I've described, elsewhere in this Forum, memories of observing class CP in my primary school. One event which sticks in my mind (no, not that one! ) dates from just over fifty years ago, when I was in my final year there. Our teacher was the senior master and, as well as using the cane in private for serious offences, he would also apply his blackboard pointer to boys' bottoms for classroom misbehaviour. It was usually just a single whack, but on this occasion the culprit was told to touch his toes again for a second as the offence was a bit more serious than usual (biting another pupil).

I remember watching the second stroke as it was being given. The teacher deliberately raised the pointer to shoulder level, paused (presumably to take aim), and then administered the blow.

That raises an interesting thought, from a scientific point of view at any rate. You can use a technique like this with a fairly rigid implement such as a blackboard pointer, or a paddle or a slipper. But clearly it won't work for something floppy like a belt or a tawse. With that, you'd need to adopt a different technique. With a reasonably thick tawse, having some twisting resistance, I suppose you could hold the far end with your other hand and then let go; otherwise, you might start with it back over your shoulder. Either of these methods would give you a start "from stationary".

There is an alternative, and that's to have a fluid backswing. With a belt, the backswing would straighten it out.

But what about a cane? You could certainly start the forward swing "from stationary"; but if you used a fluid backswing then the cane would flex backwards and store up some potential energy, giving a more powerful stroke. But maybe you'd lose some accuracy?

I wonder if anyone has any thoughts about this, either from personal experience (at either end!) or from observation.

Alan Turing This reminds me of a previous post of yours. CLICK

Yes indeed (and I've also posted before about the introductory incident with the pointer, too).

But this is a more general observation. My supposition is that you gain in power, but lose in accuracy, by taking a backswing and then in a single movement (perhaps with a flick of the wrist) turning it into a forwards movement. I might be wrong, though, so I'm asking for the opinions of our correspondents.

Even starting the forward motion of the cane from a stationary point there will be an induced curvature due to the inertia of the cane. I'm not convinced that there would be more curvature using your 'fluid backswing' technique as surely there is a limiting value of the curvature due to the stiffness of the cane?
J

Even starting the forward motion of the cane from a stationary point there will be an induced curvature due to the inertia of the cane.

Yes, of course. But with "fluid motion" the cane will be curved even at the highest point of the backswing, whereas it will be straight with a "stop, aim, fire" approach. Also, I guess the highest point would be higher in the former case than in the latter.

It's true that there's a limiting value to the curvature of a cane, but I don't know that the limit is reached during normal use. Generally speaking, when you flex a cane, you can always flex it a little more, up to breaking point, by increasing the force; the same is true when the curvature is caused by inertia.

What about the loss of energy that is used to change the direction of the cane that would more usefully be used to increase the velocity of the cane in the downward direction?

There isn't a fixed amount of energy available for each stroke of the cane, so you can't really say that the


If you include a full backswing then the muscles in your arm are working for longer, and so in principle can transfer more energy. Some of the energy from the backswing goes into the potential energy of the curved cane, and is saved for later.

(I assume that there's a limit on the power you can exert -- power is the rate of use, or in this case transfer, of energy. But I don't know enough about physiology to be certain of that.)

"Some of the energy from the backswing goes into the potential energy of the curved cane, and is saved for later."

Yes agreed, but when you start the downward stroke, the cane is travelling in the oposite direction and causing the curvature so surely you have to subtract the energy used to change the direction of the cane?
If you kick a stationary football the kinetic energy of your foot is transferred to the ball and gives it a certain velocity; but if the ball is rolling towards you when you kick it your foot has the same amount of kinetic energy but some of that is used to change the direction of the ball so its velocity is lower.

This may be a little off topic but here in the colonies biting was,is,and always has been a serious offense. I think I remember a kid getting expelled from school for that.

Also your teachers must use a different black board pointer than our teachers because the ones used in my schools were too easy to break. I think they were just pine dowel rods maybe half inch in diameter with a plastic tip.

Bob: the image I have (fuzzy, it's over half a century ago!) is of a dark wood pointer with a slight taper, maybe 18 inches long. Maybe it was dark because it had been varnished. It wasn't just a length of dowel.

Jethro: If you kick a stationary football the kinetic energy of your foot is transferred to the ball and gives it a certain velocity; but if the ball is rolling towards you when you kick it your foot has the same amount of kinetic energy but some of that is used to change the direction of the ball so its velocity is lower.

Are you sure about that? You don't need any kinetic energy at all to change the direction of a ball (think of snooker).

Suppose for a moment that the ball is perfectly elastic, and it's coming towards you at a high speed v. Block it with your foot; it will recoil in the opposite direction with the same speed v (that is, velocity -v). If you give it a kick instead of blocking it, it will recoil with a speed greater than v; the extra speed comes from the energy of the kick. That will be greater, not less, than the speed the ball would have if it had been stationary when you kicked it. It must be greater -- where else can the kinetic energy of your boot go, apart from into the kinetic energy of the ball?

I suspect that a cane is like that, because it's fairly elastic; much more so than a real football, which absorbs energy on impact and turns it into heat.

Alan - Fair enough, football was not a good example because it is elastic and so the change of shape when it hits your foot converts the kinetic energy into potential energy which restores the shape and so it rebounds without any extra energy input.

What about a 'theoretical' ball that was not elastic at all? - when it is stationary the kinetic energy of your moving foot is transferred to the ball to give it motion. If it is travelling towards you then surely when you kick it some of the kinetic energy of your foot is used to first stop it and what is left then changes its direction? Surely in that case it would be going slower than when you kick the stationary ball?

Now back to the cane - on the backstroke you must use energy to stop the backwards travel before you can start the downward stroke?

In my opinion, a preliminary backswing will contribute very little to the kinetic energy of the implement except, perhaps, by allowing a longer flight path for acceleration than might otherwise be possible.

See Some experimental data where I wrote, in part:

I have just used my kitchen scales to measure the force (applied to one end when the other is held rigid) it takes to bend a cane. It took about 1 kg force or 10 Newtons to bend the cane through about 0.3 m. The force was roughly proportional to the deflection. The average force was therefore about 5 Newtons. The elastic energy of the bent cane (force x distance) was therefore about 5 x 0.3 = 1.5 Joules. This compares with 22 Joules kinetic energy calculated earlier and an impact force of 75 kg. I conclude that the elastic energy of a cane is likely to be relatively small although not necessarily negligible. I further conclude that a carry through swing is unlikely to add much to the impact force or to the available kinetic energy because the cane will bend.


When feet strike balls it is the momentum (mass x velocity) that is conserved rather than velocity - if the collision is elastic. Normally, the foot keeps most of its momentum when kicking a ball.

Excellent scientific stuff from KK and it made me think that I've never read anything about whether new teachers received training in the use of the cane.

Was this done at teacher training college or when they started teaching in a school? With so much science involved it must have been wrong just to give a new teacher a cane and say use your common sense.

I can't resist temporarily coming out of retirement from this forum to add something to this discussion!

I have experimented with a backswing. It seemed to add little or nothing to the power of the stroke and it was less accurate, though practice might have helped with the latter. Much more important was that in two of the experiments, the cane broke just below the point at which it was held. The extent of the flexing and sudden change of direction appeared to cause far greater stress at that point on the shaft than with a normal stroke.

On a wider point, I am not sure it is necessary for strokes to be extremely hard. This forum is about school corporal punishment, which surely means causing just enough pain to be aversive without causing injury. If excessive force is used, the risk of injury is increased more than the effectiveness of the pain. Surely it is far better to give an additional stroke or two, increasing the duration of the painful experience?

For clarity and the avoidance of doubt¹, this is what I mean. First, the "point and shoot" version, starting from standstill in Frame 1. Notice the curvature of the cane.



And now the "backswing" version, again starting from standstill in Frame 1. Notice that in Frame 2 the cane is curved in the opposite direction, and that in Frame 3 the cane in direction of the handle hasn't yet reached the tip, so that the cane distorts. (This will stress the shaft and will probably cause the phenomenon observed by hcj.) I've shown the cane having a greater curvature on arrival in this version, compared to the "point and shoot" version; I believe that this is the case, although I haven't actually calculated it. I don't think that KK's observations contradict this.



In response to Jethro: if you kick a "theoretical" ball which isn't elastic at all, then it won't go anywhere -- try kicking a sandbag! You also say


You seem to have the notion that you need energy to stop a moving object. But that's not true. When you stop a moving object, you absorb energy from it. For instance, when you brake in an electric car, you recharge the battery a little -- it's called "regenerative braking". Even with an ordinary car, you absorb the kinetic energy of motion and heat up the brake pads instead. So when you say "you must use energy to stop the backwards travel" then that's mistaken. Dynamics doesn't work like that.

