Why Don't Penguins' Feet Freeze?: And 114 Other Questions - Mick O'Hare (2009)
Chapter 9. Best of the rest
In many parts of the world, people celebrate victories, birthdays and similar events by firing guns into the air with great exuberance and a seeming disregard for the welfare of themselves and others. Assuming the barrel of the gun is perpendicular to the ground when the bullet leaves it, approximately what altitude would it reach and what is its velocity (and potential lethality) when it falls back to Earth?
Auckland, New Zealand
Firing handguns into the air is commonplace in some parts of the world and causes injuries with a disproportionate number of fatalities. For a typical modern 7.62 millimetre calibre bullet fired vertically into the air from a rifle, the bullet will have a velocity of about 840 metres per second as it leaves the muzzle of the gun and will reach a height of about 2400 metres in some 17 seconds. It will then take another 40 seconds or so to return to the ground, usually at a relatively low speed which approximates to the terminal velocity. This part of the bullet’s trajectory will normally be flown base first since the bullet is actually more stable in rearward than in forward flight.
Even with a truly vertical launch, the bullet can move some distance sideways. It will spend about 8 seconds at between 2300 and 2400 metres and at a vertical velocity of less than 40 metres per second. In this time it is particularly susceptible to lateral movement by the wind. It will return to the ground at a speed of some 70 metres per second.
This sounds quite low but, because of the predominance of cranial injuries, the number of deaths and serious injury as a proportion of the number of gunshot wounds is surprisingly high. It is typically some five times more than is observed in normal firing. As might be expected, measurements of this kind are rather difficult and the above values come from a computer model of the bullet flight.
Sam Ellis and Gerry Moss
Royal Military College of Science
Swindon, Wiltshire, UK
Different bullet types behave in different ways. A .22LR bullet reaches a maximum altitude of 1179 metres and a terminal velocity of either 60 metres per second or 43 metres per second depending upon whether the bullet falls base first or tumbles.
A .44 magnum bullet will reach an altitude of 1377 metres and will have a terminal velocity of 76 metres per second falling base first. A .30-06 bullet will reach an altitude of 3080 metres with a terminal velocity of 99 metres per second.
The total flight time for the .22LR is between 30 and 36 seconds, while for the .30-06 it is about 58 seconds. The velocities of the different bullets as they leave the rifle muzzle are much higher than their falling velocities. A .22LR has a muzzle velocity of 383 metres per second and the .30-06 has a muzzle velocity of 823 metres per second.
According to tests undertaken by Browning at the beginning of the century and recently by L. C. Haag, the bullet velocity required for skin penetration is between 45 and 60 metres per second, which is within the velocity range of falling bullets. Of course, skin penetration is not required in order to cause serious or fatal injury and any responsible person will never fire bullets into the air in this manner.
The questioner may like to read ‘Falling bullets: terminal velocities and penetration studies’, by L. C. Haag, Wound Ballistics Conference, April 1994, Sacramento, California.
Melbourne, Victoria, Australia
John W. Hicks, in his book The Theory of the Rifle and Rifle Shooting, describes experiments made in 1909 by a Major Hardcastle who fired .303 rifle rounds vertically into the air on the River Stour at Manningtree. His boatman, probably a theorist unaware of the winds aloft, insisted on wearing a copy of Kelly’s Directory on his head.
However, none of the bullets landed within 100 yards, some landed up to a quarter of a mile away and others were lost altogether.
Julian S. Hatcher records a similar experiment in Florida immediately after the First World War. A .30 calibre machine gun was set up on a 10-foot-square stage in a sea inlet where the water was very calm, so that the returning bullets could be seen to splash down. A sheet of armour above the stage protected the experimenters. The gun was then adjusted to centre the groups of returning bullets onto the stage.
Of more than 500 bullets fired into the air, only four hit the stage at the end of their return journey. The bullets fired in each burst fell in groups about 25 yards across.
The bullets rose to approximately 9000 feet before falling back. With a total flight time of about a minute, the wind exerts a noticeable effect on the return point.
In my youth, I used to collect brass cartridge cases ejected from aircraft machine guns during the Battle of Britain for salvage. They drifted down slowly from the sky because, I guess, their mass to surface area ratio was low. However, they were still warm when I picked them up.
Accordingly, if the projectile is small, like a .303 bullet, it does nobody much harm when it lands. Like a mouse in a mineshaft, its terminal velocity is negligible. However, if because of its mass the projectile has enough terminal velocity, it could kill you.
M. W. Evans
Inzievar, Fife, UK
Two people lose each other while wandering through the aisles of a large supermarket. The height of the shelves precludes aisle-to-aisle visibility. One person wishes to find the other. Should that person stop moving and remain in a single visible site while the other person continues to move through the aisles? Or would an encounter or sighting occur sooner if both were moving through the aisles?
Newark, New Jersey, US
The best strategy may be to wait at the exit of the store on the grounds that the other person may eventually conclude that you have gone home and do likewise. The maximum waiting time will then be from the time you lost each other until the store closes.
A strategy of staying still only works if just one person stays still. If you both decide to stay still, then the wait time is either infinite, if you get locked in, or again until the store closes.
