# Superelevation Lennie Torgerson Engineering Applications Support Team

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Superelevation Lennie Torgerson Engineering Applications Support Team
InRoads XM Superelevation Lennie Torgerson Engineering Applications Support Team

Basics Transitions The wizard
Today’s topic will cover applying superelevation using InRoads XM. We will look at how we design the super transition: where do we begin the change, what is the rate of change, and what do we do differently when we do not use spiral curves. We will look at the equations behind calculating the length of that transition. And finally, we’ll look at the AASHTO Wizard in InRoads XM and how the wizard interprets the equation to automate the whole process.

Basics Spiral curve Tangent to curve PS PSC PC Normal crown
Tangent Runout Circular Arc Spiral Runoff Spiral curve Full Superelevation PC Runoff This slide is an isometric view that helps to illustrate how the superelevation might be applied both with and without spirals. The upper highlighted area shows a transition that uses a spiral curve. Let’s look at this from the top of the slide, with ahead on line being from the normal crown toward the PS and the curve. The Tangent Runout is the section where the outside lane lifts from the normal crown section to zero % cross slope. The Spiral Runoff is the length over which the high side continues from zero cross slope to full super, achieving full super right at the PSC. On alignments with spirals, the runoff is applied across the entire length of the spiral, with the runout applied entirely in the tangent section at the same rate. The lower highlighted section shows a transition from a tangent directly to a circular curve without a spiral. Let’s look at this from the bottom of the slide, with ahead on line being from the normal crown toward the PC and the curve. The Tangent Runout is applied in the same way – from NC to 0% and at the same rate as the runoff, but the Runoff length is calculated instead of using a spiral length. On alignments without spirals, the runoff length is calculated using an equation that takes into account the total superelevation and lane width. Then, at ODOT, 50% of the runoff is applied in the tangent and 50% in the curve. This means that full super will not be achieved until AFTER the PC. The total transition is the runoff plus the runout, whether you have spirals or not. This is a 3-dimensional issue and we can see right off that it would be a lot easier to figure this out if it can be reduced to just two dimensions. When we reduce the issue to 2-D we also apply some principles that help us produce more aesthetic and safer designs. Tangent Runout Tangent to curve Normal crown

Guiding Principles Give ‘em a good ride… Curves 1°and sharper
Use spiral transition Runoff length = spiral length Unspiraled curves 0°55’ and sharper Runoff length = normal spiral length Standard spirals cannot be attained Use longest of three solutions Give ‘em a good ride… The transition from tangent to curve is covered in ODOT’s 2003 English Highway Design Manual in section Horizontal Alignment. I have summarized the pertinent parts of the pages on Spirals and Superelevations and give you the standards for developing superelevation in three situations. What you find, reading through AASHTO Geometric Design of Highways and Streets, is that there are several formulas for calculating a minimum superelevation runoff length. For the first two situations where we are directed to use a normal spiral length, we get that spiral length from the ODOT 2003 Highway Design Manual – specifically Tables 5-3, 5-4, and 5-5. We don’t need to calculate it; just pick it off the correct table and column. These spiral lengths are all much longer than the minimum. So what does that look like with InRoads XM?

Spiraled Curves 1° or sharper
Use spiral transition Runoff = spiral With curves of 1° and sharper, we go to the ODOT Highway Design Manual and look up the spiral length for the degree of curve that we have. The maximum superelevation is listed in the same table. This sample calculation, for a 2° curve at 50 mph, shows that the ODOT spiral lengths are much longer than the minimum required to keep the transition rate below the maximum delta G of 0.5%. In the next slide we’ll see how the InRoads XM AASHTO Wizard treats the situation of a spiraled curve. From: Table 5-3 ODOT Highway Design Manual 2003 English

AASHTO Wizard – Roadway Designer
You can enter the maximum superelevation for the curve into the geometry at the same time that you are building the horizontal geometry. You pull the maximum e value off the same table as the spiral length. Use Geometry>Superelevation>Rate Calculator. In the process of designing a roadway, we develop the superelevation after we have dropped the templates. In the Roadway Designer, the Superelevation menu contains the command to launch the AASHTO Wizard. When you open the AASHTO Wizard, it reads the active horizontal geometry as well as the initial template for the corridor. If the superelevation rate column for your horizontal curve sets is blank – you must go into the Rate Calculator and enter the values before the Wizard can run. Whether you go into the Rate Calculator Editor here or out in the geometry commands – you still pull the maximum superelevation from the ODOT Highway Design Manual. Before we leave this slide – please take note of the station of the PS – this point is supposed to be the super runoff point where you have a zero cross slope. We’ll verify this in a couple of slides.

