Hi all,
I was looking through BRT help guide to find the Equilibrium Cant Equation BRT uses when calculating cant.
The Define Cant Alignment menu has the following options for Cant Method:-
I typically select Use Equilibrium Equations from the above menu.
However I wanted to know the equation BRT uses.
I calculate equilibrium Cant (based on 1435 gauge) using the following:-
E = 11.841V^2/R
Where
E Is Equilibrium Cant
11.841 Is my Equilibrium Constant
R Is the Radius
V Is the speed
I am certain BRT uses the same equation because if I compare my manual calculations against the Eq Cant values shown in the Cant Alignment Editor they are the same - however i just want to know where in the help guide it actually shows the Equilibrium Cant equation.
Any ideas?
Thanks
Yes you're right. The formulae doesn't look to be included in the help. Even universal it could appear. You can find the non compensated lateral acceleration.
Equilibrium Constant:
EC=(Center rail to Center Rail distance)/(GravityConstant*3.6^2)
Example: EC=1500/(9.809x3.6^2)=11.7999.809 is gravity constant in Paris. 11.8 is applied.
Equilibrium cant:
EqCant= EC * V^2/R
Eqcant = 11.8 * V^2/R in the example
The factor 11.82 is defined for normal gauge and takes into account g, S and the speed unit conversion from m/s to km/h.
An important fact to understand and consider is that this cant constant value – 11.82 is a conventional figure. It is defined based on a presumed conventional rail centerline distance of 1502mm, for normal gauge track and it is related to the standardised way of measuring the cant, defined in the European Norm EN13848 – Track Geometry Quality.
It is established based on general equations and it’s not defined dependant of rail type or gauge variance (as long as the track has a normal track gauge).
That is why this constant should not be changed based on the variance of the normal gauge and kept the same for a gauge of 1432mm, 1435mm, 1438mm.
The cant constant carries with it all the simplifications mentioned above. Due to these simplifications, its around the world generalised value for normal gauge is 11.8 – an acknowledgement of the level of precision used to define it.
Also, as was demonstrated above, the cant constant is computed and based on the conventional rail centerline distance (considered in UK to be 1502mm) and not on gauge (1435mm). The difference between the two is significant and considering the later when defining the cross-angle in causing a significant error in cross level and cant.
This error is summarized in table 1.
Table 1. Cant error when is presumed computed based on gauge instead of rail centerline distance.
The error becomes even more significant when is propagated over six foot for siding geometry or for canted S&C design