Superelevation Variables and Formulas
 
 
 

Use the following set of variables to calculate transition distances.

{e} The full superelevation rate. This rate is determined from the superelevation rate table, based on the design speed and curve radius.
{t} The value that is read from the transition length tables, based on the design speed and the curve radius. In most cases, such as AASHTO, this is the transition length value from Level Crown to Full Superelevation. However, this value may not be an actual length, but some other value, such as a transition rate from which the length can be calculated.
{c} The unsuperelevated normal lane slope (positive). This value is defined by the user in the Calculate Superelevation - Lanes Page.
{s} The unsuperelevated normal shoulder slope (positive). This value is defined by the user in the Calculate Superelevation - Shoulder Control Page.
{w} The normal width of the traveled way. This value is defined by the user in the Calculate Superelevation - Lanes Page.
{l} The length of the spiral, if a spiral is involved in the transition. This is the actual length of the spiral element in the curve group.
{p} The fractional part of the transition length before the start of the curve or after the end of the curve.
{q} The rate of increase of centripetal acceleration traveling along a curve at a constant speed.

The variables in the previous table are used to calculate the following:

XML Code Description Example
NC Normal Crown  
LC Level Crown  
RC Reverse Crown  
FS Full Super  

The following table describes the formulas:

LCtoFS  
The distance from the Level Crown Station to the Full Superelevation station is the value {t}, which is read from the selected transition length table. The formula assumes that the transition length table defines the runoff length.
LCtoBC   The distance from the Level Crown station to the Beginning of Curve station is a percentage of the runoff length{t} based on the variable {p}.
NCtoLC   The distance from Normal Crown station to the Level Crown Station (tangent runout) is calculated as the runoff length {t}, time the normal crown slope {c}, divided by the full superelevation rate {e}. The tangent runout length is extrapolated from the runoff length.
LCtoRC   The distance from the Level Crown station to the Reverse Crown station. (typically uses the same formula as NCtoLC)
NStoNC   Normal Shoulder point to Normal Crown point. (used for Breakover Removal Method of superelevated shoulders and Match Lane Slopes)