Archive for the ‘Electricity Generation’ Category

Care for a Danish-Style Shower?

September 1, 2014
Have you tried showering 'Danish Style'?

Have you tried showering ‘Danish Style’?

A couple of weeks ago when I wrote about the continuing Californian drought, my friend Bernard Naylor commented that in many cultures people had adapted to a climate in which rainfall was scarce.

And he mentioned in particular ‘the Danish style’ of showering. He wrote:

Bermuda was settled by the British in the early 17th century. The island has no rivers or springs and is dependent entirely on rainfall. For hundreds of years, every building was required to be constructed over a cistern (to hold its water supply) and roofed so as to maximise water collection. People are encouraged to shower ‘in the Danish style’. That is,

  • You wet yourself all over,
  • then SWITCH OFF THE SHOWER.
  • You then soap/wash yourself,
  • and finally run the shower again to wash off the soap.

This struck a chord with me because I remembered reading that when Proctor and Gambol investigated the carbon footprint of their shower gels, they found that the carbon emissions arising from heating the water for the shower was massively more than the carbon footprint of the products themselves.

So over the last few weeks I have been giving Danish-style showering a try, and it is surprisingly pleasant.

  • Firstly, the soap lathers much more easily than when the shower is continuously running and this is very pleasurable.
  • Secondly, because the lather is so much thicker, I think I use less soap/gel than I did previously.
  • Thirdly, I think I spend less time than I used to in the shower. The simple act of consciously switching off the water somehow interrupts the dreamy warmth of the showery idyll.
  • And finally, I am saving a tiny amount money

My shower – which is typical of UK showers – uses about 7 litres of water per minute. (How do I know? I just measured it using a timer and a jug).

If the water is heated from 10 ºC to around 40 ºC (a hot shower) then pausing for just one minute saves approximately a quarter of kilowatt hour (882,000 joules) – which currently saves about a penny if the shower is gas powered, and between two and five times that much if the shower is electrically heated.

So this is a little thing that saves a little money and a little water. But it is actually quite pleasant.

Care to give it a go?

 =================================

edaviesmeuk commented (below). How could I not have heard of this before!

  • Also called a navy shower:

    https://en.wikipedia.org/wiki/Navy_shower

    Don’t do it where I’m staying at the moment as the “instant” LPG boiler takes a few seconds to light as the water’s turned on allowing a big slug of cold water into the system to surprise you after the warm which was in the pipes. Will make sure to arrange the plumbing on my new house to allow restarting the shower at the right temperature for just this reason.

 

Cradle of the best and the worst

July 19, 2014
One of the three solar concentrators from the Ivanpah Solar Thermal Power Plant.

One of the three solar concentrators from the Ivanpah Solar Thermal Power Plant.

I am on holiday with my family in Nevada and California, and while shopping for beer and clothing in Las Vegas, I was reminded of the words of Leonard Cohen:

It’s coming to America first.
The cradle of the best and the worst

Lenny’ was speaking of Democracy,  but I feel that the phrase can be extended into environmental, technological and cultural realms. And in his blog I wanted to record a few thoughts about the ‘best’ of the things I have seen.

Amidst the hyperbolic kitch of Las Vegas, we stayed in the walls of a gigantic hollow pyramid that is a truly astounding architectural and engineering achievement. For example, the elevators obviously cannot run vertically but instead run at angle along the slanted edges of the pyramid.

View from the upper floors of the interior balconies of the Luxor Hotel - which is pyramidal in shape.

View from the upper floors of the interior balconies of the Luxor Hotel – which is pyramidal in shape.

Housed underneath this beautiful roof were any number of gaudy distractions. But amongst them was the Bodies exhibition. I found the exhibition dignified, tasteful and astonishingly  educational. I left with renewed wonder at my body.

We visited the Hoover Dam in which the barely mentioned reality is that the water levels are running low. But there is no denying the engineering genius and boldness of the ambition behind it’s construction.

The Ivanpah Solar Power plant may be on the wrong-side of a historic divide between solar photo-voltaic and solar thermal. But the engineering is awe-inspiring: three giant towers concentrating solar energy – one resource which is not in short supply in this part of the world.

In Los Angeles we have used the excellent public transport rail system, which is easily accessible and welcomes bicycles. Over long stretches it has been built to use the inner lanes of freeways or major roads to minimise construction costs. And nearly all the buses have bicycle carriers attached to their fenders.

