Post by: mendel on November 04, 2001, 03:27:22 PM
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.
Post by: beaujob on November 04, 2001, 07:45:11 PM
Post by: baggio on November 08, 2001, 09:02:36 AM
An alternative idea: Make all links *unbreakable* until the bridge has settled.Or just unbreakable until you click "run train or HAV." That seems like a good solution because then you won't have to make the program guess as to when the bridge has "settled".
The only problem I see is this becomes a Train Timed bridge so to speak. It's not quite the same thing, but perhaps too close.
Post by: Andy24 on November 03, 2001, 04:03:07 AM
Post by: Entroper on November 04, 2001, 09:51:27 PM
"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."
If you build an arch, the arch has a final settling point, and the beams all have an amount of stress when they reach that point. The problem is that in the initial settling, the bridge goes past the settling point, and the stresses on the beams are much greater than they are when it's finally settled. That's where it becomes unrealistic, since arches aren't just dropped into place. 
Post by: mendel on November 08, 2001, 11:28:40 AM
Post by: baggio on November 03, 2001, 09:22:32 AM
In case you are just joining us ;), I'll post a condensed version of my last message before the split:
Quote: from mendel on 5:08 am on Oct. 31, 2001 P* is an underdamped system because the bridge will bounce, and it will reach ss at sometime. You are correct that as an underdamped system, slowly introducing gravity will not elliminate a problem with bounce. However, if the bridge is allowed to reach ss before gravity is increased additionally, then the impact of that bounce on the overall design will be minimal. Of course, a poorly designed bridge is still going to collapse.
Lowering gravity will not eliminate "overshoot" or bouncing, because if damping was to eat all potential energy, the bridge would be "stuck" by friction and suddenly give when the train passed.Damping doesn't work to eliminate potential energy, it works to eliminate kinetic energy. Damping, in a mechanical sense, is a function of velocity. It will not change the final position of the system, only how long it takes to get there.
Post by: baggio on November 05, 2001, 08:54:36 AM
I approve.
I'll try to address more at a later date and time.
Post by: tombs on January 28, 2002, 01:38:20 PM
Im unsure if the intent is to make a game or to make an engineering tool.
I expect the initial aim of the Pontifex developer was to make money from selling the game. However, one is in danger of developing the game beyond the average gamers mentality into an exclusive "nerds" game which may have a low sales potential than an enjoyable gamers game. I consider myself to be a bit of both and enjoy a real good think whilst maintaining enjoyment.
I hope it wont get too techie.
Hope this doesnt spoil the thread
Post by: mendel on November 03, 2001, 09:26:13 AM
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
Post by: beaujob on November 06, 2001, 04:06:37 AM
Post by: Andy24 on November 03, 2001, 11:49:11 AM
Post by: baggio on November 06, 2001, 05:27:28 AM
Cable stay and suspension bridges are built in completely different ways. Cable stay are built from the towers out, and with suspension bridges, the cables are laid first, then the deck. How would you handle a cable stay design with two towers?
With the current system and .pxb file format, this isn't something that I can see being added.
How about, if a new system kept track of what you were adding, where, and when; and implemented gravity in the edit mode. Then you could build the bridge in a fashion that requires you to plan about where links are added, and where they are removed. Building the bridge would be half the challenge. Running the train would be the other half. Pretensioned cables would be essential if you wanted to build a proper deck. Maybe a link when placed would show you the level of stress it is receiving when you build it by changing color, and if an added piece were to break, it would change to a new color like yellow. Before you could build on, you would have to eliminate yellow links.
This would add a different element of challenge. Perhaps you would be able to add different types of anchor points now, but I think that floating anchors should be abolished. Pilons would cost a different amount than anchor points on the shore. Perhaps that amount would be dependent on the water depth, and/or how deep the pilons are set to add stability.
Easing into gravity would not be needed or even desired in this game design. Bridges could be given a rating based on how much load they can support by the cost of materials to build it. The load is a value that could be adjusted by a slider perhaps, and selecting the highest possible load could be done before the level is tested. Part of the challenge would then not be design a cheap bridge, but it would be to design the most efficient bridge. That would be a much more appropriate measure of who are truly the Pontifex Maximi.
Funding wouldn't have to be capped anymore, but you would require a certain efficiency to pass the level.
Post by: mendel on November 03, 2001, 01:06:37 PM
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[/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..
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 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.