Assuming that one person stays still while the other searches, then the maximum time is the time taken for one person to search the entire store. This depends on the layout of the store: if all the aisles can be readily seen from one vantage point, then the search is simplified. The problem is not dissimilar to that of designing prisons in which the warders can see down as many corridors as possible, or the design of forts that will give the defenders maximum cover. In order to increase the odds of being located, the person staying still should stand at an intersection of aisles.
A random search will proceed with each person moving away from their initial starting point at a rate proportional to the square root of time. The area being searched by each person is defined by two circles centred at their respective search starting points. Given that these circles will need to overlap significantly for the individuals to meet, the search time must be at least proportional to the square of their initial separation distance. If some of the aisles are blocked during this search, then the rate of movement is reduced and the problem becomes one of motion on a fractal where the rate is proportional to some fractional exponent.
St Albans, Hertfordshire, UK
To begin to answer this question, one must first know whether the two people have agreed in advance what to do if separated – for example, who should wait and who should search. If they can agree on independent search strategies in advance, the problem is the asymmetric version of the rendezvous search problem (see below); otherwise it is the symmetric version.
I discuss both versions of the problem in a paper to be published in the Society for Industrial and Applied Mathematics Journal of Control and Optimization, and several specific cases in particular search regions have subsequently been solved. In all these cases where exact solutions (to give a least expected time or minimax time) have been obtained, both searchers move at their maximum speed all the time. In these cases it is certainly not optimal for a searcher to stop while the other continues. For example, in a simplified model in which two people are placed a unit distance apart, but neither knows the direction of the other, it would take an expected time of (1 + 3)/2 = 2 for the searcher to find the stationary person (assuming visibility is nil). However, by moving optimally this time can be reduced to 13/8.
The only case I know of where a searcher and a waiter may be optimal is for two people placed randomly on a circle, and then only when the people concerned have no common notion of clockwise; otherwise one person walking clockwise and the other anticlockwise is optimal.
All these results and questions assume that the searchers find each other only when they meet or alternatively when they come within a specified detection radius. This applies to aisles in a supermarket on a crowded day, when visibility along an aisle is limited. The possibility of seeing a long distance along an aisle has not, as far as I know, been modelled.
In case anyone is interested, the full bibliography on this topic is: ‘The rendezvous search problem’, S. Alpern; ‘Rendezvous search on the line with distinguishable players’, S. Alpern and S. Gal; ‘Rendezvous search on the line with indistinguishable players’, E. Anderson and E. Essegaier. All three papers appeared in the SIAM Journal of Control and Optimization in 1995.
London School of Economics, UK
I recommend that you walk along the edge of the supermarket where the tills are, looking down the aisles for the person you seek. If you have no success, then walk back, still looking down the aisles, but also checking the tills. If you still have no success, then find the cold meat counter, as queues often develop there. Then have a final walk along the till edge, checking the aisles again. If you are still unsuccessful then you should ask for an announcement to be made on the public address system – or, if it’s not urgent, wait by the exit.
Aberystwyth, Dyfed, UK
Please read this sentence and count the Fs:
FINISHED FILES ARE THE RE-
SULT OF YEARS OF SCIENTIF-
IC STUDY COMBINED WITH
THE EXPERIENCE OF YEARS.
How many did you see? On first reading most people see only three. However, the answer is actually six. Why is this?
Cleckheaton, West Yorkshire, UK
The fact that most people can only see three Fs instead of six would only be strange if reading was entirely phonetic. In reality, several methods are used to get meaning from print, and the most common of these has little to do with individual letters and their sounds.
A reader becomes familiar with the shape of many words, particularly short, common words like ‘of’. These shapes are memorised and the reader no longer sees the words as made up of separate sounds. So, when you read the sentence, you spot the Fs in the longer, less familiar words but not in the three occurrences of ‘of’.
Exeter, Devon, UK
An intelligent seven-year-old or a proofreader would read six Fs, because they have learned to give all words equal values.
As we learn to read faster, we select the most important words, permitting our brains to fill in the gaps. The faster we wish to read, the more words we must skip. It is quite possible to read simple narrative at faster than 600 words per minute, with comprehension. Fact-packed scientific text obviously has to be read more slowly.
A fast reader must concentrate on the most important words, usually nouns and verbs. Adjectives and adverbs come next, with modals, articles, pronouns and prepositions and so on coming last. Experienced readers take less notice of the least important words which in English (as in most other languages I know) tend to be short words. So all the little words like ‘of’ are skipped, and their Fs are omitted from the count.
I can only speculate about reading speeds in Chinese or Japanese where writing systems are quite different.
Banbury, Oxfordshire, UK
I tried this on a work colleague, without using the same layout of words and characters. When I rewrote it two occurrences of ‘of’ were at the end of lines, and my friend spotted these Fs but missed the remaining one. So I would assume that the way they are placed (in the middle of the line) has an effect on their noticeability.
Obviously, someone who does not understand English would have no problem spotting the Fs. It would be interesting to see how someone who has English as a second language responds to this.
I found out by reading an optical illusions book Can You Believe Your Eyes? by J. Richard Block and Harold E. Yuker that most people think there are three Fs because they do not notice the Fs in ‘of’. This is because the F in ‘of’ is pronounced as a V, so the brain doesn’t recognise it as an F.
Bryn Hart (aged 10)
Kelmscott, Western Australia
Great shame was felt, not only at seeing only three Fs but at still seeing three after reading the answer. Then my wife sat down and announced that she saw six on first reading.
