Btw, using two cables in a V shape (instead of 1 vertical one of same length) to hold a linkbox increases its strength by more than 50%.
(Edited by mendel at 2:46 pm on Oct. 23, 2001)
The spirit of measuring these things by conducting experiments that started this thread would lead us there eventually - although Alex could probably help a lot along the way if he could find the time to write it all up :-)
A thought popped into my head... Maybe short steel members are weaker because they have less 'give'? A little bit of flexion makes an object a lot harder to break, and flexion is increased by length.... but that still doesn't account for cable... FEH!
I made up another experiment to check. It compares loading both a 20m and a 40m bar equally, and if you look closely, you see the top of the 20m bar is actually lower than that of the other! It seems it compresses even more. Stress seems to be 40% vs. 10%.
My current guess is: spring constant is unchanged for all lengths, so the short bar strains as much as the long bar (absolute length change); actually, a bit more, since the diagonals are at more of an angle. Then, stress is calculated by strain, not by strain/rest length. This would result in stress being inversely proportional to the square of the bar length (applied force being constant), which is in line with the somewhat inaccurate stress measurement.
All this is just so much guesswork; can anybody come up with better experiments to confirm this?
Notes on measuring with tspring.pxb: I used 1024x768; "Low Detail" to make the bars show up as pixel-wide lines; much "R" in edit mode so I can really zoom up close in Test mode; make a screenshot with the heights I want to compare in the same picture, preferably near the horizon; then measure pixel displacement using a gfx program; that also measures RGB values of the stress color to get the percentages.
In essence I'd started out thinking along the lines of calastigro, while trying to disprove mendel, and ended up coming to a conclusion like Falkon2's ! So I could have waited a day and had it solved for me ;)
(http://www.tjhsst.edu/~jbowman/collapse1.gif)
(http://www.tjhsst.edu/~jbowman/collapse2.gif)
(http://www.tjhsst.edu/~jbowman/collapse3.gif)
(http://www.tjhsst.edu/~jbowman/collapse4.gif)
If you look closely, you'll see that the tower with more cross-bracing will collapse sooner. If you wish, you can toy around with my bridge (http://www.tjhsst.edu/~jbowman/Three01.pxb)
Actually, congratulations on your well-reasoned article, much more exact than my off-the-cuff estimates of the percentages involved.
I don't have time right now to go into this more, so here are some suggestions:
1) Breaking strengths of 3HD and 6HD box can be narrowed down further by shortening the stick below the 2-bar at the top of the breaking column.
2) Relating cable weight to light steel weight and using short cable sections to refine things would be a bad idea because changing the connections on a structure has strange side effects. (witness replacing the 2 heavy steel sticks with light sticks and a heavy crossbeam, and both HD8 towers pop boxes)
3) Calculating Y for HD8 is erroneous because it's not the bar that breaks on this tower, it's the link box that pops. (Link boxes are still an open research question at this time.) Same goes for HD7.
I think pontifex would be more accessible (if not more fun) if the physics was more intuitive. A beginner will optimize his bridge by shortening bars to save weight (worked well in BB); pros will replace two long bars with one long bar and be more effective, but it's not easy to find that out.
If you think you'd get link boxes for free, that's not true because small bars are heavier per unit length - this is because of the proportionally longer diagonals and the absolute weight of the link boxes. Weight per unit 2HD=41, 4HD=26, 8HD=19 using VRBones's figures. Since a link box is stronger than a 2 HD bar, they're probably even heavier in proportion, making the penalty worse. And then there's the strength loss because of the diagonals' angle...
All this points to a common physics engine problem: as the construction gets stiffer, it is more likely to explode due to numerical instability of the engine.
During simulation, it may happen that beam ends move away from the joints; the engine then applies force to the beam to close that gap again, and that force can rip the beam apart if you're unlucky (and it is particularly stiff).
This problem may get worse by the non-real strain of the members as it may be prone to produce bigger gaps, especially with the diagonal cross-bracing.
Moral: don't construct stiff structures, make them loose! :-)
(I wonder if these guesses will turn out to be true... ;-)
[edit] AHA! that point doesn't exist in Pontifex! (either that or the maps simply aren't big enough...)
