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| Re: TA is obsessed with CBTC, and ''New'' tech for no reason. (579266) | |||
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Re: TA is obsessed with CBTC, and ''New'' tech for no reason. |
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Posted by Stephen Bauman on Sun Mar 2 05:58:59 2008, in response to Re: TA is obsessed with CBTC, and ''New'' tech for no reason., posted by Jeff H. on Sun Mar 2 01:54:40 2008. Now, I say it is continuous for two reasons. With ASC, your speed is continuously monitored and compared with the command. With wayside trips, your speed is based on X/T between two points, and could thus go far above the limit during part of your traversal.There is a track of length d. A train enters it going at speed v. Given that train has an acceleration of a, what is the maximum speed the train can attain on this length of track? Assume it takes time t to traverse this length of track. Then if the train is constantly accelerating, it will have an average velocity of: v + at/2 The distance traveled is: d = vt + ½at2 (1) or ½at2 + vt - d = 0 (2) solving for t we get: t = (-v ± √(v2 + 2ad))/a (3) The maximum speed is: vm = v + at (4) Substituting the value of t from (3) into (4) we get: vm = v + (-v ± √(v2 + 2ad)) or vm = √(v2 + 2ad) (5) Now, suppose we have a length of track that is D = nd long. Further suppose that d is the stopping distance for a train in emergency from speed vm and there are n timers at the beginning of each of the sections. Clearly, if the timers are set for a v = √(vm2 - 2ad) (6) then the velocity for the entire length D of the track will never exceed vm, from equation (5). That's what I meant by there being an analogy to the Nyquist Sampling Theorem with acceleration taking the place of frequency. I'm clearly viewing the wayside signals and block system as a sampled data system. I'd rather not get into a more detailed explanation involving z-transforms. I try to limit myself to high school math in my posts and quite frankly my z-transform knowledge is a bit rusty after 40 years. The other aspect of continuity is that when conditions change, the command changes instantly. You don't have to wait until the next signal for reception and enforcement. Let's separate reception and enforcement. Reception is easy. Operators are permitted to look ahead to the next wayside signal. I believe it is encouraged. Let's look at enforcement. When your leader pulls away, you get an upgrade mid-block. That's not a safety issue. Likewise, if a controlled signal is dropped in front of you, you can get a downgrade. Just how does that happen with the follower in mid-block after the follower has entered the block? A downgrade can occur at the next block boundary. A downgrade on the current block after the follower has entered it suggests that the leader has crossed an IJ in the direction going towards the follower. If that is the case and the leader has changed direction, no amount of speed control will help the follower. |
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