[OR SS4] Fillet curve transitions - offset method doesn't seem to be correct

I'm working on reverse-engineering some standard drawings so that I can repurpose them for nonstandard conditions. This leads me to making sure I have everything plotted correctly. This leads me to analyzing the attributes of the transitions and all that.

So, here I am, looking at a back deflection given on the standard drawing as 8d 32m 29.65s. The radius is 2890'. The length is 430.837'. The tangent is 215.818'.

When I draw up a curve to represent this, I set the back transition as follows: type: Curve; method: Deflection; radius: 2890'; deflection: 8°32'29.65".

I change the method to length. The length field displays 430.8369'. Great.

From my calculations (and confirming with an offset line), the lateral displacement of the PT should be offset 32.05483' from the back tangent.

When I change the method to offset, the offset field displays 16.4156'. What does this 16.4156' represent? If I manually set it to 32.05483' as it should be, I get a much wider curve, as you might expect. 

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  • It's been a while since this was a concern for me, but it is again, though I've figured out exactly what's going on and how to cover the difference.

    Here's a sample workflow, using .878:

    1. Construct any two intersecting lines A and B.
    2. Construct a fillet with a 45-foot radius and taper transitions, both of them 50' long and 10' offset.
    3. Offset each of the original lines A and B and snap to the near taper. You'll see that the offset is 10' in either case.
    4. Offset each of the original lines A and B and snap to the fillet's center of curvature. It will not be 55 feet.

    The pattern identified from the above is that offset supplied sets the offset of the PC.

    From this pattern, you might guess that in the case that you have a compound 3-center curve and you define the transition curve by the offset, you'll be telling it the offset of the PCC. If you guessed so, you are wrong.

    Sample workflow:

    1. Construct any two intersecting lines A and B.
    2. Construct a fillet with a 45-foot radius with back and ahead curves, both of them with 120' radius and 10' offset.
    3. Offset each of the original lines A and B and snap to the PCC. You'll see that the offset is not 10'.
    4. Offset each of the original lines A and B and snap to the fillet's center of curvature. It will be 45 feet + 10 feet = 55 feet.

    The pattern identified from this is that the offset supplied sets a differential offset of the fillet's CC.

    Instead of supplying the offset of the PCC, you'll need to supply the arc length or the sweep angle of the transition curve. The sweep angle is arccos(1-o/r) where o is the PCC's offset (here, 10') and r is the radius of the transition curve (here, 120'). The length of the transition arc is, of course, the radius of the transition arc times the sweep angle.

    Once you've supplied either the angle or the arc length, you can now confirm that it is drawn correctly. You should find that it is. At this point, you can choose the offset definition again, and it will report the value it had expected for this result.

    The offset reported will be equal to o + R cos theta - R, where o is the desired PCC offset, theta is the sweep angle of the arc transition, and R is the radius of the arc transition.

    Offset each of the original lines A and B and snap to the fillet's center of curvature. You'll find that it is the middle curve's radius + the offset reported by OpenRoads.

    Recommended enhancement:

    Rename this offset definition as "additional offset to center of curvature" (or something to that effect) and add another definition as "offset to PCC". And consider that sometimes we deal with curves too, which certainly complicates things at least a little.

Reply
  • It's been a while since this was a concern for me, but it is again, though I've figured out exactly what's going on and how to cover the difference.

    Here's a sample workflow, using .878:

    1. Construct any two intersecting lines A and B.
    2. Construct a fillet with a 45-foot radius and taper transitions, both of them 50' long and 10' offset.
    3. Offset each of the original lines A and B and snap to the near taper. You'll see that the offset is 10' in either case.
    4. Offset each of the original lines A and B and snap to the fillet's center of curvature. It will not be 55 feet.

    The pattern identified from the above is that offset supplied sets the offset of the PC.

    From this pattern, you might guess that in the case that you have a compound 3-center curve and you define the transition curve by the offset, you'll be telling it the offset of the PCC. If you guessed so, you are wrong.

    Sample workflow:

    1. Construct any two intersecting lines A and B.
    2. Construct a fillet with a 45-foot radius with back and ahead curves, both of them with 120' radius and 10' offset.
    3. Offset each of the original lines A and B and snap to the PCC. You'll see that the offset is not 10'.
    4. Offset each of the original lines A and B and snap to the fillet's center of curvature. It will be 45 feet + 10 feet = 55 feet.

    The pattern identified from this is that the offset supplied sets a differential offset of the fillet's CC.

    Instead of supplying the offset of the PCC, you'll need to supply the arc length or the sweep angle of the transition curve. The sweep angle is arccos(1-o/r) where o is the PCC's offset (here, 10') and r is the radius of the transition curve (here, 120'). The length of the transition arc is, of course, the radius of the transition arc times the sweep angle.

    Once you've supplied either the angle or the arc length, you can now confirm that it is drawn correctly. You should find that it is. At this point, you can choose the offset definition again, and it will report the value it had expected for this result.

    The offset reported will be equal to o + R cos theta - R, where o is the desired PCC offset, theta is the sweep angle of the arc transition, and R is the radius of the arc transition.

    Offset each of the original lines A and B and snap to the fillet's center of curvature. You'll find that it is the middle curve's radius + the offset reported by OpenRoads.

    Recommended enhancement:

    Rename this offset definition as "additional offset to center of curvature" (or something to that effect) and add another definition as "offset to PCC". And consider that sometimes we deal with curves too, which certainly complicates things at least a little.

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