(Post continued from above)
First off, I have modelled the travel times for 5, 8 and 10 inches of total superelevation (i.e. actual and unbalanced superelevation combined) in three iterations for each:
- In my first set of calculations (called "Urban Sky I" in above table), I had ignored the problem of reversed curves ("s-curves").
- In my second set of calculations (called "Urban Sky II" in above table), I had tried to somewhat approximate the combined transition length of a reverse curve and then work out the maximum level of superelevation to maximum the speed allowed after respecting the requirements for transition lengths and tangent lengths.
- In my third set of calculations (called "Urban Sky III" in above table), I only measured the tangent track between the curved sections of reverse curves and then set the maximum speed so that the spiral lengths would not exceed the length of the tangent track (i.e. the "straight segment") in between the reversed curves.
Even though the second approach closer resembles in real-life, it is impossible to measure a spiral length with the tools available in Google Earth plus, as the radius of a transition curve changes from infinity (where the track starts curving) to the radius of the main part of the curve), as shown for a hypothetical spiral curve (with a radius 650 meters and a maximum allowable speed of 65 mph) below:
View attachment 277656
Source: own work
Note: tangent track sections are where the superelevation is zero and transition sections are where the radius and superelevation change.
Consequently, it was more practical to only measure the transition lengths and to arbitrarily set the superelevations (balanced and unbalanced) in a way that the resulting spirallengths would not exceed the transition lengths, which is why I set the superelevation values to a balanced (actual) superelevation of 5 inches and a cant deficiency (unbalanced superelevation) of 3 inches, because 5 inches of actual superelevation requires a minimum spiral length of 96 meters, while 3 inches of cant deficiency in combination of a maximum speed of 65 mph requires a mimimum spiral length of 97 meters.
I refer to Part 3 of my "
modelling travel times for the Havelock alignment" exercise if anyone struggles to make sense of the above, accompanied by the following excellent video by Gareth Dennis (a UK-based railway engineer which also teaches at university and an enthusiastic audience through his Youtube channel):
Long story short, I simulated travel times between 3:50 and 3:55 for 5 inches of total superelevation, between 3:12 and 3:19 for 8 inches of superelevation and between 2:59 and 3:06, which suggests that the (previously or currently) existing alignment of the Havelock route might at least theoretically allow a travel time of 3:15:
View attachment 277657
Compiled from: own calculations with geographical and track alignment data approximated with the help of Google Earth
We will of course need to add some more of the "real-world factors" you mention, but I will of course share my spreadsheet with my calculations with you and
@crs1026 in the next few days so that you can add a few more constraints and fix some of the shortcomings, such as:
- The acceleration and deceleration capabilities of the electrical trainset I had selected for my Master Thesis (and thus also for this exercise) may exaggerate the capabilities of VIAs future (fuel-operated) fleet
- Local speed limits (in addition to those imposed by track geometry) might apply when traversing built-up areas such as around Ottawa, Peterborough and Toronto
- Tracks shared with freight traffic might permit only lower levels of superelevation than those which will be dedicated to passenger trains
Afterwards, you will also be able to estimate how much realignments are needed to get the travel time back to 3:15...
You really have to get your head around the fundamentals of cost-benefit analysis, which is calculating the Net Present Value and dividing the incremental benefits of a project by its incremental costs, as the more you re-align the existing/former ROW, the less will be the incremental benefit of upgrading later to HSR (as it's most important component is "travel time saved"), while the incremental cost will be basically the same (as you will hardly be able to justify the extra expense to design HFR with a minimum radius in excess of 4 km, like what would be required for speeds of 300 km/h and more). At the same time, I would expect politicians in Kingston to change their attitude from supportive to hostile if they start to sense that HFR is making the creation of a HSR route serving their city less rather than more likely. The challenge is therefore to design HFR in a way that keeps the capital requirements (and thus the travel time savings) minimal, but opens up the avenue for a cost-effective upgrade towards HSR. Given that quite a few curves seem to already have a radius of 3000 meters (which would allow 155 mph or 249 km/h at a superelevation of 10 inches), designing any realignments required for HFR with the same radius could ensure that they can be eventually reused by HSR:
View attachment 277677
In the end, that's how HSR was built in Germany: upgrade existing alignments where they are straight enough to allow 200-250 km/h (an approach called "
Ausbaustrecke" and used for Hannover-Berlin, Hamburg-Berlin-Leipzig and Köln-Aachen) and build greenfield HSR alignments for 250-300 km/h (called "
Neubaustrecke") wherever existing alignments are too winding to achieve speeds which would be acceptable for HSR (e.g. Hannover-Würzburg, Köln-Frankfurt and Halle/Leipzig-Erfurt-Bamberg)...
I've actually done a research trip* to Miami as I was planning to include Brightline as a case study for my Master Thesis (which at that time had a scope which was orders of magnitude larger than the small subtopic I eventually retained as my research question), but if you look at the at the actual passenger counts and revenue streams they've actually generated while operating between Miami, Fort Lauderdale and West Palm Beach (operations have been suspended since March, for obvious reasons), then running such a commuter-distance service is hardly worth it. Also, Brightline limits itself to 110 mph on all segments which are within existing rail corridors (which is the same as what Brightline is doing) and only designs its greenfield alignment between Orlando and Cocoa for 125 mph...
* admittedly, I spent far more time at the beach and sampling fast food chains (my favorite:
Pollo Tropical) you can't find here in Quebec