All posts by jarrodhart

About jarrodhart

A science & engineering geek, err, that's about it.

How to drive more efficiently

Auto, Education, Environment, Green Motoring, , , , , , , , ,

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?

Auto, Education, Environment, Green Motoring, , , , , , , , ,

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

Auto, Education, Environment, Green Motoring, , , , , , ,

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?

Auto, Education, Environment, Green Motoring, , , , , , ,

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

Auto, Education, Environment, 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

The psychology of submission to authority

Psychology, Science, Science communication, , , , , ,

What does not surviving a plane crash have to do with the “medicalisation” of childbirth? I would argue that they are both examples of how we are losing our ability to take our fate into our own hands.

When a plane crashes, some passengers die because they are waiting to be saved while those that act to save themselves are more likely to survive [1]. 

Why? Because when people hand control over of others, they find it hard to take it back again. 

So it is as you queue on the phone to buy plane tickets, you queue to check in, you queue through security, you walk down long corridors, you queue again.

To some real extent, this process is a bit like being brainwashed – it is a series of mental triggers that you are in a system, you are a subject, you are not in control. You have become a sheep.

This in itself is not a bad thing. It helps the systems to work if the people can be controlled, and certainly nothing sinister is intended; however it does mean that if the plane crashes we will be more inclined to wait for instructions than fight our way to the door.

A similar effect can play out during childbirth.  Mothers who undergo cesarean subjugate themselves to the system and in handing over responsibility, may well find taking the child back after it is cleaned-up more psychologically challenging, and are thus more likely to turn to authority (nurses, midwives etc) for help with routine things like breastfeeding and washing the baby, rather than assume responsibility; their confidence is thus eroded by the process of subjugation.

I propose therefore that both on air flights and in the maternity ward, we should do what we can to keep people in control – or at least thinking they are…

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[1] I read this claim in last week’s Sunday Times, but can’t find a reference online. However, this article hints at similar claims: 
http://www.time.com/time/magazine/article/0,9171,1053663,00.html

Open question about relativity

Cosmology, Mathematics, Physics, Relativity, Science, Time, , , , , , , , ,

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…

Cosmology, Mathematics, Physics, Relativity, Science, , , , , , , , , ,

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

Winning the toss

Mathematics, Science, Sports, , , , , , ,

WARNING: Please do not even try to read this unless you are cricket fan. If you are not it will only irritate you 😉 thx.

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Test Cricket: Australia vs. South Africa: 6 tosses to ZERO, nada, nought. Time for a change in the rules.

by Jarrod Hart

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Winning the toss in cricket can be a very significant advantage, and lead to unfairness. Let me explain…

Firstly, I am going to admit that I am an avid cricket fan. And being a nerd too, this makes me doubly susceptible to a love affair with sports statistics.

I probably learnt most of my maths skills working out how many runs Graeme Pollock required to improve his season’s average, or calculating the run rate required by Clive Rice’s Transvaal team to win the Benson & Hedges night series final at the Wanderers.

So what is my problem with the toss?

In many sports there are environmental factors that skew the game – the sun shining in your eye when you serve, the dew on the putting green, the wind behind Jonny Wilkinson, and so on.

A cricket pitch is no different. Being composed of sand and grass, it is not wholly predictable – it is also prone to evolve over time.

It can therefore be a big advantage to bat first, or perhaps to bat second. The skilled captain can often tell what the pitch will do from looking at it. To make things fair, a coin toss is used to see who gets to choose who goes first. Fine. Over the course of years, all teams will win some and lose some. However, with test matches taking five days each, the teams only play each other once every few years, so the ‘fairness’ may take a generation to arrive. 

The stats are clear. Winning the toss helps. Get the latest stats from wikipedia; at the time of writing 34.7% of toss winners had won the match. 30.8% of toss losers had won. The remainder draw/tie.

Some people will still say, oh, that’s not too big an effect, less than, say, the home advantage in football. Yes the numbers aren’t too dramatic, but what no-one seems to be pointing out is that that 3.9% difference is actually coming from a somewhat bigger difference in a smaller subset of the matches.

For example, many cricket tests are one-sided. That is to say, the favourite wins. In cricket upsets are fairly rare (rarer than in football for example). Draws yes, but complete reversals are not that common. This means that there have been lots of outclassed teams winning the toss (statistically, even the most outclassed team win the toss half the time). They have of course, mostly lost.

Secondly, there have been matches where the pitch really was constant. That is to say the toss didn’t help.

So we are left only with the matches between evenly matched teams on pitches that change. The 3.9% positive toss effect must be a stronger effect coming from this subset of the results.

I also have anecdotal evidence (all scientists, wince now). I have often watched a match, where the first team has scored 600 of a flat pitch, and then seen the second team face a ball that suddenly stays low or cuts around. We have recently seen some almighty thrashings, some by an innings plus. These by teams that were, just before the match, considered fairly equal.

Now we come to the present time. The #1 and #2 teams in the world have been locked in battle for several months. I am of course referring to the ongoing test series between South Africa and Australia. And Australia have just won their sixth toss in a row. They have won the last three matches, on ‘evolving’ pitches, and of course I am bitter, of course I am looking for excuses. But I am rational enough to see unfairness when it strikes.