AASHTO Wizard 3.5% We don’t really need to use the rate calculator – just the editor. Type in the computed rate after reading it off the table; click [OK], then click [Apply] – do this for each curve.

AASHTO Wizard In order to proceed, you have to [Add…] a section. Going by the book, you identify the CL as crown point, then left and right travel lanes as the range points. The pivot direction should be “From Inside of curve” – this will rotate the roadway about the low side edge of travel lane. Once you click [OK], the spiral lengths are applied to the entering and exiting runoffs. You can select either of the curves and [Edit…] the Superelevation Curve Information to see that “Use Spiral Length” is automatically checked on and used, if there is a spiral in the geometry. It doesn’t matter what information is entered into the upper dialog – it is ignored and the geometry is used. Note that the start station for the runoff is the station of the PS.

Superelevation Point Controls
The AASHTO Wizard creates lines for point controls. Each line will be set up to control the point name listed in the “Point” column and its reference is in the “Pivot Point” column. Here I have highlighted the point control for the TL_L – in the curve RIGHT. The TL_L references the CL, so the superelevation point control, controls the slope of the left side of the roadway as it lifts from a -2%, to 0, then to a +3.5% slope.

Superelevation Diagram - spiral
CL LETL RETL PS PSC 0.04 0.02 Slope The super diagram is drawn in the lower right corner of the Roadway Designer. It has as its axes: station along the horizontal, and cross slope along the vertical. Each line drawn in the diagram represents the slope of one segment on a template or cross section. The sign of the slope tells you whether the end point of the segment is higher or lower than the beginning point of the segment. If the end point is below the beginning, the cross slope value is negative; if above, positive. The first point is the point of rotation. This drawing is for a curve right, with the rotation point being the Right ETL (green). At station 42+00, the CL (blue) is above the right ETL on a 2% slope (+0.02). Continuing across the template, the left ETL (red) is below the CL (its adjacent point) on a 2% slope (-0.02). At station 50+00, the CL (blue) is still above the right ETL, but now on a 3.5% slope. The left ETL (red) is now above the CL on the same slope and the roadway is fully superelevated. The purpose of the Wizard is to create the control lines and to enable them for the template points. -0.02 -0.04 Station

Unspiraled 0°55’ and sharper
Runoff length = normal spiral length The second situation that we’ll look at is where you have an unspiraled curve. It is recommended that you use the normal spiral length for your degree of curve as the runoff length if the Roadway Engineering Manager approves an unspiraled curve of 1° or sharper – I took it down to 0°55’ because the table has a normal spiral length listed. Remember that ODOT spiral lengths are much longer than the minimum required to keep the transition rate below the maximum delta G of 0.5%. Just as in the first case – we can totally ignore the General Superelevation Data area of the AASHTO Wizard. Yes the upper section is for use with unspiraled curves; however, we are going to use a spiral length that we looked up! From: Table 5-3 ODOT Highway Design Manual 2003 English

AASHTO Wizard 450 The process begins the same as the first situation with [Add…] a section. Going by the book, you identify the CL as crown point, then left and right travel lanes as the range points. The pivot direction should be “From Inside of curve” – this will rotate the roadway about the low side edge of travel lane. Once you click [OK], the runoff lengths are calculated for each curve. It doesn’t matter that they are calculated incorrectly. You will need to select a curve and click [Edit…] to open the Superelevation Curve Information. The ODOT Highway Design Manual directs us to place half of the runoff on the tangent, so we leave the default 50% and enter the normal spiral length in the “Calculated Runoff Length” fields and click [Apply]. 450

