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(Edited by mendel at 12:54 am on Nov. 2, 2001)
The idea would be that concrete could be as strong as cable, cost as much as light steel (or cable) and only take compression.
Btw, http://www.chroniclogic.com/cgi-bin/ikonboard/topic.cgi?forum=3&topic=46&start=20" target="_blank">Recent research suggests that Pontifex cable can take compression if you can work with the free joint in it - as falkon announced he did (and showed to me privately) with one of the http://www.chroniclogic.com/cgi-bin/ikonboard/topic.cgi?forum=4&topic=22&start=40" target="_blank">complex levels.
(Edited by mendel at 10:57 am on Dec. 13, 2001)
I found that the final energy dissipated by the system does not stay equal with any gravity ramp (as I erroneously stated), but potentially decreases as the number of steps is increased.
I found this out by first looking at a vertical bar fixed at one end, without damping applied; if you go to 0.5 g and then take it to 1g as the oscillation is at its lower extremity, it will come to rest immediately; if you do that step at the upper end of the oscillation, you might as well not have bothered with 0.5 g.
Also note that at static equilibrium point, internal energy is equal to kinetic energy; it is half the work done by gravity (m*g*y, y being the displacement downwards) because internal beam force starts at 0 and is m*g only at equilibrium.
Now think of that same bar; at final g, let it's gravitational force be G, with an equilibrium displacement of y. Ramping up g in n steps and assuming we let the structure reach equilibrium between the steps gives us the work Wi per step i as displacement per step (y/n) * strength of gravity force at that step (i/n)*G :
Wi = (y/n) * (i/n)*G
Summing up Wi for i=1 to n gives us total work done:
W = G*y/2 + G*y/(2*n)
The first term G*y/2 is equal to the internal beam energy at equilibrium; the second term is equal to the excess energy that must be damped away. This energy decreases in inverse proportion to n.
However, this result is at best an average value when the system is not at rest between the steps.
What we do not know is how damping is affected by this; I still fear that such a procedure might increase the time the structure needs to settle, and the right timing for the steps has not been determined, either (and might vary with the structure, so might have to be dynamically computed).
In hindsight, VRBones first paragraph now makes some sort of sense to me; paragraphs 2 and 3 still leave me stranded.
Abstract: Starting the bridge on 50% of final gravity will prevent it from overshooting the final settling position, thus keeping member stress below the final settled stress. Gravity can then be increased to 75%, 88%, 94% etc.
Further down there is physics engine talk, including an attempt to explain the forces that make some constructions rip themselves apart (explode) on being born.
baggio and mendel discussing damping and gravity via icq (edited, edit approved by Baggio)
mendel: anyway, I don't have a graph plotting prog handy, but what function would describe damping? k * sin (t) bounces (k damping factor), and some others would tend to zero with varying speeds. That behaviour might depend on the specific bridge, so a general solution would be difficult to find.
Potential energy is converted to kinetic energy at the rate of speed; if you dampen speed to (next to) nothing, no potential energy gets converted, and the mechanisms "sticks". Maybe I am mislead because I think of the way brakes work (Coulomb damping)
Baggio: Ok... the general solution for an underdamped system is....
x(t) = x(0) * e(-Z*w.n*t) * ( (Z/(sqrt(1-Z^2)))*sin(w.d*t) + cos(w.d*t) )
w.n is the undamped natural frequency
w.d is the damped natural frequency
Z is the damping ratio
This is only true if v(0) is 0 though. In our case it is.
mendel: ok so it's basically e(-t) for the amplitude of the wave. that never reaches zero.
Baggio: Yes... Ae(s*t)... the sine and cosine provide your overshoot and osilation.
mendel: so if Z=1, we have critical damping, and Z>1 overdamping?
Baggio: Yes, that is correct. With the bridge, it is Z<1, underdamped.
mathematical damping models: http://mail.bris.ac.uk/~aemtak/damp/damping.html" target="_blank">http://mail.bris.ac.uk/~aemtak/damp/damping.html[/i]
mendel: Pontifex *ought* to implement material damping.. :-) as the bridge is not under water
Baggio: Water, Air.. it's still a fluid, maybe not as viscous. Coulomb damping is also used to model joint damping mechanisms. Joint damping is found in highly assembled structures. Sounds like what is needed for some parts of P*.
mendel: hmmm.. I think lowering gravity won't even reduce the amplitude. It will lower the frequency. So if the bridge bounces 3 times before settling then reducing gravity to lower the frequency might mean only one bounce.
Baggio: Ok... think of it this way, if I just barely introduce gravity, the deflection of the bridge will be ever so slight. I wait.... Then I increase gravity ever so slightly, the bridge will deflect again, ever so slightly. As G->9.81 m/s^2, the "bounce" will have been reduced to nothing.
mendel: Lowering gravity will lower the amount of potential energy energy the bridge has when it "comes into being", and the structure thus doesn't have to dissipate as much energy in the settling phase. An undamped bridge will still bounce at the same amplitude no matter what the gravity is (ok g=0 excepted).
Baggio: Yup... there isn't anything to stop it from bouncing.... That senario would never happen in real life though.
mendel: yes, but your "ever so slightly" is just not there.
Baggio: how do you mean "is just not there"?
mendel: with v depending on g and damping depending on v , the spatial movements will be the same at any gravity.
