Hi,
I would need someone to shed some light on me regarding maximum relative grade.
Could someone please explain and provide more info on this please?
Understanding fully its concept will help me on superelevation and length of spiral.
Thanks.
Regards,
Ron
https://connect.ncdot.gov/projects/Roadway/Lists/Definitions/DispForm.aspx?ID=24
Search 'maximum relative grade' on Google - there are many explanations.
Thank you for your response Mark. I just wanted to understand more the concept which i think i am missing especially when computing spiral lengths and runoffs. I see the formula of maximum relative gradient but would like to understand its principle. I'll dig and search some more for better references as you suggested. Thanks.
The maximum relative gradient controls the rate of rotation as a vehicle transitions from the normal cross-slope of the roadway to full superelevation in the curve. The rate is based partly on physics, but more so on driver comfort.
Thanks Ray, much appreciated, so it looks that the the principle from your explanation is - we don't want the road to rotate quickly/abruptly for driver/passenger comfort.
My initial thinking is that we don't want the road to rotate very slowly to prevent hydroplaning.
Standing water can be an issue depending on the profile grade of the road.
Spiral lengths are adjusted longer when more than one lane is being rotated, essentially reducing the rate of rotation. This is to limit the increase in true profile grade at the outer edge due to the compounding effect of applying the maximum relative gradient across multiple lanes.
If your roadway profile is 2% and you apply the maximum relative gradient of 0.5%, the profile grade of the outer edge of the lane is 2.5%. If you continue to apply that same relative gradient to successive lanes, the outside of the second lane will be 3%, the third lane 3.5% and so on.
Ray,
I think you are about to enlighten me, i just need more clarifications.
When you say "road profile is 2%", I think you mean also cross-slope is 2%?
To me road profile is longitudinal/vertical grade of the vertical alignment. Please correct me if my terms are incorrect.
When you say " the profile grade of the outer edge of the lane is 2.5%" - Where is the start and end of the cross-slope?
My understanding is, succeeding lanes are also 2% because the whole road has been superelevated 2%.
I think i am missing the meaning of "relative".
In researching this topic, I came to the realization that I have been applying the maximum relative gradient incorrectly in my work. I've edited my previous post to reflect that.
The relative gradient refers to the "...difference between the longitudinal grades of the axis of rotation and the edge of pavement." (AASHTO Green Book) Maybe the attached picture will help. The red and yellow lines are the left and right edges of the roadway.
Answer Verified By: ron_maneja
My big thanks to you Ray for spending time on this. I understand more in your attached diagram. My understanding is also close to yours. If i would compute, it will be ((7*12) + (2*12))/Spiral Length. That is superelevation starts & ends in the start & end of spiral. But you did it (in your diagram), maximum superelevation is the start of spiral while end of spiral is at zero normal cross-slope. Mine gives a relatvie gradient of 0.36%. I think both solutions are e are correct. Do you agree?
I think in you diagram, the annotation 0% Relative Gradient should be closer to arrow to avoid confusion to other readers.
Best Regards,
The 0% relative gradients occur in the section of full super - in the central curve - and in the tangent between the curves. The arrows indicate the limits of the spiral.
In our agency and, I believe, in most other agencies that use spirals, the cross-slope on the outside of the curve is flat (0%) at the end of the spiral (PS or PT). The remaining transition on the outside of the curve, from 0% to normal cross-slope is applied on the adjacent tangent. The superelevation on the inside of the curve mirrors that of the outside of the curve until it reaches the normal cross-slope.
If you are removing all of the superelevation - from 7% to normal cross-slope - in the spiral, I agree that your relative gradient is 0.36%.
Agreed, 0% in the whole tangent section.
Many thanks for this interesting discussion.
Much appreciated for your big help.