Tag Archives: Physics

Is the Earth like a fractal?

Have you ever spent any time looking at the Mandelbrot set? I don’t mean a cursory glance, I mean really contemplated it?

Mandelbrot set

The Mandelbrot set. The horizontal axis is the number line,

And I don’t even mean the fancy coloured versions, just the straight black-and-white one (see image on right)?

It is really far more interesting than it looks…

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At first glance it just looks like a prickly pear gone wrong, so what is so interesting?

Well, remember this graph shows a set, that is to say it divides numbers into two groups, those inside the set, and those outside.

You could easily create such a set with circle – you can define the co-ordinates inside the circle is ‘in’ the set and that which is outside the circle outside the set. Such a set can be defined in a sentence: it is all points c less than the distance r from the origin.

The Mandelbrot set is just the same – a shape that divides space into two regions – in the image, the black area shows the numbers in the set, and the white area show the numbers out of the set. The only difference from a circle is that the Mandelbrot shape is more wiggly.

It equation is not much longer to define:

It is all numbers c, where if you square the number, then add the number, then square the result and add the number again, then repeat, it does not tend to infinity.

So zero is in the set, if you square it, then add it, it is still zero.

How about 1? No, it will run off: 1,2,3, 4, …

-1, on the other hand, squared, is 1, then added, goes to zero, where it will get stuck: -1, 0,0,0…

Figuring out the contents of the set is however complicated. Bloody complicated. Infinitely complicated in fact, and one of the marvels of the mathematical world.

To get a feeling exactly how complex this set is, take a look at some animations in which you zoom in on the perimeter; you can google “fractal dive” for more…

[youtube=http://www.youtube.com/watch?v=fLrSapMYUlI]

Mandelbrot Zoom Animation

You can choose what part of the set to zoom into yourself, if you want, here: http://www.h-schmidt.net/MandelApplet/mandelapplet.html

It seems that one simple sentence has been able to define an infinitely complex boundary, and begs some interesting questions: have we created a sort of universe? What is the information content of this set?

It makes my head hurt.

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The area of specific interest to me, is the relationship between the platonic ‘world of maths’ and the real world; so are there parallels between such complexity in the world of numbers and the real world?

Clearly fractals sometimes have similarity to things in the real world – such as crystals, feathers and broccoli florets. We see many reminders of complex structure in the real world, and it brings me to think of the earth as a sort of giant 3-d fractal – where the solid matter is ‘in the set’ and the gas of the atmosphere and the vacuum of space is “out of the set”.

We can see that the interface, the earth’s surface, also has complex structure, including such things as crystal caves or the lining of your lungs – and like with the Mandelbrot, we also seem able to zoom in to many levels.

However, just as there are no perfect spheres in the real world, there are no perfect fractals, and it seems that the structure falls apart once we get to subatomic levels of zoom (or does it?)

Some part’s of the earth’s interface are fractal-like due to the iterative nature of their construction (tree growth, crystal growth, sea-shells, etc.), and you can see that a simple rule of “branching” in a plant can make a complex shape. However, some of the complexity, specifically organic and bio-chemistry, still seem different (to me anyway).

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Krzysztof Marczak Mandelbulb

Krzysztof Marczak's Mandelbulb rendering

Now it turns out that my idea of the earth as a fractal with its skin as a complex interface can be more closely matched to the newly invented (discovered?) “Mandelbulb”, the amazing 3-d set. The interesting story of their development is told by one of their key developers, Daniel White, here.

The Mandelbulb is amazing because, as with many other fractals, you can zoom in and see ever more fascinating detail, and with incredible variation, and if you zoom into it continuously it would not be unlike zooming in on planet earth using Google Earth.

This excellent video below shows the idea of zooming into the Earth off well  (it seems to be derived from a book I happen to have called “Powers of Ten“).

[youtube=http://www.youtube.com/watch?v=9BjHvwSvpOw]

So of course, you can do a similar trick on the Mandelbulb:

[youtube=http://www.youtube.com/watch?v=LxsniUIVfEM]

Enough said!

How to drive more efficiently

In this article I hope to describe some efficient driving ‘tactics’ and hopefully also explain why they work.

To do this I start with a question… what, exactly, is energy?

Many people think scientists know this, but alas, they don’t. It is one of science’s great mysteries.

On the other hand, they do know an awful lot about how it flows (they call it thermodynamics which is science-jargon for “heat-flows”). And when energy flows, we also know how to harness it.