Another_Lurker: I can't quite imagine what you mean by "going to be in the way" -- could I have a diagram, please?

Finally, on hcj's other point: I'm talking about mechanics, rather than motivation (that is, would you really want to inflict that much pain).


1. All copyright owners' rights acknowledged!

Allan's interesting drawing shows linear cane motion - the handle and business end of the cane all travelling at the same speed, or almost the same speed, and in the same direction. A recent analysis of baseball batting shows that it is the rotational motion of the bat that is important if you want to hit the ball hard (details of study not to hand/forgotten.) The same will apply to caning. The tip of the cane goes much faster than the handle. (I will try to produce a drawing the flight path of the cane tip.)

Coordinated movement of the whole body is needed to bring the cane tip to the highest speed - wrist flick, arm swing, torso unwind, etc.

In the case of a flexible strap, simple circular motion from, say, wrist flex, won't accelerate the tip. It is left behind. A more complex motion, perhaps involving an element of backswing, is required to first extend the strap before it is accelerated in a circular motion using centripedal force to keep the strap extended.

It is a relatively easy exercise to calculate the bend in an accelerating cane of known elastic properties. A bent cane travelling at speed has both kinetic energy and a much(?) smaller amount of elastic energy. What happens to the elastic energy when the cane lands is unclear but it may contribute to the "wrap" effect if the cane lands long. Wrap is most conspicuous with flexible implements. The kinetic energy concentrates in the tip as the end of the implement wraps around the target.

The pictures are only a first approximation, I'm not Leonardo!

If I were wielding a cane, I think that a lot of the power would come from an elbow movement. But however the cane is wielded, its overall motion will still be a combination of circular motions of different radii, and the shoulder motion will probably be as close to linear as makes no difference.

Actually it's not just the tip movement which is of interest; maybe 8in or more of the cane will make an impact (it obviously depends on the size of the target). If you look at photographs of cane marks, on Corpun for instance, it isn't obviously the case that the tip does most damage.

As KK says, it's a bit different if the cane wraps round, partly because there's less padding round the side.

Although it seems reasonable to expect the tip end of a cane to lag at the start of the downswing, experience suggests it is usually fairly straight by the time it reaches its target. On impact, a flexible cane bends, absorbing some of the energy back into the shaft.

The tip tends to dig in when the caner is standing too far behind the target - and of course, when it wraps. It is quite surprising how much a cane can bend as it wraps.

experience suggests it is usually fairly straight by the time it reaches its target.

I think it will depend on the acceleration profile of the motion. If the acceleration diminishes towards the end of the swing then the tip will tend to catch up; but if you can keep the acceleration reasonably high throughout then the tip will always lag behind. I guess that means bringing into play the different components of the motion, one after the other.

For the purpose of my calculations I assumed smooth, uniform, coordinated acceleration throughout the whole duration of the cane swing. Reality is likely to be more complex than this but I lack the information needed to do a better job.

I added the contributions from rotation of the wrist, elbow, shoulder and "core" and added a small contribution from a linear motion such as stepping forward during the swing to calculate the blue curve below.

The points along the line are for equal time intervals of about 1/100th of a second. The faster the cane tip, the more widely spaced the points.

The kinetic energy increases with the square of the tip speed so relatively small differences in speed have a big effect.

All the rotations add to give a single circular motion to the cane tip.

All the linear motions add together to give a single rather small linear contribution to cane tip speed.

The length of the cane affects tip speed if rotational accelerations are maintained.

If the cane is light the wrist flick is the most important contribution to tip speed.

If the cane is heavy the wrist will lack the strength to accelerate the cane and the arm, shoulders and core become much more important.

It is likely that light canes have an impact speed greater than that of heavy canes of similar length.

Good technique rather than strength is required to bring a light cane to speed.

I have some issues with the remarks made by KK in his post of 9:43pm on 15th January.

The first concerns his comment that


Well, that's not true. Combining circular motions gives a motion which isn't circular.

The simplest example comes from a rod OA of unit length, rotating with a fixed angular velocity about a fixed point O, and another rod AB of the same length, rotating in the same plane and in the same direction, with the same angular velocity relative to OA about the joint A. The tip B then moves along a cardioid rather than along a circle. (Imagine O is the shoulder, A is the elbow, and B is the hand.)

If the two angular velocities differ then the path of B will be more complicated, and may well differ quite significantly from a circular path. This might arise with a steadily accelerating shoulder movement and a late elbow movement. And adding on more components, such as wrist flicks, will make the motion more complicated still.


Why the concentration on the tip? If the motion of the tip has an instantaneous radius of curvature of, say, 1.5m (reasonable, taking into account the combined length of the arm and the cane) then the part of the cane 20cm from the tip will be travelling at around 85% of the tip speed. So 1cm of cane here will contribute around 70% of the kinetic energy of 1cm at the tip. That's why I mentioned photographs of cane marks in an earlier post: these tend to show some gradation of marking towards the tip, but not much.

I'm also concerned about the total amount of rotation shown in the diagram -- about 135 degrees, it seems to me. I'm sure that would be right for a baseball swing, and maybe for a Singapore-style judicial caning, but it seems excessive for a normal school caning. In particular, that much of a wind-up doesn't seem consistent with the reported interval of 5-10 seconds between strokes.

It's difficult to be more specific in offering criticisms, because KK hasn't given any quantitative modelling assumptions or detailed methodology. Without these, I feel that his diagram needs to be taken with a reasonably large dose of salt.

In reply to JFJ above I recall a debate in Parliament a few years ago when an ex-teacher MP told that before he went into the classroom for the first time the head teacher made him put on a boxing glove and proceeded to strap him on the gloved hand to demonstrate the technique. They then changed over and he had to strap the headmaster. On satisfactorily completing the exercise he was issued with a strap.

Unfortunately I cannot now find any record of this debate in Hansard but I am sure that my memory is correct.

GaryJ Thanks for that - sounds common sense to me but I wonder if it was widespread?

Alan You say this:
"You seem to have the notion that you need energy to stop a moving object. But that's not true. When you stop a moving object, you absorb energy from it. For instance, when you brake in an electric car, you recharge the battery a little -- it's called "regenerative braking". Even with an ordinary car, you absorb the kinetic energy of motion and heat up the brake pads instead. So when you say "you must use energy to stop the backwards travel" then that's mistaken. Dynamics doesn't work like that."

Yes I do understand why brakes work and that energy is converted from one form to another so we agree on that. Let me tell you of a real world situation that I experienced recently.

I was taking my dog for a walk and a driver entered his driveway which is on a steep slope up from the road. He got out of the car and locked it but the car started to roll backwards towards the road so presumably the handbrake was not on properly. He ran round to the back of his car and used his strength to stop the car moving by pushing against the car in the opposite direction to which it was moving.

We know the car would continue to move unless acted upon by a force to stop it and this force was provided by his muscles which were producing energy to enable him to apply the force and stop the car moving.

Applying the same reasoning to the backswing of the cane, the cane would continue to travel backwards unless acted upon by a force. This force is exerted by the arm muscles and those arm muscles are burning fuel to provide energy.

I still think that it's correct to say that, in the case of the cane, energy is used to stop the backward swing.

But the force could equally well have been provided by a great big compression spring, the lower end of which was bolted to the ground, and the upper end of which absorbed the energy of the car. You should think of the force being imposed on the car as a passive force, the consequence of Newton's Third Law (for every action there is an equal and opposite reaction). You don't need energy to create a passive force, it happens automatically as a reaction. If the driver happened to be using up energy in performing a similar activity, then the energy wasn't being used to stop the car, it was being used to make him hot and bothered.


There's a law of conservation of energy. When the cane slows down, it loses kinetic energy. Some of the tension in the arm muscles will be caused by the energy of the cane being transferred to the arm. So the kinetic energy from the cane will turn into potential energy in the muscles.

There is NO transfer of energy to the cane when you slow it down.

I forgot to mention, when commenting on KK's post, that he said


That's a misconception. If you increase the speed by 1% then the kinetic energy will increase by about 2% -- not a spectacularly big effect.

Actually the exact increase in KE will be 2.01%, but I used the approximate value 2% to make a point. The kinetic energy is proportional to v². Increase the speed to v + dv and the kinetic energy will now be proportional to (v + dv)², and that equals v² + 2 v dv + dv². If dv is small then its square will be tiny and you can neglect it.