I am an English teacher and my wife a maths teacher and there lies the difference. The reader tries to understand the passage and casually ignores the word ‘of’, which is repeated three times. The mathematical mind does exactly what the question asks – it counts the Fs. My wife sees a number of letters but I see a phrase and therefore ignore the actual task.
The splitting of words with hyphens is also important because it puts pressure on the reader to understand the text and to follow the words, diverting attention from the real task.
High Peak, Derbyshire, UK
Your correspondent will be pleased to know that English is my second language (Taiwanese is my first) and I am due to take maths A-level exams this summer. My F count on first reading was three, and it was still three after seeing the answer. I only realised that the additional Fs were in ‘of’ when I spelt it all out aloud. In fact, I only realised as I recited the second ‘O. F.’.
It is my belief that your background has no bearing on whether you spot the Fs or not. My training as a systems analyst should help me to concentrate on the task in hand (counting the Fs). As to why I missed them, two explanations remain. Either it was too late at night or I am obviously not suited to doing a maths degree and should contemplate a change of course.
As a postscript I submit the following:
IN THE WORLD
When trying to persuade a class of seven-year-olds of the need to reread what they had written, I put the above legend on the blackboard. My best readers immediately read it as ‘The silliest mistake in the world’ and I replied, ‘You’ve just made it.’ It was only when we reached the slower readers that the extra ‘IN’ was discovered. At this point the headmaster came into the room, glanced at the board, and read the message aloud, but incorrectly. A chorus from the class greeted him: ‘You’ve just made it, sir.’
The F and V confusion that was suggested by one of your correspondents cannot be the explanation here.
Stockport, Cheshire, UK
In James Bond films, a gun with a silencer is used to dispose of bad (and good) guys. How does the silencer work?
Chesham, Buckinghamshire, UK
Silencers are more properly called sound moderators or suppressors and are widely used by hunters to reduce noise levels from the discharge of firearms, particularly sporting rifles and air weapons. A sound moderator is essentially no more than a series of baffles coupled to an expansion chamber, contained within a tubular attachment which screws on to the end of the firearm’s barrel.
The noise of the discharge of most firearms is made up of two components. The first comes from the rapid expansion of propellant gases as they leave the muzzle. The second is the supersonic crack of the bullet. It is not possible to reduce the sound level of a supersonic bullet, but a sound moderator fitted to such a rifle will have some significant effect in reducing the noise signature because it controls the rate of expansion of the propelling gases.
For a sound moderator to be really effective, it must be used with ammunition whose projectiles travel at less than the speed of sound. In such cases, the noise of the discharge is greatly reduced and may not even be recognisable as a gun.
It is not possible to fit a sound moderator to a revolver because the gap between the barrel and the front of the cylinder means that about 5 per cent of the propellant gases escape, contributing to the overall noise of the discharge. Otherwise, sound moderators can be fitted to any type of firearm.
I once watched a Second World War Sten submachine gun fitted with a large, integral moderator being fired using special subsonic ammunition. The results were impressive: the only noise that came from the weapon was the clatter of its bolt.
In the public imagination, sound moderators for firearms invariably have a James Bond or underworld image. In reality, they are widely used in the countryside by hunters who wish to play their part in cutting noise pollution.
The British Association for Shooting and Conservation Wrexham, Clwyd, UK
The first successful silencers were patented in 1910 by the American inventor Hiram P. Maxim (son of Hiram S. Maxim of Maxim machine-gun fame). His devices were of the baffle type, which is still in common use today. A baffle silencer typically consists of a metal cylinder, usually divided into two sections, which is fixed to the muzzle of the firearm.
The first section, which is typically about a third of the silencer’s length, contains an ‘expansion chamber’ into which the hot gases that follow the bullet out of the muzzle can expand to dissipate some of their energy. The expansion chamber may contain a wire mesh cylinder, whose function is to break up the column of gas and to cool it by acting as a heat sink.
The second section consists of a series of metal baffles, with a central hole to allow the passage of the bullet. The function of the baffles is to progressively deflect and slow the flow of gas emerging from the expansion chamber, so that by the time the gases emerge from the silencer, their flow is cooler, they travel at low velocity and they are silenced. A motorbike silencer works on exactly the same principle.
There are also variations on this theme: some designs consist entirely of baffles, while others are based entirely on one large expansion chamber. In fact, a plastic soft drinks bottle can be made into a fairly efficient silencer that will work for a limited number of shots before it breaks up.
Silencers usually work best with cartridges that fire subsonic ammunition, since this eliminates the sonic crack which is produced by a bullet that goes faster than the speed of sound.
Some silencer designs slow the bullet to subsonic speed by means of ports cut into the barrel, with the ported section extending to protrude into the expansion chamber. These ports bleed off gas from behind the bullet, thereby reducing bore pressure and, eventually, the velocity of the bullet. In other designs, the baffles are made from an elastic material with a central hole smaller than the bullet. These ‘wipes’ are pushed open by the passage of the bullet and close when it is past. The idea is that they further slow the exit of gas. Not surprisingly, the wipes can wear out rather quickly and can affect the accuracy of the bullet.