If we consider the car, we can think of a fuel tank as bottled energy. The engine then turns that bottled energy into motion. But the laws of physics say energy is never destroyed – in only flows. So where does it go after that?

Understanding the answer to this simple question will help us all to drive more efficiently.

Here are some of the outlets for the energy from your petrol tank:

1. Accelerating your car – energy is transferred into the mass of the car. They call this ‘kinetic’ energy – kinetic is just latin for ‘movement’.

Aside for nerds: It’s the kinetic energy in a car that makes it so dangerous – when a car crashes into a tree this energy flows at a speed comparable to a bomb-blast, bending the metal and hurting the people.

2. Going uphill – the energy is also put into the mass of the car. They call this ‘potential’ energy – we’ll see why in a minute.

3. Friction – the friction inside the engine, of the wind on the car – and last but not least the rubbing of your brake shoes on your brake disks – all turn your energy into heat

Too much energy ends up in the brakes...

Too much energy ends up in the brakes...

4. Noise – some goes into people’s ears, but eventually it all just heats the environment.

And that’s it.

So the first thing to notice is that friction and noise are bad. It is not our aim to heat the world up.

So how do we avoid heat and noise? Firstly, keep your car in good nick. Keep your tyres properly inflated too.

Secondly, drive slowly. Air friction is much more significant the faster you go. Doubling your speed quadruples the frictional loss per km and multiplies the energy loss per second (power) by 8! Thus there is about 21% more energy loss to friction at 77mph than at 70mph, despite being only 10% faster. (and it requires 33% more engine power!)

My third tip is a little controversial. Try not to brake.

If you are approaching a stop, try to coast to a halt by taking your foot off the gas far in advance. If you do this, you will avoid heating your brakes and rather spend your energy on air friction, which was inevitable anyway. We will come back to braking in a minute.

Now can we do anything about the energy required to accelerate and go uphill?

Yes, we still ‘have’ this energy- so it can be recovered!

The mass in your car (including you yourself) become a store of energy when you are a) going fast, and are b) at the top of a hill.

Using potential energy...

Using potential energy...

The hill energy is called ‘potential’ energy because its got the ‘potential’ to be recovered. We generally recover it without even thinking – when we go back down the other side – gravity does much of the work.

However, we only get it all back if we don’t brake (or use engine compression) to slow ourselves. If failing to brake would lead you to exceed the speed limit, then that’s a pity, as I can’t condone breaking the speed limit, especially if my children are about.

What about the kinetic (going fast) energy? We usually also recover this – but only if we allow ourselves to coast to a stop. Again, if we use the brakes, we turn all that precious energy directly into heat, which is literally burning it.

We also tend to brake when we approach corners, again, it is more frugal to take your foot off the pedal far in advance of the corner such that you are already going slow enough to take it safely when you (eventually!) reach it.

All that might sound complicated, but it all translates to a simple rule of thumb: don’t use your brakes unless you have to. Of course this logic can be taken to its extreme (and occasionally unsafe) conclusion – take a look at the practices of the hypermiler community.

Anyway, that’s all you need to know to get a good 10-20% more miles from each tank.

That concludes this series of articles on greener motoring, I hope it has been of use. Please don’t hesitate to add your own tips in the comments section. Thanks!

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Could the internal combustion engine be greener?

For most people, fully electric cars are some way off. Most people still prefer to have a range of 300+ miles, and to fill up in a few minutes at one of several thousand filling stations.

So how bad is the car we know and love? Can it be made any better? In this article I look the most popular technologies and developments in this area.

The Internal Combustion Engine…

Until all-electric / fuel-cell / nuclear cars are fully realised – we will be stuck with the internal combustion engine. It is therefore well worth looking at how we can make the most of them.

The basics are simple – you heat up some gas, it expands and pushes a piston. In theory you should be able to get all of that heat and turn it into force.

The Internal Combustion Engine

The Internal Combustion Engine

Alas, there are details. We can’t extract all the energy because of the laws of thermodynamics – in fact the limit is about 37% given the temperature range in a typical petrol engine. Then you also have to spend some energy on sucking the gases in. You have to spend energy pumping the gases out. There is friction. There is the heat. The list goes on. Eventually we extract a pathetic 20-25%.

It is therefore not surprising that the piston-driven engine is still being improved despite nigh-on 300 years passing since the earliest versions.  There are still redesigns of the inlet manifold, of the valves, of the crankshaft – all designed to lessen the waste.

