What would the fastest track look like?

[DEW36]

Here's some old school math.

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

That is some awesome math skills!!!

 

[txchemist]

OK, after a bit of scrubbing, and recalculating to match the typical gate- timer set up from MOTM races, we have the following. Notice, the Unlimited is down to no axle friction, just a touch of rolling friction, and super low air resistance cross section and super aerodynamics. Just about close to perfect.

 

[Guest]

TX Chemist,

You have me up until you put up these charts.

Then I feel like an idiot.

Skateboarders that ride half pipe have a similar ramp. It often has anywhere from 1-3' of vertical before starting a transition over 10' vertical +/-

I would guess for the same reason.
To maximize the potential energy.

The most fascinating part of the whole thing is that the car on the cycloid track would actually travel uphill for a bit but still be quicker than a normal track.

Right?

Newton was quite a fellow to figure this one out so quick.

I am still trying to wrap my head around the geometry.

Thanks,

 

[Guest]

TX Chemist,

You have me up until you put up these charts.

Then I feel like an idiot.

Skateboarders that ride half pipe have a similar ramp. It often has anywhere from 1-3' of vertical before starting a transition over 10' vertical +/-

I would guess for the same reason.
To maximize the potential energy.

The most fascinating part of the whole thing is that the car on the cycloid track would actually travel uphill for a bit but still be quicker than a normal track.

Right?

Newton was quite a fellow to figure this one out so quick.

I am still trying to wrap my head around the geometry.

Thanks,

I am straining my brain and I am starting to grasp it.

Like GX said. A spirograph.

 

[txchemist]

...The most fascinating part of the whole thing is that the car on the cycloid track would actually travel uphill for a bit but still be quicker than a normal track.

Right?
Correct, but in the last chart, I am just showing a version of the cycloid that does not drop below the flat. Not the fastest cycloid, but faster than all other tracks.

It is showing all the different tracks starting 46" high and then vary the ramp slope, wth the BestTrack being one of the ways to do it.

 

[Guest]

Thanks for the intro to cycloids TX. They are totally new to me and I find them fascinating.

In blue is a BestTrack with the diameter of the transition also shown in blue.

In white is a circle with a diameter of 48"

In red is a cycloid.

After measuring the lengths of the arcs I see that a car on the cycloid track would travel about 4 inches less than the radius track.

 

[txchemist]

Laserman- good work, I can't tell exactly from the cad what the numbers are so here is a chart with some distances on it.