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| Re: Scheduling Capacity (1353490) | |||
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Re: Scheduling Capacity |
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Posted by Stephen Bauman on Sun May 24 10:44:10 2015, in response to Re: Scheduling Capacity, posted by Broadway Lion on Sun May 24 07:57:34 2015. Braking capacities of trains have changed. They are heavier, and what with composition brakes they do not stop as quickly. Rather than space the signals out more, they simply slowed the trains down. Actually, according to the LION \, it would have been no big problem to install emergency track brakes on the equipment to permit quicker emergency stops allowing trains to operate at higher speeds.Emergency braking rates have been specified at 3.2 mph/sec for all post WWII equipment. This means that all equipment going at equal speeds is designed to stop within the same distance, regardless of their weight or brake shoe composition. Whether the TA maintains their equipment to this design standard is another matter. The NTSB tests following the Williamsburg Bridge collision showed emergency brakes performing at less than half their design specification. Emergency braking rates don't have as much an effect on capacity as do service braking and acceleration rates. The emergency braking rate sets the safe stopping distance between trains. This distance is given by: d = (0.5*v^2)/a, where d is the safe stopping distance, v the velocity and a the emergency braking rate. A train moving at 25 mph would stop within 144 feet with an emergency braking rate of 3.2 mph/sec. An emergency braking rate of 6.4 mph/sec would stop that same train in 72 feet. It takes a train traveling at 25 mph only 1.9 seconds to travel those 72 feet. That's the potential headway reduction of only 1.9 seconds. It's not worth retrofitting the system because current service levels are way below capacity. N.B. these calculations did not include the 30% safety factor that is used for signal system design. Service braking rates are used to stop trains in stations under normal operating conditions. The service level braking rate for post WWII equipment has been 3.0 mph/sec. The braking time from 25 mph accounts for 8 seconds of the headway and covers 153 feet. The train will travel 447 feet within the 600 foot long station at 25 mph for a total of 12 seconds before applying the brake. This accounts for 20 seconds of the headway. Higher speeds may make for a quicker journey but after a certain point they increase minimum headway. The sweet spot is around 25 mph, given current service level braking and acceleration rates, dwell time and train lengths. Systems that operate at significantly higher speed do not approach even NYC's anemic service levels. CBTC could be installed to allow saturation operation. CBTC nor any other traffic control system (collision avoidance) does not increase capacity. The differences in traffic control system performance result from reaction time and the accuracy in locating trains. The reaction time savings is minimal between CBTC and today's antiquated relay based signal system. Short block lengths at station approaches make location accuracy comparable where it is needed. CBTC might raise capacity in the 60th St Tunnel from 40 tph to 42 tph. However, they are currently operating only 20 tph peak. |
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