How Big Are these Dang Hexes!?

[Anthropoid]

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

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]

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

Andrew

[jwilkerson]

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]

ORIGINAL: jwilkerson

Wikipeadia has an accurate article on the topic.

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

[Anthropoid]

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]

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]

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]

Do the math.



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

[khyberbill]

---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]

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

[khyberbill]

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]

ORIGINAL: dorjun driver

Do the math.



---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]

ORIGINAL: khyberbill

---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]

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]

are we talking African or European swallows here?

[Anthropoid]

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]

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]

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]

ORIGINAL: Anthropoid

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]

ORIGINAL: sspahr

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.