An LA Metro Train. Teh station has been built in the centre lanes of one of the wide Boulevards.

An LA Metro Train. The station has been built in the centre lanes of one of the wide Boulevards.

Many freeways have car pool lanes – in which only cars with more than one passenger may travel. Some freeways use a road pricing system –  long-discussed in the UK – in which the price to use a ‘Fastrak’ lane changes minute by minute – reaching peaks of 10 times the minimum charge at times of peak congestion. These lanes also allow fast buses to speed public transport as advertised in this excessively positive advertising video.

Of course road traffic defines LA. But driving speeds are slower in suburban streets  than in the UK’s narrower and more congested roads. In the suburban area of LA in which we are staying (El Segundo) traffic is dramatically better than Teddington.  And contrary to myth, there is excellent provision for pedestrians. And of course, California is a world-leader in legislation to control vehicle emissions.

The Hollywood Bowl

The Hollywood Bowl  is aunique cultural venue combining excellent music with the  friendly ambience of the proms and the ability to picnic as the Sun sets over the Hollywood Hills.

Culturally, the Getty Centre and Villa, the California Science Centre  (which houses the space shuttle Endeavour) and the Griffiths Observatory are among the best museums I have ever visited. And they are free.

The Disney Theatre is breathtaking and the Hollywood Bowl provides a venue for music that is unique – it felt like ‘the Proms with picnics’

The Griffiths Observatory looks over LA like a modern day secular temple to the stars.

The Griffiths Observatory looks over LA like a secular temple to the stars.

So forgive me if I pass on reciting the sins of this resource-gobbling satan. In this ‘cradle’along with ‘the worst’, are some things that I find inspiring and well-worthy of the epithet ‘the best’. And I hope that like many Californian innovations – such as vehicle emission limits – many of these will leave this cradle and spread around the world.

And to my friends: forgive me if I forgive myself for this carbon-heavy holiday.

Nuclear Nonsense in The Independent

April 28, 2014

Can you spot the difference between the two headlines below?

Two headlines for the same independent story about the plight of residents of the Chernobyl district of the Ukraine

Two headlines for the same Independent story about the plight of residents of the Chernobyl district of the Ukraine. The first one claims there are ‘cemetaries the size of cities’: this is not true.

That’s right: The first shocking headline claims the existence of’cemeteries the size of cities’. The implication is clear: that vast numbers of people have died as a result of the Chernobyl disaster.

This was not my understanding, and  I was so shocked by this claim that I tweeted the author: you can read our conversation below:

weets exchanged with Thom Davies. I have no idea if this was personal or public conversation - twitter is like that!

Tweets exchanged with Thom Davies: Thom didn’t reply to my last question. t have no idea if this was personal or public conversation – twitter is like that!

After this exchange I thought I would re-read the article and was surprised to find that the headline had changed. Indeed, I wondered if I had been mistaken in what I had seen, but fortunately I had left a browser window open and was able capture an image of the earlier page.

So what have we learned?

Firstly we learn that there are no ‘cemeteries the size of cities’ containing the unacknowledged dead from Chernobyl.

Secondly we learn that despite the absence of ‘cemeteries the size of cities’, the Chernobyl disaster was just that: an ongoing disaster played out in the lives of poor people trying to earn a living.

The ‘point’ of the article was probably to draw attention to their plight and to cause people to think twice about nuclear power in the UK. However by making unjustified and hyperbolic claims, the whole article becomes discredited: which parts should we believe?

And finally we learn that The Independent is continuing its splendid tradition of nonsense front page ‘scare’ stories. They have sadly taken down their front page story from  Sunday 20th January 2008.

That story began routinely reporting results of an unrefereed conference article which claimed that mobile phone radiation affected the sleep of a cohort of people studied. Scratching around for supporting evidence they wrote:

It also complements other recent research. A massive study, following 1,656 Belgian teenagers for a year, found most of them used their phones after going to bed. It concluded that those who did this once a week were more than three times – and those who used them more often more than five times – as likely to be “very tired”.

I would like to finish by saying that ‘you can’t make this stuff up’. Except that The Independent can. And continues to do so.

Some things to look forward to…

March 1, 2014
Swansea lagoon visitors centre

Swansea lagoon visitors centre. Picture from BBC News.

