How Big Are these Dang Hexes!? (Full Version)

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Anthropoid -> How Big Are these Dang Hexes!? (11/18/2009 3:16:03 AM)

Okay, now I'm really curious!? [:D]

I'm starting this thread so we don't keep the discussion about Chinese Tactical Nuclear Artillery off topic. Over here in this thread

http://www.matrixgames.com/forums/tm.asp?m=2293922&mpage=3&key=

We now have three different numbers for total hex square mileage: my own (probably wildly inaccurate) number of ~5900 miles; Whisper's number of ~1600 and now one by Braedonnal at about 1000 square miles.

I read in the manual on page 36 "at a scale of 40 nautial miles per hex." But does that mean the length of each side is 40 nautical miles (46.0312 Imperial miles) or the perpendicular distance between any two parallel sides is 40 miles (46.0312 Imperial miles)?



Andrew Brown -> RE: How Big Are these Dang Hexes!? (11/18/2009 3:21:07 AM)

It means that the distance between the centre points of two adjacent hexes is 40 NM.

Andrew



jwilkerson -> RE: How Big Are these Dang Hexes!? (11/18/2009 3:33:11 AM)

Which, in our case, also means that the distance between to opposite sides is 40nm.


Formulae related to hexagons can be found on the web via google. Wikipeadia has an accurate article on the topic.






DivePac88 -> RE: How Big Are these Dang Hexes!? (11/18/2009 3:43:26 AM)


quote:

ORIGINAL: jwilkerson

Wikipeadia has an accurate article on the topic.



Wikipeadia has an accurate entry... My God that is a surprise! [;)]



Anthropoid -> RE: How Big Are these Dang Hexes!? (11/18/2009 3:55:28 AM)

So Braedonnal seems to have got it right. With an apothem (and side) of 20 nm (23.0156 Imp Miles) I get 1039.23 sq nm miles (1376.25 sq Imp miles).

The ~390,000 soldiers in the hex in question where thus at a density of more like 284 soldiers/square mile. Still have the densities for Anzio based on the numbers Vaned was remembering.



jwilkerson -> RE: How Big Are these Dang Hexes!? (11/18/2009 4:23:47 AM)

The distance between opposing SIDES being 20 nm not the distance between opposing vertices.

So the 12 embedded triangles have sides of 20 nm and ~11.5 nm with the hypotenus of ~23 nm ... so the length of the "sides" of the hexagon in question are ~23nm and the area is ~1380sqnm (6 equal sided triangles with areas of ~230sqnm).



Mike Scholl -> RE: How Big Are these Dang Hexes!? (11/18/2009 8:25:53 AM)


quote:

ORIGINAL: jwilkerson

The distance between opposing SIDES being 20 nm not the distance between opposing vertices.

So the 12 embedded triangles have sides of 20 nm and ~11.5 nm with the hypotenus of ~23 nm ... so the length of the "sides" of the hexagon in question are ~23nm and the area is ~1380sqnm (6 equal sided triangles with areas of ~230sqnm).



Except that no-one in their right minds measures land area in NAUTICAL miles. You folks meed to convert to STATUTE miles and re-compute so that the numbers make some sense in this context. [:D]



dorjun driver -> RE: How Big Are these Dang Hexes!? (11/18/2009 8:56:31 AM)

Do the math.

[image]local://upfiles/20478/BFD1927CA65449B2B1E032F741CB1ED6.jpg[/image]

---And there is a nice green ball for the first to ask about knots per hour.



khyberbill -> RE: How Big Are these Dang Hexes!? (11/18/2009 9:53:31 AM)

quote:


---And there is a nice green ball for the first to ask about knots per hour
As an ex-submariner, I prefer to think in furlongs per fortnight.



dorjun driver -> RE: How Big Are these Dang Hexes!? (11/18/2009 11:16:03 AM)

Furlong per fortnight hey?  What's that, about 47.14 ft/day/parsec?



khyberbill -> RE: How Big Are these Dang Hexes!? (11/18/2009 11:42:59 AM)

quote:

