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What is Transition Length, Road Runoff and Road Runout on Tangent

Source : Design of Horizontal Curves 

Transition length is the distance required in transitioning the road from normal to full superelevation. It consists of Runout Length and Runoff Length.

Transition Length = Runout Length + Runoff Length

The customization of Runout length is a feature introduced in our latest MiTS version 2.9 which can be defined as the roadway length that is required in transitioning from normal crown (2.5%) to zero (level) superelevation.

Meanwhile, runoff length is the roadway length that is required in transitioning from zero (level) superelevation to full superelevation. In our software, the runoff length is known as ‘Spiral Length, m (for 2-lane road)’ for the spiral curve.

Now, how does MiTS compute the Runout and Runoff Length?

In MiTS, computation starts with the runoff length first, then followed by the runout length.

Runoff Length #

The computation method of runoff length depends on the horizontal curves designed by users – either as a spiral curve or a circular curve – influenced by the spiral length set under the Spread Input.

Runoff length: Spiral Curve Computation #

In the case of a spiral curve, in which the defined spiral length is set to a value that is not 0, then the runoff length will be calculated based on the Spiral Calculations Standards available in the software. The two standards are (1) Fixed mode and (2) Calculate by Max. Relative Gradient mode

Fixed Mode #

In Fixed mode, the user-defined spiral length value needs to be multiplied with the adjustment factors to obtain the runoff length.

(Under Project Parameters > Road > Design > Adjustment Factors > Click Edit)

The calculation example;

Spiral length input by user

Spiral length input by user

No. of lanes= 4; Based on the adjustment factors table, n1bw=1.5

Runoff length

= defined spiral length x adjustment factors, n1bw

= 29.000 x 1.5

= 43.5

Given, Transition chainage (at level elevation) = CH236.292

Chainage (from level to full superelevation)

= CH236.292 + 43.5

= CH279.792

Result generated from MiTS

Max. Relative Gradient #

In Max. Relative Gradient mode, the runoff value is calculated based on the transition formula [from zero (flat) superelevation to full superelevation]

The equation used in the transition length calculation can be referred as below, or can also be referred in our Appendix provided in MiTS;

$$ \text{Transition length, L (m)=}\frac{w\times e\times\left(n_1\;b_w\right)}\triangle $$

w = Road Width

e = Percentage change in superelevation

n1bw   = No. of lane Adjustment Factor (refer to the table above)

Δ = Maximum Relative Gradient

The Maximum Relative Gradient depends on the speed of the design. The values can be referred to the table below;

(Under Project Parameters > Road > Design > Maximum Relative Gradients > Click Edit)

The calculation example;

Design speed, kph = 30

Maximum Relative Gradient, % = 0.75

Design Radius, m = 30

Road Width, m = 3.6

No. of lanes = 4; n1bw = 1.5

Full Superelevation Rate, % = 6

Cross Slope rate, % = -2.5

Level Superelevation Rate, % = 0

% Runoff length on tangent = 66.667

Runoff length (on curve+tangent), based on transition length formula

= (3.6 x |(0-6)/100| x 1.5)/(0.75/100)

= 43.2

Given, transition chainage (at level crown) = CH 236.486

Chainage (from level to full superelevation)

= CH236.486 + 43.2

= CH279.686

Result generated from MiTS

Runoff Length: Circular Curve computation #

As for a circular curve, in which users have defined the spiral length as 0, the software will first calculate the runoff length based on the transition length formula. Then, the parameter ‘% of Runoff Length on tangent’ will enter the equation, which can be used to obtain the effective runoff length (length that is part of the curve). 

Circular curve computation in MiTS 2

Result generated from MiTS

The calculation example;

Design speed, kph = 40

Maximum Relative Gradient, % = 0.70

Design Radius, m = 400

Road Width, m = 2.5

No. of lanes = 2; n1bw = 1.0

Full Superelevation Rate, % = 2.8

Cross Slope rate, % = -2.5

Level Superelevation Rate, % = 0

% Runoff length on tangent = 66.670

Length of curve, m = 273.346

Runoff length (from a level to a full superelevation), based on transition length formula

= (2.5 x |(0-2.8)/100| x 1.0)/(0.70/100)

= 10

Give, transition chainage (at level elevation) = CH140.048

Chainage (from level to superelevation)

= CH140.048 + 10

=CH150.048

By using the % runoff length on tangent;

Effective runoff length

= [1-(66.67/100)] x 10

= 3.333

Length of superelevation

= Chainage (start of superelevation) + [length of curve – (2 x effective runoff)]

= CH150.048 + (273.346 – (2 x 3.333))

= CH416.728

Runout Length #

And now, to compute the runout length, the program will depend on the Run out calculation standards available that can be selected by users – (1) Autocalculate and (2) User DefinedThe difference in the computation between this two modes are;

AutoCalculate mode #

In Autocalculate mode, the runout length will be calculated based on the transition formula [from normal crown (2.5%) to zero (flat) superelevation]