To pick one example, we can look at the Atkinson Cycle. One of the many great minds to apply itself to engine efficiency was James Atkinson. He realised that if the power and exhaust strokes were designed to be longer than the intake and compression strokes (see a good animation here), you could let the hot gases expand to a greater volume then they previously occupied – and thus be cooler – so your exhaust gases carry away less embodied energy.

It really works – but is not used. Why? Well mainly because we are too committed to the current design and too much money has been spent in its evolution (which was driven by the need for power, not efficiency); to go back the drawing board has simply been too much hassle. Of course, times they are a-changing…

Another technology waiting for its time in the sun is the “VCR” engine, which stands for Variable Compression Ratio. This is a system in which the volume of the combustion chamber may be adjusted depending on whether you are accelerating, coasting or pulling a caravan up the Col du Tourmalet. It promises to constantly optimise the energy extraction. If its developers can convince major car manufacturers to trust the rather complex crank arrangement it may well be a viable alternative in as soon as 5 years from now. Watch this space.

The Transmission

Enough about the engine – what about the clutch and gearbox? That’s the “tranny” to my American friends, which means something totally different here in the UK.

The transmission’s job is to allow the car to vary speed from 0 to over 100 mph whilst the engine only varies only from around 800 – 6000 rpm, which is a much smaller range. With only 4 or 5 gears you need to use a fair range of engine revs to drive, however, the engine is not equally efficient at all speeds.

Pricnple of the CVT, with thanks to HowStuffWorks.com

Principle of the pulley-based CVT, with thanks to the brilliant HowStuffWorks.com

The idea has therefore been brewing for a device that can allow complete freedom for the engine to run at its most efficient speed, regardless of the car’s speed.

Its called the ‘continuously variable transmission’ or CVT. The most practical design is the pulley-type (see image), though others are also being developed.

In addition to allowing the engine to run at its most efficient speed,  there is also  no disruption of power flow due to gear changes. All of this will add a few vital % to your overall efficiency.

Aside: The CVT is also a vital part of an electric car using regenerative braking, as the gearing can be used to control the braking effect created by the motor/generator.

The fuel…

While hydrogen produced from renewable electricity (say hydroelectric) is one route to reduced carbon emissions, another is the idea of renewable versions of liquid fuels, the so-called bio-fuels.

While bio-fuels do not have as many issues to overcome as hydrogen, they are still far from a clear-cut solution.

Bio-fuels are simply flammable liquids made from plants (nature’s solar panels) – not only is it a renewable energy source (i.e will not run out), but the growing plants also suck CO2 from the air, so could indeed evolve less net CO2 than sources like coal-derived electricity (or hydrogen made from coal-derived electricity). On the other hand, the balance only works well if the bio-fuel is farmed in an energy (and carbon) efficient way.

The idea is fundamentally good, but as with almost all of the other ideas I have discussed, there is a flip-side.

For the first time, there is a risk of direct competition between poor farmers in remote tropical zones, and the big, fat westerner in his or her gas-guzzler. The latter wants something in their fuel tank and the former wants something in their stomach.

There was much speculation last year that the trend towards bio-fuels was responsible for the crisis in commodity food prices. This may or may not have been the cause – it may well have been the result of irresponsible speculation by commodity traders because few bio-fuel crops have directly displaced food crops. However, the question remains: will the drive for bio-fuels interfere with food supply in the future?

There is also the question of whether rain-forests may be razed to make way for the required crops (there are many choices depending on the rainfall and sunshine levels – cane, corn, beet, sorghum, rapeseed, sunflowers or palms to name a few). If an existing forest is razed it not only destroys biodiversity, but usually also results is a massive belch of CO2 into the atmosphere that will takes many years to offset.

However, bio-fuels are still too promising to let alone.

In Europe most diesel already contains a certain percentage of bio-fuel and the EU has targets for bio-fuel use in transport (5.75% by 2010). Even though the target is unlikely to be met, the trends are strong.

The technical barriers are not too serious – most diesel cars can take bio-diesel blends and can usually be made to take pure bio-diesel with minor adjustments. Bio-ethanol can equally be blended with petrol, and at 10%, many modern cars would in fact run better. However, higher levels are still the reserve of so-called “flex-fuel vehicles’ (FFV’s). These are very popular in Brazil, the world’s leading producer or sugar-based bio-ethanol. The US (especially California) is also leading in this initiative. Although to be fair, this too is not a new idea: the Model-T Ford was a FFV!