Furlong per fortnight hey? What's that, about 47.14 ft/day/parsec?
I was on the throttles once as the sub was pulling into New London and the Captain called down to make turns for 5 mph. The EOOW replied, do you mean 5 knots and the Captain came back, "If I ask for furlongs per fortnight, you will give it to me!" Needless to say, a bunch of nukes spent many a fortnight coming up with different rates of speed. The poor EOOW's nick became Furlong. I ran across that captain many years later in business and mentioned the incident and he still recalled it. He was quite a character and a good captain, the only good one I ever had. His exploits are still classified. Now and then one sees references to them in some of the books about the undersea battle of wits between the US and USSR in the 50's/60's/70's but they dont tell the whole story.



witpqs -> RE: How Big Are these Dang Hexes!? (11/18/2009 3:23:56 PM)

quote:

ORIGINAL: dorjun driver

Do the math.

[image]local://upfiles/20478/BFD1927CA65449B2B1E032F741CB1ED6.jpg[/image]

---And there is a nice green ball for the first to ask about knots per hour.


Interior Angle = 120 degrees? Times six sides that would make a total of 720 degrees! Should be 60 degrees x 6 sides = 360 degrees, right? And each of the twelve triangles that Joe mentioned would be half that, having an angle of 30 degrees at the center of the hex.

Or, am I misunderstanding what you mean by 'Interior Angle'? Please explain.



88l71 -> RE: How Big Are these Dang Hexes!? (11/18/2009 3:29:27 PM)


quote:

ORIGINAL: khyberbill

quote:


---And there is a nice green ball for the first to ask about knots per hour
As an ex-submariner, I prefer to think in furlongs per fortnight.


"My car gets 40 rods to the hogshead, and that's the way I like it!"

-Grandpa Simpson



dorjun driver -> RE: How Big Are these Dang Hexes!? (11/18/2009 4:25:13 PM)


quote:

ORIGINAL: witpqs


Interior Angle = 120 degrees? Times six sides that would make a total of 720 degrees! Should be 60 degrees x 6 sides = 360 degrees, right? And each of the twelve triangles that Joe mentioned would be half that, having an angle of 30 degrees at the center of the hex.

Or, am I misunderstanding what you mean by 'Interior Angle'? Please explain.


If you would translate the above to cubits I might be able to help you.



Kwik E Mart -> RE: How Big Are these Dang Hexes!? (11/18/2009 4:28:17 PM)

are we talking African or European swallows here?



Anthropoid -> RE: How Big Are these Dang Hexes!? (11/18/2009 8:15:10 PM)

quote:

ORIGINAL: jwilkerson

The distance between opposing SIDES being 20 nm not the distance between opposing vertices.

So the 12 embedded triangles have sides of 20 nm and ~11.5 nm with the hypotenus of ~23 nm ... so the length of the "sides" of the hexagon in question are ~23nm and the area is ~1380sqnm (6 equal sided triangles with areas of ~230sqnm).


You're kidding me! It is _that_ complicated!? You guys made this game complicated in EVERY dimension ranging from top to bottom didn't you!



sspahr -> RE: How Big Are these Dang Hexes!? (11/18/2009 8:52:54 PM)

quote:

ORIGINAL: witpqs

Interior Angle = 120 degrees? Times six sides that would make a total of 720 degrees! Should be 60 degrees x 6 sides = 360 degrees, right? And each of the twelve triangles that Joe mentioned would be half that, having an angle of 30 degrees at the center of the hex.

Or, am I misunderstanding what you mean by 'Interior Angle'? Please explain.


It's a geometry term referring to the angle at which two sides meet. http://en.wikipedia.org/wiki/Internal_angle

You don't need to know this to play the game[:)].



whippleofd -> RE: How Big Are these Dang Hexes!? (11/18/2009 9:50:34 PM)


quote:

ORIGINAL: khyberbill

Now and then one sees references to them in some of the books about the undersea battle of wits between the US and USSR in the 50's/60's/70's but they dont tell the whole story.


Amen to that shipmate.

Whipple



pad152 -> RE: How Big Are these Dang Hexes!? (11/18/2009 10:34:10 PM)


quote:

ORIGINAL: Anthropoid

quote:

ORIGINAL: jwilkerson

The distance between opposing SIDES being 20 nm not the distance between opposing vertices.

