Gravity Vehicle C

[chalker7]

If they are the same, then why is the brachistochrone so highly regarded as the fastest ramp?
Another ramp design (which I think was talked about before) would be trying to have the steepest veritcal drop and then get lowest to the floor, so that the vehicle transitions quickly from falling vertically to travelling horizontally. I plan on building some scale models to test later, but any thoughts?

There appears to be some confusion on vocab here and I think we need a refresher on different math and geometry terms, in particular brachistochrone. Brachistochrone is simply the term for the curve that will result in the lowest time for a point travelling in frictionless, gravity propelled mode from one point to another. The wikipedia page for this is pretty informative, as it explains the root of the word. Brachistos is Greek for "The Shortest" while Chrone is Greek for "Time" (the more you know!)

This definition refers to any two points, so there are an infinite number of brachistochrone curves, but only one that connects any two points. There absolutely is a brachistochrone curve for the ramp dimensions, but I haven't done the math, so I'm not sure what the exact shape or equation for it will be.

Also, I'm not convinced that a brachistochrone curve will be the absolute best shape for a ramp. If the time score was only how long it took you to travel down the ramp, it would be the best, but since your vehicle has to travel the length of the track afterwards I'm not so sure. What you (probably) want is the ramp shape that provides the highest exit velocity. While the gravity vehicle ramp brachistochrone curve will probably provide something close to the maximum velocity, it is very likely that it isn't the absolute maximum. I'm sure you could calculate that equation/shape as well, so if anyone out there loves setting up differentials and is willing to share your results, I'm sure there are a lot of us here that would love to hear what you come up with!

[Balsa Man]

If they are the same, then why is the brachistochrone so highly regarded as the fastest ramp?
Another ramp design (which I think was talked about before) would be trying to have the steepest veritcal drop and then get lowest to the floor, so that the vehicle transitions quickly from falling vertically to travelling horizontally. I plan on building some scale models to test later, but any thoughts?

There appears to be some confusion on vocab here....
Also, I'm not convinced that a brachistochrone curve will be the absolute best shape for a ramp. If the time score was only how long it took you to travel down the ramp, it would be the best, but since your vehicle has to travel the length of the track afterwards I'm not so sure. What you (probably) want is the ramp shape that provides the highest exit velocity. While the gravity vehicle ramp brachistochrone curve will probably provide something close to the maximum velocity, it is very likely that it isn't the absolute maximum. I'm sure you could calculate that equation/shape as well, so if anyone out there loves setting up differentials and is willing to share your results, I'm sure there are a lot of us here that would love to hear what you come up with!

First, I think the confusion is not so much about vocabulary, but the physics.
Second, I believe, and nobody's put up any info that says otherwise, the critical - the governing math is deceivingly simple, and a brachistochrone is actually a sub-species of red herring.

One more time, quietly from the back of the room: "For those considering/working on the building issues around a brachistochrone curve, it might be worth looking back to page 6....."
Specifically, from pg 6:
"mass * (gravitational acceleration) * height = potential energy at the top = kinetic energy at the bottom = 1/2 * mas * (velocity)^2

Mass cancels out, so the final velocity would be (simply and solely determined by) sqrt(height * (gravitational acceleration))".

It IS the (final) horizontal velocity coming off the base of the ramp that will drive your time score. You DO want as much horizontal V as you can get. No ifs, ands, or buts about it.

Once horizontal, it is actually "downhill from there."
Friction will immediately start taking "it's cut" from the kinetic energy you've gained, at some rate, depending on your design. That means V starts going down (and t -travel time to a given distance, going up - immediately). Two vehicles, same friction factor, same mass, the one with greater bottom of ramp V will get to the target distance faster. Period.

Whatever the shape of the ramp,
a) it fits (looking at it in 2 dimensions) in a 1m high by 0.75m wide rectangle.
b) "g" will act vertically over something less than 1m; the normal force of the ramp will work over about 0.75m.
c) There will be slight variance in instantaneous acceleration and v (along whatever vector) at various locations along a flat, and along a curved ramp, but they will be very small.
d) The acceleration, and velocity, at whatever point, and in whatever direction, and on whatever ramp will not be that of a perfect frictionless object.
The time the vehicle spends on any ramp that fits the rule rectangle will be VERY, very similar.
The difference in ramp travel time will be no more than a small fraction of a second.
The horizontal velocity of identical vehicles (on flat and curved ramps) is for all practical purposes - and one of our practical purposes here is, indeed, getting all we can out of the time score, going to be the same.

