Steve Long Posted April 7, 2004 Report Share Posted April 7, 2004 OK, guys, here's a challenge for you. I think we had a thread on this subject back on the old boards, but I can't find it, and don't remember the context. I could work this all out on my own, but some of you actually enjoy this sort of figurin', and can probably do it quicker. I want to include in The Ultimate Brick a table listing the weight of a "cubic hex" of various materials. I think it'll provide a handy reference for various situations. So, that means determining several issues, some of which involve annoying mathematical calculations. 1. How do we measure a "cubic hex"? A hex is a unit of ground measurement, and thus only two-dimensional. So, what's the best approach?: a. Measure the volume of a "cubic" hex that's essentially a two-meter tall hexagonal column b. Measure the volume of a sphere two meters in diameter c. Measure the volume of two cubic meters (much larger than a "cubic hex," methinks) d. Forget about "cubic hexes" and just use "cubic meters" or some other form of real-world measurement e. Something else 2. After we pick the method of establishing volume, I need formulae for a. Calculating the weight of that much material b. Converting a cubic foot into a "cubic hex" c. Converting a cubic meter into a "cubic hex" I think I can find cubic foot/meter weights for materials (in fact, I already have some). But I want to make sure I convert properly to the chosen volume (assuming the chosen volume isn't (d).) Any and all help appreciated! Quote Link to comment Share on other sites More sharing options...
Metaphysician Posted April 7, 2004 Report Share Posted April 7, 2004 Re: OK, Math And Science Experts: Cubic Hexes I'd go with the 2-meter tall hexagonal column, myself. Mainly since its easy, and you can still put together 3-d objects with them fairly easily. Quote Link to comment Share on other sites More sharing options...
BobGreenwade Posted April 7, 2004 Report Share Posted April 7, 2004 Re: OK, Math And Science Experts: Cubic Hexes The way Hero's measured three-dimensional hexes in the past (AFAICR) is 1a -- one standard hex in a two-meter column. To the best of my ability to calculate, this comes to 6.928 cubic meters (make it 7 for rounding). Quote Link to comment Share on other sites More sharing options...
mr_azrad Posted April 7, 2004 Report Share Posted April 7, 2004 Re: OK, Math And Science Experts: Cubic Hexes I like the hexagon cylinder. Also it works about to almost 7 cubic meters (making math later at least a little easier). the 2 meter tall hexagon=6.928 cubic meters (lets call it 7 cubic meters) 2 meter sphere=4.18666_ cubic meters (lets call it 4 cubic meters) 2 meter cube=8 cubic meters Volume of hexagonal cylinder= Area of hex (squared)*height of cylinder area of hex =0.866 * square of its smallest width. volume =.866*2*2*2=6.928 cubic meters volume of a sphere = 4/3 (pi) r (cubed) volume=4/3*3.14*1=4.18666_ cubic meters volume of cube=length (cubed) volume=2*2*2=8 cubic meters Conversions------- 35.31435 cubic feet = 1 cubic meter if we use the hexagon cylinder version the conversion would be 247.198 cubic feet = 1 "cubic hex" 7 cubic meters- 1 "cubic hex" Hope this helps Quote Link to comment Share on other sites More sharing options...
TaxiMan Posted April 7, 2004 Report Share Posted April 7, 2004 Re: OK, Math And Science Experts: Cubic Hexes For utilities sake, I'd go with 1m deep hexes, and let the GM double it for effects that are defined in cubic hexes. There are two ways to look at volume. Where an effect affects "cubic hexes" (say a gas attack or something), I'd define a cubic hex as a 2m hexagon that extends 2m vertically, That's 5.2m3 (assuming the 2m hex is measured from vertex to opposite vertex). So a gas attack that affects 60 "cubic hexes" can fill 312m3. The other way to look at volume is when moving / destroying stuff. If I blast dirt, how much is vaporized? In that case, I'm likely interested in how deep the hole is. So I'd take the area of the damage in hexes (2.6m2) - 1 meter deep - and see how many meters I can go through. If I'm lifting dirt the question is the same - how many meters thick can I lift? There's only a factor of 2 difference, so I'd stick with the "destroy" approach and say to double it if you are affecting a fixed volume in cubic hexes. Of course, all of my comments are from my perspective - I'm not sure why anyone should ever have to say that, but strangely, it's often needed. Edit - use 7m2 for area of a hex, since it shouldn't be vertex to vertex. Otherwise, I'm in the hex-cylinder crowd. Quote Link to comment Share on other sites More sharing options...
mr_azrad Posted April 7, 2004 Report Share Posted April 7, 2004 Re: OK, Math And Science Experts: Cubic Hexes as far as the weights of different substances I found a website that has just about everything you could want. http://www.tesarta.com/www/resources/library/weights.html just take their "pounds per cubic foot" number multiply it by 247.198 to get "pounds per cubic hex". Quote Link to comment Share on other sites More sharing options...