A second, but less common, type of silencer is the ‘wire mesh’ design. These usually have the same expansion chamber as the baffle type, but the baffles are replaced by a column of knitted wire mesh with a central hole for the bullet. Here, the wire mesh acts to disrupt the column of gas as in the baffle design, while at the same time acting as a heat sink to cool the hot gas and hence quieten it. Criminals have been known to improvise this type of silencer, using wire wool or steel pan scourers to form the mesh.
The very latest innovation in muzzle-mounted silencers is the so-called ‘wet’ silencer (or ‘wet can’ in the US). These designs allow the use of water or a lubricating oil. On firing, the hot expanding gases are cooled, and therefore quietened, by the exchange of heat into the liquid. Wet silencers allow the designer to produce much smaller or quieter designs.
An alternative approach to silencer design which dispenses entirely with the muzzle-mounted silencer has appeared from Russia. Instead it uses a special cartridge in which the bullet is pushed out by a propellant-driven piston. The piston is stopped by the neck of the cartridge, trapping the hot, noisy gas entirely within the chamber of the firearm.
It is fair to say that Hollywood takes great artistic liberties with silencers. Most real designs are very much larger than the cigar-tube sized ones typically shown on film and usually much less simple to fit and remove. Despite what is shown in films, it is usually impossible to silence a revolver because the gap between the cylinder and the barrel allows gas to escape.
Finally, forget the distinctive ‘phut’ produced by James Bond’s silencer. Real designs are more likely to produce a muffled crack, or to sound like a car door being slammed.
By email, no address supplied
Checkout operators the world over vigorously rub any malfunctioning credit and debit cards on the nearest available article of clothing. Does this actually serve any useful purpose?
From my experience, a credit or debit card will fail to ‘swipe’ correctly for one of three reasons.
First, something has permanently interfered with the magnetic strip on the card, so that the computer cannot read it. The cashier will have to type in the number manually, and a new card will probably need to be issued. Secondly, the machine is faulty and is unable to read the card.
However, the third reason the card cannot be read is the most common cause. Dust or dirt of some sort has collected on the magnetic strip. This obscures the information from the electronic reader. A quick wipe on your sleeve is all that is required to resolve this and, in the vast majority of cases, the card will swipe successfully at the second attempt.
There is no great mystery and no big science behind this practice, at least not that I am aware of. If you keep your cards in the card compartment of a purse or wallet, they should remain reasonably clean, and swipe easily on the first attempt. This should also eliminate the first problem, because they will be protected from anything that is likely to irreversibly damage the strip.
Petworth, West Sussex, UK
There is one drawback to rubbing the magnetic strip and it was something I often experienced as a supermarket supervisor. Rubbing the card can sometimes make it more difficult to read because it becomes charged with static electricity that can interfere with the electronic reader.
The instinct to rub the card in an attempt to remove any dust that may have stuck to it may work in the short term but the extra static charge the rubbing has generated will ensure that even more dust will cling to the card later on.
Why do boomerangs come back?
Barry, South Glamorgan, UK
A boomerang is like two spinning aeroplane wings joined in the middle. It is held almost vertically before it is thrown end over end. Because it spins in this way, the top wing actually goes away from you faster than the bottom wing. This makes the sideways push on the top wing (similar to lift on an aeroplane wing) stronger than that on the bottom wing, so the boomerang gets tilted over, just as you would be if someone pushed on your shoulder, and its flight pattern begins to curve.
Similarly, if you ride a bicycle and lean over, the bicycle will turn, eventually going in a circle. The boomerang does too.
Sheffield, South Yorkshire, UK
Returning boomerangs work by a combination of aerodynamic and gyroscopic effects. A boomerang is essentially a rotating wing with two or more aerofoil-shaped blades. It is thrown with its plane of rotation at about 20 degrees to the vertical and so that it spins rapidly (typically about 10 revolutions per second), with the uppermost blades travelling in the direction of overall motion. Therefore, the blade at the top moves through the air faster than the lower one. The faster-moving blades generate more lift than the slower-moving ones. This produces an overall force in the direction of turn, plus an overturning torque.
The rotation of the boomerang makes it behave like a gyroscope. When the overturning torque occurs, the gyroscopic effect makes the boomerang turn (or precess) about a different, near-vertical, axis. This continuously changes the boomerang’s plane of rotation, causing it to travel around an arc back to the thrower.
Other effects are also evident in the boomerang’s motion, such as its tendency to lie flat as it returns to the thrower – its plane changes from 20 degrees from the vertical initially, to horizontal at return. This is caused by a number of aerodynamic effects combined again with gyroscopic precession. The most significant effect is that the blades on the leading side of the rotating boomerang generate more lift force than the blades on the trailing side, because of the disturbed airflow on the trailing side. This again causes rotation which leads the boomerang to spin towards the horizontal plane. An article by Felix Hess in the November 1968 edition of Scientific American explains this process in detail.
Richard Kelso and Philip Cutler
University of Adelaide, South Australia
The simple answer to this question is that most boomerangs don’t come back and were never intended to do so. The Australian Aboriginal people made the boomerang for hunting and fighting rather than for sport or play, so they did not make the so-called returning boomerang throughout most of the Australian continent. For them, the real returns of boomerang throwing came in the form of fresh food or the beating of an enemy.
I have seen the Warlpiri people throw a karli boomerang and hit a target at well over 100 metres. Particularly skilled users of the karli throw this deadly weapon with surprising ease. The Warlpiri also manufacture the wirlki (also known as the ‘hooked’ or ‘Number 7’ boomerang), which is used for fighting.
