#5 Turnout

[WTierce1]

What curve radios will line the track from a #5 turnout with a mainline?

[OldTimer]

This keeps coming up so for those of you who are interested and are willing to spend a few minutes thinking, lets mount a quick expedition into the world of angles. 

The number of a turnout is the cotangent of the angle of the frog.  Wikipedia has a good article on trigonometric functions here:

http://en.wikipedia.org/wiki/Trigonometric_functions#Sine.2C_cosine.2C_and_tangent

and there is a numeric table of functions here:

http://www.sosmath.com/tables/trigtable/trigtable.html

For our purposes, the "side opposite" is always 1 and the "side adjacent" is always the number of the frog, 5 in this example.  The cotangent is defined as the side adjacent/side opposite, so for a #5 turnout, the cotangent is 5/1.  My table doesn't give values for the cotangent, so I need to know that the reciprocal of the cotangent is the tangent and in our example that equals 1/5 or .20.  I can look up values for the tangent in my table and find that .20 lies in between .194 (11 degrees) and .213 (12 degrees).  So....I can say with some degree of certainty (hehehe) that the diverging angle o f a number 5 turnout is approximately 11.5 degrees.   That is certainly a close enough approximation to work with the errors accepted by sectional track manufacturers so they don't have to make an infinite number of fitter pieces.

Hope this is helpful.
OldTimer

[WTierce1]

Thanks.

[OldTimer]

The rest of the answer....

I'm not at all familiar with EZ-Track, so I  had to take a break to look up the specs for Bachmann's curved track.  Turns out that 4 sections of 22" radius equals 90 degress, so one section would be 22.5 degrees and a 1/2 22" radius section would be 11.25 degrees, certainly close enough.
OldTimer

[WTierce1]

Thank You verry much!!

[Joe Satnik]

Dear All,

I measured the #5 turnout in a previous posting,

http://www.bachmanntrains.com/home-usa/board/index.php/topic,12595.0.html

and got

12.41 degrees divergent departure angle and frog angle  (which translates/calculates to a

4-5/8 (4.625) turnout # and frog # .

A 12 degree 33.25" Radius curve would be a closer fit to 12.41 degrees than a half-22" curve (=11.25 degrees).

The half-22"R curve may still be close enough to work without kinks or gaps, though, to bring the divergent back to parallel.

Anyrail.com shows a 12 degree divergent angle for the #5.

Hope this helps.

Sincerely,

Joe Satnik

[OldTimer]

LOL....the math is right...if you call an apple an orange, the answer will be wrong every time.  Just one reason I use flex track. Anyway, I'd much rather be happy than right, so thanks for clearing this up, Joe.
OldTimer