Steve Long Posted April 7, 2004 Author Report Share Posted April 7, 2004 Re: OK, Math And Science Experts: Cubic Hexes Woot! Props to mr_azrad for finding that site! I've got a good table on the subject from an old Dragon magazine, but nowhere near as complete as that, and I wasn't sure how easy it would be to find. Much work now avoided, yaaayyy. Quote Link to comment Share on other sites More sharing options...
Arthur Posted April 7, 2004 Report Share Posted April 7, 2004 Re: OK, Math And Science Experts: Cubic Hexes Actually, there was a much more exhaustive and accurate site posted on the "Ultimate Brick" thread a week or so ago. I wish I could take credit for it, but I have to nod to whoever posted it. Anyway, here it is: http://www.simetric.co.uk/si_materials.htm Densities are given in "kg / m^3". Since a 2m hex-cylinder is 7 m^3 (as has already been pointed out), just multiply density by 7 to get "Kg per hex". Quote Link to comment Share on other sites More sharing options...
Steve Long Posted April 7, 2004 Author Report Share Posted April 7, 2004 Re: OK, Math And Science Experts: Cubic Hexes Well, between those two, I think I'm definitely set for my "weight of materials" chart. And since The Sizesaurus (a book on weights, measures, and dimensions that I lucked into finding at the used bookstore t'other day) provided some other helpful info, there will be lots of things for bricks to lift mentioned in this book, that's for sure. Quote Link to comment Share on other sites More sharing options...
Gary Posted April 7, 2004 Report Share Posted April 7, 2004 Re: OK, Math And Science Experts: Cubic Hexes Do you measure the radius of a hex from the center to a vertex, or to a midpoint of one of the 6 lines? That'll affect the volume somewhat. Quote Link to comment Share on other sites More sharing options...
mr_azrad Posted April 7, 2004 Report Share Posted April 7, 2004 Re: OK, Math And Science Experts: Cubic Hexes I didn't measure the "radius" or even a side. The only measurement I had was that in Hero system a hex is 2 meters across. the area of a standard hexagon is = (squareroot of 3)/2*width of hex *width of hex or more simply=.866*width*width or =.866*2*2 or=3.464 meters(square) Quote Link to comment Share on other sites More sharing options...
Chris Goodwin Posted April 7, 2004 Report Share Posted April 7, 2004 Re: OK, Math And Science Experts: Cubic Hexes Do you measure the radius of a hex from the center to a vertex' date=' or to a midpoint of one of the 6 lines? That'll affect the volume somewhat.[/quote'] For purposes of the Hero System, it's midpoint to lines. It's two meters from the midpoint of one hex to the midpoint of the next, and that distance crosses the line segment separating the two. Quote Link to comment Share on other sites More sharing options...
Dust Raven Posted April 7, 2004 Report Share Posted April 7, 2004 Re: OK, Math And Science Experts: Cubic Hexes I vote for 2m high cylindrical hexes. From a guy who's been gaming Hero for a while, it's a lot easier to think of it in terms of "hexes" rather than try to figure out how many cubic meters fit in a hex and vice versa. Quote Link to comment Share on other sites More sharing options...
Blue Posted April 7, 2004 Report Share Posted April 7, 2004 Re: OK, Math And Science Experts: Cubic Hexes Hexes would seem to be used more for "facing" issues. I think for actually doing the cubic thing it would be easier to measure as "Cubic Inch" (2m). Other than being more... "hero like" (because it's the game with a Hexagon in it's logo)... I can't think of a single reason to be so elaborate as to measure in cubic hexagons. I mean, you don't have 6 hexes of running and 2 hexes of swimming. PLUS, if you are someone using a scale map (Like 1 hex = 8"... for some odd reason) you've got a little more math involved. Keep it inches. Quote Link to comment Share on other sites More sharing options...
JayH Posted April 8, 2004 Report Share Posted April 8, 2004 Re: OK, Math And Science Experts: Cubic Hexes Another vote for a) two-meter tall hexagonal columns. Read on for my exegesis... Any sort of attempt at geodesic-like hexagonal volumes (or spheres) would leave unaccounted space in the cracks between the figures. That just doesn't sit well. So... the only "regular closefitting shapes" available (cubes and pyramids I'm afraid) would require abandoning the very elegant hexes we all know and love. I tried working out a system of alternatingly inverted and rotated pyramids, but I got a headache when my eyeballs popped inside out. Simpler is better. You math gods rock! Quote Link to comment Share on other sites More sharing options...
