What's the most effective way to increase run time on a paper rollercoaster?

[Cyberfreeze]

For my final semester exam, where building paper roller-coaster with marbles as the coaster and one of the things were testing is ride duration. The group with the longest run time will get extra credit and my GPA could really use the boost. so i guess my question is what's the best way to increase run time? the roller-coasters will have funnels, half pipes and a jump. I've already figured out that adding lots of funnels at the correct angle will increase my run time exponentially but my teacher warned me that another group has come up with a method using the tracks and funnels that will work so well that if i don't come up with something super cleaver there's no chance of beating them. so i figured i would ask people way smarter then myself who are actually super good at physics how they would do it. sorry for horrible grammar and punctuation, i wrote this in a hurry.

 

[mfb]

Did you try rails with variable distance? Which distance works best?

 

[Ketch22]

My experience as a roller coaster designer falls into the super low category. My experience designing systems says that funnels are a red herring. Design your path so that the highest amount of energy is directed in the same direction (namely concurrent with the rails). Any device that causes a non beneficial redirection of energy will ultimately slow you down.
I assume you have parameters to work within such as height at start and overall size. Use these to best advantage. If a funnel causes a circulation of the marble it will "waste" energy, If it functions as a rail with a single point of contact it reduce expenditure. Evaluate your pathway such that the aiming of the entrance to any redirection is aligned with the intended path. Also as I commented earlier one point of contact is lower friction than two, but harder to control.
Just a few random rambling from efficiency point of view. I loved every one of my school projects like this. Keep the friction down by every means 1/sharper rails rather than blunt due to area of contact, 2/ consider air resistance, a narrow tube protects the flow but too close creates slug flow which acts like a pump, 3/small sections of single point contact can be beneficial 4/if you miss on that jump the impact will dissipate a large amount of energy, position it carefully and by trial. 4/the resistance of the air is important over time.


Which run carried more energy and how was it dissipated?

 

[mfb]

@Ketch22: The goal is to make the marble slow and run for a long time.

 

[Ketch22]

@Ketch22: The goal is to make the marble slow and run for a long time.

This is true, and after a small run the marble with the greater energy will be able to regain the greater height.
A roller coaster goes faster and then recaptures that energy by conversion of kinetic energy to potential energy. The potential is then converted again, and reconverted again. The run time only stops when the marble stops moving. It is safe to say that the overall system with the lowest loss will run the longest.

 

[mfb]

Based on the first post I don’t think you are allowed to make the track closed and let the ball oscillate as long as you can see it. A single stage of this type wouldn’t lead to a long runtime either.

 

[A.T.]

It is safe to say that the overall system with the lowest loss will run the longest.

Dropping the marble vertically would have very little loss, but the shortest duration.