So the 12 embedded triangles have sides of 20 nm and ~11.5 nm with the hypotenus of ~23 nm ... so the length of the "sides" of the hexagon in question are ~23nm and the area is ~1380sqnm (6 equal sided triangles with areas of ~230sqnm).


You're kidding me! It is _that_ complicated!? You guys made this game complicated in EVERY dimension ranging from top to bottom didn't you!


Didn't they tell you in school, that real life is complicated and that's why you need math?[X(]



witpqs -> RE: How Big Are these Dang Hexes!? (11/18/2009 11:02:10 PM)


quote:

ORIGINAL: sspahr

quote:

ORIGINAL: witpqs

Interior Angle = 120 degrees? Times six sides that would make a total of 720 degrees! Should be 60 degrees x 6 sides = 360 degrees, right? And each of the twelve triangles that Joe mentioned would be half that, having an angle of 30 degrees at the center of the hex.

Or, am I misunderstanding what you mean by 'Interior Angle'? Please explain.


It's a geometry term referring to the angle at which two sides meet. http://en.wikipedia.org/wiki/Internal_angle

You don't need to know this to play the game[:)].


Yes but I thought he was referring to the angle of the triangle formed by running lines from the edge of one side to the center of the hex (which is 60 degrees). Thanks.



JohnDillworth -> RE: How Big Are these Dang Hexes!? (11/19/2009 1:09:43 AM)

How many klicks has this thread been hijacked and how many parsecs to get back again? Screw it , I am just going to have a dram and forgt all about it!



morganbj -> RE: How Big Are these Dang Hexes!? (11/19/2009 1:29:49 PM)

I just did the math and found that jwilkerson is correct.  I got 1385.64 NM.  I haven't used trig in 40 years.  Since then sin and cosin were things you did while getting a loan.

So, Anthropoid now what?  Are you happy?  I will sleep well tonight knowing that I have a number that means nothing, since the hexes can't all represent the same distance.  Something to do with the map distortion that comes from projection of curvatures onto flat surfaces.



dorjun driver -> RE: How Big Are these Dang Hexes!? (11/19/2009 2:39:31 PM)


quote:

ORIGINAL: JohnDillworth

How many klicks has this thread been hijacked and how many parsecs to get back again? Screw it , I am just going to have a dram and forgt all about it!


It's too late in the morning for "drams". I'm gonna have a beer.



Brigs -> RE: How Big Are these Dang Hexes!? (11/19/2009 4:16:02 PM)

They say one picture is worth a thousand words, so maybe this will help make it easier to understand the math I use to
move ships around in the hexes.

Just to make all this clear, here is an accurate drawing of the game's strategic map. It's drawn perfectly to scale, so
you don't need to worry about that. As you can clearly see, it's obvious that the dotted line shows the most direct route
my ship should take to intercept the enemy. This is also the method that I'm currently using to set up my supply convoys.

I'll leave it to you to fill in the details.




[image]local://upfiles/2651/BC395719E9134EF7BBEF692670B0FB66.jpg[/image]



Anthropoid -> RE: How Big Are these Dang Hexes!? (11/19/2009 4:32:33 PM)

quote:

ORIGINAL: bjmorgan

I just did the math and found that jwilkerson is correct.  I got 1385.64 NM.  I haven't used trig in 40 years.  Since then sin and cosin were things you did while getting a loan.

So, Anthropoid now what?  Are you happy?  I will sleep well tonight knowing that I have a number that means nothing, since the hexes can't all represent the same distance.  Something to do with the map distortion that comes from projection of curvatures onto flat surfaces.


Thank you brother Morgan. Praise to the Cosigner. 1385.64 SQUARE Naughtical Miles. I'm thankful that there are those among us capable of rendering accurate, precise, valid, reliable, tasty, crunchy and insightful results from such challenging operations.