So the ratio of the new KE to the old KE is v² + 2 v dv divided by v², which equals 1 + 2 (dv / v). So the percentage increase in the KE wil be about twice the percentage increase in the speed.

And yes, you're right: this is just "differentiation from first principles" which you learn when you start studying calculus!

My diagram above is wrong.

Human motion is complex. It is usually easier to do than to analyze and model. However, adequately diligent analysis can give insight. Sports medicine is very active in this area, and movie animators too.

Models begin with simplifying assumptions and guesses at the values of various parameters. The model is then either abandoned, or corrected and refined, depending on it success or otherwise. I have presented a first attempt and admittedly rather crude model. However, it is a start and it does provide insight. It needs to be corrected and refined.

I calculated the motion of the cane tip relative to the wrist joint. I have then calculated the motion of the wrist joint relative to the elbow joint and assumed this motion is added to that caused to the tip by the rotation of the wrist, and so on. However, I failed to rotate the old axes relative to the new reference axes when adding up the various motions. This is an mistake and it can be fixed.

I assumed that all joints have the same angular acceleration and are flexed through the same angle. Unlikely in reality but easily improved.

Why concentrate on tip speed? Because the tip is a well defined location. The centre of inertia might be better, if it can be located for a rotating lever of changing shape - the cane plus arm plus body of unknown dimensions.

Yes, Alan's analysis of the effect of speed on kinetic energy is correct but so is mine, depending only on semantics.

Many have puzzled as to why some masters were able to cane so much more painfully than others. It is clear differences in cane speed was responsible. A 41% increase in speed doubles the kinetic energy. But a much smaller change in kinetic energy is likely to be important once there is nearly enough to cause injury.

Assumptions:

The cane travels in an inclined plane. Its tip position can be described by two dimensional cartesion coodinates.

The torso, and the shoulder, elbow and wrist joints are rotated by angles theta-1, -2, -3 and -4, respectively.

The cane is accelerated at a constant rate by the coordinated simultaneous rotation of the torso, shoulder, elbow and wrist. Each point of rotation remains at a fixed distance from the origin.





The rotations, lengths and accelerations are all arbitrary and can be adjusted to better suit reality as required.

One does not need science to work out how to cane a boys bottom. i cannot imagine anybody giving it that much thought at the time. I know some teachers did raise the cane above shoulder high and bring it down in an arc to land on the bottom. With something as flexible as a cabne this is dangerious. It would be hard to judge the flight path of the cane and the exact place of impact. If the boy was to moce his bottom just slightly forward or backward the arc of the cane would cause a differant part of the bottom to be struck than that intended. It could result in a more painful stroke going across the tops of the legs rather than the buttocks or worse still a stroke landing more on the lower back which could cause spine damage. In an arc motion it was far more likely that the cane would land tip first on the boys bottom cutting into it, rather than the majority of the cane landing flat. The majority of the stroke would land on one buttock not right across both as intended. The cane coming in on an arc would also be more inclinded to skim the bottom rather than land a firm stroke on it. this would, not as one may expect cause less grazing but more. The correct way is to bring the cabne in at 90 degrees from directly behind the boy, with it coming in all the time at bottom height. Any boy that moves is going to move forward, and by this method the cane will still land right on the spot intended. the cane will also land flatter, not tip first and will not cut into the buttock so much. As it will strike and push the buttocks inwards it is less likely to graze than a more glancing stroke. Added sting can be generated by a flick of the wrish just before it lands but i have always found a sharp, quick swing was always painful enough.

It's now a few days since my discussion here with JformerlyJethro about energy transfer when slowing a cane after a backswing. It's clear that he strongly believed in his point of view (that a backswing means that the cane receives less energy, because some goes into slowing it down); but it's equally clear to me that he was mistaken in that belief. I hope that I've been able to convince him about this, and I wonder if I could say a little more on the matter?

First, let's think how muscles work. (I offer the point of view of a non-expert.) Muscles contract, on command of the brain via the nervous system. For instance, if you throw a ball, various muscles contract in order to impart motion to the ball. In this way the ball gains some energy (kinetic energy, because it is moving); the energy comes, ultimately, from the food you have eaten.

You can also use your muscles to try to lift a weight. Before the weight lifts off the ground, you're trying to contract your muscles. But the weight isn't moving, so it has no kinetic energy; and the change in the potential energy of the weight (and the floor) is small. What's happening is that your muscles are in tension, and therefore possess some potential energy, again coming from the food you have eaten. This potential energy is only transferred to the weight when it lifts off the ground.

Now suppose you catch a ball. The force of the ball's movement knocks your hand backwards, and stretches some of your muscles. So your muscles acquire some potential energy because they're in tension. But this time, the potential energy has come from the kinetic energy of the ball, which has slowed down. You don't need to use the energy from food to do this.

When you slow down the backswing of a cane, the same thing happens. The kinetic energy of the cane's movement is transferred into potential energy of your muscles, which are stretched by this.

So what happens if you're not merely trying to slow the cane down passively, but you're actively trying to force it forward? Well, I accept that you're using up energy in order to do this, but the energy isn't going into the cane. It can't be, because the cane is slowing down and so losing energy. It will be slowing down more rapidly than it would have done if you hadn't been trying to force it forward, but it's slowing down nonetheless. So what's happening?

The answer is that your muscles are acquiring potential energy from two different sources. One source is from the cane slowing down; the other source is from the muscle contraction due to nerve commands. Because of this, the muscles acquire more potential energy than before (and they also acquire it faster than before).

So, with a backswing, the cane accelerates faster on the forward stroke than it would have done if it had started from a stationary position, because there's more energy in the muscle to zip it forward.

I have some sympathy with the point of view expressed by george. Why would anyone want to try to predict the path of a cane explicitly? Even if you did, I don't think that KK's approach is particularly helpful.

For a start, if you change the relative speeds of the different components then you will change the shape of the path, not merely its speed. Indeed, if one has both a shoulder movement and a wrist flick then the latter will start some way into the swing from the shoulder, and introduce a definite kink into the flight path of the tip. One shouldn't forget, either, the effect of centrifugal force pulling the cane away from the "pivot point" (if you've ever used a cane, you'll know exactly what I mean by this).

Indeed, I don't even believe that the motion is in an inclined plane, unless, as george suggests, you try to keep the path as horizontal as possible: if you start with the cane high up then you'll want to flatten the stroke out in order to avoid just slicing a layer off the receipient's backside! (This is also, of course, a source of inaccuracy when the cane is very flexible.)

My first response was not charitable when I read the critique of my attempt at modeling. Then I realized that I had not explained modeling, or my model clearly enough. The notion of models will be new to many. Also, some do not realize that this forum contains live science (and live historical research) and stuff they can participate in.

By model, I mean a set of mathematical equations that may or may not be portrayed in diagrams or graphs. The equations must be consistent with the known laws of nature. To be useful, the equations must have predictive power. However, even a model that fails to predict correctly is valuable in that it shows there is an error in the model, possibly in our understanding, or the value of one or more of the adjustable parameters (e.g. assumed arm length or shoulder motion) is wrong.

Why try to model the flight path of a cane? Why model the movements of the planets of the absorption of oxygen by blood, the weather or the growth of bacteria? It is what science is. Science has given us the modern technological world and the computer this post is being read on.

Earlier, there were discussions about the authenticity of photos supposedly showing a school caning. The question arose as to how much space is required to swing a cane and how far away would the camera have to be. The answer was found by a rough and ready experiment. It could equally be determined by modeling. A good model can deal with a much greater diversity of circumstances than is convenient to do in experiments.

In science, we begin by observation of a natural phenomenon and then try to understand and explain it, and then predict. The first models are necessarily crude. They are improved or replaced as understanding and knowledge increase. The gas law (PV = nRT) is a good approximation but it is not sufficient for real gases at high pressures. Various modifications of the law have been developed to better match reality. The simple gas law has not been abandoned.

The human body consists of rigid bones of fixed length. The rigid bones are joined by hinges with a limited range of movement. It is entirely practical and useful to model human posture and movement to perfect golf swings or to build ergonomically, using hinged bones covered with soft flesh.

The cane has been modeled as a rigid rod. This is a good approximation as any bending is small compared to its translational and rotational motion.

