[Platform 27]

For reasons that I find utterly terrifying, what I learned in high school physics has refused to ever leave my head. I can't say the same about a great many other things that would be of actual use to me on a daily basis.

Anyway, today marks a milestone, for I have been able to do something useful with that knowledge. Who knows how many decades will elapse until the next occasion?

Using every grade 10's favourite kinematics equations, I managed to derive a general formula that ought to approximate how much time a train adds to its schedule by making a stop, versus running straight through. Drumroll:

Δtstop = tdwell + (v/2)(1/a – 1/b)

where...

tdwell is how long, in seconds, the train remains stopped at the station between the moment it stops and the moment it starts again.
v is the normal continuous running speed of train, in m/s
a is the train's typical rate of acceleration, in m/s^2
b is the train's typical rate of braking, in m/s^2 (will be a negative number)

The formula assumes constant rates of acceleration and braking; I know the real mechanical engineers in the audience will tell me that in the real world you tend to see slight curves in acceleration rates on account of gear ratios and static friction and the like. The other caveat for the formula is that it assumes stations are spaced out far enough that the train in question actually does manage to speed all the way up to v before it begins braking for the next stop. Those aside, it should be a pretty good approximation.

 

[CDL.TO]

What I am missing is data on the length (in miles or kilometres) of existing railway lines that use electric propelled trains. I have a preference for EMUs, but a beggar cannot be a chooser at this time.

IE "How many miles from Heathrow to Paddington using Heathrow Connect? How many miles from Chicago to Michigan City using the South Shore Line?"

All the other data I need I can obtain form published schedules.

You're going to have an easier time finding data for EMUs than electric locos. There's also the whole problem of comparability. The lower weight of non-North American rolling stock makes a large difference in acceleration and braking time. Though you could do like-like comparisons, such as London Overgound's electrified NLL and their diesel GOBLIN.

For length, why don't you just use Google Earth or Google Maps and measure it?

 

[RedRocket191]

You're going to have an easier time finding data for EMUs than electric locos. There's also the whole problem of comparability. The lower weight of non-North American rolling stock makes a large difference in acceleration and braking time. Though you could do like-like comparisons, such as London Overgound's electrified NLL and their diesel GOBLIN.

My hope is to average out the results.

For length, why don't you just use Google Earth or Google Maps and measure it?

Last resort

Using the following:

• Metro North Harlem Line
• AMT Deux Montagnes Line
• Metro North Hudson Line
• Metro North New Haven Line
• Metro North New Canaan Branch
• SEPTA R2 Warminster
• SEPTA R3 Media/Elwyn
• SEPTA R3 West Trenton
• SEPTA R5 Paoli-Thorndale
• SEPTA R5 Lansdown-Doylestowne
• SEPTA R6 Cynwyd
• SEPTA R6 Norristown
• SEPTA R7 Trenton
• SEPTA R7 Chestnut Hill East
• SEPTA R8 Chestnut Hill West
• SEPTA R8 Fox Chase
• Metra Electric Line

You get a formula of y=20.997 ln(x) + 24.687 where y=average speed in km/h and x=avearge station spacing in km.

I want to refine this formula by adding more lines to the dataset. I have a complete dataset for Heathrow Connect and a few London Underground lines, but I don't think that subways will be comparable for this purpose.

 

[DavidJamesTO]

Electric Locos are quite rare. Most places just use EMUs. Off the top of my head:
- NJ transit
- Metro North uses dual-mode (though I don't think they use them in electric mode for stopping services)

MARC also uses electrics for some of their services to Washington, D.C. Union Station--as does SEPTA for 30th St and Suburban Stations in Philly and Long Island RR to Penn Station in NY. Some Swiss and German commuter services are electric push-pull trains, too.

 

[ShonTron]

Long Island RR is EMU, though third-rail.

