TTCI R&D
Evaluation of Minimum Recommended Tangent Distances between Reverse Curves Revisiting study on computer program dealing with wheelrail forces Alexander Keylin, Sr. Engineer II Benjamin Bakkum, Sr. Engineer II David Davis, Sr. Scientist (Retired) Transportation Technology Center, Inc. (TTCI)
R
everse curves are horizontal track curves that have opposite directions of curvature and are either located adjacent to each other or are separated by a very short section of tangent track. This type of track layout can lead to large coupler angles, especially when two coupled railcars have dissimilar lengths, long overhangs, or short couplers. When such railcars are under a large buff or draft load, this coupler angularity may cause high lateral forces at the wheel-rail interface, creating a risk of flange climb or rail rollover derailment. Lengthening the tangent track section between the reverse curves decreases coupler angles and thus mitigates this problem. This can be challenging, especially when designing crossovers in rail yards, where curves are tight, space is at a premium, and tangent length is limited by track center spacing. In 1976, the Association of American Railroads (AAR) used a computer program called Quasi-Static Lateral Train Stability (QLTS) to estimate wheel-rail forces in reverse curves and provided recommendations on minimum tangent lengths between reverse curves.1 Recently, TTCI was asked to revisit that study using modern computer simulation methods and to evaluate the American Railway Engineering and Maintenance-ofWay Association’s (AREMA) proposed new recommendations for minimum tangent lengths between reverse curves in rail yard crossovers (Table 1). Comparison between results TTCI used multibody dynamics software NUCARS to simulate one of the scenarios 6 Railway Track & Structures // March 2021
from the early QLTS study: An empty 44-ft boxcar coupled between two empty 95-ft boxcars, negotiating 9° reverse curves under 30-kip buff load at a speed of 22 mph. The following three outputs were compared between the two studies: • •
•
Maximum lateral angle between the coupler and the middle boxcar; Maximum single wheel lateral-to-vertical (L/V) force ratio, which is used to estimate the risk of flange climb derailment; and Maximum truck side L/V force ratio, which is used to estimate the risk of rail rollover.
NUCARS modeling of coupler movements, suspension elements’ deflections, wheel-rail forces, etc., is much more detailed than that of QLTS. In addition, QLTS assumes a quasi-static condition, while NUCARS calculates dynamic forces and displacements. Because of these differences, NUCARS showed coupler-to-car angles up to 35 percent lower, but single wheel L/V ratios up to 34 percent higher and truck side L/V ratios up to 30 percent higher than QLTS. Nevertheless, the trends in the two studies were similar: Increasing the tangent length between the reverse curves decreases Degree of Reverse Curves Greater than Equal to
coupler-to-car angles (up to a certain value) and generally decreases L/V ratios. Minimum tangent lengths After confirming that the results of NUCARS simulations were generally consistent with the results of the QLTS study, TTCI then selected two of the worst-case railcar combinations from the QLTS study and simulated these railcars negotiating a series of reverse curves separated by the minimum tangent lengths recommended by AREMA. Track geometry was simulated based on the numbers in Table 1. For example, a 10-ft tangent length was placed between two reverse curves whose degree of curvature was in the middle of the corresponding curvature range (2°15’) in the table for this tangent length. There were no spirals between the curves and the tangents. The simulated track geometry was nominal, i.e., no track alignment, surface, or cross-level deviations were simulated. A total of 36 cases were simulated: nine combinations of reverse curves and tangent lengths; two combinations of car lengths (an 89-ft boxcar between 95-ft boxcars, and a 44-ft boxcar between 95-ft boxcars), and two load cases (no load versus 100-kip buff load). The 44-ft boxcar was equipped with 33-in. couplers, the 89-ft boxcar was equipped with Recommended Minimum Tangent Length (feet)
0°
1° 30ʹ′
0
1° 30ʹ′
3°
10
3°
4° 30ʹ′
20
4° 30ʹ′
6°
30
6°
7° 30’
40
7° 30ʹ′
9°
50
9°
10° 30ʹ′
60
10° 30ʹ′
12°
70
12°
-
75
Table 1. Minimum recommended tangent lengths proposed by AREMA Committee 5 on Track Design.2
rtands.com