The inclined plane in my model may be inclined at any angle to the horizontal, including zero angle. The model assumes the motion is in two dimensions only, not a bad assumption as a starting point. A 3D model is likely to be better but it is more complicated and I do not have the necessary information to hand to construct it.

The diagram I posted above shows just one of an infinite number or configurations. Lengths, angles and accelerations can all be adjusted as required, and if and when better information comes to hand.

Dissatisfied with the length of the swing, or the amount of wrist flick? This is of no consequence as there are adjustable parameters in the model. You can use any values you think better.

In my time I've had a small involvement with teaching the principles of mathematical modelling.

It's certainly the case that a mathematical model will never be "correct". Even the best model can be improved -- Newtonian mechanics is one of the best, but it's still an approximation which can be improved by using relativistic mechancs for high speeds and quantum mechanics for small sizes.

And not all mathematical models have, or need, the sophistication and accuracy of Newtonian mechanics.

Sports scientists, as mentioned by KK, make good use of mathematical models. Professional sport is big business, and top sports(wo)men take advantage of anything they can in order to squeeze out the last ounce of performance. The models here are based on theory and informed by experimental evidence. Models are tested, and refined after comparison of their predictions with reality.

And that's why I don't find KK's diagram helpful. What is it predicting? As far as I can see, it tells me that the tip of a cane moves along a curved path, and gradually gets faster.

Big deal. That's as much use as saying "if you push a jelly, it'll wobble".

And even if the results were quantified, and compared with experiments in order to generate refinements, I don't see the need for them in this generality. We're not really going to have competitions for the world's best wielder of a cane, are we? Nor are we going to have training courses for people who might be required to use this technique as part of their employment.

What we're really doing is considering specific questions -- does it hurt more if you do this or do that? Or, given that the perception of pain is such an imponderable -- does it transfer more energy at a faster rate, if you do this or do that? I'd be much more sympathetic to an analysis which addressed particular questions like these.

Oh, incidentally: in response to this comment


I offer the following, which is a portion of a frame taken from a fetish movie (which is why I've cropped the image so that you can't see anything which Network54 might find offensive). There has been a backswing: do you think the bending of the cane is "small"?

Alan,

I agree with everything you say above, or at least I do not dispute anything, except about the potential usefulness of the model.

I have just constructed it using various rough guesses at lengths, rotational angles and an initial simplifying assumption that all accelerations are coordinated and uniform. Before going on to make predictions and to explore the effects of changing parameters like cane length, suppressing wrist flick, etc. I need to refine the default parameters and ensure there are no mistakes in my method of calculating. It is a work in progress, just beginning. I have published far far earlier than is customary in science.

The model is intended to give insight into the velocity of the cane just before impact. Modeling what happens to the target is more complex although the effect of lethal and non-lethal projectiles has been investigated by others. Ballistic putty or gel with properties similar to human flesh is available to aid such investigations. Kinetic energy densities of about 10 Joules per cm^2 are required for pellets to penetrate human skin. Paint gun enthusiasts have useful information on safe limits for projectiles.

The bending of canes during acceleration due to inertia or due to air drag when in high speed flight can be modeled. My rough measurement of the modulus of bending elasticity of rattan, mentioned in another post, convinced me the cane would not bend much in use so I could neglect the effect of bending in my first attempt. Bending can be added later.

The points along the curves in my diagram are equal time intervals, roughly 5-10 milliseconds. They points get further apart as the speed increases.

Straps and other flexible devices need something more than simple rotation to extend and accelerate them. Centripetal force is involved. I have not attempted to model a strap flight path.


Questions that might be investigated using a model include:

1. How much space is required to use a cane?

2. How fast is the cane going at time of impact?

3. How do the various motions torso unwind, shoulder swing and twist, elbow flex and wrist flick contribute to the speed?

4. What is the effect of changing the length of the swing?

5. What is the cause of uneven marking of left and right cheeks. Does it relate to the angle at contact or the greater speed of the tip? Flexibility is likely to be important here.


My attempt to model was triggered by Alan's linear cane motion diagrams at the beginning of this thread. I thought I could construct a better model by allowing for rotation. I encourage others to better my attempt, if they can. This is how science works. We try to build on what has gone before.

Those fascinated by the above discussions, and science in general, may find earlier related discussions of interest:

http://www.network54.com/Forum/198833/thread/1250411075/

Why do I feel so negative about the diagrams posted by KK? He's clearly put a fair amount of work into them, so why don't I feel enthusiastic?

Here's a possible reason. I occasionally get asked to referee mathematics papers for learned journals -- this is the "peer review" procedure one sometimes sees mentioned in the press. When such a paper arrives, I'm expected to offer an opinion on whether the material is correct, and whether it is significant and therefore worthy of publication.

You can tell whether the work is significant by looking just at the results. But you can't see whether it's correct without looking behind the scenes, at the concepts and calculations which support the results.

I think that's what's missing with KK's work. He's created a model, but he's just given us the results (namely the diagram) and a few of the modelling assumptions. I'd need to see much more of the workings, so that I could try out a few scenarios myself.

KK's latest post does include a little more information:


But in order to test this, I'd need to know some specific data: what were these accelerations? What are the lengths of the various components of the motion (or can I measure these from the diagram)? What was the initial configuration?

And then, to assess the significance of the paper, as this is self-avowedly a work in progress, I'd need to see the author's assessment of the main directions where the model is deficient, and how easy it would be to remedy these defects. I'd then (perhaps) be able to judge whether the model would eventually be able to help answer the specific questions listed.

The two cane-flight diagrams, their captions and the accompanying text disclose all the essential features of the model. It consists of a series of rigid levers of fixed length, connected by pivots, with all axles normal to the plane of flight. That is, all movement is assumed to be in, or parallel to, the plane of flight, which is probably not true in reality. The torso, shoulder and wrist are capable of more complex motion than simple rotation about a single axis. I have restricted myself to a 2D analysis. A 3D analysis would be better and only marginally more difficult to execute for those good at trigonometry.

The lengths of the levers, and the angles of rotation, are adjustable parameters. One particular arbitrary choice of values is shown in the second diagram above. At time of impact, all the marked angles have reduced to zero. The rotational angles have been defined so that this is so.

At first attempt, I assumed all the rotations started at the same time and the acceleration for each rotation was uniform. I did this because I presently have no information about actual accelerations, and it is the easiest to calculate. For uniform acceleration, the fractional change in each angle is proportional to the lapsed time squared.

Some may be concerned that the lack of knowledge about details of human movement limits the usefulness of the model. The reverse is the case. The model allows the possible influence of various factors to be investigated. If the model suggests a particular factor is important, it can be investigated further and an attempt made to get real information. Thus, the critical parts of the model can be identified and refined.

I do not subscribe to the notion of magic or unknowable skills that allow some caners to do a better job than others. All phenomena are susceptible to scientific study. My attempt is preliminary and probably naïve but it is a start. I am hoping others with greater knowledge or skill will be able to do better.

I remain unconvinced by KK's model, even with the additional information. Let me explain why.

In his second diagram, look at the elbow joint (purple), and the angle theta3. Now look at the elbow of your own right arm. What do you notice?

You will notice that your elbow does not bend in the direction indicated in the diagram. You can use your forearm to swivel towards the target, but not away from the target, as shown in the diagram. It is therefore not possible for all the joints to have coordinated accelerations, with everything finishing in a straight line. All models are, of course, simplifications, but I would say that to call this particular model a simplification would be excessively generous: in my view, it is wrong.

I think that it would be far better to start by concentrating on what happens with a single joint. The elbow seems simplest and most interesting. If I try to simulate the use of a cane I find that, for a hard stroke without a backswing, my elbow starts at an angle of about 45°; as the stroke continues the joint opens out until my arm is almost straight and the angle is zero; and finally, towards the end of the stroke, the angle starts to increase again.

I imagine that there many variants. In the image I posted above, the elbow angle is more like 150°. I suppose the angle could start at zero.

In any case, a constant acceleration is pretty well impossible, and modelling a constant acceleration is unhelpful. So I would suggest the following for a first attempt.

Imagine that the arm pivots from a fixed point in a plane, and moves (in the initial model) at a constant angular velocity. The forearm pivots freely at the elbow and so it will tend to straighten out. The speed at which it will do this can be calculated using the angular velocity of the arm, the distance from the shoulder to the elbow, the length of the forearm and its mass.

At some variable time after the motion has started, the elbow applies a fixed torque in the direction of motion (that is, to increase the angle by which the elbow bends). There are thus two further parameters, namely the delay (which might be zero) and the magnitude of the torque. If the torque is small, the arm will still straighten out and remain straight. If it is large then the straightening effect will be reversed.