Across Australia, even in those areas where the boomerang is not made, there is near universal use of paired boomerangs as rhythm instruments in ceremonial contexts. Such boomerangs are still traded for ritual use across thousands of kilometres.
There are and have been an astonishing variety of boomerangs from Australia. For an accessible account see Boomerang: Behind an Australian Icon by Philip Jones, published by the South Australian Museum.
Nightcliff, Northern Territory, Australia
It’s a cracker
Why does the end of a whip crack?
Farnham, Surrey, UK
The crack is actually a sonic boom, caused by the end of the whip breaking the sound barrier. This is possible because a whip tapers from handle to tip. When the whip is used, the energy imparted to the handle sends a wave down the length of the whip. As this wave travels down the tapering whip it acts on a progressively smaller cross-section and a progressively smaller mass.
The energy of this wave is a function of mass and velocity and since the energy of the wave must be conserved, it follows that if mass is decreasing as the wave travels down the whip, then velocity must increase. Therefore, the wave travels faster and faster, until by the time it reaches the tip it has attained the speed of sound.
When the wave reaches the tip of the whip it must be dissipated. Some goes to the air and some into a reflected wave that travels back up the whip. At the point that the initial wave reaches the tip and is about to embark on its return it undergoes a brief but enormous acceleration. The result is that it moves supersonically.
Lymington, Hampshire, UK
During a physics practical lesson, my tutor placed a lit candle on a turntable. When the table revolved we expected to see the flame on the candle point outwards but, instead, it pointed inwards. The school head of science couldn’texplain this. Can anyone else?
Betws-y-coed, Gwynedd, UK
Yes, they can, but, despite a large number of replies, we found we had to knit many together to get a clear picture. First of all, there was a big problem – Ed.
My first reaction to the problem was not to believe it. I tried the experiment and, sure enough, it didn’t behave as described. The flame trailed behind the candle as it orbited the centre of the turntable, just as it trails behind as you walk along with the candle.
Head of Physics
Penglais School, Aberystwyth, Dyfed, UK
After I read this question I could be found in the kitchen with a candle on a rotating cheeseboard. At a speed of approximately 60 revolutions per minute the flame simply trailed behind the candle, showing no tendency to move out or in. I repeated the experiment later in the day on a gramophone turntable at 78 rpm, with the same result. Am I missing something?
Monmouth, Gwent, UK
Yes, men of Dyfed and Gwent, you are missing something, although we commend your industry and integrity. So first of all . . . – Ed.
To see this effect, the candle must be effectively enclosed, otherwise it streams backwards. So, candle in jam jar, jam jar on edge of turntable.
Hind Leys Community College
Shepshed, Leicestershire, UK
The reason the candle flame points inwards is that the rotating table sets up a weak centrifuge.
As the air in the jam jar is being spun in a centrifuge, the denser air moves out with predictable consequences – Ed.
The candle flame bends towards the inside of the turntable for the same reason that flames move up rather than down. The heated gas of the flame is less dense than the cooler surrounding air, and the denser surrounding air moves out, forcing the candle flame in.
If I were to get really picky, I would argue that the less dense candle flame is accelerated more by the same centripetal force. Newton’s law says that for the same force, the product of mass and acceleration is the same. So if the mass is smaller the acceleration must be more. At school level, it’s simpler to think that the force has more effect on the denser air.
Sue Ann Bowling
University of Alaska
Fairbanks, Alaska, US
You can also think in terms of reference frames or do the maths – Ed.
Understanding why the candle flame points inwards is made easier by considering a similar problem in a linear reference frame. Imagine you are driving in your car and in it is a helium balloon held by a string. You brake hard. What happens to the balloon? While you slam forward against the seat belt, the balloon goes towards the back of the car. This is because the air in the car has inertia and continues forward just as you do, and the balloon reacts by floating towards the lowest pressure, lowest density portion of the air mass at the back of the car.
Similarly, the candle flame is buoyant, its shape resulting from a complex interaction between the hot burning wax at the wick and the heating of the surrounding air. So, the flame also floats in the direction of lowest pressure – towards the axis of rotation. To complete the comparison, the candle, like the car, is accelerated with respect to the air surrounding the flame, so the air is moving radially outwards relative to the candle. The flame reacts by floating inwards.
University of Tasmania, Australia
The air in a closed container would displace the less dense gases in the flame towards the centre of rotation under the centripetal force field. The flame will make an angle arctan (a/g) with the vertical (where a is the centripetal acceleration).
This effect is demonstrated by a helium-filled balloon in a car. The balloon leans forward under acceleration, backwards when braking and towards the inside of bends. The same formula applies. For a car rounding a curve of 20 metres radius at 50 kilometres per hour the lean should be about 44°.
Rector, The James Young High School
And a simpler demonstration of the same effect – Ed.
If you place a spirit level on the turntable pointing away from the centre like a bicycle wheel spoke, and rotate, the bubble quickly moves inwards. The more massive spirit has pushed the lighter bubble there.
Bradford, West Yorkshire, UK
I am well aware (having played many ball sports) of the Magnus effect which causes a ball that is spinning clockwise (when viewed from above) to swerve towards the right. Similarly, a ball struck with backspin will travel with a long, floating flight. These effects can be seen with leather footballs, tennis balls and table tennis balls. However, when applying spin to one of those plastic footballs sold at petrol stations and on beaches, the opposite is observed: clockwise spin produces right to left swerve, and backspin produces a viciously dipping shot. These balls are really only larger versions of table tennis balls, and similarly devoid of dimples and surface markings, so why should their responses to spin be opposite?
