IPAT the Difference – Technical

Its simple mathematics (part 3): subject – calculus & the Affinity Laws

Technology is the third variable in IPAT. It can be good and it can be bad. Technology allows things to be made for a much lower price on one hand, meaning that a lot more people have the ease of financial access to the products. On the other hand, technology allows more efficient use of resources, so environmental degradation is reduced by a percentage factor.

An example of the benefits of technological efficiency is found in the Affinity Laws and their application to motors. The International Energy Agency has estimated that 45% of global electricity consumption is by motors. It is estimated that 20% of global electricity consumption is by the motors that drive pumps (Pump Lifecycle Costs: A Guide to LCC Analysis for Pumping Systems, Europump and Hydraulic Institute, 2001).

The basis of the Affinity Laws is that pump and fan flow rates are related to pressure and power consumption. The calculus is as follows (assuming the impeller diameter remains constant):

Law 1a Flow is proportional to shaft speed:

Law 1b Pressure or Head is proportional to the square of shaft speed:

Law 1c Power is proportional to the cube of shaft speed:


To make the maths simple, I will explain what the key points to understand out of the above formulae:

If you reduce the speed of a pump or fan by 10%, you will use approximately 25% less power. If you reduce the pump or fan speed by 20% you will halve the amount of power consumed.

But how do you control the motor speed. Easy, with capacitors incorporated into variable frequency technology (VFD’s). Their connection to a motor is like giving the motor an accelerator pedal, allowing them to back off the gas as appropriate. VFDs are like big buckets of electric charge. The charge comes into the bucket as an alternating current at 50 or 60 hertz (depending on the country you are in). In Australia it is 50 hertz. The VFD deals out the power at the hertz rate necessary to maximise motor operational efficiency. Sensors are often connected to the VFD telling it:

“Hey mate, the motor doesn’t need to be running at maximum speed at the moment, so back off”.

Now for some rough estimates of the potential benefits of VFDs applied on a mass basis. Say there is an opportunity to reduce the electricity consumption of half the pumps and fans in the world by an average of 25% from their current consumption (by slowing their speed by 10%). This is a conservative estimate that incorporates situations where the pump has to run at 100% capacity, where VFDs are already in operation and finally, it presumes only a 10% reduction in speed. The estimate means that total global power consumption of motors could be brought down from 20% of total electricity consumption to 17.5% of the total. Given the total electricity consumption from fossil fuels will be approximately 16 TWH in 2014 (based on estimates derived from 2011 data of the International Energy Agency), then there is the opportunity here to reduce fossil fuel generated electricity consumption by 400,000 MWh in that year. Given that each MWH generated from fossil fuels causes the emission of approximately one tonne of CO-2e, the emission reduction would be of the order of 400,000 tonnes of CO2-e in 2014.

Going back to consider the algebraic consequences in IPAT, carbon emissions make up a significant part of the calculations of the ecological footprint (approximately half). Therefore, if VFD technology is introduced on a mass scale EPM/WTB estimates there will be a noticeable reduction in per capita global gha.

Finally, a specific example of the benefits of VFDs. David Bartush, the aquatics facilities manager for the Blue Mountains City Council, near Sydney, introduced VFDs to the two x 15 kWh pumps to the Springwood leisure pool. The pump power consumption has reduced by 56 MWh per annum since.

In following newsletters we will look at other ways of reducing motor power consumption with more efficient motors, correct pump and pipe sizing and power factor correction.


IPAT the difference – global footprint


Its simple mathematics (part 2): subject – algebra & IPAT

Have you ever heard of the formula:

I = P x A x T

From Ecoprofit Management: The formula’s evolution was the outcome of a debate between three guys, Barry Commoner, Paul Ehlich and John Holdren. “I” stands for environmental impact or environmental degradation, “P” is population, “A” is affluence, “T” stands for technology.

A basic tenant of algebra is that both sides of the equation have to be equal. Therefore, if you increase one side of the equation, the other side increases by the same amount.

According to the IPAT formula, if the world’s population increases by 655,000 in three days, then the other side of the equation i.e. environmental degradation, has to increase the same amount.