In the next article I will looking at the driving techniques that can get 20% more miles out of each tank.

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Green Car Technologies Explained

Let’s say you are a big-shot. You need to get around. And public transport is just not going to cut it.

You do a lot of miles and want to go the extra mile to minimise your impact – what should you do?

The answer any good car salesman would give you is: get a Prius (in case you missed it, this is Toyota’s flagship ‘hybrid’ high efficiency offering).

Sounds good, but what is a a hybrid? Is that electric? Do I need to plug it in at night? And what are the alternatives? Are there any?

In this section, I hope explain this and some of the other things coming down the turnpike.

Electric, Hydrogen and Hybrid Cars

Time to plug in?

Time to plug in?

Electric cars are not new. The idea has been around since cars were first made. The problem has always been with the batteries – you need big ones to go far, but the bigger they are, the heavier the car, and so the more batteries you need.

Add to this that batteries take hours to “fill up”, whereas you can can fill the petrol tank in about a minute, and you start to see the issues.

Once you point out that electrical energy is not exactly cheap, and that you are probably not saving the planet unless you get your power from a hydro-electric dam, and you can see why they have not taken off.

So why don’t they just make smaller batteries that charge-up quicker?

Well they are trying. The cell phone industry has driven up the ‘energy density’, but batteries are still rather pathetic compared with petrol. While 60 litres of petrol contains about 2GJ of energy, a pretty good (NiMH) battery of similar weight will muster a paltry 0.02GJ (less than 100th as much). The very highest-tech batteries – still impractical – such as Lithium Thionyl Chloride (LiSOCl2), still contain less than a 10th the energy of simple gasoline.

As a result electric cars cannot go very far on a single charge, and makes them impractical for most road users.

The smart money has not been holding its breath. The next beacon in the night was hydrogen. It packs in three times more energy in per kilogram than petrol. It makes water when it burns. How lovely.

The first problem with hydrogen is the overall efficiency – first you need to make electricity (with some inefficiency losses) – then you need to ‘make’ the hydrogen (with further losses), then you need to compress the hydrogen (yet more losses) and then you need to either burn it or convert it back into electricity in a fuel cell – both of which have more losses still. They all add up. However, these efficiencies are perhaps temporary problems…

A more permanent problem with hydrogen is its low density and thus large volume. Even when compressed to a liquid it still only contains a third the energy of an equivalent tank of petrol. Oh, and because its under very high pressure, the tank needs to be made from thick steel.

This means hydrogen cars also have poor range – and as hydrogen filling stations are rather rare, again this technology is still far from practical for Joe Public.

Due to these problems, the smart money has been looking elsewhere: a compromise solution, that tries to improve efficiency and also reduce emissions but without the short range: the so-called “hybrid”.

The Next Prius - the Toyota Prius is the top selling Hybrid

The Next Prius - the Toyota Prius is the top selling Hybrid

This is not rocket science. It is basically a car with a fairly normal engine, but also with an electric motor and battery pack.

The logic is that regular internal combustion engines waste energy when the car is running slowly or stopped at the lights. So why not switch over to an electric motor in these situations? And the electric motor runs off batteries which charge from the regular engine when it is running, though in some models the batteries can get a supplementary charge via a power socket at home .

But there is of course something extra that electric (and hybrid) cars can do: they can recover energy during braking – they call it regenerative braking.

The electrical boffins among you will know that a motor, which turns electric current into rotary motion, can work the other way too – turning rotary motion into electric current – when run this way, a motor becomes a generator.

So a car that uses an electric motor to drive the wheels can be used as a motor as you speed up, and a generator as you slow down.

The ability to recover energy from the brakes is where the big savings can be made, especially in town driving, and especially for heavier vehicles. A 2000kg car going at 40 mph has the kinetic energy equal to about 10ml (2 teaspoonfulls) of petrol, and since internal combustion engines are only about 20% efficient, that’s really about 50ml worth – which you burn every time you brake.

And that ‘s why someone came up with regenerative braking.

Aside on electric cars: Electric motors are generally quieter than standard engines. A very real challenge, believe it or not, for electric and hybrid cars, is pedestrian safety. They’re having to test simulated engine noise generators! Strange but true.

Coming soon?

Coming soon?

Why not Solar Power?

