Wednesday, February 10, 2010

david mackay: do the arithmetic

John McCarthy: He who refuses to do arithmetic is doomed to talk nonsense. (Progress and its Sustainability)

I'd forgotten a lot of my basic physics, so here is a refresher.

Power is the rate of energy conversion, or, the rate of doing work. This applies to both mechanical power, measured in joules / sec and electrical power, measured in watts

Work is done when a force is moved through a distance (W=F*D)

Mechanical force = mass * acceleration, the UNITS are kg.metre/sec/sec or Newtons
Mechanical work = force * distance, the UNITS are newton.metres or N.m or Joules
Mechanical power is work divided by time, or, Work / time, the UNITS are N.m /s or Joules / sec

Electrical power is measured in Watts. 1 Watt = 1 Joule / sec. A watt is also a volt.amp. Watts= Volts * amps

To obtain electrical energy then multiply the power * time. The UNITS here could be joules or watt.seconds. The normal units for larger amounts of electrical energy are KW.hrs. To convert watts to kilowatts divide by 1000, to convert seconds to hours divide by 3600 or 60*60.

We need to have an internalised way of having a feel for these values. A joule is the energy or work required to lift a small apple one meter straight up. If you perform that action in one second then that is equivalent to a watt or joule/sec of electrical power.

The small apple weighs 0.1 kg
The acceleration caused by the earth's gravity is roughly 10 m/sec/sec (9.8 m/s/s more accurately)
The distance we move the apple through is 1 metre
Work = force * distance
Work = mass * acceleration * distance
Work = 0.1 * 10 * 1
Work = 1 joule or 1 Newton.metre or 1 kg. metre ^2 / sec ^2, where ^2 means squared

Some other joule practical examples at the wikipedia joule page

A 40 watt incandescent light bulb produces forty joules of energy per second or the equivalent of lifting 4kg of apples 1 metre in one second. Fluorescent or LED lights achieve a similar effect with much less energy.

How much energy does a 40 watt incandescent light bulb use in one day?
40 * 24 / 1000 = 1 energy used in one day

How much energy does the average person in an industrialised country use? The figures here are for the UK

Answer: The equivalent of 125 of these light bulbs running all the time

How many wind turbines would it require to meet the energy needs of everyone in the UK?
Answer = 600,000, which would cover half of the UK. The UK currently has 2408 wind turbines

How many nuclear power stations would it require to meet the energy needs of everyone in the UK?
Answer = 300. The UK currently has 10 nuclear power stations.

Here is a video from David MacKay illustrating the need to do the arithmetic. Irrespective of whether you are an alarmist, denier or somewhere in between you still need to do the arithmetic and basic physics to intelligently discuss these issues:

David MacKay is the author of Sustainable energy - without the hot air. He has recently been appointed the UK's Department of Energy and Climate Change Chief Scientific Advisor.

1 comment:

Mark Miller said...

I agree with you about the arithmetic. I've heard engineers involved with alternative energy make claims that someday in the near future alternative energy will be our main source of power, and energy from fossil fuels will be in the minority. With the power output of alternative energy sources now, looked at on a per unit basis, it seems to me that such projections are wildly unrealistic. I don't see how a competent engineer could say these things and be honest. I'd much prefer it if more money was put into R&D for making alternative energy more efficient, rather than using it for build out.

I was talking a couple months ago with an engineer who works for an energy company. He said that from an environmental standpoint he liked wind, but it's inconsistent and it doesn't scale well.

He liked solar for specific sites, because it scales well to individual buildings, but it was only economical in certain circumstances, because you either have to choose between powering your building with solar during the day, and using the grid 100% at night, or storing power in batteries so you can continue using solar-generated power at night. The latter is hugely expensive right now, and compared to the price of getting power from the grid it doesn't make sense.

One common circumstance where he thought solar would make sense was with office buildings, especially if workers converted to electric vehicles. He thought of a design for a parking garage where everyone could plug in and recharge their vehicles while they were working during the day. As far as people's homes, he didn't see it being that practical. Most people are away from their homes during the day anyway. I have heard of people selling their surplus solar power back to the grid, but I don't know how that works out economically.

He said that using solar power plants was not all that realistic, because of all the land that's required for it, and it's inconsistent.

I have heard a few proposals for wind and solar power storage on a large scale using pumps to pump water up into a storage basin in mountainous or hilly areas, and then using that as a source of potential energy when the wind isn't blowing enough, or during the nighttime in the case of solar, but this is more wishful thinking. With wind and solar's inefficiency you have to try to preserve every bit of energy you can get from them. Just transmitting the power over large distances dissipates the energy in power lines before anyone can use it. With storage, energy would be lost in the process of storing the water, and then generating power from it. A large reserve of water would need to be used, much more than would be needed for energy storage, because the contingency of drought would need to be taken into consideration.

As far as power plant solutions, there were two that we both liked: natural gas, because it pollutes less and scales similar to coal, and nuclear. The engineer much preferred nuclear, because of the safety improvements that have been made in plant designs, and the fact that a little fuel lasts a long time. It also requires less manpower to run a plant (though the security requirements are greater). From what I remember he said there was technology for reprocessing spent fuel and reusing it for power generation as well.