If someone out there can put up some convincing math & physics that says otherwise, I, like chalker7, would also very much love to see it

[illusionist]

Okay, then would the way to maximize horizontal velocity be to have the mass/vehicle fall most vertically and then exit the ramp at the lowest point? So more of an "L" shape with a slight curve instead of a right angle?

I haven't taken physics yet, so I have very little understanding of this. Thank you Chalker7 and Balsa Man for explaining this to us.

[chalker7]

First, I think the confusion is not so much about vocabulary, but the physics.
Second, I believe, and nobody's put up any info that says otherwise, the critical - the governing math is deceivingly simple, and a brachistochrone is actually a sub-species of red herring.

I agree wholeheartedly, just it seemed like several of the earlier posts indicated some confusion about what exactly "brachistochrone" means, that's all. The rest of your post is totally correct, maximum velocity off the ramp is the critical component for this event.

Okay, then would the way to maximize horizontal velocity be to have the mass/vehicle fall most vertically and then exit the ramp at the lowest point? So more of an "L" shape with a slight curve instead of a right angle?

That's really hard to say. I'd say that if you can't set up the initial math problem, instead of struggling through it, you should just build a few different ramps and see what works best. Good luck!

[Balsa Man]

Okay, then would the way to maximize horizontal velocity be to have the mass/vehicle fall most vertically and then exit the ramp at the lowest point? So more of an "L" shape with a slight curve instead of a right angle?

I haven't taken physics yet, so I have very little understanding of this. Thank you Chalker7 and Balsa Man for explaining this to us.

No - again, caveated as before - until and unless someone comes up with some math and physics that clearly demonstrates otherwise (and I don't think its out there) - the shape - curved, or flat with a roll-out/transition at the bottom, with the same vehicle on two different ramps will not get you a materially different horizontal V.

That holds for a flat ramp that drops steeply to a transition well short of the allowable 0.75m horizontal measurement, or one that goes out pretty close to the 0.75m befort the transition curve. The simple equation I posted says it all, by the absence of any term involving the configuration through which potential energy is converted to kinetic energy. Horizontal V is determined simply by the vertical distance over which gravity has to work. It works on the center of mass of the vehicle

What ever the ramp shape, the vehicle is going to exit at the lowest point; that lowest point is the floor. How close the center of mass is to the floor (when you get there) will depend on how you design the vehicle, not the ramp.
How close the center of mass is to the top will also depend on how you design the vehicle- among other things discussed before, for example, is how a larger wheel size will prevent you getting the vehicle up as close to the 1m ceiling as smaller wheels would let you.

The difference in height of the center of mass, between where it starts at the top, and where it is at the bottom - "h" is what determines horizontal V. To maximize horizontal V, you have to mazimize the vertical distance the center of mass falls. That does not mean the distance/time/space over or through which it falls moving vertically (as in the 'almost vertical' drop-in you suggest). It means the vertical component; the height; "h" of the center of mass's movement, from the top, to the bottom. Start it as high as you can, have it be as close to the floor as you can when the vehicle gets to the floor. The clever part comes in how to do both at the same time, in the same vehicle......

You want that transition to be smooth, so the vehicle rolls through it, rather than....."slam/banging", so you don't break something, and so that the....roll-off onto the intended path is consistent. The radius of that transition curve, so that you get that smooth transition will depend primarily on your wheel radius. It has to be larger than the wheel radius, or the wheel will "bang" into the curve. You'll have to figure out whether it needt to be larger than that to not bang the floor.

[illusionist]

So the ramp shape does not matter so much in this case, but rather how far the vehicle allows its center of mass to fall, "h".

If I understand correctly, a ramp shaped like:
) (tilted so that it fits)

will have the same effect on the vehicle's horizontal v as a ramp shaped like:
/
provided that they both have a smooth transition to the floor and allow the vehicle to exit in similar manners.

Is that an accurate understanding of how ramp shape will affect the vehicles?

Edit: Nvm, I just read Balsa's post about how a more horizontal top will result in a higher position for the center of mass for the vehicle

Hopefully by the end of next week I will have data on some scale model ramps that I've built. I'll try to do some more research on the horizontal v. Once again, thanks chalker7 and balsa man for taking the time to explain this.