-----------------------
[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)
Post by: VRBones on November 07, 2001, 01:01:36 AM
Good to see some analysis on this. The idea of moving to 50%, then 75% etc is good due to the insignificance of smaller gravity values to the final result, but remember that the amplitude of the 'bounce' is dependant on the additional force applied to the system. This additional force is the difference between the current gravity and the previous gravity. As this additional force (DeltaG) approaches zero, the amplitude of the bounce approaches zero. So the best solution is to make the increments as small as possible.
Although the frequency of the bounce is not known for all bridges, if an even amount of gravity was applied on each step over the duration of one cycle, the resulting waves would more or less cancel each other out with the remaining force being proportional to the damping co-efficient. That means that if there was no damping the bridge would be in equilibrium, the more damping the less equilibrium (as the remaining force from the initial step would be dissapated by the damping co-efficient over time), but that would also have a smaller amplitude due to the damping effect.
Another way to look at it would be to have the amount of energy added to the system (gravity) to be decremented each step by the damping effect. This would keep the above equilibrium intact, regardless of the natural frequency of the bridge. This would also make an asymptotic force (like the 50%, 75% scenario) which technically would never be fully applied, but I'm sure you could drop it to G when it's as close as practical.
Update: The last section is incorrect as the damping effect for each bridge is different, thus unknown.
(Edited by VRBones at 6:25 pm on Nov. 6, 2001)
Post by: Andy24 on November 04, 2001, 10:51:54 AM
(Edited by Andy24 at 4:11 pm on Nov. 4, 2001)
Post by: mendel on November 07, 2001, 03:31:19 PM
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.
Post by: Andy24 on November 04, 2001, 03:19:31 PM
I was thinking about the bridges that are designed to fall into place. wouldn't it make them unrealisticly strong.
Post by: on November 07, 2001, 07:10:36 PM
(Edited by Chillum at 7:11 pm on Nov. 7, 2001)
Post by: VRBones on November 07, 2001, 11:25:31 PM
I got completely confused reading VRBones post of Nov 6, 6:01pm (6:25 edit) because I could not make heads or tails of the various additional forces, steps, cycles, and waves.
Sorry, was trying to put it in more layman's terms than pure math, I'll try to flesh it out a little. Made perfect sense to me at the time ;)
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 This is all without damping though. When you introduce damping, the remaining force from the initial step that is still oscillating in the system at a point in the future is proportional to the damping co-efficient (another way of stating the definition of the damping co-efficient). Since the amount of additional force is equal at each step, the net resulting force is equal to the amount of force damped over half an oscillation. The higher the damping effect, the higher the net resulting force. If you managed to work out the damping co-efficient of a bridge, you could also proportionally reduce the force at each step by that amount, therefore the resulting force from half an oscillation ago would equal the new force being added, thus returning the equation back into equilibrium. However, from some quick tests the damping co-efficient seems to vary across bridge designs (proportional to the amount of regidity across the whole bridge ?). So from all that, what's the conclusion? If you had the amount of force applied each step slowly decreasing, and the time taken to apply the whole gravity greater than one oscillation, you would get a pretty stable result. The smaller the steps the better, but means the time to apply all the gravity is more, approaching infinity (and no-one is going to wait that long ;) ). I think around 3-4 oscillations worth would be reasonable, so assuming an oscillation is one second (I've seen oscillations of .5 seconds and as long as 2 secons) and that 50% or the resulting force was damped over that time, you would have the bridge gradually sink due to the strain for 4 seconds, then have a remaining oscillation of ~4% the size of the oscillation experienced now. (Edited by VRBones at 4:27 pm on Nov. 7, 2001)
My second and third paragraphs are do do with this effect. Applying the second increase at the lower extremity of the oscillation cancels out each other due to the waves of oscillation of equal amplitude being 90 degrees apart. The same can be said if you apply the additional force in 4 stages of 0.25 G at 45 degree increments. Extending this you can see that if an equal amount of force is applied each step, and that the steps are applied evenly across the whole oscillation, they will cancel each other out. Although we don't know the frequency of the oscillation of each bridge, if we assume that all steps apply the same force evenly and that the time to apply these steps is greater than the minimum frequency of any bridge, this effect will come into play.
(Edited by VRBones at 4:26 pm on Nov. 7, 2001)
Post by: Andy24 on November 03, 2001, 03:14:23 AM
Post by: falkon2 on November 03, 2001, 03:36:21 AM