‘News’ is frequently an abbreviation for ‘Bad News’. There seems to be no end of stories about ‘things’ getting worse.

And so it is something of relief to hear of people providing solutions to our problems. Here are few things which have recently inspired me with hope.

  • Meeting some teachers today.
  • The Swansea Lagoon Project in Swansea.
  • The Solana and Ivanpah Solar Thermal Power projects in the western USA.

Teachers: Today, Saturday March 1st, I got up early and drove to Birmingham to give a talk to a group of eight physics teachers at a training day.

They were a friendly and positive bunch – but what inspired me was not their subject knowledge (which was actually excellent) but their looks. To my 54 year-old male eyes these people didn’t look like what I expected physics teachers to look like.

From this gender-balanced group there was short and tall, thin and chubby, and a range of ethnicities. They were united only in an interest in Physics and in teaching it well.

As I reflected on the long drive home, it seemed as though these people were part of the solution to a long-standing problem in physics education, and I felt honoured to be able help a little.

The Swansea Lagoon Project (BBC Story) may or not get built, but I loved the design flair in their visitors centre (main picture above), and modesty of the project.

This is not the Severn barrage which would block the entire Severn estuary and which would be able to supply 5% of UK electricity demand to the detriment of nobody but a few wading birds.

This is a much more modest lagoon off the coast of Swansea which would not even harm the birds! Its lower cost makes it much more likely to actually get built, and the technology is scalable – multiple projects could be developed one by one – something which also makes it much more investment friendly.

Map of the Swansea tidal lagoon

Map of the Swansea tidal lagoon

Two solar thermal projects in the US have recently begun operating.

  • The Ivanpah plant consists of an astonishing 170,000 parabolic mirrors each of which tracks the Sun to focus light onto a furnace at the top of gigantic tower. This heats steam which drives a turbine to generate electricity.
  • The Solana plant in Arizona is similar, but distinctly different. One difference is that it uses cheaper parabolic troughs to heat a synthetic oil which runs along a tube at their focus. But this plant can also generate electricity after dark! This astonishing engineering ‘trick’ involves storing the thermal energy in gigantic vats of molten salt. The heat can then be used to generate electricity after the Sun has gone down, allowing the generation of electricity at its time of peak demand.

These plants have been heavily subsidised. But they show that this technology is practical and I am sure the next generation of plants will be cheaper to build and operate.

However the LA times reports today that solar thermal plants are already obsolete – even as they open! – because the falling cost of silicon photovoltaic plants is making them uneconomic. That may be true – but photovoltaics definitely don’t work in the dark!

The future is not obvious. But when I see the diversity of people teaching physics and wanting to do it better. And when I see the range of emerging options for sustainable energy generation I feel able to hope that even if I don’t recognise it immediately, the future will arrive all by itself – and that it will not be all bad.

Signs of change

January 6, 2014
An electric car charging in central London.

An electric car charging in central London. How long might it be before such a sight is commonplace?

I don’t often walk through central London: I find the place mystifying and alienating. But one can sometimes see things there before they become common in other places.

Earlier in 2013 I remember spotting hydrogen cylinders on top of a fuel-cell powered bus. And just before Christmas as I shopped for gifts, I wandered past two electric cars being charged. I had previously seen the charging stations all over the place, but I had never seen them being used.

So how long might it be before such a sight becomes commonplace? Well I don’t know – it’s a question about the future – but it is likely to be decades. And of course electric cars are currently mainly powered by coal and gas burned in power stations, not renewable energy.

Scientific American recently published an article about the slow rate at which ‘new’ sources of energy have historically been adopted. I adapted the data and re-plotted it below.

Graph showing the number of years it took various fuel sources reach a give share of world energy supply - after they reached 5%. What realistic growth rate can we expect for renewables?

Graph showing the number of years it took various fuel sources reach a given share of world energy supply – after they reached 5%. What realistic growth rate can we expect for renewables (3.5% in 2012)?

Notice that throughout the 19th Century, coal was never more than 50% of world energy supply: the world was still burning wood. And notice that the ‘switch to gas’ is still underway.

Each of these transitions represents colossal financial investments from which people will not simply walk away. And since ‘World Energy Supply’ now is vastly larger now than it was in 1850, it is inevitable that change will be slow.