Walsall, West Midlands, UK
This phenomenon was dealt with in some detail in a feature called ‘The seamy side of swing bowling’ which appeared of New Scientist on 21 August 1993, and is best explained in terms of ‘boundary-layer separation’.
When a ball travels through the air its surface is covered by a thin coating of air that is dragged along with it. Beyond this lies undisturbed air. Between the dragged air and undisturbed air lies a thin boundary layer. At the front of the ball, this layer moves slowly. But as it travels round the ball, it speeds up and exerts less pressure (as dictated by Bernoulli’s law, which states that the faster a fluid flows, the less pressure it exerts).
At some point, the boundary layer separates from the ball’s surface. If the ball is smooth and not spinning, this happens at the same point all round the ball. But if the ball is spinning, the boundary layer separates asymmetrically, so the boundary layer covers a larger area on one side than on the other. The result is a larger region of low pressure on one side of the ball than the other, which pushes the ball to one side.
In a conventional swing (produced by the Magnus-Robins effect), the spin of the ball carries a very thin layer of air along with it. This pushes the point of boundary-layer separation towards the back on the side of the ball where the spin is moving in the same direction as the surrounding airstream, and towards the front on the side that is moving against the air stream. The result is lower pressure on the side where the boundary layer has become extended, which causes the ball to swing in that direction. That’s why a clockwise spin causes the ball to move from left to right. (Another way of describing what happens is to say that the shift in the point of boundary-layer separation pushes the flow lines of the air round the ball – the ball’s wake – to one side, so that the ball swerves to the other.)
All this assumes that the flow in the boundary layer is laminar, with smooth tiers of air on top of each other. In practice, part of the airflow may be turbulent, with air moving chaotically throughout the layer, and this is where reverse swing can occur. Experiments show that turbulent layers stick to the surface of the ball longer than laminar layers. So if the boundary layer is turbulent on one side and laminar on the other, the pressure will be lower on the turbulent side and the ball will swing to that side.
Under certain circumstances, turbulence can develop first on the side of the ball which is moving against the airstream, so that the boundary layer here separates later. The result is a reverse swing. Whether turbulence will develop depends on the type of ball, its speed, size and spin, so reverse swing is seen more commonly in some sports than others (see the following answers).
Sports such as cricket, which use balls with seams, give bowlers additional opportunities to produce both swing and reverse swing through turbulence. Skilful players can bowl so that the ball spins with its stitched seam always facing at a particular angle to the oncoming air. The seam affects the airflow, making the boundary layer turbulent on only the seam side of the ball. The boundary layer thus separates later on this side of the ball and the result is avicious swing.
Bowl fast enough and that swing can be made to reverse. At the very high speeds produced by world-class bowlers (more than 130 kilometres per hour), the air moves so fast that the boundary layer becomes turbulent even before it reaches the seam of the ball. In this case the seam pushes the boundary layer away, encouraging it to separate from the ball earlier on the seam side. The ball then unexpectedly swerves in the opposite direction from usual. This is the notorious ten-bob swerver.
The effect can be produced by ordinary cricketers too, if their ball is scuffed, as a rough surface allows a turbulent boundary layer to develop more easily. Deliberate scuffing is, of course, against the rules – Ed.
The reverse swerve on a plastic football is due to boundary-layer separation. On the side of the football where the relative velocity of the air and football is larger, the flow in the boundary layer becomes turbulent. On the other side it remains laminar. The laminar boundary layer separates from the ball’s surface once the airstream is no longer pushing it onto the surface. By contrast, the turbulent boundary layer remains in contact with the surface farther round the ball. This results in the wake behind the ball being deflected in the opposite direction to the rotation of the ball. And it produces a force towards the side of the ball that is moving in the opposite direction to the airstream (from right to left for a ball spinning clockwise).
Experiments show that the main factor governing the direction in which a ball swerves is the ratio of the rotational speed of its surface to the ball’s translational speed. The reverse swerve occurs when this ratio is small (less than 0·4), while the Magnus effect occurs at higher ratios, which probably explains why the faster-spinning tennis ball swings in the opposite direction to the football.
University of Leeds
West Yorkshire, UK
The swerve of a spinning ball is commonly ascribed to the Magnus effect but, more than a century before Heinrich Magnus, Benjamin Robins studied spinning cannon balls and in 1742 he published a description of why, even on windless days, they swerved off course.
Wellington, New Zealand
Many publications do now refer to the Magnus-Robins effect. It is perhaps worth remembering that Isaac Newton commented in 1672 on how the flight of a ball was affected by spin – Ed.
What causes the colours that form on a clean iron or steel surface after it has been heated and cooled for tempering? The colours range from yellow when the metal is heated to about 200 °C, through gold, brown, purple, blue and finally black when heated to about 600 °C. And because the oxidised blue or purple finishes on steel mechanisms have often survived unmarked in clocks from the last century, what is the physical nature of this transparent and very durable coloured layer?
