Speed that maximizes throughput of a track

I believe many earlier suggestions are correct, but I think we've mentioned the most obvious. Some freight trains today are almost two miles long - one would think that statistic would determine the shortest block length. I can't ever foresee a block length ever being shorter than the length of the longest train....

electricron wrote:I believe many earlier suggestions are correct, but I think we've mentioned the most obvious. Some freight trains today are almost two miles long - one would think that statistic would determine the shortest block length. I can't ever foresee a block length ever being shorter than the length of the longest train....

the block lenght is not determined by train lenght but by braking distance under worse circumstances at max speed for any train.
even if a train was 10 miles long it can occupy multiple blocks , you still have the normal block signal sequence behind last car.

Therefore, with a two mile long freight train that takes a mile to stop, it'll need at least three miles of block clearances (1 mile before and 2 miles for its length); no matter how long each block is? If all the blocks are the same and I doubt they are, assuming 1/4 mile blocks, that train requires 12 blocks?
I'm assuming a following train is assigned the block clearances behind the original train....

Of course, the shorter the block's length, the more blocks you'll have, and the more expensive the signal system is.

What is the standard block length in New Jersey for the NEC?

electricron wrote:Therefore, with a two mile long freight train that takes a mile to stop, it'll need at least three miles of block clearances (1 mile before and 2 miles for its length); no matter how long each block is? If all the blocks are the same and I doubt they are, assuming 1/4 mile blocks, that train requires 12 blocks?
I'm assuming a following train is assigned the block clearances behind the original train....

Of course, the shorter the block's length, the more blocks you'll have, and the more expensive the signal system is.

What is the standard block length in New Jersey for the NEC?

The implications of long block lengths are significant. Unless you allow stop and proceed at intermediate signals you automatically add 2 miles to the space each train occupies Consider the following parameters;

2-mile signal blocks (10,560 ft)
9800ft freight trains
gently undulating terrain causing train speed to vary between 56 and 60 mph for both trains
typical 3 signal indication sequence (GYR)
Requirement to have speed below 30 mph after passing Yellow indication, expecting to stop at next signal.
Signal may be readable only at 600 ft distance.

At a minimum the two trains have 8 track miles tied up. Almost continually 12 miles tied up (while crossing from one block into another which will be most of the time when moving. Adding another indication doesn't really help, as it pushes the tail back distance for running at track speed further behind.


The NEC in New Jersey likely has less than 2 mile block lengths, but they also have more sophisticated signalling systems.


If you really want to understand railway control, the implications of train speed, block lengths, signalling systems, in a format intelligible to non-railroaders, though still rigorous, see this website for books on the subject;

http://www.vtd.net/index.html

The best current University to study Railway Management right now.

The Friedrich List Institute of Transportation and Traffic Science, Dresden University of Technology - Dresden, Germany
http://en.wikipedia.org/wiki/Dresden_Un ... Technology

No US University offers that rigorous a program, at least not yet.

electricron wrote:Therefore, with a two mile long freight train that takes a mile to stop, it'll need at least three miles of block clearances (1 mile before and 2 miles for its length); no matter how long each block is? If all the blocks are the same and I doubt they are, assuming 1/4 mile blocks, that train requires 12 blocks?

The NYC subway system is a good example of a system where the block length is substantially shorter than one train length.

I don't know if a block is shorter than a stopping distance (what DutchRailNut more precisely calls "braking distance under worse circumstances at max speed for any train", but I suspect it is. I do know that between stations, you can see multiple block signals showing yellow and, in the distance, a red signal.

This system is probably a good example of a system which is, or at least needs to be, optimized for maximum throughput (i.e., trains per hour.) During rush hour, many of the lines are at (or over?) capacity.

amm in ny wrote:I'm not sure why everyone keeps throwing in "block lengths" and "improved signaling."

David Benton wrote:I'm only guessing here but I would say block lenght affects the time it takes to get the info to the following train .

Correct ... If one sets the signals based on stopping distance large blocks keeps the train behind further back than it needs to be.

Signalling that conveys information more than two blocks ahead can be used to slow the following train and reduce the stopping distance allowing the following train to approach the lead train closer and perhaps avoid a stop if the lead train is able to get moving again.

electricron wrote:I can't ever foresee a block length ever being shorter than the length of the longest train....