But the lesson of this graph is this: Take Heart. Looking back coal, oil and gas seem like they were somehow ‘obvious’ or inevitable, but that is probably just hindsight. Was it obvious that we would overcome the seemingly impossible engineering challenges required to sink mines, drill wells and capture natural gas?

So when it comes to renewables – and this refers only to ‘modern’ renewables: mainly wind and solar – the rate of rise in usage is unlikely to exceed that seen for coal, oil or gas. But that does not mean that change is not coming.

The slow rate of growth is not something to be proud of, or to rejoice in: but neither is it a cause to berate ourselves and say ‘nothing is happening’. It’s just a measure of how much energy we use, the colossal investment in existing infrastructure, and how much more we need to do.

Hopefully new sights will become visible to us in the decades ahead as we build a new world which doesn’t require fossil fuels to make it work.

Candles at Christmas

December 13, 2013

My colleagues at NPL have just finished making a video of my talk about candles so I thought I would share it with you while it was fresh.

Thanks to Lloyd for the video and thanks to everyone who helped with the talk. Personally I hate watching myself, but I hope you enjoy it.

You can follow up on the topics in the talk with the links below:

Looking on the bright side

December 10, 2013
A parliamentary 'standard candle' - made from spermaceti - a substance found only in the heads of sperm whales.

A parliamentary ‘standard candle’ – made from spermaceti – a substance found only in the heads of sperm whales. Click for a larger view.

I gave a 20-minute talk last Thursday – a Christmas talk about candles. As usual with these things, I started out knowing a little, but the process of preparing the talk involved learning lots of interesting things. And then not mentioning them.

I spoke to colleagues all over NPL to ask for help: one lent me a precision balance to weigh a candle as it burned, and another built me a device to power an electric torch from a candle! I thought that was very cool.

When I asked my colleagues in the optical team about measuring the spectrum of light from a candle their eyes lit up and I could barely stop them talking – they knew so much.

After lending me a spectrometer, they mentioned that they had an old ‘standard candle’ in their office. In the ‘old days’ it was a candle such as the one in the picture at the top that formed humanity’s standard for ‘an amount of light’.

And even though our modern standard  – the candela – is defined quite differently, its magnitude can still be linked back to the amount of light given off by a standard candle.

Gazing at the candle I was astounded. Had a whale really been killed in order to make this candle? The answer was ‘Yes’: I felt like I was holding ivory in my hands.

The idea that we would kill whales in order to extract oil and make candles is now so bonkers that we can hardly credit it. And this made me feel a little better.

It made me realise how desperate people must have been for light, and that for all its faults, our civilisation has now all but solved this problem. And that made me smile – and momentarily reflect on the brighter side of humanity’s adventure with energy.

Candle Mass and Candle Power

November 5, 2013
Weighing a candle. By determining the rate at which the candle lost mass, I could work out the rate at which it was using up the chemical energy of the wax.

Weighing a candle. By determining the rate at which the candle lost mass, I could work out the rate at which it was using up the chemical energy of the wax.

The other day I was looking at a slender candle flame when the thought occurred to me: “How much energy does a candle use to produce that light?“. After a moment of reflection, I thought of two ways to estimate it:

The first method was to weigh a candle as it burned and estimate the mass loss per second. Then I would need to look up the chemical energy of wax per gram (its so-called calorific content) and multiply the two numbers together to get the rate at which energy was released per second.

The second method was to measure the heating power of the candle. To do this I would need to put the candle under a container with a known heat capacity. Then by measuring the rate at which the temperature rose, I could work out the rate at which the candle had delivered energy to the container.

The experimental details are below, but here – for the impatient amongst you – are the results.

  • The candle lost mass at a rate of 1.78 mg per second. Multiplying this by what Wikipedia tells me is the calorific value of wax (43,100 joules per gram), I calculate that the candle is consuming chemical energy at a remarkable 77 watts. Wow!
  • That’s a lot of power and it is pretty clear that the candle is not producing anywhere near 77 watts of light – I guess the efficiency for producing light must be below 0.1%. Most of the energy must be producing heat.
  • I repeated the weighing experiment on a second (nominally identical) candle and I calculated that it consumed chemical energy at a rate of approximately 73 W. Within the uncertainty of measurement, I think this is consistent with the first measurement.
  • I used the second candle to heat 250 g of water in a lightweight (105 g) camping saucepan. The rate of temperature rise indicated that the candle was delivering energy at a rate of approximately 44 W.
  • So approximately 59% of the chemical energy was being delivered as useful heat. This seems reasonable given my previous experience heating water with flames, and considering that some of the wax may go un-burned (to make the soot in the flame)

So these two quite different experiments seem reasonably consistent, which is pleasing. But the results beg the question: “Could we use that 40 watts of thermal power to produce light more efficiently than a candle can?”.

