e.g. the radius of part of an easement.
- Harry
3 points define an arc.
Take 3 points on the arc. Use a compass to bisect them. Where the bisecting lines meet is the fulcrum. the length back to the point is the radius.
Dave
Lackawanna Route of the Phoebe Snow
The bisecting the arc method is correct for an arc, bu what is being asked about is not an arc, but a spiral. I'm pretty sure you would need the formula for the spiral to determine the radius at a given point.
One reason I use the 1/2 inch offset method marking spirals. Works just as well and no math to worry about.
Dave H.
Dave H. Painted side goes up. My website : wnbranch.com
He just asked how to determine the radius. He didn't say what he intended to do with the information. Bisecting 3 points very close together will get him the radius in a specific location.
I agree with the bent stick transition, if in fact he is trying to calculate a transition. Easy and no math.
Thanks to both Phoebe and dehusman. My question was worded badly, so I think dehusman had the technically correct answer, but Phoebe answered the question I was trying to ask.
Phoebe, I hate to admit it, but I don't remember enough HS geometry to apply your answer. So if you have the patience, how do I use a compass to bisect the points?
Arbitrarily pick 3 points on the same rail. The closer together they are, the smaller part of the curve you will be measuring.
Label them from one end. A,B,C
Place the point of the compass on A. Draw a small arc inside the curve, and a small arc outside the curve. Then WITHOUT CHANGING THE SETTING OF THE COMPASS, put the point of the compass on B. Do the same thing you did from A. The arcs should intersect at 2 points, one inside and one outside. Connect those intersecting points.
Now do the same with points B and C.
Extend those 2 lines you just made. Where they cross is the center of the circle. The distance from that intersection to any of the original points is the radius.
If you used the inside rail, add the distance to the center of the track.
Phoebe Vet wrote:Arbitrarily pick 3 points on the same rail. The closer together they are, the smaller part of the curve you will be measuring. Label them from one end. A,B,CPlace the point of the compass on A. Draw a small arc inside the curve, and a small arc outside the curve. Then WITHOUT CHANGING THE SETTING OF THE COMPASS, put the point of the compass on B. Do the same thing you did from A. The arcs should intersect at 2 points, one inside and one outside. Connect those intersecting points.Now do the same with points B and C.Extend those 2 lines you just made. Where they cross is the center of the circle. The distance from that intersection to any of the original points is the radius.If you used the inside rail, add the distance to the center of the track.
From the far, far reaches of the wild, wild west I am: rtpoteet
R. T. POTEET:
I am not trying to argue here. And I don't profess any mathematical expertise.
You are still trying to indicate that my system will not allow you to project a spiral. I understand that and agree with that. I don't believe that that is what he was trying to do. Perhaps I should have added that what he will measure is the average radius between points A and C. But we are not in need of great precision here. He doesn't need to know down to a fraction of an inch, and I don't believe he is trying to build a spiral. I believe that he just wants to know how sharp his turn is so he can tell what rolling stock he can use. If he is trying to build a transition, he can use the results of the proceedure I described and apply the offset that you recommended. But he does have to know "offset from where?".
If you believe he is trying to calculate a spiral, feel free to post the formula and/or proceedure. Don't just keep telling me I'm wrong. Submit what you believe to be the right answer. He can then choose the one that will acomplish his goal.
Phoebe Vet wrote: I believe that he just wants to know how sharp his turn is so he can tell what rolling stock he can use.
If thats what he is trying to do then the answer is "it doesn't matter".
Assuming the easement is between a curve and a tangent or between two curves, the smallest radius will be the curve or smallest of the two curves. The radius of the easement will always be larger than the radius of the smaller curve.
dehusman wrote: Phoebe Vet wrote: I believe that he just wants to know how sharp his turn is so he can tell what rolling stock he can use. If thats what he is trying to do then the answer is "it doesn't matter".Assuming the easement is between a curve and a tangent or between two curves, the smallest radius will be the curve or smallest of the two curves. The radius of the easement will always be larger than the radius of the smaller curve.Dave H.
I agree with that. Does it answer his question?
On the topic of Spirals:
I'm not sure of the exact formula, but to figure a spiral radius you need to triangulate points on the radius'd leg in relation to the tangent and beginning of curve:
Interesting thread. Thanks Phoebe Vet for telling me how I can figure out the 'average radius' of a curve on my layout, something I've oft wondered how to do.
Your method certainly will do that and no mathematics are involved. The problem has always been trying to find the center of the circle!
Thanks fer learnin me somethin today!
Joe Daddy
Another quick way to find a line through the center of an arc is to get a small 45-45-90 triangle, set longest side so each end touches the arc. Mark where all three points are. Flip it over, keeping the longest side on the same two points on the arc. Mark the point of the 90 degr angle is. Draw a line connecting the point inside and the point outside the arc. Move the triangle over a couple inches or so and repeat.
You are doing the same thing as bisecting the arcs, but with triangle. Since a lot of small carpenters squares (speed squares) are 45-45-90 triangles its a handy method.
HarryHotspur wrote: e.g. the radius of part of an easement.
I drew you a diagram.
This system will find the center of a perfect circle that intersects all three points. Therefore, if the radius is changing, as in an easment, the closer A and C are together, the more acurate it will be.
As another poster noted, to calculate an easment find the center of your fixed radius circle, and offset that center. That will result in the last (or first) segment of the curve having a greater radius.
You can find all kinds of fancy formula.
First when you draw your radius, keep it 1/2" away from the straight section your comming off of. Other wise you can't create a transition. That goes for both ends of the radius!
I use a fishing pole tip end. I just keep the big part in line with the straight section i'm comming off and bend the tip around to the other straight section or where ever I want to end the transition. I use nails to hold the butt end in place before bending and something heavy or nails at the tip behind the tip line guide. Use the pole to trace your transition line.
May sound stupid but if you look at a fishing pole natural bend It's a transition curve.
Guy's ask, " How did you do such nice transitions?".
Jules