why are we talking monorail the set form of transport has been fixed

If you don't want to pay enough attention to the discussion to even understand that much, that's cool too.

It originated as an idea for a more efficient way to spend the $10 billion that a second harbour tunnel is rumoured to cost. It then proceeded more along the lines of metros. The areas discussed have been the northern beaches, Parramatta-CBD and Parramatta-Epping. Very little to do with the NWRL, but still completely on topic.

It originated as an idea for a more efficient way to spend the $10 billion that a second harbour tunnel is rumoured to cost. It then proceeded more along the lines of metros. The areas discussed have been the northern beaches, Parramatta-CBD and Parramatta-Epping. Very little to do with the NWRL, but still completely on topic.

Are you kidding?  A NWRL metro thread discussing a Northern Beaches monorail?  It's barely on the right website much less the right thread!

For mine, "a more efficient way to spend the $10 billion that a second harbour tunnel" is a very low bar for any proposal.  

That said, and this isn't really meant to as derogatory as the previous two comments: I think a monorail - almost anywhere - fails the "what problem are we solving here?" test.  I think that's a much higher bar, because I think the NWRL project also fails to pass that test too.

Are you kidding?  A NWRL metro thread discussing a Northern Beaches monorail?  It's barely on the right website much less the right thread!

Because clearly discussing an elevated metro (in the form of a monorail) and a second harbour crossing in a thread labelled "metro/harbour crossing" is very obviously in the wrong place. Yep. Sure. You got me.

NWRL hasn't been most people's definition of metro since they threw that metrolink proposal out. You know, that northwest/west/southeast/lowernorthshore stuff.

I think the NWRL project also fails to pass that test too.

I agree, but saying so in Sydney will be shouted down.

...Accel/decel rate = 1m/s^2
...
I've done these same calculations for a few existing metro/monorail systems as well, just to check that it was reasonably accurate. It comes out consistently 1-2 minutes under the correct total time for Copenhagen metro and Tokyo monorail (30s dwell time each), Osaka monorail (60s dwell time) and the Sao Paulo monorail (with a 90s dwell time). Admittedly this is assuming minimal sharp corners for all those systems, and the only one I can verify for that is Copenhagen, but I think that's a fairly safe assumption.

So going by all this, I expect that the monorail in Sao Paulo has a 90 second dwell time for some reason. I have no idea why, but there you go. That sort of time is also pretty consistent with several of the other metro lines they have there, so it's plausible.

Having spent the last few days re-levelling my backyard from 6% to 6°, some more thinking on this.  If you look at the Bombardier page for the São Paulo it mentions a "fully equipped" capacity of 48000 people per hour per day (fully equipped is in quotes this time because it is what the manufacturer says, not because I have an irrational bias against Bombardier).  Given the units I assume that this is specified past a peak loading point on the system, not in terms of total trips along the length of the system.

Based on Bombardier published specifications this appears to be based on the system ultimately being configured with eight car sets running at 75 second intervals (i.e. every 75 seconds an eight car set turns up with 1000 people on board).  That's not going to work with a dwell time of 90 seconds, unless you've got bifurcated platforms or similar - the switching at elevation associated with those would not be pretty and it would be nasty to retrofit.  

Perhaps they are planning on dwell time reducing in the future from what ever nominal figure they have now, but I think it would be a brave transport planner that assumed dwell time reduced as utilisation increases.

Even 60 seconds is cutting it tight - it only then gives you 15 seconds of cycle time to accelerate away, wait for vehicle safety clearance and then deaccelerate the next set in.  Something like 30 seconds dwell is probably a reasonable component of the total cycle time.  That suggests that you are back to looking at in-transit dynamics explaining the total travel time.

In terms of system balance, it also doesn't make sense to me to have a vehicle that belts in and out of stations at an acceleration that is at the upper end of what is comfortable for standees, only to then sit around for 90 seconds to wait for people to step a metre or two through some generously proportioned doors.