Superelevation Diagram – no spiral
CL LETL RETL PC 0.08 Slope This diagram is for a curve right with a maximum e value of 8%. The rotation point is the Right ETL (green). Before the circular curve, the CL (blue) is above the right ETL on a 2% slope (+0.02). Continuing across the template, the left ETL (red) is below the CL (its adjacent point) on a 2% slope (-0.02). After the runoff and well into the curve, the CL (blue) is still above the right ETL, but now on an 8% slope. The left ETL (red) is now above the CL on the same slope and the roadway is fully superelevated. The 450’ normal spiral was applied as the runoff length with 225’ applied on the tangent and 225’ applied after the PC. We achieve full super 225’ past the PC. 0.02 450’ -0.02 Station

Non-standard spirals or runoff
The last situation that we’ll look at is where you can’t fit a standard spiral or runoff. In this case, you may want InRoads to calculate the minimum runoff for you. Here’s where we finally get into the math. Note #5 on Table 5-3 in the ODOT HDM gives us an equation for the Superelevation Runoff length. This is another form of AASHTO’s minimum length of runoff equation. InRoads uses yet another form of this same equation to calculate a minimum length of runoff based upon the MAXIMUM RELATIVE GRADIENT. For the examples I’ve worked with, this equation gives a longer runoff length than the other two, and you are instructed to use the longest. So we’ll move forward with the topmost equation and see how it relates to AASHTO’s and how InRoads interprets it. But first we need to understand what the relative gradient is. From: Table 5-3 ODOT Highway Design Manual 2003 English

LETL RETL CL Though AASHTO speaks to the longitudinal grade – we can remove the actual vertical alignment grade from the equation because we are talking about the difference between the longitudinal grades of two points as we move horizontally. Because all points on the template follow the vertical alignment, the thing that causes the difference is the effect of the superelevation. In a non-supered situation, as we climb a vertical grade, there is no difference between the elevations of our axis of rotation (RETL) and our edge of pavement (LETL). When a super is applied, however, the grade difference between the axis or rotation and the edge of pavement is straightforward to calculate: width of the rotated plane x %super. “…the length of the superelevation runoff should be based on a maximum acceptable difference between the longitudinal grades of the axis of rotation and the edge of pavement.”

Relative Gradient – spiral or spiral runoff
From my earlier example of a 4°30’ curve, 50 mph, with an 8% super, runoff length of 450’, and 2-12’ lanes rotating about low side ETL: The relative gradient is the rate that the grade difference is applied: grade difference/runoff length. We can see from my calculations that our 450’ runoff without a spiral does not exceed the maximum relative gradient of 0.5%.

The math AASHTO ODOT InRoads XM
Lr = minimum length of superelevation runoff, ft max = maximum relative gradient, % n1 = number of lanes rotated bw = adjustment factor for number of lanes rotated w = width of one traffic lane, ft ed = design superelevation rate, % Ls = length of superelevation runoff, ft s = relative slope, % (same as ) W = distance from ETL to ETL, ft ed = design superelevation rate, % Lr = length of superelevation runoff, ft  = maximum relative gradient, % bw = adjustment factor for number of lanes rotated, based upon number of points on template between Pivot and furthest Range Point. Dp-e = distance from Pivot to furthest Range Point, ft ed = design superelevation rate, % The ODOT formula is pretty simple and we can see that the runoff lengths will be a bit shorter than those produced by the AASHTO or InRoads formulas by setting an adjustment factor (bw) of ½ and not allowing it to vary based upon the number of lanes. What this means, is that for a one lane rotation, the runoff length will be half what you would normally calculate. InRoads interprets the AASHTO formula – so if it is your goal to use ODOT’s simple formula, you can still use the AASHTO Wizard in InRoads to create your control lines, just as we did with the no spiral situation.

Example From my earlier example of a 4°30’ curve, 50 mph, with an 8% super, and 2-12’ lanes rotating about low side ETL: 192’ is a far cry from 450’ that we got from the spiral table. We can force InRoads XM to use this value and put 50% of it on the tangent like before. We can also force it to ignore the maximum delta G.