In answer to your query concerning my present psychodynamic state: I _AM_ happy though I suspect that might have more to do with the meds I'm taking than with the number 1385.64 Naughtical Miles. Well, maybe the Naughticoms in _interaction_ with the meds, and the realization that once 3PM hits I can get out of this godforsaken office next to the noisy asbestos abatement project which the facilities planners in their infinite wisdom decided to schedule during the middle of a semester just as I initiated a cutting-edge, state-of-the-art, multi-hundred dollar experimental psychophysiological study of gamers in my lab . . .

But I digress . . .

With respect to your assertion that the hexes would be different sizes, obviously that is hogwash; It was proven long ago that maps are flat.

I look forward to your responding to my Navy SEAL thread. I await a suitable mod that represents SEAL Team 1 complete with HALOs, HAHOs, UDTs, BUDs, LITEs, PINGs, SBIs, HOHOs, CHOCOs, and all the other high-tech gear and paraphanelia that have led the coalition forces to victory in the war on raggedy tribesmen.

ADDIT: @ Brigs: I _think_ you might have made a slight miscalculation. I did not get my skinfold's calipers out to check for certain, but I think that the angle that you've depicted represented at MOB' (by which I am guessing you are showing "maximal organizational banzai?") should in fact be more obtuse.



Mike Scholl -> RE: How Big Are these Dang Hexes!? (11/19/2009 4:43:40 PM)


quote:

ORIGINAL: bjmorgan

I just did the math and found that jwilkerson is correct. I got 1385.64 NM. I haven't used trig in 40 years. Since then sin and cosin were things you did while getting a loan.


AGAIN I ask..., who the bloody devil measures LAND in nautical miles? This thread began with a question about troop density per square mile (not knot) in China. So how about some math whiz crank up his brain box and give us some useful information in statute miles?



USSAmerica -> RE: How Big Are these Dang Hexes!? (11/19/2009 4:55:27 PM)


quote:

ORIGINAL: Mike Scholl


quote:

ORIGINAL: bjmorgan

I just did the math and found that jwilkerson is correct. I got 1385.64 NM. I haven't used trig in 40 years. Since then sin and cosin were things you did while getting a loan.


AGAIN I ask..., who the bloody devil measures LAND in nautical miles? This thread began with a question about troop density per square mile (not knot) in China. So how about some math whiz crank up his brain box and give us some useful information in statute miles?



2000 yards in 1 nautical mile.

1760 yards in 1 statute mile.

You do the math.



JWE -> RE: How Big Are these Dang Hexes!? (11/19/2009 6:43:46 PM)


quote:

ORIGINAL: USS America
2000 yards in 1 nautical mile.

1760 yards in 1 statute mile.

You do the math.

Sounds like my Marine buddy Jeremy. Every time he gets on the boat and checks the GPS he complains; "what is this nautical mile crap, how the hell do I change this stupid piece of crap to read in kilometers?"



witpqs -> RE: How Big Are these Dang Hexes!? (11/19/2009 7:09:35 PM)

Not so fast!

Have a look: http://en.wikipedia.org/wiki/Nautical_mile

A Nautical Mile can be:

1,852 meters (exactly) international convention formulated in 1929 but not adopted by the USA until after WWII (1954).

1,853 meters (exactly) [also called Admiralty Mile/UK Nautical Mile/Imperial Nautical Mile] beginning in 1970.

6,080 feet (exactly) [also called Admiralty Mile/UK Nautical Mile/Imperial Nautical Mile] before 1970.

6,000 feet (2,000 yards) [also called Tactical Mile or Data Mile] used by NATO navies.

6,080.20 feet (based on the US foot of 1893) [also called US Nautical Mile] was used from 1893 to 1954 by the USA.

This is a period game 1941 to 1946 involving nations with varying definitions of 'Nautical Mile'. So which one did Andrew use? [;)]



morganbj -> RE: How Big Are these Dang Hexes!? (11/19/2009 7:37:12 PM)


quote:

ORIGINAL: Anthropoid

I'm thankful that there are those among us capable of rendering accurate, precise, valid, reliable, tasty, crunchy and insightful results from such challenging operations.

...

With respect to your assertion that the hexes would be different sizes, obviously that is hogwash; It was proven long ago that maps are flat.


These two statements demonstrate that you are certainly NOT one of the precise posters. Maps are not flat when they are rolled or wadded up. So there! [:-]




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