## Mathematics Of A Bi-Mode Aventra With Batteries

This article in Rail Magazine, is entitled **Bombardier** **Bi-Mode Aventra To Feature Battery Power**.

A few points from the article.

- Development has already started.
- Battery power could be used for
applications.*Last-Mile* - The bi-mode would have a maximum speed of 125 mph under both electric and diesel power.
- The trains will be built at Derby.
- Bombardier’s spokesman said that the ambience will be better, than other bi-modes.
- Export of trains is a possibility.

It’s an interesting specification.

**Diesel Or Hydrogen Power?**

Could the better ambience be, because the train doesn’t use noisy and polluting diesel power, but clean hydrogen?

It’s a possibility, especially as Bombardier are Canadian, as are Ballard, who produce hydrogen fuel-cells with output between 100-200 kW.

Ballard’s fuel cells power some of London’s hydrogen buses.

The New Routemaster hybrid bus is powered by a 138 kW Cummins ISBe diesel engine and uses a 75 kWh lithium-ion battery, with the bus being driven by an electric motor.

If you sit in the back of one of these buses, you can sometimes hear the engine stop and start.

In the following calculations, I’m going to assume that the bi-mode |Aventra with batteries has a power source, that can provide up to 200 kW, in a fully-controlled manner

Ballard can do this power output with hydrogen and I’m sure that to do it with a diesel engine and alternator is not the most difficult problem in the world.

**The Mathematics**

Let’s look at the mathematics!

I’ll assume the following.

- The train is five-cars
- The empty train weighs close to 180 tonnes.
- There are 430 passengers, with an average weight of 80 Kg each.
- This gives a total train weight of 214.4 tonnes.
- The train is travelling at 200 kph or 125 mph.
- A diesel or hydrogen power pack is available that can provide a controllable 200 kW electricity supply.

These figures mean that the kinetic energy of the train is 91.9 kWh. This was calculated using Omni’s Kinetic Energy Calculator.

My preferred battery arrangement would be to put a battery in each motored car of the train, to reduce electrical loses and distribute the weight. Let’s assume four of the five cars have a New Routemaster-sized battery.

So the total onboard storage of the train could easily be around 300 kWh, which should be more than enough to accommodate the energy generated , when braking from full speed..

I wonder if the operation of a bi-mode with batteries would be something like this.

- The batteries would power everything on the train, including traction, the driver’s systems and the passenger facilities, just as the single battery does on New Routemaster and other hybrid buses.
- The optimum energy level in the batteries would be calculated by the train’s computer, according to route, passenger load and the expected amount of energy that would be recovered by regenerative braking.
- The batteries would be charged when required by the power pack.
- A 200 kW power pack would take twenty-seven minutes to put 91.9 kWh in the batteries.
- In the cruise the power pack would run as required to keep the batteries charged to the optimum level and the train at line speed.
- If the train had to slow down, regenerative braking would be used and the electricity would be stored in the batteries.
- When the train stops at a station, the energy created by regenerative braking is stored in the batteries on the train.
- I suspect that the train’s computer will have managed energy, so that when the train stops, the batteries are as full as possible.
- When moving away from a stop, the train would use the stored battery power and any energy used would be topped up by the power pack.

The crucial operation would be stopping at a station.

- I’ll assume the example train is cruising at 125 mph with an energy of 91.9 kWh.
- The train’s batteries have been charged by the onboard generator, on the run from the previous station.
- But the batteries won’t be completely full, as the train’s computer will have deliberately left spare capacity to accept the expected energy from regenerated braking at the next station.
- At an appropriate distance from the station, the train will start to brake.
- The energy of the train will be transferred to the train’s batteries, by the regenerative braking system.
- If the computer has been well-programmed, the train will now be sitting in the station with fully-charged batteries.
- When the train moves off and accelerates to line speed, the train will use power from the batteries.
- As the battery power level drops, the onboard generator will start up and replace the energy used.

This sequence of operations or something like it will be repeated at each station.

One complication, is that regenerative braking is not one hundred percent efficient, so up to thirty percent can be lost in the braking process. In our example 125mph train, this could be 27.6 kWh.

With an onboard source capable of supplying 200 kW, this would mean the generator would have to run for about eight and a half minutes to replenish the lost power. As most legs on the proposed routes of these trains, are longer than that, there shouldn’t be too much of a problem.

If it sounds complicated, it’s my bad explanation.

This promotional video shows how Alstom’s hydrogen-powered Coradia iLint works.

It looks to me, that Bombardier’s proposed 125 mph bi-mode Aventra will work in a similar way, with respect to the batteries and the computer.

**But, Bombardier Only Said Diesel!**

The Rail Magazine article didn’t mention hydrogen and said that the train would be able to run at 125 mph on both diesel and electric power.

I have done the calculations assuming that there is a fully-controllable 200 kW power source, which could be diesel or hydrogen based.

British Rail’s Class 150 train from 1984, has two 215 kW Cummns diesel engines, so could a five-car bi-mode train, really be powered by a single modern engine of this size?

The mathematics say yes!

A typical engine would probably weigh about 500 Kg and surely because of its size and power output, it would be much easier to insulate passengers and staff from the noise and vibration.

**Conclusion**

I am rapidly coming to the conclusion, that a 125 mph bi-mode train is a practical proposition.

- It would need a controllable hydrogen or diesel power-pack, that could deliver up to 200 kW
- Only one power-pack would be needed for a five-car train.
- For a five-car train, a battery capacity of 300 kWh would probably be sufficient.

From my past professional experience, I know that a computer model can be built, that would show the best onboard generator and battery sizes, and possibly a better operating strategy, for both individual routes and train operating companies.

Obviously, Bombardier have better data and more sophisticated calculations than I do.

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