Hawksmoor Posted April 8, 2004 Report Share Posted April 8, 2004 Re: OK, Math And Science Experts: Cubic Hexes Hexes because all movement is based upon them. 2m Hexes because existing Champions mechanics are based on it. Ignore the incomplete filling of a Hex by "awkward" real world shapes. Motorcycles do not fill *all* of two hexes with their width and length and girth do they? No. Abstraction is our friend. Hawkmoor -See Steve is just one of the guys, he is omnipotent in his sphere but not omniscient ------ Newsflash Joan! I'm Omniscient! You don't have to explain your thought process to me! Whoah! Are you being snippy? GOD is snippy! Ok Joan, I am God. I am beyond your experience. I don't look like this. I don't sound like this. I look like this so you can relate. If I seem snippy it is because you understand snippy. --God to Joan -Joan of Arcadia Quote Link to comment Share on other sites More sharing options...
caris Posted April 8, 2004 Report Share Posted April 8, 2004 Re: OK, Math And Science Experts: Cubic Hexes I favor a sphere one meter in radius. It seems more consistent with the way that area effect powers work. How do you describe the shape of an Explosion, Darkness field, etc.? Quote Link to comment Share on other sites More sharing options...
Hawksmoor Posted April 8, 2004 Report Share Posted April 8, 2004 Re: OK, Math And Science Experts: Cubic Hexes I favor a sphere one meter in radius. It seems more consistent with the way that area effect powers work. How do you describe the shape of an Explosion' date=' Darkness field, etc.?[/quote'] In inches which are Hexes Hawksmoor Quote Link to comment Share on other sites More sharing options...
CorpCommander Posted April 8, 2004 Report Share Posted April 8, 2004 What comes in these shapes? What comes in the shape of a cubic hex? Not much stuff. What comes in the shape of a sphere? Lots of things. What comes in the shape of a cube? Even more things. I am not sure cubic hexes mean much. Conceptually harder than cubes, they also have some other issues in that namely doing math with them is more difficult. I think the example of the motorcycle is a good one. Though it rests in 2 hexes, it does not come close to filling 2 cubic hexes. I wish I could be more constructive and offer an alternative that is clever and wise but I am going to have to think on this one a bit more. Quote Link to comment Share on other sites More sharing options...
Steve Long Posted April 8, 2004 Author Report Share Posted April 8, 2004 Re: OK, Math And Science Experts: Cubic Hexes Thanx for all the help, guys! I've gone ahead and made my chart with both a "cubic foot" and "cubic hex" columns, which will hopefully satisfy everyone, and I've provided some handy conversion formulae to boot. Quote Link to comment Share on other sites More sharing options...
CorpCommander Posted April 8, 2004 Report Share Posted April 8, 2004 Re: OK, Math And Science Experts: Cubic Hexes Sounds like The Ultimate Brick is going to be one great product. I am really looking forward to it. Gadgets and Gear is out at my FLGS so I'll get that in the mean time! Quote Link to comment Share on other sites More sharing options...
Blue Posted April 8, 2004 Report Share Posted April 8, 2004 Re: OK, Math And Science Experts: Cubic Hexes Thanx for all the help' date=' guys! I've gone ahead and made my chart with both a "cubic foot" and "cubic hex" columns, which will hopefully satisfy everyone, and I've provided some handy conversion formulae to boot. [/quote'] Your generosity knows no bounds. (Though I'm sure you've got a chart to tell me how much it weighs) Quote Link to comment Share on other sites More sharing options...
SCUBA Hero Posted April 8, 2004 Report Share Posted April 8, 2004 Re: OK, Math And Science Experts: Cubic Hexes OK' date=' guys, here's a challenge for you. I think we had a thread on this subject back on the old boards, but I can't find it, and don't remember the context.[/quote']There was a thread, and I can't find it with the Search function - I think it was to determine hex volume for air, but I'm not sure. I'm also not sure, but I think you ruled at that time that the volume of a hex was 8 cubic meters. Just something to keep in mind if there's a mismatch with the 7 cubic meter figure later. Quote Link to comment Share on other sites More sharing options...
caris Posted April 8, 2004 Report Share Posted April 8, 2004 Re: OK, Math And Science Experts: Cubic Hexes In inches which are Hexes Hawksmoor While I use hexes as a convient unit of measure on a hex - mat, I do not describe an explosition as having the nice regular sides will all the angles that a hex would have. Quote Link to comment Share on other sites More sharing options...
Steve Long Posted April 8, 2004 Author Report Share Posted April 8, 2004 Re: OK, Math And Science Experts: Cubic Hexes Your generosity knows no bounds. (Though I'm sure you've got a chart to tell me how much it weighs) As a matter of fact, you need at least STR 31 to lift my generosity, according to the table. Quote Link to comment Share on other sites More sharing options...
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