Sheer bow

The Blossbogen is a form of a transition curve that is used in track construction , e.g. B. at Deutsche Bahn AG . It represents an alternative to the clothoid . The course of the curvature is clearly defined by the cubic polynomial , which transitions tangentially from one curvature to the other.

The curvature between the beginning of the transition curve (ÜA) with the curvature zero and the end of the transition curve (ÜE) with the curvature of the subsequent radius is defined as: ${\displaystyle k}$

${\displaystyle {\begin{aligned}k(l)&={\frac {3}{R\cdot L^{2}}}\cdot l^{2}-{\frac {2}{R\cdot L^{3}}}\cdot l^{3}\\&=\left(3-2{\frac {l}{L}}\right)\cdot \left({\frac {l}{L}}\right)^{2}\cdot {\frac {1}{R}}\end{aligned}}}$

in which

• R = radius of the connection arc
• L = total length of the transition bend
• l = intermediate length of the transition curve section, viewed from the ÜA.

Table of values :

Job	${\displaystyle l}$	${\displaystyle k}$	annotation
Spiral start	0	0
	${\displaystyle {\frac {1}{4}}L}$	${\displaystyle {\frac {5}{32}}{\frac {1}{R}}}$	d. H. ${\displaystyle k<{\frac {1}{4}}{\frac {1}{R}}={\frac {8}{32}}{\frac {1}{R}}}$
	${\displaystyle {\frac {1}{2}}L}$	${\displaystyle {\frac {1}{2}}{\frac {1}{R}}}$
	${\displaystyle {\frac {3}{4}}L}$	${\displaystyle {\frac {27}{32}}{\frac {1}{R}}}$	d. H. ${\displaystyle k>{\frac {3}{4}}{\frac {1}{R}}={\frac {24}{32}}{\frac {1}{R}}}$
Spiral end	${\displaystyle L}$	${\displaystyle {\frac {1}{R}}}$

literature

• Bloss: The transition arch with a curved superelevation ramp . In: Organ for the Progress of the Railway System . tape 91 , no. 15 , August 1, 1936, ZDB -ID 552263-8 , p. 319 f .

See also

• Transport engineering