One might then investigate the interplay between these two additional parameters in terms of the final speed of (effectively) the wrist.

I feel that starting by looking at more realistic motion of fewer components is much more likely to give an understanding of what's happening than looking at oversimplified motion of all the components. That's because adding components is fairly straightforward, whereas eliminating the oversimplifications is much more difficult.

I am a little confused about this discussion. I understood the original question was whether drawing the cane back quickly before the downswing, causing it to bend, would then provide additional acceleration as the cane was propelled towards its target.

As a result of practical experiments, it seemed that there was perhaps a small extra acceleration, but with two disadvantages. The "unwinding" of the bend caused by the backswing is not necessarily perfectly aligned with the direction of the downswing, as flexible canes tend to "flutter". This leads to inaccuracy. Second, the cane tends to be stressed near the handle, probably because of distortion of the shaft into an S-shape and may be weakened.

The discussion now seems to centre on the elements that contribute to the downswing. I suggest that these are not unlike a golf swing and there is perhaps useful data available in the scientific studies of that sport.

One rarely mentioned factor is the follow through. In a golf shot, there is nothing that the player can do to influence the flight of the ball after it has left the club, so why is a follow through important? It ensures that the club is maintained at full speed right up to the moment of impact.

The same is true of a cane stroke. If you aim right through the bottom, visualising that you are trying to hit the chair or desk beyond, it is easier to ensure that the cane does not decelerate before it strikes the target. I suspect this is one of those "magic" factors that mean some seem to hit harder than others.

hcj: You're right, the discussion has widened a bit, but I'm not too bothered about that.

As far as the backswing is concerned, I did mention the possible loss of accuracy in my original post. Certainly there will be a greater possibility of lateral movement caused by the flexibility of the cane; there might also be the fact that switching the direction of the muscle action might itself modify the direction of motion.

As far as the follow-through is concerned, an expert on the matter told me a few years ago that it was essential, and indeed used the same form of words as you.

(I'm reminded of a craze for karate which arrived soon after I moved to my grammar school in 1961. Boys would move a couple of desks until they were about ten inches apart, and then put a length of wood across the top of them. They would then hit the wood, aiming to break it. The first time I tried it, I just hurt my hand. But then I realised that you have to assume the wood will break, so that you don't instinctively slow down, and I managed to smash a foot-length of 2 x 1 in half.)

Alan,

Unlike you, I have not lectured on model building but I have used modeling to design a successful commercial process. The process involves an enzyme reaction. The cost of the enzyme, the reaction temperature and the size and number or the reaction vessels had to be optimized, and the process scaled to match an existing continuous plant, all in a very limited space.

I began with a simple rough model and then refined it, paying most attention to the elements that the model suggested were important. The alternative would be to model every element of the model perfectly at the start and then to assemble the perfected elements. Unfortunately, in most cases, we do not have the information required to do this to hand and must do many experiments and make difficult measurements to get the details for each element, some of which later turn out to be unimportant. In addition, the design of each element often affects the operation of other elements. You then find the apparently perfected element is imperfect and needs to be further refined.

Rough complete models can be immediately useful after little work whereas perfected elements are usually not useful until they are assembled - after much work and delay.

I am attempting to do the same here, that is, to begin with a rough model and to refine it. Yes, the model as disclosed is far from perfect. I am endeavouring to get others involved very early, as in a discussion with colleagues over coffee. To be told the model has no merit because it is imperfect is not helpful. Much better is to be told how to improve it, or to be offered a better alternative model.

The human body is made up of bones. These are essentially rigid and of fixed length. Okay, they can bend a very little, especially in the young but for our purposes were can totally ignore the tiny amount of bending.

The bones are joined together by flexible joints. Very roughly, in the case of dry bones :

    Your toe bone connected to your foot bone
    Your foot bone connected to your ankle bone
    Your ankle bone connected to your leg bone
    Your leg bone connected to your knee bone
    Your knee bone connected to your thigh bone
    Your thigh bone connected to your hip bone
    Your hip bone connected to your back bone
    Your back bone connected to your shoulder bone
    Your shoulder bone connected to your neck bone
    Your neck bone connected to your head bone

Some of the joints such as those at the knee, elbow and in the fingers are simple hinges with a single axis of rotation. Others, like the shoulder and wrists, are capable of bending in two directions and of twisting.

The angles between the bones can be described in various ways. It is not necessary to use the lines connecting the joints at the ends of the bone as the reference when defining the angles. For example, the elbow may be straight to start, and then bend. The elbow angle at the start is not zero but it is zero at time of impact. In addition, if the elbow was bent and fixed through the entire stroke, as likely for horizontal strokes, the rotation attributed to the elbow would come from twisting of the arm at the shoulder joint.

Human movement can be modeled accurately using bones and joints.

There is presently great uncertainty as to the accelerations although it is likely some information is available in the literature, which I cannot easily access. The accelerations may depend upon on the resistance or the inertia, especially of the wrist where the muscles are weak. It the absence of specific information the assumption of continuous if not uniform acceleration is reasonable. It is consistent with the notion of carry-through aiming for a point beyond the target so acceleration continues right up to impact. It is also consistent with the notion that the bigger the windup the harder the stroke.

As explained previously, it is easy to apply more complex accelerations to the model, when information comes to hand. If the model were to suggest that the rotation of a particular joint was important then it would be worthwhile trying to model the movement better.

At present, the model calculates the 2D coordinates at fixed equal arbitrary time intervals by calculation the various angles at each time.

In all likelihood, useful sophisticated unpublished, published and proprietary black-box models already exist. Badminton might be the sport with the closest match although tennis is more likely to have been studied.

KK, I'm genuinely impressed by your industrial experience. I've never done anything "real" like that. I also understand the feeling of loneliness if you do a fair amount of work and someone who you think might be able to contribute instead just spends his time carping. In my defence, I'd say that you really need dynamics rather than just kinematics, and so you need some idea of how muscles behave in order to provide the forces. As I've said on previous occasions, I don't have that knowledge.¹

I also think that the process development you describe is rather different. There, the objective was to make the enzyme as quickly and inexpensively as possible (I guess). I don't think it's quite the same with caning, because you're trying to analyse rather than synthesize.

I do, really, think that it would be worthwhile considering just the shoulder and elbow joints. As Doctor Dominum has described, some canings, not the most severe, could be described in this way. So this wouldn't be a component which might, when assembled, have to be discarded; it would be a genuine instance which would add to our understanding. So when you say


then, in the present context, I would respectfully disagree with you.

1. But I'd be willing to learn. If you were able to explain to me in simple terms how, in particular, the muscles controlling the elbow joint work (biceps and triceps?) with, perhaps, the ranges of forces they can exert and the configuration of the connections with the bones, then maybe I could have a go.

The model is not intended to replace the real thing but rather to provide insight.

The following drawing shows the master in a possible "neutral" position, perhaps just before delivering a stroke.

The cane is parallel with the ground and the master slightly stooped in order to position the cane at the correct height. If the caner was substantially taller than the canee a greater stoop or partial squat would be required. Diagonal strokes are inevitable if the master's hand is higher than the target.

A weak stroke could be applied using wrist flick alone while keeping everything else still.

A weak stroke could be applied using only hip, torso and shoulders rotation about a vertical axis.

A weak stroke could be delivered by raising the straight arm and bringing it down.

A coordinated combination of these and other movements would produce a far more powerful stroke.




After a brief glimpse at the biodynamics of bandminton, and photos of players in action, I conclude it is not much like school caning as I knew it, and my model is very crude. See, for example:

http://projekter.aau.dk/projekter/files/42678547/ArticleDone.pdf

A bird's-eye view of the scene shown in the drawing above.




Apparently, good bandminton players attain racket head speeds in the range of 30 to 50 metres per second (108 to 180 kmph)

Reflectors are often attached to elite and would be elite athletes bodies, and their equipment who are the filmed at very high speed simultaneously from several different angles. The movement of the markers in 3D space and relative to each other is recorded and analysed, a complex task. This paper describes a method for doing this analysis and conveniently describing the motions.