The calculation example;

Design speed, kph = 30

Maximum Relative Gradient, % = 0.75

Design Radius, m = 30

Road Width, m = 3.6

No. of lanes = 4; n1bw = 1.5

Full Superelevation Rate, % = 6

Cross Slope rate, % = -2.5

Level Superelevation Rate, % = 0

Runout length, based on transition formula

= (3.6 x |(-2.5-0)/100| x 1.5) /(0.75/100)

= 18

Chainage (from normal to level crown)

= CH218.486+ 18

= CH236.486

Result generated from MiTS

User Defined mode #

In User Defined mode, the runout length will be based on ‘Table 4.8: Desirable Length of Spiral Curve Transition’ in ATJ 8-86 Pindaan 2015. Do note that users can override the runout length as he or she wishes, though.

Runout length based on Table 4.8

Runout length based on Table 4.8;

Chainage (from normal to level)

= CH219.292 + 17

= CH236.292

Result generated from MiTS

To help users understand better on how the computation is being carried out in the software, we provide you with the spreadsheets and project file for two sets of combinations – User Defined, Fixed & AutoCalculateMax. Relative Gradient – for your reference.

How User-Defined Runout Length affects the vertical detailing for Spiral Curve? #

In MiTS, the Vertical Detailing diagram not only shows the transitioning of the road from Normal Crown (2.5%) to a full or partial superelevation of your road design in the form of line, but it also provides users with the value of gradient change per meter (%/m). This parameter reflected on the diagram is fully derived based on the chainage table in the Superelevation Report, which can be acquired using the following formula.

$$ \frac\%{\text{m}}=\frac{\text{∆gradient}}{\text{∆chainage}} $$

Provided below is the example of how this parameter is being computed, when the runout is ‘AutoCalculate’ by the software and the runoff is using Fixed Spiral Calculation Standards for both circular and spiral curves.

Input for IP1 and IP2

Chainage (IP1 - Circular Curve)

Cross Slope Rate (%)

Gradient/meter (%/m)

Left

Right

Left

Right

88.895

-2.50

-2.50

-

-

106.895

-2.50

0.00

0.00

0.14

124.895

-2.50

2.50

0.00

0.14

140.842

-4.71

4.71

-0.14

0.14

156.788

-2.50

2.50

0.14

-0.14

174.788

-2.50

0.00

0.00

-0.14

192.788

-2.50

-2.50

0.00

-0.14

$$ \frac\%{\text{m}}=\frac{\left(-2.5-0\right)}{\left(\text{88.895-106.895}\right)}=0.1389\approx0.14 $$

IP1 Vertical Detailing that is reflected from the change in gradient based on Superelevation Report

Chainage (IP2 - Spiral Curve)

Cross Slope Rate (%)

Gradient/meter (%/m)

Left

Right

Left

Right

218.167

-2.50

-2.50

-

-

236.292

0.00

-2.50

0.14

0.00

254.417

2.50

-2.50

0.14

0.00

279.792

6.00

-6.00

0.14

-0.14

294.568

6.00

-6.00

0.00

0.00

319.943

2.50

-2.50

-0.14

0.14

338.068

0.00

-2.50

-0.14

0.00

356.193

-2.50

-2.50

-0.14

0.00

$$ \frac\%{\text{m}}=\frac{\left(6-2.5\right)}{\left(\text{294.568-319.943}\right)}=-0.1389\approx-0.14 $$

IP2 Vertical Detailing that is reflected from the change in gradient based on Superelevation Report

Through the analysis of the Vertical Detailing provided, a consistent value indicating a steady gradient change per meter is observed in both IP1 (circular curve) and IP2 (spiral curve) during the transition. This consistency extends to other curve configurations, including those utilizing the Max Relative Gradient as the Spiral Calculation Standards, except for cases where runoff length is user-defined in a spiral curve.

In this particular scenario, the inconsistency in the gradient change arises due to the combination of two fixed values; a fixed gradient change of 2.5% to 0% over a specific length and a fixed runoff length that encompasses a gradient change from 0% to a full superelevation curve. These two values may not coincide, making it impossible to achieve a consistent gradient change per meter along the entire superelevation.

Spiral Curve with User-Defined runout length under Spread Input

Chainage (IP2 - Spiral Curve)

Cross Slope Rate (%)

Gradient/meter (%/m)

Left

Right

Left

Right

219.292

-2.50

-2.50

-

-

236.292

0.00

-2.50

0.15

0.00

253.292

2.50

-2.50

0.15

0.00

279.292

6.00

-6.00

0.13

-0.13

294.568

6.00

-6.00

0.00

0.00

321.068

2.50

-2.50

-0.13

0.13

338.068

0.00

-2.50

-0.15

0.00

355.068

-2.50

-2.50

-0.15

0.00

IP2 Vertical Detailing for spiral curve with user-defined runout length

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