Having spent the last few days re-levelling my backyard from 6% to 6°, some more thinking on this.  If you look at the Bombardier page for the São Paulo it mentions a "fully equipped" capacity of 48000 people per hour per day (fully equipped is in quotes this time because it is what the manufacturer says, not because I have an irrational bias against Bombardier).  Given the units I assume that this is specified past a peak loading point on the system, not in terms of total trips along the length of the system.

Based on Bombardier published specifications this appears to be based on the system ultimately being configured with eight car sets running at 75 second intervals

Perhaps 48kPAX/hr is in both directions?  => a 150sec headway in each direction.

Perhaps 48kPAX/hr is in both directions?  => a 150sec headway in each direction.

No - note stupid typo on my part - their docs explicitly state 48000 people per hour per direction, not per day as I wrote.

No - note stupid typo on my part - their docs explicitly state 48000 people per hour per direction, not per day as I wrote.

So it is (having just checked), using a 75 second headway or 48 tph.  A "safe" stopping time for 1m/s^2 deceleration from 80kph is ~45 seconds, leaving a 30 sec dwell, so I suppose it's possible.  That's with a substantial reduction in safety vs "real" rail systems.  Safety to Aussie standards would require a top speed of less than 40kph when operating at these densities.

A dwell of 30 seconds is probably possible too, given the door ratio.  7 x 36m^2 of standing space, so ~250m^2 @ 4/m^2 is 1000 PAX per train, so that makes 48kpax/hr.  They are ordering enough trains for at most 36tph.  

1.6m doors are a bit tight, but it's still 2 channels per door, 4 per car or 1:25PAX.  1000PAX/train and a 30sec dwell are probably not possible simultaneously, but it's in the ballpark.

If you look at the Bombardier page for the São Paulo it mentions a "fully equipped" capacity of 48000 people per hour per day

...

Based on Bombardier published specifications this appears to be based on the system ultimately being configured with eight car sets running at 75 second intervals (i.e. every 75 seconds an eight car set turns up with 1000 people on board).  That's not going to work with a dwell time of 90 seconds, unless you've got bifurcated platforms or similar - the switching at elevation associated with those would not be pretty and it would be nasty to retrofit.  

Now the weird thing here is that the monorail in Sao Paulo is 7 cars, not 8. Also, at the usually quoted 4 pax/m^2, even with 8 cars and 48 tph you can't cram 48000 pphpd into it. Something strange is going on there.

So it is (having just checked), using a 75 second headway or 48 tph. A "safe" stopping time for 1m/s^2 deceleration from 80kph is ~45 seconds, leaving a 30 sec dwell, so I suppose it's possible. That's with a substantial reduction in safety vs "real" rail systems. Safety to Aussie standards would require a top speed of less than 40kph when operating at these densities.

Since you've just checked, you won't mind providing a source on that, right? The physics of what you're saying makes no sense, so I'm interested in the justifications for such safety standards.

7 x 36m^2 of standing space, so ~250m^2 @ 4/m^2 is 1000 PAX per train, so that makes 48kpax/hr

No. Specifications for 4/m^2 are 356 for a 4 car train. That gives about 623 for 7 cars, although that's still not quite correct because it doesn't take end/middle car differences into account.

Now the weird thing here is that the monorail in Sao Paulo is 7 cars, not 8. Also, at the usually quoted 4 pax/m^2, even with 8 cars and 48 tph you can't cram 48000 pphpd into it. Something strange is going on there.

My assumption (but not conclusions) were incorrect.  The quoted hourly capacity was after the system was "fully equipped", which I took to be additional complete sets plus intermediate cars to bring existing sets to 8 cars, because that was the supposed maximum car count per set for the generic system (assumes that platforms etc were built in anticipation of 8 car sets).

Specifications that I found later show indicate the capacity is based on 1000 people per seven car set on a 6 people per square metre (presumably "standees per area available for standing" basis) including 122 seated per set.

