Coal and Math

[CombatWombat51]

@Aluvial - Ok, imagine a jet plane zooming right over your head. That's what all that math was to me Thanks for all the info, but all I know about stuff like "tan" is that it's one of the buttons on my calculator I never touched for fear that it would bake me or somethng

@die kludge - :bows: I was hoping for two short and sweet answers, but I suppose I should have known better...

@Agemegos - Thanks for all that info! That certainly has convinced me to now place any special value on coal IMC.

@DanMcS - ok... heh, I think I halfway got what you were talking about... You said that CRG's original was 3cm * 3cm *2.598. Ok, so that means side^2 * 2.6

Then you say 2.6*radius^2! Radius?! Did you mean side? Please someone say he did, then my math illiterate self can be content

Sorry I'm being so thick about all this math stuff. I had no idea that there were so many different ways of getting the area of a hexagon... I think I should have saved everyone some trouble and cut a hex into 12 right triangles, and gone with that Oh well, I'll continue begging for now

 

[DanMcS]

Yes, the side of a hexagon is the correct distance to use. It's the same as the distance from the center of the hex to one of the points, because you can think of the hex as being made up of 6 equilateral triangles. I called it the radius because, um, I had a brain fart, and also, I was thinking about it in terms of the formula for the area of a circle, which is pi*r^2, a formula familiar to everyone, so I wanted to phrase it similarly.

 

[CombatWombat51]

Alright, side^2 * 2.6. I can do that

So a hexagon with an area of 25 mi^2 has a side ~ 3.1 miles long?

3.1^2 *2.6 = A

9.61 * 2.6 = A

24.98 = A

And that's close enough to 25 for me. 3 miles, instead of 3.1, is close enough, too. Everything look good with that?

Thanks again for the help everyone

 

[CombatWombat51]

A bump to make sure I got everything right with the math

 

[Coredump]

A bump to make sure I got everything right with the math

Accepting rounding errors... your math is correct.

(A regular hexagon with side 3 mi.; will have an area of 23.38 sq.mi.)

.

 

[Umbran]

You seem to have gotten answers about the hexagon, but I will mention...

Any polygon can be broken down into a number of rectangles and triangles, whose areas are easy to calculate accurately. Find the areas of each piece, and sum them up.

 

[CombatWombat51]

Thanks for the confirmation, Coredump

Yeah, I figured I could just cut a regular hexagon into 12 right triangles, and figure the area that way, but I saw this as an opportunity to learn something new. And it's much easier to beg

 

[Dogbrain]

You are going to have to be careful about this, because a lot of what was called 'coal' in early records was charcoal (made by charring wood), not mineral coal.

By AD1050, mineral coal was used for fuel in Great Britain under the name "sea coal", having been worn off cliffs and washed up on the shore. The Boldon Book of 1183 mentions a coal mine in Escomb (Durham). Durham coal mining was a monopoly of the Bishops and made up a big part of the economy of the area by at least the 13th century. By the beginning of the 14th century, coal was Newcastle's dominant export.

The coal was not used for iron making or smithing because it had a lot of sulfur and ruined the metal. However, it was used for other fuel purposes, including cooking, heating, etc. Once coal to coke conversion was developed in the 1700s, the steel era could start.

 

[ph0rk]

I'm doing some mapping stuff for my campaign, and I have two seperate questions that I figure some kind souls here could help me with

1. What was coal used for before steam power? Was it heavily mined?

2. How can one calculate the area of a hexigon?

charcoal and coal were used for clay firing and metal smelting; and eventually for making carbon steel; all well before the english colliers were mining it for steam engines.

 

[Phineas Crow]

Not to beat a dead horse, but here is an excerpt from the book Coal: A Human History by Barbara Freese

In the summer of 1306, bishops and barons and knights from all around England left their country manors and villages and journeyed to London. They came to participate in that still novel democratic experiment known as Parliament, but once in the city they were distracted from their work by an obnoxious odor. These nobles were used to the usual stenches of medieval towns--the animal dung, the unsewered waste, and the rotting garbage lining the streets. What disgusted them about London was something new in the air: the unfamiliar and acrid smell of burning coal. Recently, blacksmiths and other artisans had begun burning these sooty black rocks for fuel instead of wood, filling the city streets with pungent smoke. The nobles soon led popular demonstrations against the new fuel, and King Edward I promptly banned its use. The ban was largely ignored, so new laws were passed to punish first offenders with "great fines and ransoms." Second offenders were to have their furnaces smashed.

Had the coal ban held up in the centuries that followed, human history would have been radically different. As it happened, though, in the late 1500s the English faced an energy crisis when their population rose and their forests dwindled. They learned to tolerate what had been intolerable, becoming the first western nation to mine and burn coal on a large scale. In so doing, they filled London and other English cities with some of the nastiest urban air the world had yet seen. They also went on to spark a coal-fired industrial revolution that would transform the planet. The industrial age emerged literally in a haze of coal smoke, and in that smoke we can read much of the history of the modern world. And because coal's impact is far from over, we can also catch a disturbing glimpse of our future.