pondering the maths of code 55 streamline

[phonebook]

before I begin, I accept that this probably serves no useful purpose

a peco medium radius code 55 point is supposed to have a radius of 18 inches, now, this is for the curved bit, and not an average of the point itself- from its heel to the toe that bends out.

because

i've been trying in xtrckd to find the correct return piece

if I put two points together- bendy toe to bendy toe, then they return correctly to streamline spacing of (as near as makes almost no difference) 1 inch

but

an 18 inch radius 10 degree custom curve is nothing like the return for it

messing around and experimenting suggests I need a 37 inch radius to do the job and even then its not EXACTLY right

so

my old schoolboy trigonometry can give me a helping hand:

the track spacing is 27mm

the angle is 10 degrees

the Opposite is 13.5mm - thats half the track spacing as the bendy toe must terminate in the middle (so two of them together make a crossing)

so the lenght of the Hypotenuse (the track centers at the end of the bendy toe of the point to the end of the curve i desire) must be 76.56mm - SIN 10 = 13.5/Hypotenuse

That Hypotenuse slots into a circle, the curve I require is the Arc from one end of the Hyptenuse to the other, and the radius of that circle is the correct radius I'm looking for.

the trouble is, I don't have the maths in me!!

can anyone point me in the right direction?

The answer is probably very very close to 37 inches 939.8mm as that would mean that a long point would be the outside parallel curve against a code 55 curved point when spaced correctly appart.

[Bufferstop]

If you get down to the level of checking the radius of the curve you will find that Streamline points, just like the real thing don't have a constant curvature starting at tip of the blade and continuing through to the exit rail, in fact the exit rails are straight from the frog (crossing) onwards. The answer to the return curve to come back to parallel is a piece of flexible track. As you surmise the calculations don't lead anywhere as there are no set track sections that fit the requirement, so you will have to use flexible in the end.

[phonebook]

i absolutely agree with you, but still I'm keen to discover the rhyme, reason and relationship of the different track pieces.

yes, it serves no practical purpose- other than to tax the mind

but musing it did lead me to the interesting discovery that a curved point seems to fit one streamline spacing inside a long point

[locoworks]

i get almost exactly ( i know , i know ) 34.5 inches constant radius in a 10 degree arc to give streamline centres from a code 55 large raidus point. this was done using 'cadrail' drawing a tangent arc, but i don't know how ( or even if ) it is possible to strike the arc from the the point so i placed two points nose to nose and drew a tangent arc on one point and dragged it's radius until it just touched the other point.

[phonebook]

i get almost exactly ( i know , i know ) 34.5 inches constant radius in a 10 degree arc to give streamline centres from a code 55 large raidus point. this was done using 'cadrail' drawing a tangent arc, but i don't know how ( or even if ) it is possible to strike the arc from the the point so i placed two points nose to nose and drew a tangent arc on one point and dragged it's radius until it just touched the other point.

thanks for that- while chelsea beat spurs, i was being a busy bee as well and googled the maths it seems i need the height of the arc to calculate the radius, well i added two points together so the height would be half spacing- this got me the result of 39- which it certainly isnt

then i realised that the hieght is a little more than half spacing because the straight toe sticks out a tad more than the bendy one- but only a tad. which gets me closer to the 37 or so that I believe it to be

so i would imagine that your 34.5 inches is an underestimation, as I think you've made a similar mistake to me only in the other direction- but i am quite prepared to be wrong!

[locoworks]

i get almost exactly ( i know , i know ) 34.5 inches constant radius in a 10 degree arc to give streamline centres from a code 55 large raidus point. this was done using 'cadrail' drawing a tangent arc, but i don't know how ( or even if ) it is possible to strike the arc from the the point so i placed two points nose to nose and drew a tangent arc on one point and dragged it's radius until it just touched the other point.

thanks for that- while chelsea beat spurs, i was being a busy bee as well and googled the maths it seems i need the height of the arc to calculate the radius, well i added two points together so the height would be half spacing- this got me the result of 39- which it certainly isnt

then i realised that the hieght is a little more than half spacing because the straight toe sticks out a tad more than the bendy one- but only a tad. which gets me closer to the 37 or so that I believe it to be

so i would imagine that your 34.5 inches is an underestimation, as I think you've made a similar mistake to me only in the other direction- but i am quite prepared to be wrong!

i have my cad set to inches, i have track centres in code 55 @ 1.05 inches ( this may be where the issue is if that isn't correct? ) but with 1.05 centres it is definitely a 34.5 inch +/- radius arc of 10 degrees to get you to those centres from the points diverging route. i redrew the standard template in the cad package as it was wrong! not by much mind. but i printed out full size 1 -1 a complex station throat for a planned club layout using code 55 and with 3 slips sandwiched between 2 large radius points, so 5 large radius items in a row, it was within a couple of mm tolerance in the total length so i'm happy the template is correct to the actual physical pieces of trackage.