Anyway, they certainly are not planning on having 90 second dwell times!

Specifications that I found later show indicate the capacity is based on 1000 people per seven car set on a 6 people per square metre (presumably "standees per area available for standing" basis) including 122 seated per set.

Anyway, they certainly are not planning on having 90 second dwell times!

Which then implies that something unknown is going on, because 50 minutes total trip time, 75 second headways and 80km/h top speed does not add up for that route.

Which then implies that something unknown is going on, because 50 minutes total trip time, 75 second headways and 80km/h top speed does not add up for that route.

Not if the maximum speed is not reached because of a) a combination of an average acceleration that is less than what you are assuming and b) an inability for sets to run at that maximum speed because there is insufficient distance to the set in advance of it.

Not if the maximum speed is not reached because of a) a combination of an average acceleration that is less than what you are assuming and b) an inability for sets to run at that maximum speed because there is insufficient distance to the set in advance of it.

Except neither of those things make sense. Inability to maintain acceleration or reach top speed under a passenger load of 4-6/m^2 with those inter-station distances would seem to imply manufacturer dishonesty, and the physics of it should mean there is enough room for top speed operation with 75s headways and 30s dwell times.

Now the weird thing here is that the monorail in Sao Paulo is 7 cars, not 8. Also, at the usually quoted 4 pax/m^2, even with 8 cars and 48 tph you can't cram 48000 pphpd into it. Something strange is going on there.

Since you've just checked, you won't mind providing a source on that, right? The physics of what you're saying makes no sense, so I'm interested in the justifications for such safety standards.

No. Specifications for 4/m^2 are 356 for a 4 car train. That gives about 623 for 7 cars, although that's still not quite correct because it doesn't take end/middle car differences into account.

It adds up if there are no seats.  11m x 3m x 7 cars x 4PAX/m^2 = 924 ~= 1000 PAX/train.

The physics is very very simple (to the point it's probably not correct enough for these purposes).  Calculating Stopping time using v=at where a=-1 & v = 80kph = 22.2m/s = 22.2s.  A "safe" separation in NSW is (at least) twice that, so 44.4s, or near enough to 45sec.  Actually, to split hairs I should add the 3.6 sec it takes an 80m train to pass a point at 80kph.

I wish I could give you a link for this, because all the signalling standards used to be published on the safety authority's web site, but they made a decision make all of that "need to know", which probably says something about what they might be planning.  In any case, (and this is from memory so I hope someone can point me to a link confirming this), NSW standards are/were that signals must be as stop far enough back so that a train passing the signal at stop (SPAD) travelling at the maximum allowable line speed can come safely to a complete stop.

To avoid a SPAD the trailing train needs to start decelerating at the absolute latest a full stopping distance before a signal at stop, and that by definition must be at least one full stopping distance behind the first train.  Ignoring driver reaction time, the imprecision of block signalling and traverse time of the train length (the first two are negligable with fully automated moving block signalling and train ops), that means 2 x stopping distance is the absolute *minimum* allowable separation.

There are some good formulas for this in Wikipedia which should be simple enough for, I'll have a hunt for them and post what I find.

There are some good formulas for this in Wikipedia which should be simple enough for, I'll have a hunt for them and post what I find.

This is what I was thinking of.

The physics is very very simple (to the point it's probably not correct enough for these purposes).  Calculating Stopping time using v=at where a=-1 & v = 80kph = 22.2m/s = 22.2s.  A "safe" separation in NSW is (at least) twice that, so 44.4s, or near enough to 45sec.  Actually, to split hairs I should add the 3.6 sec it takes an 80m train to pass a point at 80kph.

I wish I could give you a link for this, because all the signalling standards used to be published on the safety authority's web site, but they made a decision make all of that "need to know", which probably says something about what they might be planning.  In any case, (and this is from memory so I hope someone can point me to a link confirming this), NSW standards are/were that signals must be as stop far enough back so that a train passing the signal at stop (SPAD) travelling at the maximum allowable line speed can come safely to a complete stop.