Many people have suggested that solar panels, aka photovoltaic (PV) cells, may have utility for electric and hybrid cars. Surely it would help to add some panels on the roof and bonnet?

It sounds good, but alas, solar power is fairly dilute – about 1kW per square meter is an estimate used in the industry. And while a few kW may drive your household’s minor appliances, it doesn’t do much for a car. Even small car engines pack over 50kW. There is simply not enough return, even if solar panels were 100% efficient.

When you add the fact that the real “insolation” (power of sunlight) is about 1/10th of the industry claimed 1kW/sqm, and that solar panels are typically only 20% efficient you can see where this is going.

Energy storage

We have already noted that energy storage is key to the challenge. Petrol and diesel pack a punch, but are not renewable and belch carbon dioxide, while batteries would need to be enormous and take ages to recharge.

Nickel Metal Hydride Battery

Nickel Metal Hydride Battery

Hydrogen is not dense enough so you need a colossal reinforced tank if you want to go any distance, and pocket-sized cold fusion reactors are still firmly in the SF domain.

There are however a profusion of ways to store energy, so what other options do we have?

Motorsport fans may have heard about the new F1 regenerative braking systems, called KERS (Kinetic Energy Recovery System), will also know that they are looking at flywheels and capacitors as alternatives to batteries.

A flywheel

A flywheel

The flywheel is simply a spinning disc which stores the kinetic energy in rotational form. This sounds simple, and can be very efficient but requires a fantastically strong flywheel, and will disintegrate if over-charged. Flywheels also have an annoying habit of resisting turns – that is to say their axis of rotation likes to stay pointing the same way, and so would probably need to be mounted within gimbals to allow a car to go around corners…

Flywheels can however achieve pretty good energy densities (comparable to batteries) and are very efficient. They can charge up and down faster and more often than batteries, but are, on the downside, far more expensive.

Ultracapacitors from Maxwell

Ultracapacitors from Maxwell

Capacitors are much cheaper – and can also charge and discharge quickly and many times. The capacitor is the electrical equivalent of a spring. You apply the electric equivalent of pressure (voltage) to the capacitor and it creates an electric field which stores energy. It is fundamentally different to a battery in which an applied voltage supplies electrons which drive reversible chemical reactions; it can charge and discharge much quicker too.

So what’s the catch? Rubbish energy density. Significantly worse than batteries or flywheels (which are of course already pretty poor compared with hydrocarbon fuels).

There are many other clever ways to store energy – in springs, elastic bands, compressed gases, raised weights – plenty for inventors to think about, but, alas, too many to cover here.

Despite this profusion, neither batteries or any of the alternatives pack the punch of petrol, so it’s going to figure in our future.

In my next article I ask: what we can do to make the most of our friend, the internal combustion engine? I look at their efficiency and also take a detour of perhaps a ‘green’ way to keep using them: with biofuels.

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What makes an efficient car?

Q: why are some cars so much more efficient than others?

Many people will say small=good, big=bad.

That’s a pretty good start, because big cars are probably heavier and also have more wind resistance.

But the rule does not work universally. Sports cars may be small – and look aerodynamic, but may still use lots of fuel so what’s going on there?

The sad reason for that is that the cars and trucks we drive have most often been optimised for speed, power and appearance and not necessarily for efficiency. This may be due to the circumstances in the 20th century – in which the vehicles we use today evolved – where the supply of oil appeared more-or-less infinite and where there were apparently no consequences for burning it.

So what factors determine how efficient a car or truck will be?

#1 Engine type

Petrol or diesel?

Petrol or diesel?

There are two major competing technologies – petrol and diesel. 

Diesel engines were not promoted for many years (for cars) as they tend to be sluggish and noisy. However they are the more efficient technology in terms of miles per gallon and carbon dioxide emissions (CO2 is the main ‘greenhouse gas‘).

However they have become steadily smoother and more refined and really took off in the 80’s – helped somewhat by government incentives (mainly in mainland Europe). However, they soon became implicated in city smog problems, so many incentives were dropped.

The engines continue to improve with efficiencies now perhaps 20% better than the equivalent petrol version – and as concern over CO2 grows diesel engines are again increasing popularity.

So why are diesel engines more efficient?

This is for two reasons: firstly, the engine internal losses are lower; petrol engines control their speed by ‘throttling’ the air supply to the engine – that is to say they hold back the air and make the engine suck it in through a small gap – a tactic which takes a lot of energy. Diesel engines just let the air in with arms wide open.