[phonebook]

i get almost exactly ( i know , i know ) 34.5 inches constant radius in a 10 degree arc to give streamline centres from a code 55 large raidus point. this was done using 'cadrail' drawing a tangent arc, but i don't know how ( or even if ) it is possible to strike the arc from the the point so i placed two points nose to nose and drew a tangent arc on one point and dragged it's radius until it just touched the other point.

thanks for that- while chelsea beat spurs, i was being a busy bee as well and googled the maths it seems i need the height of the arc to calculate the radius, well i added two points together so the height would be half spacing- this got me the result of 39- which it certainly isnt

then i realised that the hieght is a little more than half spacing because the straight toe sticks out a tad more than the bendy one- but only a tad. which gets me closer to the 37 or so that I believe it to be

so i would imagine that your 34.5 inches is an underestimation, as I think you've made a similar mistake to me only in the other direction- but i am quite prepared to be wrong!

i have my cad set to inches, i have track centres in code 55 @ 1.05 inches ( this may be where the issue is if that isn't correct? ) but with 1.05 centres it is definitely a 34.5 inch +/- radius arc of 10 degrees to get you to those centres from the points diverging route.

1.05 is ok- in xtrckd its 1.044

what i meant is, that I don't think the methodology is a good one because peco streamline points are the kind that overlap slightly on the straight to when they are joined bendy to bendy- hence i can't calculate the exact height (i underestimate it a little) and you are measuring a length slightly shorter than it ought to be- you're straight toe is slightly protruding!

i did this in xtrckcad : put two points together back to back and find a circle (by trial and error) that joins the two bendy toes

then i get as near as makes no difference 37 inches (but to me it does make a difference- because i want to KNOW!!)

perhaps there is wild variations in the parameters of the software- i would probably believe that to be honest

[locoworks]

yes the straight outlet protrudes slightly with 2 points joined curce to curve, but it doesn't change the centres, the 2 straight parts of the points are still parallel. you don't measure between track centres at the end of the straight bits, you measure perpendicularly from the end of one straight bit to where ever it hits the straight bit of the other point. what messes it up, and what you also mentioned earlier is that the straights on the point either side of the arc are different lengths so there is not, as i mentioned earlier a single radius curve that has ends that will match up to where the ends of the straights are on the point.

look at it this way, if you pin a point down and lay a straight edge accross the two rail ends at the toe and draw a perpendicular line towards the curve side of the point, and then do the same from the rail ends on the curved route, where they intersect will give you point at which you could in theory stick a compass point in. but if you measure the length of the lines they are different lengths. set the compass to one length and it will be inside the centre line on one side, and set it the other length and it will be outside the centre line the other side.

[phonebook]

you are correct and i am wrong!

but my radius argument is better but your curve is the best- regard the two diagrams, my two long points fit exactly into 37 inch circle, the inner circle is your 34.5 inch circle- as you can see it overlaps

but

the other diagram shows how your 34.5 inch return curve (top) is a better fit than my 37!

and i am beginning to understand why- ish- but surely my method does tell me the radius that the point fits into!

[locoworks]

no it doesn't tell you a radius because it isn't a circle, it is a series of same radius arcs joined by short straights, as the frog angle is 10 degrees and the curved route is straight after the frog i expect it takes 36 points to produce your 'circle' that isn't?? what it does tell you, is how wide a baseboard would need to be to fit it onto. what makes it a nice symetrical/mirror image ( ignoring the unused straight route ) is that if you use all the same hand point all the short straight sections are made up from one long and one short straight so they are all the same length. if you did the same with half the 'circle'?? done with the same hand points and the other done with half left hand and half right hand fitted toe to toe and curve to curve the two halfs wouldn't quite meet. the one made up 50/50 would be slightly short and finish slightly inside the other one. and so would also be very slightly wider/fatter. ( i just did it to see )

[phonebook]

ok so not a circle but a series of arcs and straights

thing is i had imagined (wrongly as it turns out) that working that out would lead me to the return curve- because the track center of the bendy toe must be half the spacing (otherwise two together toe to toe wont make a good crossing).

I'm starting to get some clarity on this at last, it must be that the bendy toe has a little bit of straight at the end- otherwise all three points (small medium and large) would not be able to have different radii and still keep to the same track spacing when forming a crossing

after all, the 34.5 inch curve works equally well for all the points in the range

many thanks for indulging me this curiosity and further info is much much appreciated