Allesyree, Derbyshire, UK
The hot furnace gases that are used for heat-treating steel oxidise the alloying elements, such as chromium, to form a thin surface film. These surface films interfere with visible light waves to produce the colours that your correspondent mentions.
The thickness of the films determines the apparent colour of the steel as it interacts with light of different wavelengths. Thinner films, which are formed at lower temperatures, seem yellow or gold. Thicker films make the steel appear light blue. The thickest films seem midnight blue and finally black.
Temper colours on clean, bare steel are actually quite fragile, and are quickly lost if rusting thickens the surface film by depositing layers of hydrated iron oxides. Many parts of the hundred-year-old clocks mentioned in the question owe the durability of their temper colours to the practice of dipping the tempered steel in sperm whale oil. The sperm oil gives a transparent, waxy protective covering to the oxide films, preserving their colours for posterity. Widespread use of this technique has had the obvious disadvantage of producing a serious shortage of sperm whales.
Dhahran, Saudi Arabia
We have tried the experiment taught by science teachers in which a candle standing in water is covered by an upturned glass. The candle goes out and the water level rises in the glass.
We are taught that the rising water level is caused by oxygen being consumed by the burning candle. However, if we have four candles burning under the glass instead of one, the water level rises much more. Why?
Emma, Rebecca and Andrew Fist
Norwood, Tasmania, Australia
Emma, Rebecca, and Andrew’s questioning of the seemingly well-understood candle experiment demonstrates how young and inquisitive minds are able to demolish false explanations propagated through school physics over the decades.
The consumption of oxygen may well contribute to the rising water level to a certain extent, because a given mole volume of oxygen will burn the wax’s carbon into roughly the same mole volume of carbon dioxide and the hydrogen into two mole volumes of water vapour respectively.
The former will partly dissolve into water, the latter will almost completely condense into liquid water. This will certainly lead to a net decrease in gaseous volume.
However, this is a minor consideration: the important influence is the heat created by the burning candle(s). By the time you cover the candle(s) with an upturned glass, an increased number of candles will have increased the air temperature around themselves more than a single candle would.
As soon as the candle(s) go(es) out, the surrounding air contracts as it cools and the ratio of contraction is directly proportional to the initial average temperature of the air volume under the glass. So more candles lead to more heat, a higher temperature and a higher water level upon cooling down.
All this tells us that we should never believe science teachers without asking a few pertinent questions first.
Congratulations to the children who experimentally disproved the common textbook misconception about the candle, the upturned jam jar, the dish of water and the alleged removal of all oxygen from the jar.
By observing that four burning candles cause the water to rise significantly higher up the jar, they have shown that the principal cause of this effect is the heat from the candles, causing the air in the jar to expand. They will also have noticed that the expanded air makes a ‘glug, glug’ sound as it escapes around the rim. There is a short pause after the candles go out, and only then does the water level rise as the remaining air cools and contracts again.
A candle flame goes out after only a small percentage of the available oxygen has been used up. So it is wrong to claim that this experiment demonstrates the proportion of oxygen in the air in some quantitative way.
Interactive Science Limited
High Peak, Derbyshire, UK
The effect is partly caused by the thickness of the three extra candles. You get the same effect using single candles of different thickness. The thicker the candle, the higher the water will rise.
The water drawn in is squashed into the space between the candles and the glass. The narrower this space, the higher the water will rise.
Greenock, Strathclyde, UK
Why do helium balloons deflate so quickly? When my children bring balloons home from parties, the ones that are filled with helium are often small and wizened by the following morning. I realise that some of the size reduction is caused by deflation but something else must be at work because standard air-filled balloons stay inflated for much longer.
Great Corby, Cumbria, UK
Helium gas is not only very light, it is monatomic – its particles are all made of a single atom. As a result, helium is made up of the smallest gaseous particles possible. The atoms are only 0.1 nanometre in diameter, and are quite capable of diffusing through metal films. Because it so readily diffuses through small pores, helium is used to help test for leaks in industrial and laboratory vacuum systems. Nitrogen and oxygen molecules have a much larger diameter than helium atoms which means that they are much less capable of diffusing through the balloon walls. It’s like the difference between trying to get sand and small pebbles to pass through a sieve – the sand goes through much more easily because it’s made from smaller particles.
The second factor which helps to increase losses by diffusion is that balloons are made from viscoelastic materials whose structure is a tangled mass of polymer strands – a bit like a plate of spaghetti. The polymer strands cannot pack closely together, and have channels through which the helium can diffuse, so even at low pressure the helium will diffuse out through the walls. When the balloon is inflated, the polymer stretches, so the balloon walls become thinner (the helium has a shorter distance to diffuse out), the molecular structure becomes slightly more open (making diffusion much easier), and the increased pressure provides a driving force for the diffusion. These are the reasons why deflation is very rapid to begin with, but then gradually slows down as the balloon gets smaller.
Commercial helium balloons are made from non-porous inelastic materials and are coated to reduce the losses even further, although even they still lose a significant percentage of helium per day, certainly enough to disappoint children (and grown-ups) the morning after buying a balloon.
Heriot, Borders, UK
The helium atom is very small and very light. It is able to diffuse through the thin, stretched rubber of the balloon quite easily, finding its way through atomic-sized pores. Air molecules (oxygen and nitrogen mainly) are larger and heavier and diffuse through much more slowly. In addition to the increased pressure inside the balloon which pushes helium out through the sides, there is another factor that increases helium flow outwards.
