I am not sure that site exits in English ?
Skate is shown! ;)
but ..." but apparently, there was no cycloidal ramp construction".

http://www.mathcurve.com/courbes2d/brachistochrone/brachistochrone.shtml

Thank you Pilou.
Your link translates well to English, with Chrome translate.
It has the friction equations as well.

Some scripting may be attempted this weekend, as well as searching for "Solver" code...

- Brian

English link to same site:
http://mathcurve.com/courbes2d.gb/brachistochrone/brachistochrone.shtml

Cool!

I just find how have the English Page of the Mathcurves.com !
One more time the Symdrom of Edgard Allan Poe of he Purloined Letter has made a victim ! :)

And what about my silly conjecture of the Orient / Line - Line use ?

Thanks for all the replies.

I originally came across this VSauce episode which inspired my interest in building a skateable version.
https://www.youtube.com/watch?v=skvnj67YGmw

@Bemfarmer here are the rules guiding the curve(shown in red but not accurate).
Basically point A needs to be tangent to ground plane and the height of point B needs to be 5 feet or so but cannot go beyond vertical(ideally 70-80 degrees).

Great link about the skate ramp Pilou, and all your other links.

Maybe you know him, it was a SktechUp Master! ;) Jeff Hammond
Now I believe that he uses Rhino or Moi ;)





By Jeff Hammond

2 curves are in tangency as soon as 4 control points following are aligned!

Hi Yakas,

The existing CycloidInterp script will work, with aRadius = bRadius = 2.5 feet+, mirrored upside down, using half of one cycle.

At a radius of 2.5 feet, the height difference is 5 feet, and the upper tangent is 90 degrees.
At a radius of 3 feet, the height difference is 6 feet, and with one vertical foot removed from the top of the cycloid,
the tangent is about 65.9052 degrees from the horizontal, as measured with Michael's Angle script.

Some more options may be added to the script...

- Brian

(No calculus needed. It has already been proven that without friction, the brachistochrone is a cycloid)
(The CycloidInterp script uses the Trochoid formula. When aRadius = bRadius, the trochoid is a common cycloid)

Great!

Thanks so much.