On 01-03-2014, Ed workman replied to my post on another thread, but regrettably I am often off line for days at a time, thus missed his question.

> Alright OldPole
> Isn't headway a function of speed?
> That is, if the trains go slooooooow the headway can be tighter?
> And the reason I ask is cuz I think I remember the Bridge Ry was signalled for 90 second
> headway. But I don't remember for what speed. Instead of cash, SP[IER] pledged the cars
> for the cost of the [ ATS/cab?] signals, and the cars thus went to the Bridge Authority
> upon abandonment by IER service.
> thanks
> regards
> Ed



Yes, I did mean two minutes per mile -thanks for the correction. And yes, attainable headway is a function of design speed, but not a linear one, nor a pure one.

Yes, the Bay Bridge railway was designed for 90 second headway at 35mph max; the limiting factor being a station stop at Yerba Buena. But when that was skipped, they regularly attained as tight as 62 seconds between trains. That was possible because the tracks fanned out to multiple tracks or platforms at both ends. But if a stop was made on the island between those track fan-outs, the extra time in the Yerba Buena block wrecked that.

To my knowledge, no one has ever managed better than aprox 90secs between trains through an individual platform track. Not even in Sydney Australia, where they do that all day long. And not even with CBTC or other fancy new "moving block" systems - not even theoretically - 86 secs being the best theoretical CBTC number I've ever heard of, and that turned out to be by fudging certain vehicle performance numbers.

Most studies I've done seem to show the best headway numbers are attained at a schedule speed of between 25 and 35 mph. The exact number seems to vary somewhat, depending the most on acceleration and braking capabilities of the vehicles themselves, which are non linear in their effect. But whatever those capabilities are given as, the lower apex of the schedule speed vs track capacity curve, seems to always fall near 30mph.

This occurs because the time it takes for a train to enter a block and traverse the distance to where the 2nd block is cleared, is almost linear with speed. But the required braking distance, and hence block length, goes up by the square with speed. Thus the higher the planned speed, the longer is the distance (by the square) that must be traversed at a linear increase in speed.


But in the case at hand (single track over the GG Bridge), this rule ends up overshadowed by another consideration; loading limitations on the bridge. Despite the use of an optimum speed, headway is still limited by the bridge loading limit, permitting only one train on the bridge at a time.

The use of this reduced speed in my calculation was not intended to optimize headway, but to limit dynamic loading that might lead to undesirable harmonics in the bridge structure. I believe that was a contributing reason for this speed limit on the bay bridge as well.

The whole exercise was intended to see if the resulting loss of track capacity caused by these expected bridge loading restrictions, would still permit a viable public service over the bridge. While these GGB limitations will not permit the BART Transbay Tube's capacity of 21,000 seats per hour in each direction (could have been 28000 per hour, but that's another post), they will still allow as much as 5000 per hour in the dominant direction. Plenty enough for a relatively small population to be viably served. And still doubling the current people capacity of the bridge.

Hope that helps.