What would the fastest track look like?

[Crash Enburn]

... when you do these strange track calculations...

I find the question rather strange, then. "I want to build a bridge from point A to point B that a PWD car would traverse the quickest," instead of "I have a magical 42' track, which configuration would be the quickest?"

I guess under your bridge proposition, that an arc with a radius of something like 20', starting at vertical at A, then going below the horizontal, and rising back up to the horizontal, where it would then continue to B. At the bottom of the curve (running horizontally) it would be going far faster than the car that stays above the plane, slowing down to the same 4.78 m/s speed when it returns to the horizontal.

However, now the question strikes me as somewhat silly and irrelevant to actual PWD racing.

- Eric

 

[txchemist]

Just letting everyone think of what they can. The correct answer does end up in a reasonable PWD track, so we will first find the answer, and then add air resistance and then wheel friction and then rolling friction and then "drift". So it will become more relevant.

 

[chromegsx]

I guess I don't understand by what is meant by no friction or am oversimplifying it. If it takes longer to fall 46" and move laterally 42', then it does to just fall 46", it seams there is another force other than gravity is acting on the car slowing it's acceleration.

I get what you are trying to accomplish (ask), but I'm confused by the parameters.

I'm guessing a track that dips slightly below 46" at some point will be closer to what your looking for. Since the max speed of the car to go laterally would be increased for a moment prior to finishing the race at 46" drop and 42' out.

 

[txchemist]

Chromegsx is on to something- I will tell the story of the first tuning board and how the fast ramp was discovered soon

 

[chromegsx]

Not sure I know how to do the calcs on a curve, I'm more of a straight and to the point kinda guy.

Wish I had the time to try though. Thanks for the entertainment though txchemist. I'm intrigued.

 

[txchemist]

The story of Grandpa Mooseman (not his real name)

GM was poor. He was so poor he had no watch, so he made his own measurement system by letting water flow out of a bucket through a small hose into a cup so the different amounts of water collected could be weighed and used as a sensitive timer. He only had a few tuning boards ( one was 21 ft. long ) and he was trying to figure out what was the fastest way to get from point A to point B if you could change the height of A to anything you wanted. He noticed that when the angle between A and B was zero ( the board was level). Nothing moved. The more he lifted the tuning board, the faster the car made the run. He plotted out the time and distance to see if the change was a perfect straight line, or if it was some curve. When he went past 45 degrees, even though the car was going faster at the end of the run, the board had to be longer to make the larger angle and the total time started to increase. That is when he discovered the 45 degree angle gave the fastest straight line to cover the distance between A and B. He was over 70 when this happened, and he died soon after finishing his book, He used to say " I can slow down gravity and measure it when I make the car or ball roll on my wood board". Then he thought, " What if I use two smaller boards to cover the A to B distance?. Even if it is a longer distance, is there any combination that is faster?. Well in a short time he found plenty of examples and when he plotted them out, they made a section of a circle, so he made a ramp the shape of his circle and it was the fastest way he found. He wrote in his notes it would make the fastest ramp. If you have a restriction on the height of A, the fastest track is to make the circle ramp of radius A to drop to the flat and then continue straight. A few years after he died, another fellow came along and discovered faster circle ramps, and then discovered the fastest shape of all.

 

[chromegsx]

parabola!??? Parabolics are always better. /images/boards/smilies/wink.gif

 

[txchemist]

Chromegsx- You just came up with a solution better than Grandpa Mooseman- and just a tiny bit slower than the correct shape.!!!
Good thinking

 

[txchemist]

There are solutions that dip below the flat. The parabola has to dip earlier than the best solutions. We do add the extra restriction now that we have to manufacture this track and not go below the flat. Below is the parabolic answer compared to the correct answer at the restriction of the flat, and below that we see a nice long track with both if we could build such a track..
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We also add the super Kinser in green, a drop below the floor, roll to the finish and hop back up again, and a super BestTrack in cyan that drops below the floor and hops back up.
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

 

[RickRacing]

Inverted Cycloid?

 

[txchemist]

Bingo!! and now the answers
1 who first asked this question, --- Johann Bernoulli ( you know, the same guy that did the fluid dynamics equations for wind resistance etc.)
the Brachistochrone Problem

2. in what year did he ask it. --- 1696
3 Who missed the answer.---- Poor Grandpa Mooseman AKA Galileo who by the way coined the term Cycloid, and if he had been alive for the contest- he might have re-thought his circle answer. He really did build ramps of grooved wood lined with polished parchment and used polished brass spheres to roll around and figure out the equations of gravity and motion.
4 who got it in 12 hours--- Issac Newton who hated the snooty Frenchman- an interesting read

http://www-history.mcs.st-andrews.ac.uk/HistTopics/Brachistochrone.html

and we will continue later with a few more practical tracks and then start to add friction!!

 

[Kinser Racing]

You intellectuals really make me feel dumb. /images/boards/smilies/smile.gif

 

[IAE Racing]

You intellectuals really make me feel dumb. /images/boards/smilies/smile.gif

+1

Although very interesting material

 

[chromegsx]

Ah man oval or ellipse was my next guess...which looks a lot like inverted cycloids. had to look that one up as I don't remember that one from high school geometry and calculus.

 

[GravityX]

Great read Txchemist! I'm sure they weren't thinking about pinewood derby cars back then.... or were they??? Either way an interesting read. Now... is the spirograph just a bunch of cycloids traced out to make various designs?

 

[Guest]

That Was So Cool!!!!

TX chemist,

When are you writing a book?

I will definitely line up to read it!

Thanks!!

 

[txchemist]

GravityX, yes- the Spirograph is all different kinds of cycloid.
I will polish off some summary charts later.
I got most of the info from the Internet, and then I put it into Excel to see if correct. I also have a track and car modeling software program. ( fun, but won't help you tune and rail run).

Here is a neat You Tube- ignore the Russian- good graphics- can't get it to start at 53 sec. you might manualy jump it to the good stuff.

Shows both typical cycloid and one that goes beyond halfway. also shows 3 sleds starting at different places on the hill, and crosing the finish line ( if just at the bottom of the hill) at the same time if the ramp is the perfect cycloid.

[video]http://youtu.be/k6vXtjne5-c?t=53s[/video]

 

[Rocket car]

You intellectuals really make me feel dumb. /images/boards/smilies/smile.gif

This goes for me too. Anything harder than 2+2=5 is to hard for me.

 

[Crash Enburn]

Anything harder than 2+2=5 is to hard for me.

2 + 2 does equal 5 for large values of 2. /images/boards/smilies/wink.gif

 

[GravityX]

Here's some old school math.

[video]http://youtu.be/oJS8GszWJuQ[/video]