Computer Methods in Biomechanics and Biomedical Engineering

Volume 13, Issue 2, 2010, pages 171-183

A computationally efficient optimisation-based method for parameter identification of kinematically determinate and over-determinate biomechanical systems

M.S. Andersena, M. Damsgaardb, B. MacWilliamsc & J. Rasmussena

Abstract: This paper introduces a general optimisation-based method for identification of biomechanically relevant parameters in kinematically determinate and over-determinate systems from a given motion. The method is designed to find a set of parameters that is constant over the time frame of interest as well as the time-varying system coordinates, and it is particularly relevant for biomechanical motion analysis where the system parameters can be difficult to accurately determine by direct measurements. Although the parameter identification problem results in a large-scale optimisation problem, we show that, due to a special structure in the linearised KarushKuhnTucker optimality conditions, the solution can be found very efficiently. The method is applied to a set of test problems relevant for gait analysis. These involve determining the local coordinates of markers placed on the model, segment lengths and joint axes of rotation from both gait and range of motion experiments.



There are many more similar papers. Biomechanics is a large and active field of study.

Lots of torso / core windup, arm back but no elbow bend.

http://www.cliffsnotes.com/study_guide/topicArticleId-10453,articleId-10414.html

Mechanics Defined

Mechanics is the study of the motion of material objects. Classical or Newtonian mechanics deals with objects and motions familiar in our everyday world. Most people possess some intuition about classical mechanics; we all have watched a ball fly through the air or a bicycle tire spin. You should not be afraid to connect the formalism with your intuition. Indeed, this is often the easiest way to see the answer to a difficult problem. Allow the formal physics and math to illuminate what you already know.


A gentle intro to the rotation of rigid bodies:

http://www.cliffsnotes.com/study_guide/Rotational-Motion-of-a-Rigid-Body.topicArticleId-10453,articleId-10419.html


A frightening esculation:

http://www.cs.cmu.edu/~rapidproto/mechanisms/index.html#mechindex

Biomechanics

http://en.wikipedia.org/wiki/Biomechanics

Free software: http://en.wikipedia.org/wiki/Simtk-opensim

The OpenSim software looks interesting, but I see that I need to join their community before downloading it, and I'm not sure that it would be appropriate for me to do that. Apart from that, I suspect that this would be a suitable tool for investigating these questions.

As far as the mechanics is concerned: well, I can do mechanics. I even write research papers on some of the more obscure aspects of mechanics: for example, motion subject to nonholonomic constraints -- such as car parking in the smallest possible space. I can do cars; but shoulders, arms, etc. need a greater knowledge of anatomy than I possess.

Incidentally, I find the lower image in the post of January 28 2012, 2:59 AM quite unconvincing. It looks like a horizontal golf swing. But if you tried a horizontal golf swing, I bet you'd fall over!

Alan,

You would seem to be very well qualified to calculate the bend in a uniform cane of known modulus of bending, held at one end and in a state of constant linear acceleration, as in your diagram above. You may neglect air friction and assume the bend is small / the cane is stiff (sin theta = theta) if that helps. Refer to Sir Isaac if you wish.

What is the torque experienced by the accelerating hand?

KK: What is the torque experienced by the accelerating hand?

I'm not entirely sure why I need to know the torque that the care will exert on my hand; I'd be much more interested in the range of force or torque that I can apply to the cane, and the resulting effect.

Still, here are a few comments on this problem. The first is that, strictly as stated, I can use Einstein's "principle of equivalence" to formulate the problem in a simpler manner. This principle states that, if you are in a lift (elevator), there is no difference between experiencing a constant linear acceleration in free space, and being at rest in a gravitational field. It's just the choice of a different (non-inertial) frame of reference. So I will imagine a lift, with the cane fixed to the wall and sticking out into the interior. Real gravity, which will have only a small effect, will be neglected; I shall replace the acceleration of the lift/cane combination with a (horizontal!) gravitational field.

It is now clear what happens. Take moments about the fixing on the wall. The torque must equal the "weight" of the cane, with an appropriate value of the gravitational constant, multiplied by half the length of the cane. This will be the case if the cane is rigid, and approximately the case if the cane flexes slightly.

In fact, I imagine that KK didn't really mean that the acceleration shold be constant. He meant that it should be a Heaviside step function, zero up to a certain time, and then some constant positive value afterwards. A first attempt at modelling this would be to imagine a support along the length of the cane, and suddenly removing this support at the critical time.

For a rigid cane, this makes no difference. But if the cane is flexible then it will start to deform under the "gravitational field". Thus, taking moments, the torque at the fixing will equal the difference between the "weight" and the effect of the angular acceleration of the centre of mass about the fixing. This can be determined by solving equations involving the elasticity of the cane. In fact the cane will tend to oscillate about its equilibrium position. That's because Newton's Law (force equals mass times acceleration) gives rise to families of second-order constant-coefficient ordinary differential equations, whose generic solutions are either oscillatory or exponential, and in this model the sign gives oscillatory solutions.

In fact, the scenario described above isn't quite what happens. You cannot make the whole cane accelerate suddenly like that when you are holding one end (and so you can no longer model it using the Einstein principle). In fact a ripple moves along the length of the cane when the acceleration starts.

Perhaps you don't believe that? Well, you'd certainly believe that a wave moves along a whip when you crack it, because you can see it happen. A flexible cane, at least for the first few milliseconds after the acceleration starts at one end, behaves like a rather stiff whip. The ripple is much shallower than in a whip, and it moves much faster, but it's there. Whether it is significant will depend on the numerical details.

And that's as far as I'm going to go with this.

A further comment on KK's diagram.

While a moderate cane stroke could be administered with a straight elbow, I don't believe that it is possible to keep your elbow straight when using a full wind-up.

Why? Because, unlike a golf swing, which is essentially in a vertical plane (and so doesn't have much of an effect on lateral position of your centre of gravity), a cane stroke does move your centre of gravity horizontally. So you'll need to keep your balance. You might try some footwork, or you might bend your knees to help. But I'm not convinced that you'd really do that; instead, I suspect it would be more likely that you would instinctively adjust your elbow angle (and hence the position of the centre of gravity of the arm unit) in order to maintain balance while aiming at the target.

Bent elbow

Above, a crude attempt has been made to apply biomechanics. The science of biomechanics began more than 300 years ago.


Giovanni Alfonso Borelli is often described as the father of biomechanics. He was born in Naples in 1608. His De Motu Animalium, published in 1680, extended to biology the rigorous analytical methods developed by Galileo in the field of mechanics. Borelli calculated the forces required for equilibrium in various joints of the human body well before Newton published The Laws of Motion Borelli was the first to understand that the levers of the musculoskeletal system magnify motion rather than force, so that muscles must produce much larger forces than those resisting the motion. Borelli died in Rome on December 31, 1679, but his impressive body of original work helped inspire a great number of future scientists, microscopists, and inventors. The highest honor bestowed by the American Society of Biomechanics is the Giovanni Borelli Award.

http://en.wikipedia.org/wiki/Giovanni_Alfonso_Borelli


I am guessing that few members of this forum have much interest in the application of the physical sciences. Is there point in posting such science here?

KK wrote:

I am guessing that few members of this forum have much interest in the application of the physical sciences. Is there point in posting such science here?

Thank you KK. Having an interest in the science of CP, I would welcome any relevant information.

Corporal punishment usually involves a series of inelastic collisions, often involving the buttocks.

A perfectly elastic collision is defined as one in which there is no loss of kinetic energy during the collision.

No collisions between real objects are perfectly elastic but some come close such as those between billiard balls.

An inelastic collision is one in which part of the kinetic energy is changed to heat or used to cause permanent deformation. Strapping, caning, paddlings, etc. involve inelastic collisions.

Momentum is conserved during both elastic and inelastic collisions.

It is difficult to track kinetic energy during a collision since some of it is converted to heat etc. Momentum is more easily tracked.

The ballistic pendulum (see below) can be used to measure the transfer of momentum. When the pendulum is struck by a bullet, cane or other fast moving object it will swing.

If the mass of the pendulum is know it is possible to calculate the momentum transferred to it during the collision directly from the change in height of the bob during its swing. Alternatively, the angle of the swing or its length can be used in the calculation if the length of the pendulum is known.

The strike plate or "cheeks" on the pendulum can be changed from near elastic (hard rubber) to human flesh like (ballistic clay or gelatine). This enables the dissipated energy to be measured by difference.

Roma Plastilina(TM) No.1 is a soft, homogenous non-hardening, oil-based modelling clay used for ballistic tests. It is plastic and undergoes permanent deformation when struck. The depth of penetration relates directly to the kinetic energy density of the impact. Clay is a little harder and denser (1.5 g/mL) than real flesh.

