## Express On A Perpetual Motion Machine. Scientists Create An Electric Train That Will Charge By Gravity

The title of this post, is the same as that of this article on The Saxon.

These are the first two paragraphs.

The world’s first “infinity train” will recharge its electric batteries during deceleration using the force of gravity.

Scientists and engineers from the Australian company Fortescue Future Industries have begun developing the world’s first train that will be powered by gravity. The company plans to spend $50 million on this development over the next two years, according to the Daily Mail.

**How Does The Train Work?**

According to the article, the sequence of operation appears to be as follows.

- The train starts at the high end of the line.
- The train rolls down the hill to the low end of the line.
- As it descends, it will pick up kinetic energy due to gravity.
- Regenerative braking on the train will be used to charge the battery.
- The train will have a full battery, when it reaches the low end of the line.
- The full battery will then power the empty train back up the hill.

I have a feeling that this will work, where there is a full train coming down the hill and an empty one going up.

In an example, I will assume the following.

- The high end of the line is 100 metres above the low end.
- The train weighs 100 tonnes.
- The full load weighs 100 tonnes.
- Regenerative braking is 100 % efficient.

I can calculate these energy values for a train running down and then up the line.

- A full train just about to descend, which weighs 200 tonnes and is 100 metres up will have a potential energy of 54.4 kWh.
- Whilst descending, this energy will be converted to kinetic energy and the regenerative braking will transfer this energy to the battery, which will then contain 54.4 kWh of electrical energy.
- After descending, the full train, which weighs 200 tonnes and is zero metres up will have a potential energy of 0 kWh.
- After emptying, the empty train, which weighs 100 tonnes and is zero metres up will have a potential energy of 0 kWh.
- After ascending, the the empty train, which weighs 100 tonnes and is 100 metres up will have a potential energy of 27.2 kWh.
- When the train reaches the high end, there will still be 27.2 kWh left in the battery.

Note.

- After a trip, there will be some energy left in the battery to start the train rolling down the hill on the next trip.
- Effectively, the train is powered by the weight of its cargo, which in Fortescue’s case is very dense iron ore on its trains from Pilbara to the coast.
- In some ways the Infinity train carrying iron ore is a bit like an overshot water wheel, where weight is added to the wheel and this makes the wheel turn.
- The train is driven by the weight of the cargo.

It may look like perpetual motion, but the train needs to be loaded for each trip to increase its potential energy.

I will now look at a passenger train on the same route.

- The high end of the line is 100 metres above the low end.
- The train weighs 100 tonnes.
- I will assume there are 50 passengers in both directions.
- I will assume each weighs 80 Kg with baggage, bikes and buggies, which gives a weight of 4 tonnes.
- Regenerative braking is 100 % efficient.

I can calculate these energy values for a passenger train running down and then up the line.

- A passenger train just about to descend, which weighs 104 tonnes and is 100 metres up will have a potential energy of 28.3 kWh.
- Whilst descending, this energy will be converted to kinetic energy and the regenerative braking will transfer this energy to the battery, which will then contain 28.3 kWh of electrical energy.
- After descending, the full train, which weighs 104 tonnes and is zero metres up will have a potential energy of 0 kWh.
- After emptying and reloading, the empty train, which weighs 104 tonnes and is zero metres up will have a potential energy of 0 kWh.
- After ascending, the the empty train, which weighs 104 tonnes and is 100 metres up will have a potential energy of 28.3 kWh.

Note.

- After a trip, there will be almost no energy left in the battery to start the train rolling down the hill on the next trip.
- If the regenerative braking has an efficiency of less than 100 %, it would be unlikely to work.

But it would work, if an appropriate amount of energy were to be added to the battery at either or both ends of the route.

**Could A Passenger Train Like This Work On A Real Route?**

In the UK, there are several lines, where a rail line climbs a few hundred metres.

- Cardiff Central and Aberdare
- Cardiff Central and Ebbw Vale Town
- Cardiff Central and Merthyr Tydfil
- Cardiff Central and Rhymney
- Cardiff Central and Treherbert
- Glasgow Central and East Kilbride
- Llandudno Junction and Blaenau Ffestiniog
- Manchester Piccadilly and Buxton
- Manchester Piccadilly and Glossop

For the trains to work, I suspect the following is needed.

- Regenerative braking efficiency must be as close to 100 % as possible.
- The total number of passengers going down during the day needs to be at least the same as the total number of passengers going up.
- For passenger trains to work, an appropriate amount of energy needs to be added to the battery at either or both ends of the route.

Freight trains which are transferring weight down the hill will generally always work.

**Conclusion**

The Infinity Train will work well with heavy freight, but will probably need supplemental charging to work with passenger trains.

Both heavy freight and passenger trains will use less energy, than one working to traditional principles.

I reckon Fortescue should develop a long distance cable ropeway like this

Just in case your calculation isn’t followed:

As you say potential energy depends on the mass of the object (m) in kilograms, the height above a reference point (h) in metres. In addition to that it’s also depends on the gravitational force (g) in metres/s.s, so that potential energy (PE) = m.g.h. in Joules

As we’re talking about the standard force due to gravity on Earth (9.806m/s.s)

PE = 200000 . 9.806 . 100

PE = 196.12MJ

this converts to MWh by dividing by 3.6

PE = 54.477 MWh

It’s interesting that the first effort to regenerate energy from braking was first achieved by a US Railroad around 1916, however the use of DC motors was rather inefficient. I think it was less than 20%, possibly as low as 10%. Today with modern AC motors and traction control systems that figure is going to be around two-thirds of that theoretically available.

Comment by fammorris | March 18, 2022 |

I use Omni’s potential energy calculator.

Comment by AnonW | March 18, 2022 |