Streety McCarface
Senior Member
I meant bored, my mistake.
225.5 MJ (E=mgh (205,000kg * 10m/s^2* 110m) was just a quick calculation for the more important power, which is of concern when going up such steep gradients. Also, the energy density of petrol is 34.2 MJ/L, or about 6.6 litres of gasoline. It may not seem like much, but when you have 20 trains going up that hill every hour, that difference adds up to more than 140K L of fuel annually. Given that the efficiency of thermal generation is around 40% (even less if generated by a locomotive), that number is closer to 350.4K L annually (and that's just for the difference, it would actually be ~1.5M L wasted annually). 1L of gas equates to 8.8 kWh, so every time a train goes up the hill, it uses at least 58 kWh. Now, while that's only about 9 dollars worth of power, it adds up over a long time. Over a year, it wastes close to $790K in electricity alone (without considering waste energy and without considering regenerative breaking earnings from going down the hill).
I should have clarified later, that the focus of this entire statement was assuming that we started from a cut-and-cover level at pape and travelled down 110 meters over 2 km, in which, the grades would be 5.5% (which would be a cause for concern for the TTC). For most steep grades in the system, I'd assume that they'd have sections of straight track or low grade track for the train to accelerate to a safe speed, then enter a steep gradient. If this happens, then the power required at any given time does not exceed 3,100 kW for the entire train. If there were stations between the don valley and Bloor, then this would not be possible without stopping the train on a 5.5% grade or increasing the grade significantly, neither of which are good ideas.
I don't fully understand that third bullet point. Are you suggesting the the train does not require any work to go down the hill? While this is true and would generate power due to conservation of energy, there are plenty of other factors (as you mention later) affecting the net gain of electricity from regenerative braking. Realistically, given that these numbers are constant whether you are going up or down the hill, they can be left out. They would also affect the trains heading up the hill, which would in term require that more power be used to get up the hill. Say, if friction does 100MJ of work while the train is going down the hill, it is also going to do around 100MJ of work if the train is going up the hill, and if the train is traveling along a 0% grade, that difference is irrelevant since it applies to all scenarios. While it is true that electricity would be generated from regenerative braking, at most, the efficiency of this is 70%, and because there's so much energy that has to be dissipated in such a small amount of time, that number is going to be even less (Probably less than 40%). Even if this number is applied, close to $400K in electricity annually is wasted just by keeping the train underground. In capital expenditures, it's not much, but it's close to 1/3 of all advertising revenue the TTC makes. If the train has to go back up after the don valley, that number doubles. Again, the claim that going down the hill would be a huge waste of money was just a general claim based on the shear distance they need to cover. The real point (and I should have made this clearer), was that the wear on the train itself would have not made this proposal feasible in any sense.
EDIT: All those numbers assume an empty train at all times. Since that load is live, the amount of wasted electricity is likely up to 30% too low.
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