AASHTO Wizard 192 We leave the “Percent Runoff on Tangent” set to the 50% default and simply key in the ODOT value into the “Calculated Runoff Length” fields and click [Apply]. The start and stop stations are 96’ (192/2) before the PC and after the PT. 192

Superelevation Diagram – short runoff
PC 50% 0.08 Slope The 192’ runoff length is applied 50% on the tangent and 50% on the curve. Remember that the runoff goes from ZERO cross slope to full super. The runout is extended back to the normal crown on the same slope. I want you to take a look at some more math here, because I think it is important to point out that in rotating about the low side edge of travel lane with no spiral and a short runoff – that the relative gradient exceeds the AASHTO maximum. 0.02 192’ -0.02 Station

Relative Gradient – short runoff
Example of a 4°30’ curve, 50 mph, with an 8% super, runoff length of 192’, and 2-12’ lanes rotating about low side ETL. Exceeds max. relative gradient! A value of 1% is twice the maximum relative gradient given by AASHTO. It is the ODOT equation for the short runoff that results in this larger relative gradient. How can you mitigate that?

Relative Gradient – short runoff
Example of a 4°30’ curve, 50 mph, with an 8% super, runoff length of 192’, and 2-12’ lanes rotating about centerline. Rotation about CL reduces gradient! Changing the axis of rotation to the CL can reduce the relative gradient back to 0.5%. w is the distance between the axis of rotation and the edge of pavement (or TL)

Superelevation Diagram – CL rotation
LETL RETL Slope The left half of the roadway rotates upward and the right half rotates downward. This can cause ponding in flat areas – so beware. Station

What if you did want InRoads XM to calculate a non-spiraled runoff for you based on the maximum relative gradient, lane widths, design superelevation and all that? I’ll explain how InRoads interprets the AASHTO minimum length of runoff equation and how you might need to modify entries in the Wizard. The Maximum Delta G and % Runoff on Tangent fields are for use when you do NOT have spirals in your geometry. Here you would set the Maximum Delta G to 0.5 (I will be changing our defaults to that value soon). The % Runoff on Tangent is correctly set to 50% for ODOT. The radio buttons on the right in the General Superelevation Data section describe how to apply the runoff when you have a geometric spiral. You can define the PS to begin back at the NC point - then the spiral covers both the runout AND the runoff. It is ODOT’s way to place the PS at the zero cross slope and that’s how the default is set. In these sample dialogs, I am setting up the wizard to calculate control lines with the axis of rotation being the inside TL.

Lr = length of superelevation runoff, ft  = maximum relative gradient, % bw = adjustment factor for number of lanes rotated, based upon number of points on template between Pivot and furthest Range Point. Dp-e = distance from Pivot to furthest Range Point, ft ed = design superelevation rate, % Dp-e bw ed max (looked up) The “Maximum Number of Lanes from Pivot” is achieved by InRoads counting the number of points on the template from the pivot to the farthest edge (most points away) and subtracting 1. RETL, CL, LETL is 3 points, minus 1 gives you 2 lanes. It is just totally counting points, though and cannot distinguish between a median and a lane. It will also see any extra points in between that you have placed, perhaps for face of barrier. What I’m trying to say is that it may not count the number of lanes well. For our example, the Distance from pivot to edge is 2x12’ or 24’. The design superelevation is read from the geometry – you can change it here is you wish. The Max. Delta G was filled in on the very first dialog. AASHTO discussion on the adjustment factor says that this case of one lane on either side of the CL, rotated about the low edge is considered a ONE LANE ROTATION. Note what happens when we simply change the number of lanes from 2 to 1 – the reduction factor changes AND the runoff lengths are calculated below. Clicking [Apply] uses the calculated values in creating the control lines. (1st dialog)

Cross Section in Super A curve right and curve left cross section – controlled by superelevation control lines created by the AASHTO Wizard – shoulder rollover locks have not been applied. Note that when superelevated, the vertical alignment is not applied at FG on the template (cyan dot at CL). May make matching in at mid curve difficult.

Basics - review Spiral curve Tangent to curve PS PSC PC/PT
Normal crown PSC Tangent Runout Circular Arc Spiral Runoff Spiral curve Full Superelevation PC/PT Runoff Tangent Runout Tangent to curve Normal crown

Guiding Principles - review
Curves 1°and sharper Use spiral transition Runoff length = spiral length Easy to use AASHTO Wizard without editing Unspiraled curves 0°55’ and sharper Runoff length = normal spiral length Edit “Calculated Runoff Length” in Wizard Standard spirals cannot be attained Use longest of three solutions

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Give ‘em a good ride…

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