Secondly, diesel engines have a higher compression ratio which allows them to extract more energy (according to the laws of thermodynamics). Petrol engines cannot compress their fuel any more than they already do because petrol will spontaneously explode if compressed too much, and push the compressing piston backwards. It was this very problem that led Rudolf Diesel to invent the Diesel engine in the first place. In his design the fuel is only added after the air is compressed, totally side-stepping the issue.

#2 Car Dimensions

The most important measurement is the frontal projected area; this is unfortunate because a big cross section is what makes a nice roomy car. Tall cars are bad, wide cars are bad. It’s best to use the length if you need volume – which is the trick trains use.

It also turns out that nice fat tyres are also bad. Sorry. Biscuit wheels have less rolling resistance.

Sportcars do not slip through the air, they push it upwards...

Sports cars do not slip through the air, they push it upwards...

What about aerodynamics though? Surely a Ferrari slips through the air? Yes, to a degree, but not as much as you might hope – for one thing, Ferraris are surprisingly wide, but more interestingly, they are not actually designed to slip through the air – they are in fact designed to push the air upward in order to get downforce. Those big wings at the back are not there to cut through the air – they’re there to give the tyres more grip…

#3 Car Mass

It is hard work to lug a heavy suitcase around. It is obviously hard work to lug a heavy car around. That said, the laws of physics say that heavy items also have more momentum and so will roll further once moving – so you can in fact recover much of the energy if you take advantage of that momentum. The energy is really only ‘lost’ when you use the brakes and turn it to heat. 

This energy recovery trick, combined with ‘regenerative braking’ can reduce the impact of car weight, however generally speaking all additional weight is bad.

PS. I will cover efficient driving tactics and also ways to recover energy from the brakes in forthcoming articles in this series.

#4 Transmission

I know automatic gearboxes are nice. They free up the brain to worry about other things. But they are still bad for fuel efficiency – and for some interesting reasons.

Firstly, fuel efficiency depends on always being in the right gear to get the most out of the engine. However even the best and newest models still don’t change gear at the ideal time – whereas a skilled driver could.  Why not? Surely the brainy chaps at Toyota have perfected it all by now? Alas, no. The reason is this: the gearbox doesn’t have all the information the driver has. The driver may know he or she is about to crest a hill or hit some traffic. The gearbox can’t know this – it simply has to make a judgement based on the angle of your foot on the pedal and the current applied torque.

Secondly, some automatic gearboxes are less good at ‘coasting’ (i.e disconnecting the wheels from any internal machinery to reduce friction and engine resistance).

Aside for health and safety officials from the government: Some might say coasting is unwise; it is suggested that having the power to both slow down or speed up a short notice may improve safety; it is also suggested that engine braking is safer than foot braking because it is less inclined to the lock the wheels. These arguments do actually hold some water. While it is in fact possible to use engine braking to put the car into a skid, it is, in general, wise to take corners in gear as you will have more precise control over speed, and in the (rare) case of brake failure (or the more likely case of a foot slipping off the brake pedal), control is more likely to be maintained. I suggest therefore that coasting should only be done in safe conditions and at low speeds.  

The last problem with automatic gearboxes is all the fluid. While manual gearboxes do have some oil to churn,  the average automatic gearbox is a veritable fountain. The engine connects to the gearbox through a torque converter, which is a cunning clutch-like device based on discs spinning in fluids.

In the gearbox itself, the rotating shafts are used to pump fluids at high pressures through various tight channels and orifices in order to drive actuators that engage and disengage the absurdly clever planetary gearing. All this fluid-flow has inherent frictional loss, and thus reduces efficiency.

#5 Efficiency of Utilisation

What do I mean by ‘utilisation’? Well answer me this: what is more efficient, a Toyota Prius or a Grand Voyager? 

The answer is clear: it depends  – on how many people you are carrying.

Much can be said for using the vehicle right for the job. If you need a big van once every six months, look at renting or borrowing one, and drive something smaller.

#6 Age and Embodied carbon

This time I am asking: what is more efficient, a nice new Prius or your 3 year old one? You might think a new one would have the edge, but what you need to remember is that it takes an awful lot of carbon to make a new car, and it may take years to work that off. Rather keep your three-year-old in tip-top shape and hold onto it until its efficiency starts to dip –  until the new model really is significantly better.