[chalker7]

No - again, caveated as before - until and unless someone comes up with some math and physics that clearly demonstrates otherwise (and I don't think its out there) - the shape - curved, or flat with a roll-out/transition at the bottom, with the same vehicle on two different ramps will not get you a materially different horizontal V.

That holds for a flat ramp that drops steeply to a transition well short of the allowable 0.75m horizontal measurement, or one that goes out pretty close to the 0.75m befort the transition curve. The simple equation I posted says it all, by the absence of any term involving the configuration through which potential energy is converted to kinetic energy. Horizontal V is determined simply by the vertical distance over which gravity has to work. It works on the center of mass of the vehicle

What ever the ramp shape, the vehicle is going to exit at the lowest point; that lowest point is the floor. How close the center of mass is to the floor (when you get there) will depend on how you design the vehicle, not the ramp.
How close the center of mass is to the top will also depend on how you design the vehicle- among other things discussed before, for example, is how a larger wheel size will prevent you getting the vehicle up as close to the 1m ceiling as smaller wheels would let you.

The difference in height of the center of mass, between where it starts at the top, and where it is at the bottom - "h" is what determines horizontal V. To maximize horizontal V, you have to mazimize the vertical distance the center of mass falls. That does not mean the distance/time/space over or through which it falls moving vertically (as in the 'almost vertical' drop-in you suggest). It means the vertical component; the height; "h" of the center of mass's movement, from the top, to the bottom. Start it as high as you can, have it be as close to the floor as you can when the vehicle gets to the floor. The clever part comes in how to do both at the same time, in the same vehicle......

You want that transition to be smooth, so the vehicle rolls through it, rather than....."slam/banging", so you don't break something, and so that the....roll-off onto the intended path is consistent. The radius of that transition curve, so that you get that smooth transition will depend primarily on your wheel radius. It has to be larger than the wheel radius, or the wheel will "bang" into the curve. You'll have to figure out whether it needt to be larger than that to not bang the floor.

Just to clarify (for anyone who may be following along), you are assuming that the only thing contributing to the velocity of the vehicle is the potential energy of the vehicle on the ramp (found through U=mgh). Presuming you are maximizing m at 2.5kg and g is a constant, you are saying the only way we can increase energy, and therefore, the speed, of the vehicle is by increasing h. Fundamentally, you're absolutely correct, however you're treating the internals of the system like a black box when in actuality there are two major components you are glossing over.

The first is the physical length of the ramp/travel time internally. This is where a brachistochrone curve (b-curve) matters. However, I suspect the differences between a perfect b-curve and a fairly smooth guess will be on the order of hundreths of a second (so....probably not worth fretting).

The second, and much more important issue is losses due to friction. If you have a very long path, you are going to lose more energy to friction. Also, if you have a flatter path (with a larger normal force vector), you are going to lose more energy due to friction. This is where your energy delivery distribution (shape of the curve) is going to really matter (in addition to lessening the impact at the end of the ramp). While I have no calculations to back this up, I suspect a flat ramp would lose more to friction. I say this because a flat ramp will provide constant acceleration/energy delivery, but also constantly lose energy due to friction (effectively lowering g by some small percentage). However, on a ramp with a very steep initial drop will deliver the bulk of the energy initially with very little loss to friction, due to a very low normal force.

Now, the big question is....does this really matter? I suspect it won't matter that much. I am willing to bet that any teams with well-built ramps could swap ramps (but not vehicles) and have runs within a couple tenths of a second of their own ramp. In my opinion, the real optimization for this event will come from friction reduction during the run (from high quality bearings/wheels) and vehicle adjustment (being able to travel perfectly straight and pinpoint stopping accuracy). Of course, I'm always thrilled when a Science Olympian proves me wrong with an awesome device, so I don't want to discourage anyone from building an awesome ramp, but I would highly recommend not focusing on the ramp so much that you neglect the vehicle itself.

[Balsa Man]

First, and most importantly, I absolutely agree with your conclusion, Chalker7. And, yes, I intentionally glossed over/black-boxed length of ramp and friction during the ramp run. There are at least a couple other aspects I can think of where “t” (time) is a factor in the defining equations, but that factor is very small, and they’re not worth going into. My conclusion of “the same” was carefully and intentionally stated as, “for all practical purposes”, and “not...materially different.”