I've seen it. It shouldn't be an issue as long as the appropriate warning is given to following trains. What difference does it make if a train occupies one block or 10 as long as the signals convey to the following train where it needs to stop to avoid collision with the train ahead?

amm in ny wrote:

JayBee wrote:On the French LGV (High Speed Line) Jonction which acts as a belt line around the east side of Paris, peak traffic in each direction of a double track railway is 26 trains per hour, or one train every 2' 20"....Stopping distance for a French TGV or German ICE from 300 kph (186mph) is about 9 kilometers (5.59 miles),...

You don't say what you are trying to show by giving these figures, but I am grateful to have numbers that are used in real life. Anyway, I thought I'd see how the train spacing compares with the time to come to a complete stop (9 km)

300 kph = 1/12 km / sec.
2' 20"= 140 sec / train = ~12 km train spacing.

This looks like one stopping distance, with a safety factor thrown in. It also sounds like they are getting close to the theoretical maximum capacity of one track.

Of course, if the trains ran only 150 kph, the stopping distance would only be 2.25 km. Adding 1.5 km or so for safety, you could run one train every 90-100 seconds. This is what I meant by "increased speed leads to decreased throughput."

It's not just physics, we are dealing with people here, and people don't behave entirely predictably.

40 to 45 mph is the rule of thumb for the maximum capacity of a limited-access highway. The primary reason for that is human behavior. As long as traffic is moving at 45 mph or more drivers brake gently and are able to maintain a nearly constant speed and nearly constant distance with the car ahead. But when traffic slows to less than 45 mph, drivers are prone to over-react and brake harder, sending a shockwave of brakelights down the highway behind them. The whole roadway comes to a standstill.

Similarly, the minimum headway between trains is around 2-1/2 minutes. Start with that and work backwards to determine the maximum speed. The reason for this is that somewhere along the line, the train has to stop at a station. Now the typical dwell time may be only about 45 seconds, but it may be shorter or longer depending on passenger behavior. Passengers alighting from the train have to wait for the train to come to a complete stop, for the doors to open and for all of the passengers in front of them to get off first. Passengers boarding have to walk half a car length to the nearest door, wait for the alighting passengers to get off, and then board the train in an orderly fashion. After all the passengers have boarded, the conductor gives the signal. Another 3 seconds are allowed before the doors close and only once the doors are closed can the train proceed. Large crowds, unfamiliar riders, or slow walkers delay the process. At less than about 2-1/2 minutes headway, all it takes is one old lady with a walker to cause a domino effect down the line that stops the whole system.

jstolberg wrote: It's not just physics, we are dealing with people here, and people don't behave entirely predictably.

40 to 45 mph is the rule of thumb for the maximum capacity of a limited-access highway. The primary reason for that is human behavior. As long as traffic is moving at 45 mph or more drivers brake gently and are able to maintain a nearly constant speed and nearly constant distance with the car ahead. But when traffic slows to less than 45 mph, drivers are prone to over-react and brake harder, sending a shockwave of brakelights down the highway behind them. The whole roadway comes to a standstill.

Above 125mph the European don't believe in a color light signalling system and don't depend on humans. To see the German LZB system, and for an explaination of its variants see this well written Wikipedia article.

http://en.wikipedia.org/wiki/Linienzugbeeinflussung

jstolberg wrote:40 to 45 mph is the rule of thumb for the maximum capacity of a limited-access highway. The primary reason for that is human behavior. As long as traffic is moving at 45 mph or more drivers brake gently and are able to maintain a nearly constant speed and nearly constant distance with the car ahead. But when traffic slows to less than 45 mph, drivers are prone to over-react and brake harder, sending a shockwave of brakelights down the highway behind them. The whole roadway comes to a standstill.

I don't see how this is relevant to trains. Trains normally are required to leave at least one full stopping distance between one another, whereas the recommended spacing for automobiles is simply one reaction time, and most people drive even closer than that. Trains operate according to rules, often enforced by signalling systems, that pretty much guarrantee that collisions cannot occur, whereas collisions are simply accepted as inevitable facts of life in automobile traffic. BTW, according to the people I know who model traffic flows, the shockwave phenomenon has more to do with traffic density than speed.