To avoid a SPAD the trailing train needs to start decelerating at the absolute latest a full stopping distance before a signal at stop, and that by definition must be at least one full stopping distance behind the first train.  Ignoring driver reaction time, the imprecision of block signalling and traverse time of the train length (the first two are negligable with fully automated moving block signalling and train ops), that means 2 x stopping distance is the absolute *minimum* allowable separation.

Ah, minimum separation rather than stopping time (the phrase you used before), that makes more sense. Twice the minimum stopping time is what I would have guessed as the minimum safe separation. Good to know.

There are just a few things I'd like to add. These monorails are designed to be fully automated as a means of obtaining these extremely small headways. Not sure about what sort of signalling they're meant to use. The other main thing is that the service braking rate is not necessarily the emergency braking rate. Bombardier doesn't have these specs freely available to my knowledge, but Hitachi for example has -1.11m/s^2 and -1.25m/s^2 respectively. Such a minor difference could make up for the traversal time of the train length.

The part you said before that I really found strange was that such densities would require top speeds of under 40km/h to comply with Australian standards. Your clarifications don't really seem to support that, unless that was stated assuming that drivers and block signalling were involved.

Ah, minimum separation rather than stopping time (the phrase you used before), that makes more sense. Twice the minimum stopping time is what I would have guessed as the minimum safe separation. Good to know.

...

The part you said before that I really found strange was that such densities would require top speeds of under 40km/h to comply with Australian standards. Your clarifications don't really seem to support that, unless that was stated assuming that drivers and block signalling were involved.

You're right, I think I stuffed up and transposed stopping distance/time and minimum separation in my head before posting that comment about 40kph.

BTW, with 3 phase block signalling (we actually have 5 phase on CityRail) the absolute minimum achievable separation is effectively 4 stopping lengths.  That's because the trailing train "has" (AFAIK there are no hard an fast quantitative rules on this yet) to decelerate prior to passing a signal at caution (this adds 1), and even 3 stopping lengths is only right when the trains are optimally positioned relative to the blocks.  The separation will vary between being 100% optimal for block placement, and 100% non-optimal regarding block placement, which means you need to add and extra block, effectively another stopping distance.

The other thing you need to consider is these stopping distances need to be calculated based on the fleet's worst performing vehicles in the worst (reasonably) possible conditions ie, wet/lubricated braking surfaces, fully loaded vehicles at the wrong end of their maintenance cycle.

Except neither of those things make sense. Inability to maintain acceleration or reach top speed under a passenger load of 4-6/m^2 with those inter-station distances would seem to imply manufacturer dishonesty, and the physics of it should mean there is enough room for top speed operation with 75s headways and 30s dwell times.

I don't think that's what DTMW is talking about.

I'm no mechanical engineer but for what it's worth:  Acceleration is not constant, *power* is constant, which is E/t (rate of energy consumption).  And because Energy is half mass velocity *squared*, you need more energy to maintain a constant acceleration as speed increases.  But as power is the constant, acceleration tails off as speed increases.


E=1/2mv^2
v(t)=sqrt(2Pt/m)
Differentiate with respect to time to get
Acceleration a(t) = sqrt(P/2m) / sqrt(t)  (I think).

This is obviously not a complete description, because at t=0, acceleration is infinite, and there is no maximum speed.  At the lower end you need to consider the efficiency of the motors at low revs, adhesion (apply too much power and you spin the wheels rather than propel the vehicle forward) and at the upper end wind and rolling resistance.  

Because of all this, acceleration is not a constant with respect to velocity.  That's just a convenient assumption to make high school physics possible with simple equations and no calculus.