Classic Cortina

Classic Cortina

If however you don’t have a Prius but have an old guzzler, the carbon may balance out rather more quickly – it really won’t do to keep driving your 3-litre Cortina for ever.

#7 On-board computer

If you get a car with an instantaneous fuel consumption display, you may find yourself trying to set a record – and learning a lot on the way. 

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In my next article I discuss some of the innovative green car technology that is on the horizon.

 

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Series home…

The Beginner’s Guide to Green Motoring

The 20th century has the seen the rise of the car in the western world. It has impacted the evolution of our cities, our roads and our houses – and we have therefore become rather dependent on them. We co-exist!

However, the effects of carbon emissions are emerging now and we find ourselves on the horns of a dilemma – to drive, or not to drive?

For those of us who can’t give it up, I have written a series of articles looking at the environmental impact of the motor car and looking at what we should be doing to minimize our impact.

hummer

Gas guzzler.

1. What makes an efficient car?

2. Green car technologies explained…

3. Making the internal combustion engine greener

4. How to drive more efficiently

That’s it for now, but I will hopefully add more in time.


©Jarrod R. Hart 2009

Open question about relativity

A quick open question for physicists:

If you accelerate off in one direction, and keep accelerating until you are travelling fast (a relativistic speed), special relativity supposedly says the universe contracts in the direction of your travel. Fine, I can see how that makes some sense.

Now consider a massive body, such as the sun – it warps space time in its vicinity, presumably roughly equally in all directions, creating a symmetrical ‘dent’ in the fabric of space-time (if you like the trampoline analogy).

But if you fly past at a relativistic speed, and space is contracted in the direction of your travel, will the sun’s sphere of influence also be contracted, turning it from a “sphere of influence” into an ‘oblate spheroid of influence’?

Or will its shape be maintained for some beautiful reason (which is what I suspect)?

Thx.

The interesting implications of our theory of gravity…

The evidence is now pretty strong that Gravity is just a symptom of ‘curved’ space time.

While it’s cool to have gravity all figured out, like so many matters in science, the answer raises even more interesting questions.

Like what is the nature of the curvature? Well, people (including me) are still trying to figure this out. In the meantime it is a good pastime to pontificate about the implications of curved space time. Here are two of my most recent theories/perspectives…

Perspective 1: Trees and apples switch places…

Each mass has a ‘destined path’, a path it will follow if left to its own devices. Just as Newton suggested in his First Law of Motion, things only change velocity when experiencing a net force.

However, he thought that gravity was a ‘force’ that made apples drop, however, the new theory of gravity suggests the apple was stationary – it was the tree and the meadow that were accelerating (upwards), a result of being pushed by the ground.

It lets us think of falling objects as ‘free from force’, and obeying Newton’s First Law.

Now, switch gears. Think what would happen if you could walk through solid things like walls. You may think it useful, but it would certainly cause some inconvenience, as you would presumable fall through the floor and plunge into the Earth’s molten core. You would fall past the centre and then start slowing; you would then briefly surface on the other side of the Earth, only to fall again. You would thus oscillate on some sort of sine wave. This is your ‘destined path’, the straight line through space time that your mass and location intend for you, where you to follow Newton #1. It is simply all the floor tiles and rocks preventing you from going straight in space-time. You are thus constantly being pushed, and thus curving off that path, thanks to the force of the floor. Lucky thing really.

Perspective 2: Slow time really is a drag…

A gravitational field can also be thought of as a gradient in the speed of time. It is possible (to me at least) that rather than supposing space-time is curved, it may well be that it simply varies in ‘density’. How? Well if time passes at different speeds in different places, that can be thought of as a density difference.

Now, we know that even when standing still, we are still plunging ahead – through space-time – in the direction of time. However,  thanks to Earth’s gravity, time is going slower down at your feet, they are sluggish, stuck in the mud. Now if you have a pair of wheels on a fixed axle, what happens if your right wheel gets stuck in the mud? It slows and you turn to the right… and in the just the same way, your body is trying to ‘turn’ downwards toward your feet – the gravity you feel!

When I first thought of this model, I was smug and pleased with myself. Until I found someone else[1] had already used it to accurately model planetary orbits. Read about it here – they have shown that waves (and therefore particles) will curve for the above reason combined with Fermat’s Principle. Bastards! 😉

 

Refs:

[1] Landau, LD; Lifshitz, EM (1975). The Classical Theory of Fields (Course of Theoretical Physics, Vol. 2) (revised 4th English ed.). New York: Pergamon Press. pp. pp. 299–309. ISBN 978-0-08-018176-9

Gravity explained in 761 words

People seem to be harbouring the impression that there is no good theory of Gravity yet. I asked a few friends – most thought Newton had explained it, but couldn’t explain it themselves. This is rather sad, 80-odd years after a darn good theory was proposed.