I was not going to write about it. I knew it would come over as whining. Until a friend pointed out a simple solution: they could have one toss at the start of the series and then alternate the choices for the remaining tests, thereby preventing one team heaping the unfairness too high.

Today’s sixth win in a row for Australia was too much. We need a change in the rules. The South Africans have lost their #1 ranking to the toss, and it stinks.

The last 6 tests:

Test no. 1899 Toss won by Australia, match by SA (In Australia)

Test no. 1902  Toss won by Australia, match by SA (In Australia)

Test no. 1904  Toss won by Australia, match by Australia  (In Australia)

Test no. 1910 Toss won by Australia,  match by Australia (In SA)

Test no. 1913  Toss won by Australia,  match by Australia (In SA)

Test no. 1916 Yes, Toss won by Australia,  match ongoing (In SA)

Foot-note: Being a cricket stats nerd, it was of course sad news to hear that Bill Frindall, a peerless cricket analyst had died. He acted as the eye of a the nerd-storm that has been raging for years, about which most of the world was blissfully unaware. His death has left us all without bearing, little squalls in the night.  CricInfo is not not quite the same. Yes, it’s rammed full of passionate staff, many of whom are nerds and scholars of the game, but it seems to lack the Frindall touch. I ask you this: who will care about this problem with the toss in this new world order? Bill would have.

The Economics of Advertising Warfare

Economics, Science, The scientific method, , , , ,

Picture the scene. Acme Corp’s toothpaste business AcmeDent is a profitable enterprise; and so is that of their biggest rival Ace.

One day, however, they hire a new marketing and sales manager, let’s call him Bob. He is ambitious and full of ideas – ready to shatter preconceptions, break the mold, think outside of the box, etc, etc.

After a few days in the office he realises that the market is saturated. People are just not going to start brushing at lunchtime. The only thing for it is to increase market share. He calls a team meeting.

“We either have to increase sales or increase our margins. We have already cut ourselves to the bone cost-wise, and increasing price will lose market share. If we cut prices, we lose market share – so it looks like stale-mate.” But Bob, being new, felt this was old fashioned reasoning. Surely we could do something to get market share? “Any ideas?”, he asks.

The room is quiet. No one wants to say anything risky in front of the new boss. Looking around at his team, his eyes settle on Sheila, the head of brand management. “What are you doing to get market share?”

Now Sheila wanted Bob’s job. She’s not is a good mood, but knows to be cautious. “Well Bob, as you will know from the report I prepared for you, our advertising budget is tight; your predecessor seemed to think we just needed to match Ace’s spend.”

“What? Why?!” Bob sits up. He can smell an opportunity.

“Don’t ask me, I asked for more. He was very conservative.” There’s a murmur around the table. They all know Sheila is being polite. Before being headhunted, Bob’s predecessor had a reputation for being tighter than duck’s arse.

A few weeks later, the new ad campaign cranks into life. Bob is surprised by how much it cost, but he knows 10% more market share will make it more than worth while. He starts to study his sales figures with care. Will it work?

The end of the quarter looms. What will the results show? Bob reads the business news – Ace’s chairman has made some comments. They are very critical and accuse Acme of “destroying the market”.

“Ha!” Bob exclaims out loud. Excellent, they are hurting.

The results roll in. They are good. 12% additional market share, mostly taken from Ace. No wonder they’re moaning.

That night, he sees the new TV ad from Ace. He has to admit it’s good.

“Why didn’t we think of that?” he booms to Sheila the next morning. “It’s a great idea.”

Sheila is unruffled. “We did think of it; we just thought it would be too expensive.”

“Hell!”, Bob is on a roll with the benefit of hindsight, “we’ve seen that advertising can gain us market share – of course it’s worth it. What you can do if I double your budget?”

“Well…”

Ace’s campaign works and Acme loses most of their new-found market share. The next month brings Acme’s bigger and better campaign – tying together TV, print, competitions, star endorsements, the whole shebang. Again is works like a charm. Market share is back up.

—

Freshly sun-tanned from two weeks on the Keys, Bob is feeling pretty pleased with himself at the AGM. The CEO will surely make a point of congratulating him on a job well done. He is getting on too, and will surely be eyeing up replacements.

The meeting starts well and soon enough they came to the the financial performance of AcmeDent toothpaste.

“Bob,” the CEO starts, “what the hell is going on here?”

Bob is taken aback by the look of displeasure on the CEO’s face. Oh, well he has a reputation for being grumpy, maybe this is him having a joke. “Well, you see, we have increased market share by 10% this year, our revenues are at an all time high…”. He searched the CEO’s still stony face.

“But what about profits? What are they?”

“Well, you see, this year we made significant investments, so it doesn’t look great, but rest assured, next year…”

“Investments?”

“Yes, we invested in major advertising campaigns…”

The CEO is shaking his head slowly.

Bob is suddenly feeling a nervous. “Well, we had to spend money to get the market share, but now we’ve got it, we will see a profit next year.” That should calm him down.

“But what about Ace’s latest trick? While you were away, they’ve started a new fad amongst teenagers for luminous teeth or something.”

“Well sir, it is a bit of an arms race…”

“A race to where exactly?”, the CEO looks very serious now.

“Well…”

“Bob, can’t you see, they have to match our advertising spend to protect their business. All you’ve done is pissed both company’s profits down the plughole.”

The CEO leans over to his assistant, “How much to get the other guy back?” he whispers.