What we need is a common unit of measurement to apply to the formula. This is where the calculation principles of ecological footprinting come in handy. It uses global hectares (gha) as its unit of measurement. The total gha of the earth is calculated as all the productive land and sea available to provide the natural resources needed for all the things humans consume. Wealthier per capita countries like the USA (8 gha per person) and Australia (6.8 gha per person) have higher per capita footprints than countries like India (0.9 gha per person). This is because wealthier countries consume more things on a per capita basis. So for the USA, 8 gha represents the amount of productive land and sea needed per person to not only meet the demand on natural capital, but also to allow the natural capital consumed to be regenerated and all associated waste assimilated.

Currently we are in overshoot. The average global per capita footprint is 2.7 gha.The average global biocapacity is 1.8 gha per capita. That means humans need the earth to be another 50% bigger in order for it to be able to meet the demand on natural capital. At the current rate of increased consumption, the world will need to be three times as big to meet demand by 2050.

We are turning resources into waste faster than waste can be turned back into resources and depleting the very resources on which human life and biodiversity depend.The result is collapsing fisheries, diminishing forest cover, depletion of fresh water systems, and the build-up of carbon dioxide emission. Overshoot also contributes to resource conflicts and wars, mass migrations, famine, disease and other human tragedies and tends to have a disproportionate impact on the poor, who cannot buy their way out of the problem by getting resources from somewhere else.

So what is the impact of the extra 655,000 people on earth in the 3 day period? All we have to do is multiply the net increase in people by the average per capita gha (i.e 655,000 x 2.7 gha) which equals 1,768,500 gha. This is how much extra global hectares are needed. Over a year it will be 216 million gha (80 million extra people x 2.7 gha). The “I” in IPAT must therefore increase by the same amount and is reflected as an extra 216 million gha in overshoot.

The next variable in IPAT is affluence. This is where one looks at not only the bigger consumersin the west, but also the rise of the middle class in economies such as China and India. Worldwide 700,000 TV sets and 5 million phones have been sold in the last 24 hours. For the year, 20 million cars have been manufactured and 85 million computers have been sold. Just today, 5 billion dollars has been spent on the military enterprise.

In both China and India, the average per capita income has increased significantly in the last 30 years and is reflected in the rise of the middle class. Over this period the average per capita gha in China has risen from 1.3 gha to 2.2 gha now. In India it has risen from 0.7 gha to 0.9 gha over the same period. Worryingly, India’s biocapacity has collapsed in the same period by almost half down to 0.4 gha per person. This means it is regenerating its own natural capital at half the previous rate.


World Meters – Population

Its simple mathematics (part 1): subject – multiplication & the population

Direct from Ecoprofit Management newsletter: Recently I had cause to travel from my home in the Blue Mountains (west of Sydney) to Perth on the other side of Australia. It was the trains, planes and shuttle bus thing. On the way back passengers have the option to catch the redeye flight, an overnight flight. I chose that option.

While I waited in the Perth Airport terminal I had time to kill. Out came the laptop. For some odd reason I decided to look up the estimated world population at that time on www.worldometers.com. At 7pm (Perth time) the website showed the total as 7,223,729,300 people. After that I did the emails response/catch-up thing and before I knew it, it was time to board my flight.

Observing the passengers as they waited at the baggage return once we arrived in Sydney, I was able to confirm that the person who came up with the nickname redeye wasn’t a creative genius. No doubt too, others were looking at me and going, wow that guy needs a sleep bad.

Anyhow, I was so glad to get home to my family and before I knew it, it was Saturday. At 10pm on that night I had a sudden thought: its 72 hours since I looked up the world population at the Perth airport terminal. Why don’t I look up how much it is now? I was shocked. The number of people on the earth, after allowing for deaths was 7,224,384,300.

That’s a 655,000 net increase in human beings in three days.

My first thoughts were: how many people are aware of the rate of increase in the human population? It works out to an 80 million per annum increase.

This thought reminded me of Paul and Anne Ehlich’s 1968 book The Population Bomb that predicted mass starvation events in the 1970’s and 80’s as a result of the inability of agricultural output to match the predicted population explosion. The book content was essentially an extension on Malthusian Theory.

The Ehlichs were incorrect in the timing of their forecast, but their prediction has every chance of coming true, with the population expected to rise to 10 billion by 2062, and especially when the spectre of the fall-out from global warming is thrown into the mix.