JayBee wrote:TGVs have four braking systems, Tread Brakes, Multi-Disc Brakes, Regenerative Brakes, and Eddy-current Brakes. The tread brakes are only used at low speeds, and the Eddy-current brakes are only used in an Emergency.

Tread brakes are used only on the powerheads, because Alstom couldn't fit disc brakes due to space constraints. They only cut in when the regeneratives are unavailable during air brake application (and to arrest the train during standstill), though.

The TGV does not have eddy current brakes. It doesn't have track brakes either, which does it no favors regarding our method of calculating braking power. That's why it's not allowed to do more than 155 kph (at best) with 160 kph being the general limit on non-LZB tracks in Germany. This is similar to the ICE3 which does indeed have eddy current brakes (the only train in the world to use them), but they are only used as operational brakes on the Cologne-Frankfurt and München-Nuremberg HSL. On a very restricted part of the conventional network, they only see use during an emergency brake application. Eddy current brakes are allowed on perhaps 10% of the network, which means a top speed on non-LZB non-eddy current tracks of 140kph for the ICE3.

JayBee wrote:What you model doesn't consider is signal block length which typically is 2-miles for North American freight railroads, but can easily be as short as half a kilometer in places on European High Speed lines, though one kilometer is standard.

Not on high speed lines, would be pointless there. The Hannover-Berlin HSL for example is divided into 4800 meter LZB signal blocks on perhaps half its length. Cologne-Frankfurt should be around 3000m, Hannover-Würzburg is between 1000 and 1500 meters. However on the non-HSL track between Offenburg and Basel, the shortest LZB signal blocks are 400 meters in "length". Makes sense there because that line is awfully crowded day and night with everything from ICEs to freighters.

JayBee wrote:Stopping distance for a French TGV or German ICE from 300 kph (186mph) is about 9 kilometers (5.59 miles), without using the Emergency brakes.

Sounds a bit too long to me, at least on a level track. May be true on certain parts of Cologne-Frankfurt, though.

AX-330 wrote:

JayBee wrote:Stopping distance for a French TGV or German ICE from 300 kph (186mph) is about 9 kilometers (5.59 miles), without using the Emergency brakes.

Sounds a bit too long to me, at least on a level track. May be true on certain parts of Cologne-Frankfurt, though.

Actual stopping distances vary a lot with conditions. (The problem with dead leaves on Metro-North tracks come to mind.) The "stopping distance" that's relevant to train spacing is

DutchRailnut wrote:[the maximum] braking distance under worse circumstances at max speed for any train.

To put it differently, if you were strapped to the front of a 300 km/hr train, and they decide to stop, and you knew there was a concrete wall across the track some distance ahead, how far away would it have to be for you to feel safe?

FWIW, according to my calculations, to stop from 300 km/hr in 9 km requires a constant deceleration of about 0.4 m/sec^2. (And 216 secs.)

amm in ny wrote:To put it differently, if you were strapped to the front of a 300 km/hr train, and they decide to stop, and you knew there was a concrete wall across the track some distance ahead, how far away would it have to be for you to feel safe?

Feel safe? 300km would do (although I could probably be convinced to feel safe about 30km). Be safe - that's where your math comes in.

I think of rollercoasters that are a lot safer than they feel. They are deliberately designed that way to add thrill but they still must be safe. Being safe in a 300km/hr trains is always being able to stop before contacting something ahead of you. Feeling safe is being able to stop before recognizing something ahead of you as a threat.

Its not about feel safe but about fail safe, the stopping distance is determined by whatever it takes to stop the worse stopping train, traveling the effected area.
if that happens to be a unit ballast or coal train the signal blocks will be long, or freight speed very low like on MNCR.
The railroad does not just take a number out of a hat, there numbers are set by certain tabels in certain government offices.

For purposes of mid speed and high speed rail, is there a way to determine what the practical maximum passenger speed on light, moderate, and heavy freight lines are? I know 90 mph is often cited by the freight industry as the practical maximum on shared track. But I'm guessing that's heavy freight. What's the freight volume like on the Chicago-St. Louis line now being upgraded for 110 mph? And don't forget that VIA runs up to 100 mph on CN's Quebec-Windsor corridor, though it's mostly a 90 mph maximum east of Montreal and west of Toronto.