Hi all,

I have been comparing notes between C-Track geometry and K-Track geometry, and wondering why there are some geometric differences between them.

The C-Track standard curve point is 24.3° and the K-Track standard curve point is 22.5°. Why are they different ?

The C-Track standard length is 360mm (188mm + 172mm) and the K-Track equivalent lengths are 324.9mm (168.9mm + 156mm). Why ?

The C-Track spacing between tracks is 77.4mm and the K-Track standard spacing between tracks is 64.6mm Why ?

Both of these C-Track and K-Track forms have complications, and there are numerous articles on how to construct different layouts where the tracks fit together. Some of these are really interesting shapes, but go to a lot of trouble to make things fit. Those 5.7° C-Track curves are difficult to work with and you only get them in R2.

I think that C-Track got the distance 360mm right but the angle wrong, and K-Track got the angle 22.5° right but the distance wrong.

I believe that a best-in-class track would combine the best features of both of these.

__In my theoretical world, __1) the standard curve point should be 22.5°. Because 2 x 22.5° = 45°, and 4 x 22.5° = 90°. All angles become easy to join, whether you are doing reverse loops or X-crosses or anything.

2) The standard length of 2 tracks should be 360mm. Because this fits nicely with the R1 radius curve and allows for subsequent concentric circles. We need to eliminate the small straight sections required in the K-Track range to make up the 360mm.

Combining the best of these C-Track and K-Track features, I believe that the optimal spacing between tracks is calculated to be 71.61mm.

(see calculations below)

A track line spacing of 71.61mm will allow the perfect match incorporating 22.5° points and 360mm combined straight sections.

All crossings will be completely seamless and will fit snugly into the track geometry.

All points will be able to curve at 22.5° and curve up to 45° with no problems, or curve back to parallel tracks, go to reverse loops, etc.

In C-Track terms,

instead of the 24188, we would have a 24184, and instead of a 24172 we would have a 24176, and instead of a 24077 we would have a 24071.

In K-Track,

it would not be necessary to have all of those small sections like 2204 and 2208, etc to get back to the 360mm.

Using a little trigonometry, one can calculate these angles and distances using SINE and COSINE functions.

It's just something that I have been thinking about for a while

And having a bit of fun with maths !

Regards

John