I've been trying to weigh the difference between a 4-length of heavy steel and 4 1-lengths, but my studies are hindered by the brittleness of 1-lengths. go figure.
[/edit]
(Edited by Calastigro at 2:11 pm on Oct. 23, 2001)
I think it is in part due to the elasticity of the cable and the moment of the supported beams. If you slow down the break, the center beam is the first joint to break. (Incidently on the joint, and not on the cable as has been mentioned) The reduced tension on the center, causes an elastic snapback that is felt on the common cable segment.
This translates down the other two cables and gives them an ever so slight tug. This additional force is enough to break their joints and send the entire structure crashing.
I find odd that once all this weight is releaved though, the cables do not recoil consistant with the tension that they had been placed under.
Ask anyone in the Navy, line snapback is a very really, and potentially deadly event. Those cables should be going every which way.
For example, here are three Heavy Steel pillars (just to give a common footing) supporting the highest tower that won't collapse with 1-unit, 2-unit and 4-unit light steel beams:
As you can see, the 4-unit beams can have 9 beams without collapse (10 collapses after several seconds), 2-unit beams can only go up 5 beams, and 1-unit beams, wow... it can't even support anything beyond the weight of itself! This has got to be a physics bug of some sort (mat-c may have mentioned the problem here?) The same issue is apparent with cables - short ones can't support much at all
This is high on my priority list of things that should be fixed, I think...
I used to think this was physically ok, because the short box diagonals are at more of an angle (45° for 1x1 as opposed to 14° for a 4x1 box). However, setting 100% as the bar breaking load, a 4-box can take 1176% against 1-box 965%, and even with the added relative weight of short boxes (15.3 vs. 12.2 per unit length), this does not account for the strength loss you've observed.
In real life, the longer a (solid) bar gets, the more likely it is to fail by buckling outward, so the compresive strength actually decreases with length. (If you pull, you have no buckling, so strength against tension remains constant).
I like it the way it is, though. As it is now, you have to strike a balance between strength and budget for lateral supports. If the members for the short bars were as strong as the long ones, you can make lateral supports all 2 units and this would make it really easy to arrive at the cheapest possible solution (as opposed to constant tweaking currently needed to get the right balance)
edit: By lateral supports, I mean bars that connect two arches or pillars together so that their tension/compression is distributed. I.e. cables between a heavy steel arch and the deck
If the short pieces could withstand the same load as the long pieces, 4 2-unit long members instead of a 8-unit member would give you free joints (because the joints cost nothing). Thus, there wouldn't be any reason to build your members longer than 2 or 3 units.
(Edited by falkon2 at 5:44 am on Oct. 23, 2001)
The discussion of internal structural-elment angles and such shouldn't apply here, should it? A cable is, well, just that, there's no joints, angles, etc (or at least there shouldn't be). So what's the deal here?
In the case of cables, they don't snap in half, they break at the joint with the steel - the steel isn't any different no matter how long the cable, so it can't be the steel breaking, but why should the strength of the cable be dependent on its length?
Something unusual I did stumble across. Remember that objects-fall-at-equal-rates theory? Well, doesn't seem to work in Pontifex:
You can see in the first shot that the longer beams broke first and yet just before they hit the ground, you can see that the 1-unit beams are falling much faster than the 2-unit ones... (ignore the 3-unit beams, they've already partially crashed into the ground in the 2nd shot). Why is this? Shouldn't be air resistance (if that's even factored into the engine) since they all have the same horizontal surface area, and other than air resistance, all objects should fall at the same rate, right?
The length of cable seems to affect the strength of the link box it attaches to.
If you're using a cable which has two joint = 3 section, and only the middle section is short, it will hold much more weight than it would if you attached a box to the short piece (or switched the short section down).
Of course, with an anchor at top, you don't need a top section really.
You can also use a cable joint to attach more cables, like an inverted Y. Even if they're the same length, the lower cables will tear first (from the box).
See http://pontifex.mendelsohn.de/forum/sthang1.pxb and sthang2.pxb.
[corrected URL]
(Edited by mendel at 9:08 pm on Oct. 23, 2001)