Ballistic gelatine is designed to simulate living soft tissue. It is the standard for evaluating the effectiveness of firearms against humans because of its convenience and acceptability over animal or cadaver testing. Ballistic gelatine resembles a very firm jelly. It is made by dissolving gelatine in hot water and allowing the mixture to cool.

Ballistic Pendulum

I have found the following. Have I missed any substantial science threads or messages?


Paddling: how it works. Alan Turing, July 31, 2009
http://www.network54.com/Forum/198833/thread/1249030390/

The science of strap (and paddle weight) and pain. KK, August 15, 2009
http://www.network54.com/Forum/198833/thread/1250290818/

Sex, gender and pain the science. KK, December 18, 2009
http://www.network54.com/Forum/198833/thread/1261177459/

Backswing. Alan Turing, January 14, 2012
http://www.network54.com/Forum/198833/thread/1326544185/

Questions to Maureen. Trackoid, November 30, 2011.
http://www.network54.com/Forum/198833/message/1322630448/

Injustices or not. Steve M, January 2, 2009
http://www.network54.com/Forum/198833/thread/1230930900/

You need to be careful when discussing the conservation of momentum.

I have taken KK's ballistic pendulum and screwed the wooden block onto a brick wall. I fired a bullet at the wooden block. The bullet entered the block, and stopped.

What has happened to the momentum of the bullet?

Alan,

I do hope you had permission.

When the gun was fired the recoil was transmitted to planet Earth. A short time later the impact of the bullet was transmitted to planet Earth, restoring the rotation to its proper rate.

That is, of course, absolutely right. But it illustrates the problem. A very small movement of the Earth can swallow up a large amount of momentum, and we can't really measure that movement (we can only deduce it from the quantities we can measure, and the conservation law). That means we can't really use the conservation law to tell us anything, because there will always be the nagging doubt "but perhaps the Earth has moved".

Talking of bullets etc, the recoil of the gun and impact of the bullet on the target, and the effect it has on the earth.
What happens or will happen if we build more wind farms to produce energy. A windmill provides resistance to the wind, and is converted to rotational power. As most winds in this country are from the west, if we were to build many more wind farms, would this result in the rotation of the earth increasing in speed ? The same could apply to tidal barriers built to utilise an east/west tidal flow.

But the Earth's rotation is slowing anyway, as a result of tidal drag. So maybe that will help!

Does that mean we'll end up with more hours in a day?

If so, I'm all for it!

Lotta, I hope you live that long!

The Earth's rotational kinetic energy is about 2 x 10²⁹ J, whereas human energy use over the entire planet in 2008 was around 5 x 10¹⁸ J. (Sourced from Wikipedia, but it's not going to be ridiculously wrong.) That's a big difference. I don't know the exact figure for tidal drag, but again it's pretty small.

You may not have noticed but a leap second was recently added to atomic clock time (Coordinated Universal Time) to keep it aligned with the slowing rotation of the Earth. So, if 30 June seemed a long day, it was.

I do not think extracting energy from wind or tide will have much effect on the Earth's rotation as most of the extracted energy would have gone directly to waste anyway.

If there is an air or water pressure difference between two connected points fluid will flow. The speed of the flow depends on the resistance to that flow. Steady state conditions are quickly achieved. The flow does not get faster and faster if the pressure stays constant. The work done in overcoming the resistance is converted to heat or converted to kinetic energy in rotating turbine blades.

Impeding tidal flows may reduce the tidal slowing of the rotation.

There is currently a lot of scientific interest in "non-lethal" or "less lethal" weapons suitable for use by police (and repressive regimes). Guns of various kinds are most common. Chemical irritants and electric shock devices are becoming more common but usually lack the accuracy and / or the range of rubber bullets, bean bags and the like.

The less-lethal weapons are designed to incapacitate or to deter by causing pain without causing serious injuries (and preferably, without leaving marks). There would seem to be overlap with the science of corporal punishment.

There is also interest in body army for the military, and wounds caused by paintballs and air gun pellets.

Some of the research has been done on dead bodies and test animals. Work has also been done on models of, or surrogates for, human flesh and various body parts such as the head or chest. Ballistic gelatine or clay may be used on its own or behind armour.

The blunt criterion (BC, see equation below) is used to estimate the injury likely to vital organs when the chest or abdomen is struck by a hard blunt projectile. There is a 50% chance of moderate injury for BC = 0.37. Serious injury or death is likely for larger values. The criterion does not purport to indicate injury to the skin or surface of the body. The BC value for straps, canes and paddles is likely to be well below the 0.37 value although they cannot be characterized by a single diameter.



Kinetic devices can be characterized by their impact speed and mass. The following diagram is borrowed from a paper concerned about the safety of small unmanned aircraft. Canes etc, may reach speeds of a few tens of metres per second and may weigh up to a few tenths of a kg. That is, devices used to inflict CP occupy the left bottom corner in the diagram.





The following recent paper illustrates the sort of research being done.


Forensic Sci Int. 2012 Jul 10;220(1-3):126-9. Epub 2012 Mar 8.

Skin penetration surrogate for the evaluation of less lethal kinetic energy munitions.

Bir CA, Resslar M, Stewart S.


Abstract

Although the benefits of the use of less lethal kinetic energy munitions are numerous, there is a need to evaluate the munitions prior to deployment to ensure their intended effect. The objective of the current research was to validate a surrogate that could be used to predict the risk of penetration of these devices. Existing data from biomechanical testing with post-mortem human specimens (PMHS) served as the foundation for this research.

Development of the surrogate involved simulating the various layers of the skin and underlying soft tissues using a combination of materials. A standardized 12-gauge impactor was used to assess each combination. The energy density that resulted in a 50% risk of penetration for the anterior thorax region (chest) (24 J/cm(2)) from the previous research was matched using a specific combination of layers.

Twelve various combinations of materials were tested with the 50% risk of penetration determined. The final validated surrogate consisted of a Laceration Assessment Layer (LAL) of natural chamois and 0.6 cm of closed-cell foam over a Penetration Assessment Layer (PAL) of 20% ordnance gelatin. This surrogate predicted a 50% risk of penetration at 24 J/cm(2). Injury risk curves for the post-mortem human specimens and surrogate development work are presented.

I'm intrigued that the BC formula is logarithmic in the kinetic energy. The D in the denominator is to be expected, because the same impulse on a smaller area will have a greater effect, although presumably when D gets small the projectile stops being "blunt".

I guess a paddle would be blunt. Is a cane blunt?

What kind of correlation is there between injury and pain? Presumably this depends on the part of the body being hit.

I do not think the BC is purported to be, or is, a linear function of injury or pain. Rather, the logarithm is used to compress the scale and reduce its apparent precision to better match the real precision. BC is only rough and ready assessment tool.

There is a scale for injury: http://en.wikipedia.org/wiki/Abbreviated_Injury_Scale

Apparently, it is much easier to make effective flexible body armour than rigid. The energy must be spread as well as absorbed. Deformation of the body must not exceed 44 mm, enough to break ribs in some people. Part of the absorption is by the flesh beneath which is sacrificed to protect the vital organs from otherwise penetrating projectiles.

A large amount of work is being done to make both munitions and armour "better". Much of the research seems very unsavoury and it is not an area for the squeamish or those inclined to moral considerations. There is a demand for cadavers and amputated limbs.

Paintballs seem to be the best model for canes in terms of the impact energy density, wounding and size, if a sphere can approximate for a cylinder.

Tattooists rate various body parts for sensitivity. Hands and feet rate high and the buttocks low.

First of all, thank you KK, for posting the information.

I have had difficulty so far picking out the most relevant factors. However, you have just beaten me to the keyboard in saying that paintball seems to have interesting similarities to caning.

The form of weals is quite similar, though different in shape. The contact area of a paintball, weighing about 3 grams is quite small at about 2.5 sq.cm. A cane is perhaps ten times heavier, but has a contact area correspondingly greater.

A few fascinating things I have picked up are:

Paintballers use similar strategies to school pupils when it comes to reducing pain. Loose clothing over several pairs of underwear are common - though referees deprecate this. Maybe they are the "headmasters" of paintball?

Paintball strikes to the unprotected hand are considered some of the most painful, especially those where the ball bounces off rather than breaking. This corresponds with my experience of the cane, where a brief contact with an almost instant release can seem more painful in the short term than a stroke which remains on the skin for longer. It is almost as if the cane "sticks" to the skin, drawing it upwards as the pressure is released.

