Gravity Vehicle C

[bearasauras]

What seems to be at question here, and it's the hard part to get one's head around, is whether that means an object coming off the brachistochrone curve ramp will have a higher horizontal velocity than the object off the flat ramp. Psychology/human perception bumping into physics. It would seem so, but, as I now understand it, that is not how it works

Here's an interesting paper- see page 2 onto 3 particularly.
http://uweb.cas.usf.edu/~drohrer/pdfs/Rohrer2003M&C.pdf

If someone can shoot a hole this, and the basic physics (that I noted, and that are reflected in this paper), I'd really like to see it. I'm thinking about putting a couple simple ramps together this weekend for marble testing to confirm this.....non-intuitive conclusion.
There are a lot of other pieces to the puzzle of optimizing a gravity vehicle; getting the right trade-offs of maximum velocity, and minimum lateral and linear error, and predictability/repeatability- all together. Fun stuff!

I've only looking quickly over the paper, but in general, if you want to know which curve will have a higher horizontal velocity coming off the ramp (ignoring friction), then I think all you need to do is take the slope of the ramp right before the vehicle leaves the ramp. Assuming there's no friction, all the potential energy you started out with (assuming you have a point mass) will be converted into kinetic energy at the bottom of ramp. The more "flat" your ramp is at the end, the the more horizontal energy you'll have. Looking at the brachistochrone above, the slope at the end isn't as steep as a line connecting the top to the bottom, but I would say it's still kinda steep.

[chalker]

I think everybody is chasing a red herring here. Clearly the majority of the effort in this event should be in trying to alter the effect of gravity on the vehicle. I mean we wouldn't have called it Gravity Vehicle if we didn't expect that right? So here's the magic formula for winning this event.

1. Get 2 standard, off the shelf gravity lenses (any model should do)
2. Build ramp around one of the gravity lens such that the focus of the lens is on the starting position of the vehicle
3. Dial that lens up to 11 (resulting in 11 times the potential energy as normal on the vehicle to start)
4. Build the vehicle around the other gravity lens such that the focus is on the wheels
5. Dial that lens down to -1 (resulting in no friction between the wheels and floor)
6. Launch vehicle
7. Win


I'll leave the actual implementation as a simple exercise for the reader;)

[bearasauras]

Chalker, I think your post is a little bit misleading. Your typical gravity lens will not be able to focus on all 4 wheels. You'll need a model like this one here (http://goo.gl/Iy4Yr) which allows for 4 separate focusing locations.

[Balsa Man]

I like the gravity lens idea, Chalker. Now if you could just get the model Bearasaurus spotted moulded out of Unobtanim alloy, it might just work.

But, back to which "curve" will induce a higher horizontal velocity at the end, that, I believe, is where the red herring is truely being chased.

It doesn't matter, at least in the (frictionless) descending point case; shape/trajectory of descent doesn't change it. The parts of the paper discussing perceptions vs physics are really worth reading carefully... Only the distance the center of mass drop matters. Flat ramp, curved ramp; for a given h & l, V-horiz is the same. As I said before, if I have this wrong, I'd love to hear/see the proof.

That means to get max energy, and therefor speed leaving the ramp, you want to maximize the vertical distance the center of mass drops.
Center of mass as high up at start as you can, as low down as you can at the bottom.

When you move from a frictionless point dropping, to a wheeled vehicle, you obviously want a curved transition from sloped to horizontal. Wheel size, wheel base (length), and where you concentrate mass all play into how best to do that.
Cheers,

[thedoctor]

While I can't claim to understand everything you guys are talking about just by reading through these posts quickly, I think we should all realize that building a good, curved ramp is going to challenging. It's kind of like helicopters; all the theory in the world is pretty hard to put into practice. This is why i love SciOly

[haverstall]

I think I'm learning more physics here, than in my class right now. Not that I understand a lot of what's going on though..

My partners and I are hung up on one thing when we're thinking about building the curve.

Regarding maximizing the potential energy at the start and following the Brachistochrone. I think the confusion comes from people looking at the picture of the curve and not understanding where it comes from. Here's a picture of the curve for going 100 units down and 75 units across. Like Chalker said earlier, you can have a brachistochrone and still maximize your potential energy.


Image generated by a Mathematica® file found online.

So, is the brachistochrone curve half a cycloid? Because if so, wouldn't that mean the brachistochrone that Bear has is technically not a cycloid, simply because the length of the cycloid is 200 cm and the height is 75 cm? Or am I seeing this completely incorrectly, and should be facepalming?

[fishman100]

Just wondering how would you build a Brachistochrone curve? I don't think you can curve wood easily without it splintering and my next guess would be plexiglass, but IDK...

[illusionist]

Thin sheet of metal nailed to a frame? Or perhaps plastic?

[nerpas]

I used to work on crew for the theatre at my school, and we used a very bendy type of plywood for building curved surfaces. I don't know what it's technically called, but it exists.

[thedoctor]

I used to work on crew for the theatre at my school, and we used a very bendy type of plywood for building curved surfaces. I don't know what it's technically called, but it exists.

What'd you have to do to it to make it hold its shape?