8.7.2.3 IfcAlignmentVerticalSegmentTypeEnum

8.7.2.3.1 Semantic definition

The IfcAlignmentVerticalSegmentTypeEnum indicates the type of a segment of a vertical alignment segment (IfcAlignmentVerticalSegment).

Vertical curvature	Segmenttype	Enumeration Values
No vertical curvature	constant gradient	CONSTANTGRADIENT
Derivative of gradient with respect to horizontal projection of alignment is constant	Vertical curve, parabola	PARABOLICARC
Derivative of vertical angle with respect to 3D arc length along the alignment is constant	Vertical curve, circular	CIRCULARARC
Variation of vertical curvature is constant	Vertical curve, clothoid	CLOTHOID

Table 8.7.2.3.A

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
θ	(Greek "theta") Longitudinal slope angle (incline or decline)	rad
g	gradient (math); g=tan(θ)
x(s)	variable longitudinal coordinate of the projection of the alignment / track centreline into the ground plan.	length
y(s)	variable transverse coordinate of the projection of the alignment / track centreline into the ground plan.	length
z(s)	Variable vertical coordinate of the projection of the track centreline in plan in a Cartesian coordinate system in the vertical direction.	length
z_c(s)	Ordinate of the vertical circular arc of measured away from the tangent line at position s.	length
L_V	length of vertical radius radius (inverse curvature)	length
R_V	radius (inverse curvature) of the track centreline at a point in the elevation diagram (longitudinal section)	length
κ_V	(Greek "kappa") Vertical curvature	1/radius_V
Z_G	Distance of the tangent intersection from the chord of the vertical circular arc	length
Z_M	Distance of the centre of the vertical circular arc to the tangent intersection point (stitch height)	length
l_T	Length of the tangents of the vertical circular arc	length

Table 8.7.2.3.B

References to EN 13803/2017

EN 13803/2017 covers "Track alignment design parameters". As such it is not fully compatible with definitions for IFC Alignment. Therefore rail specific terms like track have been replaced with more general terms also applicable to road design.

Referenced content of EN 13803/2017 "Table 2 - Elements for vertical alignment" has been modified as follows:

Vertical curve, parabola: Derivative of gradient with respect to chainage is constant
Generalized: Derivative of gradient with respect to horizontal projection of alignment is constant

Vertical curve, circular: Derivative of vertical angle with respect to sloping length along the track is constant
Generalized: Derivative of vertical angle with respect to 3D arc length along the alignment is constant

EN13803 clause 3.5: Chainage: longitudinal distance along the horizontal projection of the track centre line.

8.7.2.3.2 Type values

Type	Description
`CIRCULARARC`	Vertical alignment segment where the derivative of vertical angle with respect to sloping length along the track (3D length) is constant. The curvature for vertical circular arc segment is provided by: $$ \kappa_v = \frac{1}{R_v(s)} = \frac{d\theta}{ds} $$ The length for vertical circular arc segment is provided by: $$ l_V =\Delta s_v = \frac{\Delta \theta}{\kappa_v} = \Delta \theta \cdot R_v $$ The distance between point on segment to tangent is provided by: $$ z_c(s) = \frac{s^2}{2\cdot R_v} $$
`CLOTHOID`	Vertical alignment segment where the derivative of vertical angle with respect to sloping length along the track (3D length) obeys a linear change. The curvature equation of the vertical clothoid segment is provided by: $$ \displaylines { \xi = \frac{s}{L} \\ \kappa_v(s) = \kappa_{v1} + \xi \Delta \kappa_v } $$
`CONSTANTGRADIENT`	Vertical alignment segment with constant gradient.
`PARABOLICARC`	Vertical alignment segment where the derivative of gradient with respect to distance along is constant. General equation of the parabolic arc segment is provided by: $$ y = a x^2 + b x + c $$ The gradient (slope) of this curve at any point (first derivative) is provided by: $$ \frac{dy}{dx} = 2 a x + b $$ The rate of change of gradient of the parabolic arc segment is constant. The variation of curvature is therefore provided by: $$ \frac{d^2y}{d^2x} = 2 a $$

Table 8.7.2.3.C

8.7.2.3.3 Formal representation

TYPE IfcAlignmentVerticalSegmentTypeEnum = ENUMERATION OF
	(CIRCULARARC
	,CLOTHOID
	,CONSTANTGRADIENT
	,PARABOLICARC);
END_TYPE;

8.7.2.3.4 References

IfcAlignmentVerticalSegment