Two questions:
1) What's the weight of a Tesla battery?
Approximately ~500 kilograms -- only 1% the weight of a BiLevel coach (50,000kg per coach). Though the shielding will add some.
It's a question of how big a catenary-free hop we need to clear, with enough safety margin (more than a 5x factor) for long track blockages that includes winter heating for stranded passengers.. Realistically I'd say we need 5% of a coach weight to be battery (300 KWh per coach, plus shielding) to do a Hamiltion top with safety margin.
2) How long will a Tesla battery deliver to that maximum output? Even if the peak power is there, Zero to sixty in a small number seconds on a highway ramp is a relatively short burst of power, and therefore a different battery drain, than Run 8 to track speed (and maintain).
This question is already answered in bullet #10 -- continuous to depletion (no time limit) if overengineered to the point where there's no battery heating considerations. What will happen is parallelism which vastly reduces power requirements to -- where only a mere 5%-10% of battery max output can still out-horsepower the new Tier4 locos. That's all that is needed for revenue operation.
Does not have to be Tesla branded, but they are easy mathematically for napkin exercises. Mathematically, with the equivalent of about "36-Tesla-battery-equivalents" (about 3½ megawatt-hours).
True, it is not that simple -- but understanding parallel-vs-series -- the napkin math is within stone throw of a bilevel EMU battery train that likely will be manufactured in Europe in about 5 years from now.
Electricity torque is much higher at low end than gas/diesel, and you got the EMU traction.
For reference:
-- a Stadler KISS is about 6 megawatt max, 4 megawatt continuous, and it
accelerates a 6-coach at 1.1 m/s^2
-- The GO train locos
accelerate a 12-coach at only 0.33 m/s^2 (appeared to be full throttle, accelerated to 50kph in one trainset-length)
But you don't necessarily have to go max. You can simply accelerate slightly slower during catenary-free sections. Say at only ~2 megawatts or so, and for a whole 12-coach. Say 3000 HP. You can accelerate like a bat out of hell under catenary to Burlington, and just gently accelerate after your Aldershot/Hamilton dwell.
Mathematically to do a standard ~3000 HP acceleration (approximate output needed to out-accelerate a 12-coach noticeably faster than a diesel)
-- You'd only need to draw 80 kilowatts per Tesla-pack-equivalent if there were 36 Tesla-pack-equivalents spread throughout,
only 16% the max output of a typically sized Tesla-pack-equivalent battery capable of 500 kilowatts per Tesla-pack-equivalent module, at 36 modules per 12-coach trainset.
MATH: Theoretical 18 megawatts max, but only needing 2.2 megawatts (3000 HP) to accelerate faster than a GO train due to all-wheel traction
-- You'd only need to draw 22 kilowatts per Tesla-pack-equivalent (
only 4.4% the max output) if there were 100 Tesla-pack-equivalents per train.
MATH: Theoretical 50 megawatts max, but only needing 2.2 megawatts (3000 HP) to accelerate faster than a GO train due to all-wheel traction
Note: Figures are approximate.
Point proven: You'll still be accelerating faster than a diesel GO train at only a tiny fraction of the max output of the battery
You never use max output, for battery longevity. It was only merely to simply prove my point -- that excess safety margin is definiitely becoming available --- to out-accelerate diesel --
without needing to use remotely close to battery max output..
If we needed route extenders sooner than specs were available, we'd choose diesel dual modes instead until that happened anyway. It's a flex-choice, backwards compatible, not a corner-back-into'er like Hydrogen. No need to worry ourselves to death. Let's wait for Europe to put a bunch of catenary-recharged battery trains out, and mature them, release bilevel models, and then that'll definitely catch attention of Metrolinx. It's all backwards compatible.
TL;DR: This doesn't matter for currently funded core RER. This discussion is all academic for RER Phase I, as this graceful battery-train introduction discussion really won't matter till 2030s or 2040s, since we'd be going catenary-only at first. I view dual mode battery trains will be electrification route-extenders past freight infrastructure (etc), only if they become available.