I've been pondering about the extent to which extent I can implicate myself in the joint effort of modelling travel times for the HFR route and I believe that I will draw the line by taking the model I developed for my
Master Thesis, apply it to the HFR route on the existing ROWs route and then hand the file over to you to play around with whatever realignments or bypasses you can think of.
However, at every step, I have to be transparent about where my assumptions come from (e.g. from my Thesis rather than anything I might or might not have seen at work), which means I need to first explain to you how I arrived to the adapted model and I'll loosely follow the structure I used in my Thesis:
- Parameters
- Train
- Superelevation
- Data
- Route
- Curves
- Modelling
- Speed limits
- Uniform acceleration
- Fixed blocks vs. variable blocks
- Model Solving
- Ignoring s-curves
- Respecting s-curves
Okay, shall we?
1. Parameters
1.1 Train
The only practical way to model train running times is to assume uniform acceleration, by which only two parameter determine a train's capabilities to accelerate and decelerate (one parameter for each) along its route, which I explained in all detail in Section 6.2.
As you could also read in Section 5.3, I selected four different train types for the Toronto-Kitchener service I was modelling:
View attachment 270743
Source:
my Master Thesis (p. 60)
Needless to say, that the "Inter-City" train is the most appropriate train profile as the closest equivalent to the Siemens trains which would serve the HFR route.
1.2 Superelevation
As I explained in Subsection 5.7.2, I identified that the maximum allowable total superelevation (note that this is the sum of
balanced and
unbalanced superelevation) under FRA rules is 10 inches, but opted to only assume the same 5 inches which Caltrain's host railways were willing to accept for its commuter rail network. I found an
interesting article (on p. 24) about Brightline in which they mention that its host railroad's tracks (i.e. those of FEC) were banked by 2 inches of actual banking (i.e. balanced superelevation), which suggests that the 3 inches of "cant deficiency" (i.e. unbalanced superelevation) Paul has mentioned are an industry standard. More interestingly, it mentions that the actual banking along the shared segments was increased to 5 inches, which presumably translates to a total superelevation of 8 inches. Given that a passenger railroad was able to obtain 5 inches of banking from its host railroad, it appears reasonable to assume that a passenger railroad sharing
its own tracks with infrequent freight trains could at least impose the same banking onto its curves. Therefore, I will assume a total superelevation of 8 inches for modelling the HFR route.
Unfortunately, "s-curves" (e.g. a right-curve directly leading into a left-curve) pose a problem here: the more banking is applied to the curves, the earlier the banking has to start so that the target value has been achieved
before the train enters into the curve (and the same has to be reversed at the end to the curve until the tracks are horizontally levelled). I will therefore limit the total superelevation to 5 inches for any adjacent curves which bend in opposite directions.
The last point actually brings me to a remark towards the many friends of tilting trains here: the only thing what a titling train does is increasing the cant deficiency by adding an additional superelevation to the banking which was already applied to the route (thus offsetting part of the underbalance which results from the centrifugal forces at the speed at which the train travels around the corner. However, in the context of s-curves a tilting train which tilts with an additional 2 inches (to throw a number around) over a curve with a banking of 5 inches has the same total superelevation (i.e. banking of tracks plus permittable cant deficiency plus the banking of the train, thus: 5+2+3=10 inches) as a conventional train train operating over a curve with a banking of 7 inches and thus requires the same distance to become horizontally levelled without passengers becoming uncomfortable. Therefore, even if an FRA-compliant non-electric tilting train design was available for the North American market (I'm not aware of any), it would not allow to run faster around s-curves than the non-tilting train which is currently in production for VIA...
2. Data
2.1 Route
I extracted the routing from the excellent Ontario Railway Map Collection and only modified the relevant lines to cut them as required (and to make them meet each other at Agincourt). The only line I actually had to draw was the bypass northwest of Smiths Falls, for which I simply placed a circle with a radius of 3000 meters (i.e. sufficient to allow a maximum speed of 110 mph even with a total superelevation of only 2 inches, see next section), which touched the lines extended from the Smiths Falls and Belleville Subdivisions:
View attachment 270752
The result is the following route:
View attachment 270944
2.2 Curves
Let's move on to the tricky part, the curves: using the only perk of Google Earth Pro about which I care (i.e. the circle drawing tool), I have measured every single curve I could spot (by drawing tangent lines between those curves I could spot) - and believe me, there are a lot! Long story short, I identified 270 curves along the alignment, of which 229 were located on the Havelock Subdivision (thus 85%, despite only accounting for only 73% of the total distance:
View attachment 270945
No less surprising, the most Eastern segment of the Havelock Subdivision (i.e. between Tweed and Glen Tay) has 8 times as many curves (per 100 km) as the Smiths Falls Subdivision:
View attachment 270943
Before I continue with determining the speed limits, I'll give you my
.kmz file and some time to explore the curves I've identified and to find any curves I might have missed. Also, please let me know if you have any questions so far or struggle to see where I derived my assumptions from! As I said at the beginning, full transparency and exclusive dependence on publicly accessible sources is the only way for me to help you with modelling the HFR route...