Steve Jackson Games Forums HexVolume
 Register FAQ Calendar Mark Forums Read

 03-31-2017, 10:07 AM #1 Refplace     Join Date: Nov 2008 Location: Yukon, OK HexVolume ANyone have the volume of a standard hex? __________________ Looking for group in my area My GURPS official contributions Buying them lets us know you want more! My GURPS fan contribution and blog: REFPLace GURPS Landing Page My List of GURPS You Tube videos (plus a few other useful items) My GURPS Wiki entries
 03-31-2017, 10:11 AM #2 Varyon   Join Date: Jun 2013 Re: HexVolume A standard hex is one yard wide and 4 yards tall. Assuming a circular base, it ends up being exactly pi cubic yards in volume.
 03-31-2017, 10:45 AM #3 Diomedes   Join Date: Mar 2008 Location: Dallas, TX Re: HexVolume Th area of a 1-yard hex is (3/4)(sqrt) 2 square yards, 0r 1.06 square yards. At 4 yards high, that comes to 4.24 square yards.
03-31-2017, 10:47 AM   #4
Captain Joy

Join Date: Nov 2006
Location: Heartland, U.S.A.
Re: HexVolume

Quote:
 Originally Posted by Varyon A standard hex is one yard wide and 4 yards tall. Assuming a circular base, it ends up being exactly pi cubic yards in volume.
This wasn't immediate obvious to me, so I thought I'd run the numbers for you doubters.

Area of a cylinder = pi•r^2 • height

In our case, the radius, r = ½y
and height = 4y
where y = 1 yard

So, pi•(y/2)^2•4y = pi • (y^2 / 4) • 4y = pi • y^3 • 4 / 4 = pi•y^3
= 3.14 cubic yards

I'm surprised it's so much less than the hexagon value.
__________________

Last edited by Captain Joy; 03-31-2017 at 11:01 AM. Reason: added comparison to hexagon and corrected an error Prince Charon pointed out

03-31-2017, 10:53 AM   #5
Prince Charon

Join Date: Dec 2012
Re: HexVolume

Quote:
 Originally Posted by Captain Joy This wasn't immediate obvious to me, so I thought I'd run the numbers for you doubters. Area of a cylinder = pi•r^2 • height In our case, the radius, r = ½y and height = 4y where y = 1 yard So, pi•(y/2)^2•4y = pi • (y^2 / 4) • 4y = pi • y^3 • 4 / 4 = pi•y^3 = 3.14 square yards I'm surprised it's so much less than the hexagon value.
Did you mean cubic yards, there?
__________________
Warning, I have the Distractible and Imaginative quirks in real life.

"The more corrupt a government, the more it legislates."
-- Tacitus

Five Earths, All in a Row. Updated 3/23/2020: Earth-1 American Command Crew Rosters article has been posted.

 03-31-2017, 11:03 AM #6 Ulzgoroth   Join Date: Jul 2008 Re: HexVolume I get a different value for the hexagon area. 3*1/(2 sqrt(3))*1 square yard, leading to a 3.464 cubic yard volume. __________________ I don't know any 3e, so there is no chance that I am talking about 3e rules by accident.
03-31-2017, 11:15 AM   #7
Daigoro

Join Date: Dec 2006
Re: HexVolume

Quote:
 Originally Posted by Ulzgoroth I get a different value for the hexagon area. 3*1/(2 sqrt(3))*1 square yard, leading to a 3.464 cubic yard volume.
Is your hex 1 yard from corner-to-corner or side-to-side?
__________________
World Wikis:
Cyberpunk: Duopoly Nation
Fantasy: Dominion Cross
Space Opera: Behind the King's Eclipse
Steampunk: Colonial Steam

03-31-2017, 11:24 AM   #8
Captain Joy

Join Date: Nov 2006
Location: Heartland, U.S.A.
Re: HexVolume

Quote:
 Originally Posted by Ulzgoroth I get a different value for the hexagon area. 3*1/(2 sqrt(3))*1 square yard, leading to a 3.464 cubic yard volume.
A hex is basically six equilateral triangles. The area of a triangle is ½bh. A GURPS hex is 1 yard wide, from side to side.