Yes, something like that.  As speed increases I expect (I don't know, because the Innovia 300 monorail track in my backyard got damaged while I was re-levelling it) that the acceleration is only the initial acceleration (or acceleration at lower speeds), at higher speeds traction power will be limiting.  On top of the kinetic energy consideration, losses typically rise with velocity squared.  I don't expect a manufacturer to kit out the mechanicals and electricals of a system such that it can do that design acceleration at speeds approaching its maximum.

I have a route simulation for a 30 second dwell time for multiple vehicles running on 75 second headways that gets to ~40 minutes transit time.  Add a minute or two for people to climb up and down stairs, chuck in a lateral or vertical curve or two that stop you running at 80 km·h-1 max, vary the station spacing a bit and you'd get to 50 minutes transit time without forcing it too much.



[In terms of derivation, if you want to come at it from kinetic energy point of view (I think this is effectively reversing the definition of kinetic energy):

 E = 1/2 . m . v^2

Ignoring losses (all traction power goes into kinetic energy):

 P = dE/dt = d/dt (1/2 . m . v^2)

If the driver has remembered to close the doors, then m is constant with respect to time.  v is (hopefully) a function of time though.

 P = 1/2 . m . d/t (v^2)

Chain rule...

 P = 1/2 . m . d/dv (v^2) . dv/dt

   = 1/2 . m . 2 . v .dv/dt

dv/dt is acceleration.

 P = m . v . a

Simpler approach is to consider the unit increment of work, force by distance (a dot product, but hopefully the monorail doesn't vary too far off its path), noting that distance increment is velocity by time increment and Newton sorted out the force to acceleration thing a while back (ignoring losses - traction force is only used for acceleration along the path).

 dW = F . dx = F . v . dt = m . a . v . dt

Power is dW/dt, so divide through by dt and you've got the same outcome.]

And this all proves they should be making the NWRL tunnels suit double deckers.

I think a monorail - almost anywhere - fails the "what problem are we solving here?" test.  I think that's a much higher bar, because I think the NWRL project also fails to pass that test too.

The NWRL is a glorified Monorail that won't be compatible with the rest of the network. Given the excellent CDC bus coverage of the north west it's simply a double up of services in the area.

This is about future planning. I guess the next stage is the easy bit, getting to St Leonards.
Some things are obvious-
All trains will be identical so platform doors can be taken as a given
Trains without drivers are old hat, they have been operating all over the world for many decades, Victoria Line (the man in the front does not operate the train) and Docklands in London, Vancouver Skytrain, Paris Metro and dozens more. Train frequencies can be less than 2 minutes through the core and dwell times are critical hence the current DD stock is not suitable.
There is no way the two systems can share tracks, when the link through the CBD is in place, the Bankstown line will be Metro only.
There will be no direct Hornsby via Macquarie Park services, change at Epping.
Increasing the bore size for tunnelling is not insignificant as suggested, any reduction is worth a lot of money, an ECRL size bore is about twice the area of a Metro bore.

The video is interesting, anybody know why two pantographs per car? No platform screen doors either.

With the ECRL, Epping - Hornsby has an improved 15 minute service.

The Strathfield-Epping section still has the old 30 minute service, off peak.

AFAIK, this is partly to allow for freight.

Once the NSFC is built, will Strathfield-Epping improve to a 15 minute service?

With the ECRL, Epping - Hornsby has an improved 15 minute service.

The Strathfield-Epping section still has the old 30 minute service, off peak.

AFAIK, this is partly to allow for freight.

Once the NSFC is built, will Strathfield-Epping improve to a 15 minute service?

Also to do with train balancing. You want to run 15min, then they need to go somewhere once past the City. Also more buses running to the city south of Epping.

Note that platform doors can be used even with manually driven trains, and can be designed to be compatible with all variations in door arrangements, such a system is used on the Madrid metro. And DD rolling stock may actually dwell faster at busy stations with Olympic park style platforms than a single decker could at a similarly busy station with a platform on only one side.

Note that platform doors can be used even with manually driven trains,

I would think you would need some automated system for stopping on the mark though.