I asked my colleagues at work – and the answer is most definitely ‘Yes’. You can see a device which does this in action in the movie below, and download instructions on how to make it here.

Experiment#1: Candle Mass

Graph showing the mass loss of candle (in grams) versus time (in seconds). The vertical grid-lines are every 3600 seconds - or one hour. Teh best-fit to the rate of mass loss is 1.78 milligrams of wax per second.

Graph showing the mass loss of candle (in grams) versus time (in seconds). The vertical grid-lines are every 3600 seconds – or one hour. The best-fit to the rate of mass loss is 1.78 milligrams of wax per second.

The rate of mass loss is rather slow. My weighing scale had only 1 g resolution so I needed  to measure for several hours to get a reasonable estimate of the rate of mass loss.

Experiment#2: Heating effect

Graph showing the temperature versus time of 250g of water in a 107 g aluminium container  of candle (in grams) versus time (in seconds). The vertical grid-lines are every 60 seconds - or one minute. The best-fit to the rate of temperature rise is 0.038 °C  per second.

Graph showing the temperature versus time of 250 g of water in a 105 g aluminium container of candle (in grams) versus time (in seconds). The vertical grid-lines are every 60 seconds – or one minute. The best-fit to the rate of temperature rise is 0.038 °C per second.

This is the raw data of temperature versus time taken using a thermocouple thermometer. I took care to stir the water before taking a measurement.

Time (s) T (°C)
0 15.2
60 16.9
120 20.2
180 22.6
240 25.3
300 27.6
360 29.5
420 31.1
480 32.9
slope 0.038056 °C/second

I then worked out the heat capacity of the water and the aluminium

Water
Mass 250 g
Specific Heat capacity 4.2 J/g/°C
Heat Capacity 1050 J/°C
Aluminium
Mass 105 g
Specific Heat capacity 0.904 J/g/°C
Heat Capacity 94.92 J/°C
Combined Total Heat Capacity 1144.92  J/°C

Then I multiplied the  heating rate (0.038 °C/s) by the heat capacity (1145 J/°C) to get the rate of energy input (43.6 J/s – or watts).

Our Energy Trilemma

November 3, 2013
Our energy trilemma is that Energy policy needs to balance three goals that defy simple solutions.

Energy policy needs to balance three goals that defy simple solutions.

“The development of stable, affordable, and environmentally-sensitive energy systems defies simple solutions. These three goals constitute a ‘trilemma’, entailing complex interwoven links between public and private actors, governments and regulators, economic and social factors, national resources, environmental concerns, and individual behaviours”

I couldn’t have put it better myself, so I simply quote from a report by the World Energy Council. And “No”, I have no idea who they are either. But I am grateful to them for enunciating clearly the three strands of the problem. If only our own political parties could speak to us so intelligently.

At the moment the UK’s labour party and the governing coalition are battling over issues of social equity. The labour party advocate an energy price freeze and the coalition advocate some kind of ‘improved’ market.

I don’t think anyone on either side seriously thinks either of these policies addresses longer term issues of social equity. And the arguments ignore the impact on the other two strands. Lower prices are bad for the environment. And in a society that has adopted a market-based way to provide energy, reducing the profitability of energy supply companies is bad for future energy security.

Similarly even the looming environmental threats from climate change cannot justify ignoring the other ‘horns’ of this trilemma. Increasing the price of energy or restricting its availability will have impacts on social equity and energy security.

And focussing on energy security – which means prioritising coal because of its widespread availability – has obvious devastating effects on any attempt to build a sustainable energy infrastructure.

So What?

It is only when we recognise the ‘three-pronged’ structure of our problem that we realise that a rational energy policy – whatever components it contains – will have one key feature:

  • A rational energy policy will disappoint all vocal advocates of one horn of the trilemma.

