I am putting in a 180 degree curve. One side will start with a 32" radius curved turnout that I would like to transition into a 30" radius curve by the time it comes out the other end. My question is, with a nice smooth tightening of the curve from 32 to 30 what will be the diameter of the curve? Thanks
Brent
"All of the world's problems are the result of the difference between how we think and how the world works."
Well, I am no math whiz...but considering the diameter of a 32 inch radius is 64 inches and the diameter of a 30 inch radius is 60 inches, I'm going to say that the diameter of your transitioning curve will be 62 inches.
If that's not close enough, you really do need a math whiz.
There is no true answer as we can't factor in what we don't know.
Since diameter and circumference are connected in the equation, without knowing the length of the portion at 32 vs the length of the portion at 30 its impossible to calculate.
Find someone with spare card board, cut to 90° segments of each radius, then over lap the 30" segment over top the 32". Adjusting the two pieces to give you the desired transition, then measure.
I can tell you from experience the resulting parabola will be slightly longer than it is wide, if done a full 180°. Meaning the radius from start to 90° may be slightly shorter than 32" at the apex or apogee of the curve the radius will be slightly longer the 32" due to stretch.
In reality the measurement is minimal really.
Good Luck
BlueHillsCPRWell, I am no math whiz...but considering the diameter of a 32 inch radius is 64 inches and the diameter of a 30 inch radius is 60 inches, I'm going to say that the diameter of your transitioning curve will be 62 inches.If that's not close enough, you really do need a math whiz.
Okay give me the Darwin award. It's been a loooong day. Maybe I'd better not work on the layout tonight, we wouldn't want any catastrophic engineering failures.
I'll go along with BlueHillsCPR. Here's why.
From your description I assume that the curve is making a smooth transition and the center of the curve doesn't change during the transition. If the center changes, then the final distance could be anything, but I wouldn't call the line from one side to the other a "diameter" in that case.
|/ \| <------- 32 in --------> o <--------- 30 in -----> |
Total from one side to the other is 32 + 30 = 62 in.
Ok, ok, you guys are right...I'm a math whiz.
J/K of course! When it comes to the tough math I run for my spouse, who actually enjoyed Algebra and passed Calculus!
If you are actually going to be concerned with transitions on either end then the effective radius will be in the 63 inch range because you will ease out the curves on either end. 8-)
Dave H. Painted side goes up. My website : wnbranch.com
The transition (or easement) curve between 32 and 30 inches can be any length you desire. Since the two here are so close together, there really isn't much operational need beyond making sure you have smooth flowing track. Transition length from tangent to curve is usually given as the length of your longest car, but if you look at the distance between the 30 and 32 points you'll find it much shorter than that at around 1-2".
See MR's templates http://www.trains.com/mrr/default.aspx?c=a&id=290
Enjoy
Paul
okay this is what i did,
i went into autocad and drew two circles one at a 32" rad. and another at a 30" rad. both having the same center point. i took both and cut them into a 180 degree arcs. i then grabbed the end of the 32" rad. arc and snapped it onto the end of the 30"radius arc. then i went into the properties of this new arc and it came out to be a 31.0161" radius. now this did change the orginal center point of the 32"rad. arc. at 1.4142 at 45 degrees if 0 is at east on a compass. and also changed the 180 degree arc to a 184 degree arc.
so i hope this helps
later
glenn
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Yes but! If the curve is to be a continuous lessening from 32" to 30" it will have different radius at any given point since it is continuously changing. In other words it is getting smaller and smaller until it is down to 30" radius. The two ways I would lay this out are an easy way and a little harder way.
Easy way
Since the only 32" segment is the turnout I would lay out a 30" radius curve from the opposite side for at least 180 degrees. i would then locate the turnout to allow an easement ( a continual tightening radius) until it reachs 30" between the two and connect it to the curve.
Harder way
Same idea but locate the easement between a roughly 90 degree section of 32" radius and 90 degree section of 30" radius using the same center for the curves. Since the only known 32" radius needed is the turnout there is really no reason to make it this hard.
My plan is to put the curved track 1/2 inch inside the nominal curve and transition the curve one car-length before and one car-length after where the straight track would have ended if the curved track wasn't laid a half-inch inside the drawn nominal curve. For example on a 180-degree turn, the straight tracks would be 60 inches apart using a nominal 30-inch-radius with the non-transitioned part of the curved track laid on a 29.5 radius. Hope that's clear.
Mark