the horizontal distance travelled as
sqrt(2*r*D - D^2), with D the depth and r the radius of the earth. Plugging in the actual values, the submarine would travel around 80000 feet in 24.67 minutes

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rabinoz

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Re: A Question For Those Good At Math
« Reply #15 on: January 17, 2016, 05:00:52 PM »


You want some sums?

There is one simple point I have posted before.  Surprise, surprise - essentially no comment!
Thanks to Napoleon the definition of the metre was originally one ten millionth of the distance from the equator to the North Pole along the line of longitude through Paris.
And the (British) nautical mile (now accepted as 6080 ft) was defined as one sixtieth of one degree at the equator.
I don't see how anyone could argue that these are very much in error.
So presumably we can accept that on the Flat Earth map the radius of the equator is close to 10,000 km, or 6214 miles,
hence the Flat Earth Equatorial circumference has to be 2xπx6214 miles or 39,042 miles.
We know, however that the earth has an equatorial circumference of very close to 360x60 = 21,600 nm or 24,873 miles.

Maybe some kind proponent of the Flat Earth map could explain this readily proven discrepancy!

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frenat

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Re: A Question For Those Good At Math
« Reply #16 on: January 17, 2016, 06:47:07 PM »
The technician guy, if I remember correctly, said they would travel a long way in a straight line according to their instruments and they never adjust for the supposed curvature of water.
Nor should they have to.  If they set a depth they will stay at that depth.  As they move and stay level the boat will self adjust to gravity.  It still works no matter how ignorant you or your technician guy is.

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th3rm0m3t3r0

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Re: A Question For Those Good At Math
« Reply #17 on: January 17, 2016, 06:48:46 PM »
*Image*
As far as the dispute over straight lines goes, speaking from a RE perspective, Jane is correct.
There aren't any straight lines when following the surface of a spheroid. Only arcs.
Usually, a straight line would be following one of these arcs. (In RE thought.)

As far as the math goes, Jane is also correct enough.
My math worked out to 24.4368338968 minutes.
I'm not sure who is more correct, I would guess Jane, as I used Pythagoras' Theorem. I would assume some well executed trigonometry would be a bit more accurate, and it also depends on the accuracy of the input figures. I'm not sure the method Jane used to come up with her number.

I would say with certainty that the number is somewhere around 24 minutes. 5 is not correct - that much can be said for sure.

Earth r - 150 = 20903370 ft. (a)
Earth r = 20903520 ft. (c)

a2 + b2 = c2
436950877356900 + b2 = 436957148390400
436957148390400 - 436950877356900 = b2 = 6271033500
20903370 + 79189.85730508674177125 = 20903520
32 knots = 54.0099 ft/s
79189.85730508674177125 / 54.0099 = 1466.21003381 seconds.
1466.21003381 / 60 = 24.4368338968 minutes.
« Last Edit: January 17, 2016, 07:28:47 PM by th3rm0m3t3r0 »


I don't profess to be correct.
Quote from: sceptimatic
I am correct.

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rabinoz

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Re: A Question For Those Good At Math
« Reply #18 on: January 17, 2016, 08:01:07 PM »
The technician guy, if I remember correctly, said they would travel a long way in a straight line according to their instruments and they never adjust for the supposed curvature of water.
Sure they either set their navigation computer to the desired depth, and voile!
Or the Helm, maybe assisted by Outboard, will keep the depth constant.

Likewise on a plane either the desired altitude is entered into the flight computer,
or the pilot in command will maintain the desired altitude with throttle and flight controls.
Since I am neither a pilot nor submarine officer, feel free to pick fault!

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Son of Orospu

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Re: A Question For Those Good At Math
« Reply #19 on: January 17, 2016, 09:14:48 PM »
The technician guy, if I remember correctly, said they would travel a long way in a straight line according to their instruments and they never adjust for the supposed curvature of water.
I'm not an expert in submarines, but don't they need to do something with air tanks to rise.

I think they are called ballast tanks. 

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Rayzor

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Re: A Question For Those Good At Math
« Reply #20 on: January 17, 2016, 11:19:02 PM »
Submarines use inertial guidance systems.   These systems use Schuler tuning to correct for the earth's curvature.

Schuler tuning is a modification to the electronic control system used in inertial navigation systems that accounts for the curvature of the Earth. An inertial navigation system, used in submarines, ships, aircraft, and other vehicles to keep track of position, determines directions with respect to three axes pointing "north", "east", and "down". To detect the vehicle's orientation, the system contains an "inertial platform" mounted on gimbals, with gyroscopes that keep it pointing in a fixed orientation in space. However, the directions "north", "east" and "down" change as the vehicle moves on the curved surface of the Earth. Schuler tuning describes the modifications necessary to an inertial navigation system to keep the inertial platform always pointing "north", "east" and "down", so it gives correct directions on Earth

https://en.wikipedia.org/wiki/Schuler_tuning

So if the straight line is determined by the navigation system,  the submarine will remain at 150ft until it encounters something that causes it to change.
The answer is indefinite.


« Last Edit: January 17, 2016, 11:21:23 PM by Rayzor »
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