Set y = 1 yard.
This means the area of each triangle, ½bh = ½ • (1/SQRT(3))y • (½)y
= (1/(4•SQRT(3)))•y^2.
Since six of these triangles make a hex, hex area = (6/(4•SQRT(3)))y^2.
The volume is 4y high, so hex volume = 4y•(6/(4•SQRT(3)))y^2 = (6/SQRT(3))•y^3
= 3.46 cubic yards, in agreement with Bill Stoddard, which pleases me no end.
__________________

Last edited by Captain Joy; 03-31-2017 at 11:59 AM. Reason: several, until I got it right

03-31-2017, 11:31 AM   #9
whswhs

Join Date: Jun 2005
Re: HexVolume

Quote:
 Originally Posted by Varyon A standard hex is one yard wide and 4 yards tall. Assuming a circular base, it ends up being exactly pi cubic yards in volume.
A hex does not have a circular base, but a hexagonal one.

Assume a distance of 1 yard from hex center to hex center. Then the distance from hex center to the middle of a given edge is 0.5 yard. We can divide the hex into six equilateral triangles. Taking the line from the hex center to the middle of the edge as the adjacent side, and applying a bit of trigonometry, we get that the line from the center to the vertex is 0.57735 yards, and therefore any exterior side must be the same length, because the triangle is equilateral. Its area is therefore 0.1443 square yards, and the area of the entire hex is 0.866 square yards, or just about 13/15 square yards. Since the height is 4 yards, the volume is 3.464 cubic yards.

For comparison, an inscribed circle has radius 0.5 yards and area 0.785 square yards, and a circumscribed circle has radius 0.57735 yards and area 1.047 square yards. The former gives volume equal to pi; the latter gives volume equal to 4.1888 cubic yards.
__________________
Bill Stoddard

A human being should know how to live fast, die young, and leave a beautiful corpse. Specialization is for insects.

 03-31-2017, 11:46 AM #10 Varyon   Join Date: Jun 2013 Re: HexVolume GURPS hexes are, to my knowledge, meant to be approximations of circles. What the actual volume works out to depends on which side of "circle" you err - if you treat a GURPS hex as being the largest hexagon that will fit within a 1 yard diameter circle (the points of the hexagon touch the circle), you'll end up with volume less than pi. If you treat a GURPS hex as being the smallest hexagon that a 1 yard diameter circle will fit inside of (the edges of the hexagon tough the circle), you'll end up with a volume greater than pi. With the way GURPS hexes are arranged - going from the center of one hex to the center of another (a nominal yard) passes through an edge, not a point - I believe the latter interpretation is more correct than the former, so you'd expect a volume greater than pi. That's only if you treat the approximation as literal truth, but in that case movement is going look a little odd. EDIT: Partially ninja'ed by Bill. I feel my point about it being an approximation of a circle stands.

 Thread Tools Display Modes Linear Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Fnords are Off [IMG] code is Off HTML code is Off Forum Rules
 Forum Jump User Control Panel Private Messages Subscriptions Who's Online Search Forums Forums Home Illuminati Headquarters     SJ Games Discussion     Daily Illuminator     Forum Feedback and Help Warehouse 23     Warehouse 23 General Discussion     Warehouse 23 Digital     Pyramid Munchkin     Munchkin 101     Munchkin     Munchkin Collectible Card Game     Other Munchkin Games Roleplaying     Dungeon Fantasy Roleplaying Game         DFRPG Resources     GURPS         GURPS Resources         GURPS Character Assistant     Transhuman Space     Traveller     The Fantasy Trip         The Fantasy Trip: House Rules     In Nomine     Roleplaying in General     Play By Post Board and Card Games     Car Wars         Car Wars Old Editions     Ogre and G.E.V.         Ogre Video Game         Ogre Scenarios     Board and Dice Games     Card Games     Miniatures The Gnomes of Zurich     The Industry     Conventions     Trading Post     Gamer Finder

All times are GMT -6. The time now is 03:05 PM.