DIFFERENTIAL-GEOMETRIC DETERMINATION OF MOTION CHARACTERISTICS IN HIGH-SPEED CURVES

Correct geometric layout of railway routes for speeds between 120 and 200 km/h and speeds beyond 200 km/h calls for exact determination of the motion characteristics (speed, acceleration and "h" vectors, etc.). In high-speed train running there is a change in the significance of the individual vectors governing motion and in addition to speed and acceleration the higher-order kinematic characteristics ("h" vectors, etc.) become determinative for the rail-curve geometry. Employing the differential-geometric method, the author describes the determination of the higher-order vectors by way of vector analysis. This is a new and hitherto unused method for the geometric layout of high-speed rail routes. Bearing in mind the determination of the motion characteristics, it can be seen that using higher-order kinematic vectors as scalar quantities is a very coarse approximation. The need to employ the method described here is all the more apparent if one does not assume a constant speed, but takes into account the actual speed conditions. It can therefore be seen that the correct geometric layout of high-speed rail routes calls for the vectoral determination of the actual motion characteristics, as described in this article.