Of course there is still some controvery and the odd contradiction with other beloved theories, but the heart of the General Theory of Relativity really does a great job of explaining gravity and it is really wonderfully beautiful, and can be roughly explained without recourse to jargon and equations.

This is a theory that’s just so darn elegant, it looks, smells and tastes right – once you get it. Of course, the ‘taste’ of a theory doesn’t hold much water; for a theory to survive it needs to make testable predictions (this one does) and needs to survive all manner of logical challenges (so-far-so-good for this one too).

This is not a theory that needs to remain the exclusive domain of physicists, so for my own personal development as a scientist and writer, I thought I might try an exercise in explaining what gravity is – according to the general theory of relativity.

For some reason, my wife thinks this is strange behaviour!

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The story really got started when Einstien realised that someone in an accelerating  spaceship would experience forces indistinguishable from the gravity felt back on Earth. 

He or she could drop things and they would fall to the floor (assuming the spaceship is accellerating upwards)  just as they would fall on earth.

So perhaps that’s all gravity is… some sort of accelleration? Let’s see.

In the spaceship, it’s clear to us that the objects would appear to fall to the floor, but in reality, it is the floor of the spaceship that is rushing up towards the objects – this explains why things fall at the same speed whether heavy or light, matching Galileo’s own test results when he dropped various things, supposedly from the leaning tower of Pisa. It further implies that things will ‘fall’ even if they have no mass at all… such as light beams.

The thought experiment goes thus: Consider if you had a laser-beam shining across the spaceship control room; it would curve slightly downwards, because the light hitting the opposite wall would have been emitted a little time ago, when the spaceship was a little way back, and going a bit slower (remember, its accellerating).

We know the light is not bending, it is just that the source is accellerating, resulting in a curved beam. Imagine a machine-gun spraying bullets across a field – as you swing the gun back and forth the bullets may form curved streams of bullets, but each individual bullet still goes straight.

So Einstein suggested that perhaps light beams will bend in this same way here on earth under a gravitational field. Now Newton’s theory of gravity says light beams may also bend if they have ‘mass’, but the mass of light is a dodgy concept at best (it has inertia but no rest mass, but that’s a whole different blog posting). Anyway, even it it does have mass, it would bend differently from what Einstien predicted. So the race was on to see how much gravity could bend light…

This bending of light prediction was proven by a fellow called Eddington who showed that during a solar eclipse, light from distant stars was indeed bent as it passed near the sun, and by exactly the predicted angle.

Einstein went further though, suggested that light beams on Earth are, just like on the spaceship, really travelling straight, and only appear to bend, and that this can be so if space-time itself is curved. They are going straight, but in curved space.

We know that the shortest distance between two points is a straight line, but if that line is on a curved surface, supposedly straight lines can do strange things – like looping back on themselves. Think of the equator. This model therefore allows things like planets to travel in straight lines around the sun (yes, you read right).

The model has been tested and shown to work, and gives good predictions for planetary motion.

So what can we take home from all this?

Well mainly, if this model is right, we need to let it sink in that gravity may not be a force at all, but an illusion, like the centrifugal ‘force’ you experience when you drive around a corner.

Secondly, it is an open invitation to think about curved space and its marvellous implications!

The trouble with academia…

I have had enough exposure to scientific academia (6 years full time, and now 6 years as an industrial PhD supervisor) to have seriously lost faith. Some of the issues well put by Jonathan Katz, a physicist in his article Don’t become a scientist.

Perhaps ‘lost faith’ is too kind. “Fed up with”, is perhaps more precise. Perhaps I just want to whine. The complaints I would add to Dr Katz are the following opinions I have come across:

  1. The assumption that unless you are a professor at a tedious university, you have no intellect.
  2. The idea that unless your ideas are published in a the ‘preferred’ peer reviewed journal, they are not worth bothering with.
  3. The idea that research with some practical use is somehow inferior.
  4. The idea that anyone deserves to get public money to ponder their theories without a feeling a gratitude and indeed an obligation to pay this kindness back.

Perhaps I am just envious and wish I was a don at Oxford… 😉