Why? Because the big question is, indeed, “does this really matter.” The question of “what matters?” is, I would suggest, is the first and most important question for ANY event. It is the “sharp point” of good analysis.

When the rules come out, read, re-read, ponder. Put into your thinking pot, and stir around, three things; 1) the basic physics/engineering (from what you know, and enough research to get a....working understanding, and quite possibly some “proof of concept” experimentation); 2) the scoring system (how is it set up, how does it work, what “pays off” more and less – run some numbers- what happens to your score when you change the value of the various factors by a bit?); and 3) building practicalities and time consideration - think things through – get a handle, best you can, on “what would it take to make?”/”how long would that take?”. The ramp shape question we’ve been discussing is a fine example - how much time would it take, first to figure out how to actually construct a ramp with a surface that follows a b-curve, then to do it? How much time would it take to do a flat one with a bottom transition curve? Is the time difference worth what it will get you in points? Are there other aspects where the same, or maybe less time will get you more, or equal points?

We’ve been discussing this same fundamental, “what matters” question/issue over in the towers thread. The time we (kids, coaches, event supervisors, etc.) have to devote to Science-O, and a particular event, is limited by the other time demands in our lives; “t” is a finite resource.

The more effectively you focus your time to what matters most, the better you are going to do. No caveat words here; simple and absolute truth. A key to that is figuring out what are red herring, and what are....good eating fish.

In discussions on this board, with people having a wide variety of experience and depth of understanding, there is going to be a mix. It’s easy to wander off down what may seem like a really cool path that’s .....actually leading nowhere that matters. Along with red herrings, watch out for solutions that, on analysis, would require unobtanium. There are always practical limitations. An example might be something else we’ve been discussing; how small diameter wheels might be advantageous. Hmmm, if small is good, smaller is better.....with quarter-inch diameter wheels,,,,oh, cool found a website where I can get 0.125” diameter ball bearings, little rubber O-ring around em- that would do it. Hmm... the center hole in those puppies is 0.01”, so for axles, I need some 1/100th of an inch diameter rod....and it needs to hold up 2.5kg....hmm... actually significantly more than that as it rolls through the transition curve at the bottom of the ramp....calculate....hmm, going to be pulling1 and a half g....that's almost a kilo on each wheel....mmmm, brass?.....no; mild steel?.....no- ....high-carbon tool steel?, darn, no again...ah, unobtanium will do the job, though. Maybe a frivolous example, but I threw it in to illustrate the sort of “constructability analysis” that will save wasted build time (and money).

Last, let me echo Chalker7s last thought (last sentence) about awesome devices- that do, and will turn up. The folk that do REALLY well are very often those that stir one more ingredient into the “thinking pot” – after some good analysis, stepping back, and doing some “out of the box” thinking.

That is, in most cases, where real breakthroughs in science (and Science-O) come from. Conventional wisdom; the body of knowledge; the current state of understanding, is both good and important. It is not to be ignored. It is not perfect, though. Ever since man has been “doing science”, it has been evolving, changing, growing; by plodding, little incremental steps, and by flashes of insight that allow great leaps into a whole new picture/perspective. So, awesome possibilities are out there – don’t be afraid to look for, and go for them.

[illusionist]

Okay, so I get that the distance that the center of mass falls is what influences the velocity, but I still can't seem to grasp that a ramp shaped like this (turned 90 degrees so that the the longest side will be vertical) will result in same speed as a ramp shaped like this.

Since the first ramp is steeper and allows the mass to fall most vertically down without being deflected horizontally, won't it result in greater speeds? I've been re-reading your posts, but I still dont get it... >.< Surely the difference in ramp shape between the first and second images has an impact on velocity right?
Edit: You've said that the "almost vetical" thing doesnt affect horizontal v, but rather how high and low the center of mass is. I understand the yes-or-no part, but I dont understand the why.

This isn't related so much to my planning for the event right now, but just personal learning.

Okay, another question, relating to the rules. It says that the release mechanism must be a pencil (line 3.h), but it does not state unlike last year's mousetrap rules that the pencil must be used in a vertical manner. So based on that line of the rules, I can use the pencil to pull out a release mechanism right? I just want to confirm it. And I know this isn't the place for official clarifications, these are solely opinions, etc.

[questionguy]

Can someone go more in depth about the possibility of using elastic devices? I am a little confused as to what would be allowed and the extent they would help the vehicle.