Baggio: It is dependant on g, but only the acceleration portion... only x double dot is used, but then the mass is divided through.
Baggio: This is a bit hard to convey in text form.. http://www.pontifex2.com/iB_html/non-cgi/emoticons/smile.gif" border="0" valign="absmiddle" alt=':)'>
mendel: Insight: "ever so slightly" is correct because beam internal energy does NOT scale with g. If you look at a settled bridge it has internal energy stored in the beams that it is equal to the potential energy in the bridge in start configuration at final gravity. Lowering gravity at the start does not reduce that final figure. It will just serve to eliminate high kinetic energies in the process. correct?
Baggio: Yes... that is what I've been trying to convey on the message board. The final outcome would be the same, but those peak kinetic energies could fail the bridge before it is ever tested by the train. In levels where few cars are used, this means that the bridge may be failing because it can't settle nicely, and might have been able to support the train.
mendel: but I knew that before (and posted on it). So at 0.5 g the bridge would probably not overshoot because the energy is not (yet) in the system - it would need to get at least 0.5 * final internal energy in kinetic energy to overshoot, because at 0.5g the bridge settles to internal energy levels of 0.5 full; when kinetic state passes this, deceleration sets in, so kinetic energy must be 0.5 full at this time to reach 1 full at peak displacement. But peak kinetic cannot be 0.5 full because potential energy is just that much, and kinetic can't be higher than that :-) So we'd ramp up to 050% 75% 88% 94% etc.
Baggio: Well, it will still overshoot, meaning it will still have bounce, but that bounce may not exceed the final resting position of the bridge.
--> this means the internal stress is less than in the final position, too!
I've been thinking about it, and I think you are right about the frequency though. I think the frequency will be less, and perhaps the time constant will be to.
Interesting... it is kinda hard to visualize this because there is no place on earth that I've been able to observe .5g.
here is where the physics engine part starts
mendel: Pontifex physics are not of this earth.
Baggio: Don't I know it... if they'd change the k of the steel though, I'd be happy. That is really causing some odd behaviors.
mendel: Having less bouncy cables alone would make sus bridges easier (and the physics engine more unstable).
Baggio: More unstable by being less bouncy?
mendel: more unstable as in - likely to generate huge forces out of nowhere (see rip-apart tower)
Baggio: Ahh... I see your point.
mendel: physics engines watch that members joined stay joined, and when they drift apart they apply a force ex machina to get them to stay together. this can cause explosion.
Baggio: I think that is also in part to the k not scaling with length. I guess that is a problem with the joints trying to stay at the same verticies.
mendel: That's what I meant.
Baggio: Yup... I'm in agreement. That matches what I've observed... in a way this is kinda neat. We are pioneers, not unlike Newton before us, trying to discover what makes the "world" work the way it does.
talk about open source physics engines and project bcon deleted - contact me for details
Baggio: Before I turn in, did you see this slide? http://www.q12.org/ode/slides/slide13.html" target="_blank">http://www.q12.org/ode/slides/slide13.html Is that the short link bug or what?
mendel: yes. gamasutra had a review of physics engines a while back (1998) and some of these commercial examples showed exploding, too.
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[no changes in this edit except to state that the log is now approved by Baggio]
(Edited by mendel at 3:07 am on Nov. 5, 2001)
On another thread, you profess the desire to keep this forum "alive"; however, the quality of a forum is not the number of posts on it, but rather the "signal-to-noise" ratio, a term that denotes the ratio of interesting, thought-provoking, well-thought-out posts to the rest that you have to read through to get at the gems.
Why do I mention this?
Because as the signal-to-noise ratio drops, people get fed up with a given forum and stop using it.
Now ask yourself: you may be a "Junior member" by the number of posts, but is the quality up to it? How often have you, in effect, said "yeah, I like that, too"? How often have you, yourself, posted off-topic (I am thinking of recent posts in "Contest Bridge", "Extreme Calm" and "mirror function", to name a few)? You don't have to keep those remarks in; an acceptable way would be to use the "Message" link to tell the author you (don't) like his post; this will encourage authors of posts you like to repeat their performance, thus enriching the forum.
Also, double-posting within minutes is very annoying; show you know how to use the "Edit" feature if you wish to add to what you've said.
Continuing on your present course will mean you'll have the "Member" title real soon, but by that time everyone will be so annoyed with the majority of your posts that noone will read them. If this should come to pass, I would probably ask ChronicLogic to give you a custom title.... "hobo" as one who sleeps under bridges, perhaps, but let's hope you are conscious of your improved rank and improve the quality of your posts (and reduce the quantity).
Best Wishes
Michael
I was aware of that, that's why it has an "abstract" up front so people can just read that and skip the rest.
A bridge that falls into place can be compared to a pre-fabricated bridge put in place by cranes, so easing the "fall" for those could be realistic.
Because the level editor manual says
"Holding down Ctrl key while editing the landscape will snap the height of the landscape to the grid."
Though I must admit, it took a friend to tell me this before I used it, too. http://www.pontifex2.com/iB_html/non-cgi/emoticons/smile.gif" border="0" valign="absmiddle" alt=':)'>
Maybe we need a FAQ item: What things are in the manual that you can't figure out by just using the game?
