Chainage on a Sine half-wavelength diminishing tangent curve

[Anonymous]

Below is a screenshot of a Sine half-wavelength diminishing tangent curve which I have measured the distance between two 20m chainage intervals. The straight line distance is 18.567m, I would presume the curve distance is slightly longer but this is still significantly shorter than the 20m chainage. Do you know why this is the case for this spiral, cubic parabola and Japanese parabola? Is chainage on a spiral defined differently to that on a straight line? Is the curve length defined whilst drawing the alignment the actual curve length or something else?

[rl_jackson]

Short answer yes it is defined differently. Hence the reason for a forward and back station along alignments. 

[wfberry]

Rick:

I will admit I very seldom use Spirals but the only time I have ever use back and forward stations is where we have equations in the alignment.

Length along a spiral should be the actual length in my estimation.

Bill

[Anonymous]

Bill/Rick,

Thanks for your replies, Rick do you know of any documentation that describes this behavior? I couldn't find anything. If not I would be grateful for a longer answer if you have time.

Also the chainage at the beginning and end of the spiral is correct in that i drew a 200m spiral and that the chainage difference is 200m (so im not sure why it would require a station) although the spiral draw length is c 195m. On the arc the chainage is proportioned exactly 20m apart. The chainage is just proportioned differently along the length of the spiral. The amount by which it is proportioned on the spiral appears to be relative to the curvature. In that when the curve is shallow the distance between the chainage ticks increases, whilst as the curve increase the distance between the chainage ticks decreases. 

Bill, I thought the length along the spiral would be actual length as well. The input was for a 200m long spiral the resultant drawn spiral was around 195m.

Cheers,

Richard

[rl_jackson]

What I was referring too is that in most cases when I've had DOT R/W plans that used either a regular tangent curves or a spiral curves, they almost always had a forward and reverse(back) station calculation so that the PI of the curve would match up with the station value of the forward PI shown on the plans. Its just the nature of using a curve as a curve is always longer than the incoming/outgoing tangent.

As Bill said, I to rarely do this on subdivisions or any other work I've done as its usually not necessary to show or label a PI, but if you calculate the tangent from the PC to the PI to the station to the PT it will ultimately have a different station value and that's what the station equations corrects the issue.

[cwr-pae · Accepted solution]

When stationing curves presents issues I always think of Chord Definition. See this old thread for a discussion of C3D & chord definition curve issues. Note that newer versions of C3D include a setting under alignments to measure (station?) rail curves on the cord (Settings, Alignment edit feature setting, rail alignment options). I confess I don't understand the chord definition method, I just know it exists and frequently causes people headaches. Net search Chord Definition stationing for more info if you want.

[Anonymous]

Thanks Rick and CWR. I think you are right about the chord stationing. Ill do some reading!!

Thanks everyone for your help.

[Anonymous]

Saying that, i have done some reading but it doesnt account for the differing lengths between what is requested to be drawn (Spiral in length of 200m) and what is drawn (resultant curve length of approx. 195m). Do you have any suggestions?

[cwr-pae]

Can you post a drawing the alignment?

[Anonymous]

Please see attached ZIP file.

[Anonymous]

Repost for some reason!!