8.7.2.1 IfcAlignmentCantSegmentTypeEnum
8.7.2.1.1 Semantic definition
The IfcAlignmentCantSegmentTypeEnum indicates the type of a segment of a cant alignment segment (IfcAlignmentCantSegment).
Cant is defined as the amount by which one running rail is raised above the other running rail, in a track cross section.
For 3D modeling both the cant value and the cant angle (bank angle, lateral angle, cross slope angle) are relevant.
The relation between cant value D, Railhead distance b and cant angle ψ is shown below.
$$ \displaylines { \psi = \arcsin \frac{D}{b} \\ \sin \psi \approx \psi \approx \tan \psi } $$
Variation of Cant  Segmenttype  Enumeration Values 

0  both rails without relative elevation  CONSTANTCANT 
constant in the complete segment, <> 0  elevated rail  CONSTANTCANT 
variation along the segment  Transition with linear cant variation  LINEARTRANSITION 
variation along the segment  Transition with nonlinear cant variation  HELMERTCURVE, BLOSSCURVE, COSINECURVE, SINECURVE, VIENNESEBEND 
8.7.2.1.1.1 Cant variation in high performance transition bends
While for combinations of horizontal clothoids and linear cant transitions the extension along the base line differs in some cases, curvature transition and cant transition for high performance horizontal transition bends are expected to have the same start position and end position. In some regulations the same linear extension requirement is mandatory for high performance transition bends.
Whether the cant variation is defined by the same base formula as the curvature of the corresponding horizontal high performance transition bend or by a linear ramp also might differ between regulations.
8.7.2.1.1.2 Used Symbols and their meaning
Symbol  meaning  Unit, value range 

L  full length of segment  positive length L > 0 
s  current position on segment  0 < s < L 
ξ  = s / L (Greek "xi") standardised, dimensionless path length along the alignment / track centre line  0 < ξ < 1 
D  cant .... amount by which one running rail is raised above the other running rail, in a track cross section  length 
D_{1}  cant at beginning of the alignment segment  length 
D(s)  variable cant at station "s" along the alignment cant segment.  length 
b  Railhead distance; distance between the nominal centre points of the two contact patches of a wheelset (e.g. about 1500 mm for nominal track gauge 1435 mm)  length 
ψ  (Greek "psi") Angle of cant (cross slope angle, bank angle)  rad 
φ  (Greek "phi") Directional angle (azimuth, bearing)  rad 
8.7.2.1.2 Type values
Type  Description 

BLOSSCURVE

Non linear cant variation according to Bloss curve base formula. Base formula (Cant) $$ \displaylines{ \xi = \frac{s}{L} \\ D(s) = D_{1} + (3  2\xi) \cdot \xi^2 \ \Delta D } $$ 
CONSTANTCANT

For horizontal straight lines, compensation of lateral acceleration is not required and should be avoided. Therefore the applied cant value is constant 0. For horizontal circular arcs, compensation of lateral acceleration is very common. In these cases the applied cant value is constant value greater 0.
Base formula (Cant) $$ D=Const $$ 
COSINECURVE

Non linear cant variation according to Cosine curve base formula. Base formula (Cant) $$ \displaylines{ \xi = \frac{s}{L} \\ D(s) = D_{1} + \frac{1}{2} \cdot (1 cos(\pi\xi) \ ) \Delta D } $$ 
HELMERTCURVE

Non linear cant variation according to Helmert curve base formula. Base formula (Cant) $$ \displaylines{ \xi = \frac{s}{L} \\ \text{First half: } D(s) = D_{1} + 2 \cdot \xi^2 \ \Delta D \\ \text{Second half: } D(s) = D_{1} + ( 1  2 \cdot (1  \xi)^2) \ \Delta D } $$ 
LINEARTRANSITION

Linear cant variation. This is the "natural" formula for horizontal clothoids. Base formula (Cant) $$ \displaylines { \xi = \frac{s}{L} \\ D(s) = D_{1} + \xi \ \Delta D } $$ 
SINECURVE

Non linear cant variation according to Sine curve base formula. Base formula (Cant) $$ \displaylines { \xi = \frac{s}{L} \\ D(s) = D_{1} + ( \xi  \frac{1}{2\pi}\cdot sin(2\pi\xi) \ ) \ \Delta D } $$ 
VIENNESEBEND

Non linear cant variation according to Viennese bend base formula. The determining influence of the cant variation for the curve in the horizontal Cartesian 2D coordinate space is unique within all other transition curves. .Base formula (Cant) $$ \displaylines { \xi = \frac{s}{L} \\ \psi = \arcsin \frac{D}{b} \\ \sin \psi \approx \psi \approx \tan \psi \\ \psi(s) = \psi_1 + \Delta\psi \cdot \xi^4 \cdot (3584\xi + 70\xi^220\xi^3) } $$ 
8.7.2.1.3 Formal representation
TYPE IfcAlignmentCantSegmentTypeEnum = ENUMERATION OF
(BLOSSCURVE
,CONSTANTCANT
,COSINECURVE
,HELMERTCURVE
,LINEARTRANSITION
,SINECURVE
,VIENNESEBEND);
END_TYPE;