That means that almost everyone will fight to block it  and that almost no-one will speak up for it. You don’t believe me? Well consider some of the following – any or all of which could be part of a rational energy solution:

  • Fracking – which if implemented well could potentially help both energy security and reduce the use of coal (38% of UK supply today)  – is met with vehement ‘green’ opposition.
  • Wind turbines – which sustainably generated 6.4% of UK electricity supply today – are objected to almost religiously, and its energy generating capacity erroneously dismissed.
  • Nuclear Power – which for all its faults actually works and generated 21% of UK supply today – is objected to because despite being ‘low carbon’ it is not genuinely sustainable
  • The Severn Barrage – which could sustainably generate 5 GW (~7% of UK demand) of electricity for the same cost as Hinkley C – is objected to because of its effects on wading birds.
  • Coal-fired power stations – which generated 38% of UK electricity supply today at the lowest cost – are objected to because they are emit more carbon dioxide than gas-fired Power Stations.
  • Gas-fired power stations – which generated 25% of UK electricity supply today while emitting half the carbon dioxide – are actually being moth-balled rather than opening because they are ‘uneconomic’.
  • Increased energy costs – which are essential to pay for energy investment of whatever kind, and inevitable in any case because of increased worldwide demand – are objected to by almost everyone.

So although I don’t have ‘the solution’, I think that we do collectively have access to all the elements of a rational energy policy. But if we are to choose a rational policy, then we need to understand the nature of our trilemma. If we don’t understand this then democratically more people will object to every aspect of the solution than support it. And proponents of one aspect or another of energy policy will seek ‘victory’ or fight ‘defeat’. And using that language to describe our situation will make us all losers.

P.S. ‘Today’: This post was written on Saturday 2nd November 2013

Do we really want lower energy prices?

October 31, 2013
Graph from the Daily Mail, 16th August 2013. It shows that increases in prices of electricity has resulted in a reduction in consumption. The question is

Graph from the Daily Mail, 16th August 2013. It shows that increases in prices of electricity has resulted in a reduction in consumption. The question is this: “Is this a good thing, a bad thing or just an ‘obviously true’ thing?”

The gist of news stories about our energy supply in the last few weeks is that energy – electricity and gas – is ‘too expensive’. However I disagree: I think that energy is not just ‘too cheap’, it is much too cheap. Let me explain.

Cheap energy feels great. When energy is cheap, poor people can keep warm in winter: in the vernacular of the press, they can heat and eat. And importantly they don’t worry about their fuel bills which makes them both warm and happy. Likewise transport becomes cheaper, and everything that we manufacture or grow becomes cheaper to produce and move – and so we make more things and sell more things to people who are not using their money to pay fuel bills. So the economy grows, and we all – on average – benefit.

However there are two problems with cheap energy. Firstly  when energy is cheap we use more of it. And then we spend less on things which helps us reduce energy consumption. For example, if energy is cheap it makes less sense to insulate houses well. Then when energy prices do rise, we will find ourselves doubly disadvantaged. The cause of this expected rise is not to do with the environment but simply that many more people on the planet want to use the finite amount of coal and gas to which we have access. Of course, if we took advantage of cheap energy to increase our investment in energy-saving measures then that would make sense: but sadly that is the opposite of what happens.

The second problem is that cheap energy is dirty energy. Cheap electricity comes from coal and gas and is associated with emissions of carbon dioxide into the atmosphere. As I mentioned in a previous post, the amount of carbon dioxide emitted is phenomenal and rising year on year. To the best of our knowledge and understanding, it has, in our lifetimes, changed the climate of the planet and we expect the effects to increase over the coming decades. This effect is irreversible. Energy sources which don’t cause this pollution are all much more difficult in one way or another than burning fossil fuels. In other words, energy produced sustainably is more expensive.

So cheap energy feels good, makes everyone happy (except me), and gives rise to economic growth. However, it causes us to reduce investment in energy-saving measures and makes sustainable energy generation uneconomic. It also makes the effects of Global Warming – whatever they turn out to be – worse.

So what can we do? The only realistic way to reduce energy consumption is to increase the price of energy – see the graph at the head of the page. This makes sense in the long term, but results in suffering in the short term. Is it still possible to imagine a United Kingdom in which some sense of social justice could ameliorate the effects of increasing energy prices? I would like to think it is, but I am not sure.


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