The only electromotive-pulled electric railways in North America are Amtrak (standard Metroliner equipment, not Acela Express) Northeast Corridor, Empire Service (via hybrid diesel/third-rail, including the Maple Leaf Toronto-New York service) and the Keystone service; New Jersey Transit, MARC (the Penn Line which runs through Penn Station Baltimore to Union Station Washington from Delaware), and the Metro-North Harlem and North Hudson (New Haven is entirely EMU, though switches from third-rail to overhead in the Bronx before joining the NEC though New Rochelle and Connecticut).

I believe that CalTrain was looking at electric locomotives pulling Bombardier Bilevels and other commuter equipment, at least to start, so I thought that was a worthwhile link.

Canada had other locomotive-pulled electric systems into the 1990s, such as the Deux-Montagnes line before the 1995 upgrades, the CN Tumbler Subdivision in BC and the Inco Railway in Sudbury.

The former Kowloon-Canton Railway in Hong Kong might be a worthwhile alternative to look at as well.

 

[DavidJamesTO]

This is an EMU?

 

[Second_in_pie]

This is an EMU?

Doesn't look like it. If you look at it, there's a separate locomotive from what looks like regular Bi-Level cars.

 

[RedRocket191]

This is an EMU?

No, but this is:

http://goinglocoinyokohama.files.wordpress.com/2009/06/lirr10.jpg

515 is a dual mode loco.

 

[kettal]

Why shouldn't GO use third rail power? Especially on lines with no level crossing?

 

[ShonTron]

Snow, limited speeds, leaves on tracks. That's for starters.

The only third rail systems for railways (not so much subways, though many newer systems use overhead) are legacies - such as the lines leading out of South London station, Penn Station to Long Island and north on the Empire Service trains, etc. They also don't host heavy freight usage, which even some GO-owned lines might still see.

 

[drum118]

I agree that there is no need to have stops every km as there is nothing there now or 30 years from now to need a station in the first place. In many places you have industries there, but sadly no rail service to them.

I only see 6 locations where stations should be put in for the current west line. A couple requires major development.

Even looking at the east end, only a few stations will be needed on top of what there now.

Going up on the Milton line, 7 more stations.

Georgetown will need 7 more stations also.

I would never use 3rd rail. Overhead is the way to go as well being EMU's.

 

[RedRocket191]

I agree that there is no need to have stops every km as there is nothing there now or 30 years from now to need a station in the first place.

For the record, I'm not trying to say that we SHOULD put a stop every kilometre. I'm trying to find out how many stations CAN be added without slowing it down more than 2009 levels.

 

[vegeta_skyline]

Why shouldn't GO use third rail power? Especially on lines with no level crossing?

Every line has level crossings and many of them. (not including foreman, farmers or utility crossings)
Richmond Hill has the least with 6(2 of which are pedestrian only but have the same requirements as a road crossing) + 1 rail crossing
Lakeshore East has 9
Lakeshore West has 12
Milton has 14 (used to be 17 up until a year or two, thank you population explosion Milton)
Georgetown has 14 & 2 rail crossings
I'm not even going to get into how many Barrie has suffice to say it has more than all the above put together!
Stouffville has a lot as well with 32 (1 pedestrian)

It would cost billions to grade separate them all and there'll be many more to cross with expansion.

 

[drum118]

For the record, I'm not trying to say that we SHOULD put a stop every kilometre. I'm trying to find out how many stations CAN be added without slowing it down more than 2009 levels.

You should look at hop scotching also.

I have said there should be different type of service compare to what we have today.

1. Milk run that stops at every existing station and the new ones.
2. Hop scotching where you stop at every other one or 2.
3. Regular stops that exist today.
4. Mid express that runs from one station to Union
5. Express like there is today.
6. Long express-regular service where trains will run express to say Oakville and then regular service to the end.
7. Long haul that starts at the last current station and go beyond the current area of operation.

Depending on the type of service as well quality, some trains would be 3, 5, 7, 10, 12 cars long. This has an impact on acceleration and deceleration also.

 

[RedRocket191]

I'm not disagreeing that all those should be options, but the only way to do an apples to apples comparison is to compare milk-run to milk-run.