Because there is almost no helium in the air, far more helium atoms are hitting the inside of the balloon than the outside, and there is a net flow outwards. However, you will notice that the balloon does not completely deflate. This is because some air moves in as, conversely, more air molecules hit the outside than the inside.
This leads to a truly bizarre effect if the balloon is filled with the gas sulphur hexafluoride, which has large, very heavy molecules which hardly diffuse through the rubber at all, and so cannot get out. But once again, as in the helium example, there are more air molecules outside than in, so air diffuses inwards and the balloon slowly increases in size.
Department of Electronics and Computer Science
University of Southampton, UK
If you find yourself in a free-falling lift is there any action that you can take to reduce the effect of the collision? Would jumping just before you hit the bottom of the lift shaft help?
Amersham, Buckinghamshire, UK
First of all, Hollywood clichés notwithstanding, it’s almost impossible for a lift to fall down its shaft, thanks to Elisha Otis’s 19th-century patent acceleration-sensitive safety brake. The instant a car starts to fall, multiple spring-loaded arms pop up and wedge it in its shaft.
As for improving your survival prospects, probably the best thing you could do is lie face-up with your back on the floor and your hands under your head to minimise the impact, although this would be difficult to do if you’re in free fall.
Jumping just before impact would merely delay your own impact by a few milliseconds. Besides, how would you know when to do it? If you jumped a moment too soon, first you’d bang your head on the ceiling, then you’d be slammed to the floor when the lift hit the bottom.
Even if you could time your jump precisely, to do any good you’d have to exert the same force required to jump to the height from which the lift fell from (for example, if the lift fell 100 metres, only someone capable of jumping 100 metres in the air could save themselves that way). If they could do that they probably wouldn’t need the lift.
Schofields, New South Wales, Australia
If you jumped a moment before hitting the bottom, giving yourself an initial upward speed, relative to the lift, equal to that of its downward velocity, you would head swiftly towards the roof of the lift compartment. There would be problems with jumping as you would probably be weightless, but with handles to let you pull against the floor it ought to be possible.
Fortunately, just before you hit it, the roof would suddenly accelerate very quickly away from you (assuming the lift kept its shape after impact!) until it had the same (relative) upward velocity as you. Also, the floor would do the same, but towards you. You could then land lightly from a few inches off the floor and walk out of the lift on to the ground floor, which would be travelling upwards at the same (relative) velocity.
However, there are one or two problems with this. To achieve such a velocity, you would have to be capable of jumping the height from which the lift dropped. And even if you could do this, one surmises that the acceleration produced in order to jump would be comparable to that experienced on hitting the bottom.
Even so, by similar reasoning, you would suppose that even a small jump would lessen the impact.
Tuffley, Gloucestershire, UK
I can see three ways of increasing your survival chances, although only slightly. The first has already been mentioned – jumping as vigorously as possible before you land in order to cancel out some of the upthrust. The second is to get any soft objects you have with you, your clothes for example, and place them underneath yourself prior to impact. This would increase the deceleration time of the collision, and slightly reduce the amount of damage done. If you aren’t bothered about your legs, I suppose you could try standing up, and have them act as ‘crumple zones’, although this could be fairly messy. The third is hardly worth mentioning. You could try to spread yourself out as much as possible while holding on, in order to increase the lift’s surface area. This should decrease its terminal velocity by some indiscernible amount.
Tollerton, Nottinghamshire, UK
In black and white
While working at a factory that produces carbon powder, I noticed I had made a large black thumbprint on one of my sandwiches. This set me wondering why bread, or for that matter potatoes, rice and sugar, which are mostly carbon, are not black.
Holywell, Flintshire, UK
The best way to explain is with an example. Sodium reacts violently on contact with water, while chlorine is a highly toxic greenish-yellow gas. However, sodium chloride, the compound which contains these two elements, is harmless common salt, showing the properties of an element are very different from the properties of that element’s compounds.
The black powder used to produce a photocopy is finely ground carbon in its elemental form. The particles are extremely small and arranged at random. Any light which falls on them is absorbed and not re-emitted, so the powder looks black. The sandwich certainly contains carbon but not in its elemental form. Here, it is combined with oxygen and hydrogen as carbohydrates. These compounds have their own properties which are nothing like the properties of their constituent elements. The slices of bread emit light of many wavelengths reasonably well, so when we look at bread in daylight, it appears white.
Carbon is normally found as an amorphous solid, which means it lacks a definite crystalline structure. Because of this, and because of the position of certain electrons in the outer orbits of the carbon atom, light is absorbed and not reemitted. This means the carbon atoms in graphite, soot and carbon black appear black.
Diamond, which is also carbon, is normally clear, because its crystalline structure alters the electrons and their positions to create a colourless crystal. Diamonds can be coloured if other atoms, usually metals, are present and alter the electron bonds to create blue, yellow, pink and green versions.
H. William Barnes
Warrington, Pennsylvania, US
Carbon, as present in foodstuffs such as bread and potatoes, is in hydrated form – the carbon has been chemically bonded with water and so does not appear black. To get the black carbon back you need to remove the water, usually by heating. This is why burnt toast is black.
Sugar is also carbon and water. But add concentrated sulphuric acid and you’ll see black carbon appear as the acid efficiently sucks out the water.
Farnham, Surrey, UK