The Mega City Electric Car – Doing the Numbers

ELECTRIC MOTORING

Driving our Mega City electric “car” must be a strange experience for any driver under 50. By modern standards it is a very light (plastic) and somewhat cramped vehicle which manages about 35mph on a level road, for maybe 35 miles, on a single 8 hour charge. Downhill (with the wind behind it) it can manage 40mph. Uphill, or with the wind against it, it has trouble making 20mph. It is quite unlike a petrol or diesel car, all of which will do 70mph, most on any but the most extreme terrain.

IT’S A MATTER OF POWER.

The smallest readily available conventional car is the Smart Car, and the diesel model gets 85 mpg and 84mph from a 33kW (45hp) engine. It weighs 770kg, and its frontal area is similar to the Mega City’s, which is an important factor in determining the speed any car can do, and how much power it needs to do it.

The Mega City’s electric motor produces 12kW (16hp) about a third of the Smart Car. It weighs 750kg – about the same – over half of which is battery. There are 12 batteries, storing 10kWh of electricity between them when charged. 10kWh is a lot of electricity – more than many houses use in a day – but it’s a tiny amount of power for a car.

To see how tiny, consider that a litre of diesel weighs less than a kilogramme, but stores about 10kWh of thermal energy when burnt. An engine can only convert about 50% of this into mechanical power – the rest goes up in smoke (or heat, which in the winter is still “useful” to passengers). 2 litres of diesel therefore store about the same amount of mechanical energy as the Mega City’s batteries, but the Mega City can propel itself nearly 50 miles on that, the equivalent over 110 miles per gallon. The Smart Car gets about 37 miles from the same amount of energy, albeit at 50mph.

The Smart diesel may have 33kW of power available, but it doesn’t require all of that to drive on level roads at moderate speed. So, for example, 50mph only needs about 14kW, or less than half maximum power.

The Mega City motor has a low power mode which limits power to 4kW, about a quarter of the Smart diesel’s 14kW cruising power. In this mode it can just about reach 30mph on level ground, and we can assume the motor is putting out the full 4kW to do that. The Mega City’s low power range is 50 level miles, which would take an hour and forty minutes at 30mph, so should only consume around 6.64 kWh of battery. Since the batteries hold a usable 9kWh, why can’t it do 70 miles?

Mega City’s manufacturers say that it consumes 180 Watt-hours per mile on low power at its most economical speed, which is about 20mph. At 20mph, 180 Watt-hours per mile translates to 3.6 kWh consumed per hour – in other words 3.6kW. 3.6kW will drain a 9kWh battery in 2 ½ hours, giving us that maximum range of 50 miles, but at 20mph.

The Mega City can’t travel 70 miles at 30mph because of air resistance. Air resistance goes up with the square of the speed. On a level road, at higher speeds, most of a car’s engine power is used to push the air out of the way. That’s why during fuel crises the government lowers speed limits. A car will use noticeably less fuel at 50mph than it does at 70mph, and for the same reason the Mega City uses much less electricity at 20mph than it does at 30mph. Flat out, or on high power, it won’t go anything like 50 miles before running out of battery.

AND WHAT ABOUT HILLS?

The term “level mile” is a little hollow (or steep) to describe motoring in the Brecon Beacons National Park. Very few of our roads are flat for very long, and the “A” roads – which have the gentlest gradients – are not terribly welcoming for cars with only enough power to do 30mph on level ground.

To climb a hill you need much more power than to go the same distance on level ground, where the engine only needs to overcome air resistance and the friction in the engine itself, the drive train and the wheel bearings. When climbing a hill, the engine power also has to lift the weight of the car, its passengers and its cargo. This is when the Smart Car diesel’s extra power comes in handy, while the Mega City starts to suffer.

The Mega City suffers because it needed 4kW just to overcome the air resistance of moving at 30mph. If it has to lift itself, its batteries, and its payload up a slope as well, it can’t maintain 30mph, even on high power. Putting your foot down, as you would with a normal car, will not work because there is no more power available.

We can calculate how much extra work the Mega City has to do to climb a hill. The car with its batteries weighs about 750kg, and with two traditionally built passengers that rises to, say, 900kg. The gravitational force acting on a kilogramme at the Earth’s surface is roughly 10 Newtons, so raising 900kg by 1 metre against gravity consumes 10 by 900 = 9000 Joules of energy. Climbing 100 metres with 2 passengers will consume 900,000 Joules, or about ¼ of a kWh, and that’s in addition to the power required to move forward through the air at whatever speed you can manage.

If we take a trip from the A470 roundabout in Brecon to the top of the Storey Arms pass we’ll climb 300 metres in 10 kilometres. Just raising our 900kg Mega City and passengers those 300 metres will consume at least ¾ of a kWh over and above the energy required to drive the 10km at whatever speed the car can manage. The slower the car goes, the less energy will be needed to overcome air resistance. We already know that moving at 20mph on the flat uses up 3.6kW. Climbing to Storey Arms at 20mph, which takes about 20 minutes, is therefore going to consume 1.2kWh to overcome the air resistance and 0.75kWh raise the car and its cargo, for a total of about 2kWh.

THE BOTTOM LINE

So the Bad News is that the Mega City, on unrestricted roads in this area, is going to seem rather slow, even slower when climbing hills. But the Good News is that the back roads in the Brecon Beacons National Park are also used by cyclists, and by tractors pulling muck spreaders. The Mega City is quicker and drier than a bike, and can easily keep up with the muck-spreader you wouldn’t be able to pass even in a Porsche! The Mega City will comfortably get us into town where, of course, it’s as fast as anything else.

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One Response to “The Mega City Electric Car – Doing the Numbers”

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