The off-season is a difficult time for theme park-goers since everything around us is closed... So no big coasters. Normally, I would just open up NoLimits and build some failed rides. Another thing that I'm beginning to do is actually build a theoretical roller coaster on paper. Its a very complicated task because of all the factors you have to take in account. I created this topic for all the math and physics jocks to talk about the science of a roller coaster (mechanical, electrical, structural), and maybe some others will be interested in the science. Feel free to discuss other things related to the science, but if anyone is interested I have a problem of my own that I added below.
Now, the first "basic" thing I want to present is how does a lighter train affect the speed of a roller coaster at the bottom of a drop? For example, X2 got a lighter train during its transformation, or Raging Bull with all seats filled vs none filled. Did it make the train go faster at the bottom of the first drop or slower? High school physics says mass doesn't matter, but I think there may be a slight variation.
This is what I have (mechanical): To begin, I know that I can't assume that Potential Energy (PE=mass*gravity*height) at the top equals Kinetic Energy (KE=.5*mass*velocity^2) at the bottom because of the energy lost to heat. If I assume that they are equal (mgh=.5mv^2), then a change a mass won't change velocity at all because the m variable cancels out. The tricky part is when I take friction into account. I did some research and I found that the coefficient of (kinetic) friction of nylon on steel is approx. µ = 0.3. Having that, I can solve for the Force of Friction(F=µ*Normal Force). The normal force is constantly changing because of centripetal forces acting on the train and the changing angle between the train and the ground (because of gravity).
I'm certain that the lighter train will go faster, but I want to prove it and taking rolling friction with different forces seems hectic. I didn't really write out the whole problem because I'll end up getting frustrated.
Here are some of my givens. Momentum is not constant due to the decreasing of velocity from lost energy by heat. I'll say that mass is 10,000kg (to keep it clean) of the empty car and 15,000kg of the full train. The 5000 kg gap should emphasize the difference of speed. So... anyone have some ideas?
Lighter and Heavier should go at exacty the same top speed at the bottom of the first drop. Heavier train will hold it's momentum longer though, and end up taking later track at slightly higher speed.
Favorite Wood Coasters: The Voyage, Ravine Flyer II, Thunderhead, Balder Favorite Steel: Voltron Nevera, Steel Vengeance, Expedition GeForce, Olympia Looping Parks visited: 232, Coasters Ridden: Steel: 894, Wood: 179, Total: 1073
Does it qualify me If we had to create physics roller coaster designs to submit to great america (not actually) in the fifth grade?
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If you have a perfect system, then the mass of the train and the angle of the drop shouldn't matter as long as the initial height is the same. It starts to get tricky once you account for frcition and wind resistance. If you want to you could find the wind resistance by taking one of those scale Statix train models and figure it out.
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Well, also the weight of the train affects it slightly due to the fact the momentum has to change directions. Grab a 10 pound back pack and whip it around your head like star wars kid. Then take a 20 pound back pack and whip that around your head. You wont feel it while its traveling in a straight line due to it having its own momentum but when you have to change its direction, you feel it a lot more. That's why they switch to lighter trains, less stress on the rails.
Now, the weight of the object doesn't affect the gravity of the fall in a freefall (think about the whole hammer and feather in a vaccum thing, still goes at 9.8m/s). The biggest issue is all of the wind resistance. there is a lot more wind resistance if you have say the Klumps family reunion on there instead of a pro anorexia march, but that little bit is negligible but still countable.
The biggest issue to me is the slant, since gravity will always pull straight down relative to the earth and the drop is slanted at lets say 60 degrees, it seems like it should pull at the same speed since whats pulling it never changes.
[quote="jackluver18"]^Doesn't have a Signature[/quote]
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[quote="David"]What's really funny, is that you think I'm from the GP (General Public). When indeed, I most likely know far more about the coaster, as I've rode it multiple times. [/quote]