A Bridge Building Design Environment with "Force" Feedback by Alexander Repenning, ralex@cs.colorado.edu, March 21, 1997
An extended version of the simulation including instructions for teachers with questions and answers is featured on the PBS website: http://www.pbs.org/teachersource/mathline/concepts/architecture/activity3.shtm The instructions have been created by Dr. David Barnes from the Show-Me Center http://www.showmecenter.missouri.edu
Build your own bridge and experience forces. Remove as many bricks as you can to reduce the cost of the bridge but .. in the case of instability your bridge will collapse under the load of cars driving over it. Computing the forces in all the bricks the bridge provides you with feedback (some call it critique) by colorizing bricks indicating structural tension.
Load any of the worksheets and run the simulation
Remove bricks with the eraser tool
Add bricks again with the pen tool
The best bridge is the one that uses the minimal number of bricks. How many does it take? Hint, you will need to have some bricks under tension (glowing red) to build the best bridge.
In order to succeed in building the best or at least a pretty good bridge the user has to make a big conceptual shift that took human kind many years. The simulation supports this because unlike a physical artifact it visibly illustrates mechanical forces. This kind of computational feedback/critique, after some time, encourages to abandon their first design. Most people playing with this simulation start with removing vertical slices. This leads to a good but not optimal design. In essence this is a Greek bridge design. Optimal bridges require some kind of arch design. This is what the Romans learned.
In this Greek to Roman design context this simulation could be linked to a number of educational issues including: architecture, physics, design, history, geometry, algebra, calculus, etc. Ideally these links would be captured in a medium such as the Web allowing the learner to follow some of these dimensions.
Educational tidbits. One thing we learned with this simulation is that constructionism can be more effective when used in some DEconstrutivist context. Learning about something by building things from scratch can be extremely powerful but also frustrating to the point where learners give up.
In the case of the bridge builder people seem to be learning just as much if not more by REMOVING elements of a design. Combined with the "force" feedback most of the users we observed eventually migrated to arch designs. This process could be aided with some instructionist tools.
This is a completely distributed model of computation. Traditional approaches (e.g., finite elements) are based on the notion of one global equation matrix. We wanted to have a more decentralized model in which every brick would be able to compute it's contribution to the stability of a construction that it is part of. After all, physical bricks do not communicate with all other bricks of a bridge either with the goal of setting up a global equation.
Bricks take into consideration things on top of them that could push them down, things on their side, e.g., to which they could be glued, and things below them that could support them. These forces are communicated localy in diffusion process.