The energy of a paintball at the muzzle of the gun must not exceed 5.7 joules. I think this is rather less than some of the figures previously suggested for a cane stroke. I am not sure how to compare the actual velocity of the ball with that of a cane tip as the paintball decelerates over distance whereas the cane is accelerating towards its target.

Far more research has been done on paint balls than on canes. Paintballs are "soft", deform, and burst on impact, unlike the cane. They deliver kinetic energy at roughly the same density as a light school cane (Joule/cm^2), depending on the range. The wounds are very similar in type with the damage occurring at the edges of the impact zone, probably due to shearing, tearing and capillary bursting. There is little or no damage apparent at the centre of impact

The photo below shows mild/moderate wounds on the hip, probably an hour or two after impact. There is no redness around the wounds but the wounds have not yet darkened or turned purple. The impacts were reported to have hurt.

It would be interesting to determine with the risk of pain is a significant part of the attraction of paint ball sport. Risk taking for its rewards requires "real" consequences.

http://www.jabfm.org/content/25/1/124.long

Journal of the American Board of Family Medicine. 2012 Jan-Feb;25(1):124-7.

Target lesions and other paintball injuries

Sbicca JA, Hatch RL.

Paintball is a popular combat game, with more than 5 million participants per year. As it has increased in popularity, the incidence of paintball-related injuries also has increased. The most common injuries are classic, benign skin lesions that are easily recognized if one is aware of them. Devastating eye injuries also may occur if participants do not wear face masks. Other reported injuries include musculoskeletal injuries, solid organ injuries, and vascular pseudoaneurysms. Rarely, paintball-related deaths have been reported. This article is the first to review the full spectrum of paintball injuries; in addition, the article emphasizes the importance of encouraging participants to adhere to appropriate safety measures, particularly wearing an appropriate face mask at all times during the game.

The diagram shows the predictions of mathematic equations for a steel ball dropped onto a slab of ballistic clay.



The relatively slow-moving (6 m/s) but dense ball hits the clay at about 3 milliseconds. It immediately begins to slow, deforming the clay and shedding kinetic energy (purple line). The ball reaches its deepest penetration at about 12 ms when its kinetic energy becomes zero. It then rebounds because of the elasticity in the clay (green line).

Some 10 Joules out of the 20 J of the initial kinetic energy is used to plastically deform the clay.

The clay oscillates as elastic and the kinetic energies interchange but this is quickly damped by viscous effects which have been neglected in the calculations.

The clay is a rough analogue of human flesh. It is rather more dense (1.57 g/mL), homogeneous and isotropic than flesh, and more plastic and less elastic. Clay is useful because it has a memory it is permanently deformed by impact which allows the deformation to be measured. The size and depth of the crater relates to the energy of the impact.

The steel ball is a rough analogue for a cane. It has similar impact energy to a cane but it is going much slower and is much heavier.

There are some other matters; I can't say how significant they are.

The kinetic energy of the ball can't have been constant before 3ms (it was falling, and so accelerating). I'm not clear why it should be constant (and non-zero) after 18ms.

The ball also has potential energy (that's how it managed to gain kinetic energy, by reducing the potential energy). The potential energy wasn't constant when it was in the clay, because the ball's height varied. (A cane also has potential energy, caused by its enforced curvature).

When a cane hits its target, the flesh ripples away from the impact. But the flesh is attached to rigid bone structures, and so the ripples seem to be reflected and interfere with one another. This phenomenon does not appear to occur in the ball experiment.

Alan,

Thanks for your interest.

I do not understand the study by Callahan of the impact of a steel ball into clay. It involves the modeling of stresses and strains in four-dimension space-time.

The 1.043 kg, 63.5 mm diameter steel sphere was dropped from a height of 2 m. It produces an impact crater 21.5 mm deep and 67 mm across.

The block of clay measures 140 x 610 x 610 mm. Some six parameters are used to describe its properties (density, elastic, Poisson's ratio, plastic, strain hardening). Some of the parameters are adjusted to give the best fit of the model to the drop experiments rather than being measured independently.

It is stated that the effects of gravity are neglected during the impact. I calculate it took 640 mS for the steel ball to fall 2 metres, neglecting air friction. The ball loses it energy in about 10 mS. (The zero time in the figure above appears somewhat arbitrary.)

What would be of the greatest interest is the zone of plastic flow - the region where the clay is sheared and permanently displaced. Are the circular wounds produced by paint pellets (or the tram tracks produced by canes) explained by the clay model? Why does the point at centre of impact remain, apparently, uninjured?

KK wrote:

Are the circular wounds produced by paint pellets (or the tram tracks produced by canes) explained by the clay model? Why does the point at centre of impact remain, apparently, uninjured?

As I have always understood it, the white zone between the tram tracks shows where pressure has forced the blood and lymph out of the surface capillaries into the surrounding tissue, causing it to swell. The capillaries continue to leak, causing a contusion to develop, which then spreads downwards under the force of gravity. The discolouration eventually appears to cover a much larger area than the original injury, but the point of impact, even if not obviously injured, remains tender when touched.

I'm not sure the steel ball is a close enough analogy to a cane to tell us a great deal. What interests me most is the elastic rebound and how it interacts with the flexibility of the cane. In other words, what determines whether you should choose a more flexible or less flexible cane?

hcj,

I believe you are right about how the wound is produced but there is another possible mechanism. The tissue surrounding the impact crater is stretched and vulnerable blood capillaries may tear and bleed. This mechanism is proposed in some forensic medical texts. This could be what happens when blood is drawn. I will provide a drawing soon.

The steel ball / clay mathematical model can be modified to better match caning. The weight, diameter and speed of the ball can be made more cane-like.

The clay in the model calculations can be made more elastic and less plastic but must remain homogeneous and isotropic, quite unlike human flesh.

Some experimenters have coated the clay with materials that mimic some of the properties of skin.

Using the model involves inserting appropriate values into a computer program. I do not have access to the program.

I am not certain that the model allows adequately for bulk displacement of clay and I doubt that it can deal with the displacement of fluid in a porous elastic medium.

Tram tracks formed by tearing

Tram tracks formed by blood displacement in the capillaries

Photos of impacts show impact craters are much wider than the implement.

Very high pressures are generated immediately under the impact zone. Fluid is displaced either side to where pressures are lower. The high pressure inside the capillaries cause them to rupture.

KK, Your first drawing shows the effect of rectangular (tawse tail?) and round section (cane) impacts. I am not sure whether the differences in the depth of penetration are deliberate?

I have very little experience of the tawse, but I do not recall tramline type marks characteristic of the cane, even when the tawse tails were of a comparable width to a typical cane.

I should have acknowledged the source of the first (B&W) drawing.

I found it in a couple of places and do not know its original source. There is no significance in penetration distances and they do not relate to specific devices as far as I know.

http://www.pdn.ac.lk/med/departments/forensic/BUDHUSARANAI/tram-ansr.htm



The following is a further diagram from the mathematical modeling of a steel ball hitting clay.



The ball has struck the clay from above and penetrated some distance into it.

Von Mise's stress is the total combined force per unit area at a particular time and point in the clay. The dark blue areas are uneffected by the impact and the red and yellow greatly affected. The stress decreases in all directions the greater the distance from the ball.

The predicted stress pattern does not match the annular wounding caused by a paint pellet.

Ballistic clay

Soft modeling clay, wetted with non-volatile oil rather than water, is used for ballistic studies because of its plasticity and memory. The clay is deformed when struck. The deformation is permanent and can be measured later, at the experimenters convenience. The clay is similar to Plasticine(TM), once a popular plaything for children.

Clay is very different in structure to human flesh. The wounds produced in clay by blunt force trauma differ from those produced in flesh. Gels made with gelatin and hot water are a closer analogue to human flesh but are harder to prepare and to study.


Ballistic Gelatin

Gelatin gels consist of a three dimensional network of tangled strands of elastic protein with water filling the spaces between. The average separation of strands is about a micrometer. The protein occupies only a few percent of the volume and water the rest.

The protein strands straighten or buckle when the gel is subject to shear or compression, as shown in the diagram. If the distortion of the gel is too great the protein strands break.

Water may leak from or be forced from the gel. Its movement through undamaged gel is greatly impeded by the protein as the channels are very narrow even if very great in number. The channels are generally narrower, more irregular, less defined and tortuous than blood capillaries.

Mechanical shocks travel through the gel at near the speed of sound in water (1 mile per second).

Most of the studies of ballistic gelatin either have been destructive or have involved small, relatively slow deformations only. In the destructive tests, the minimum force or energy required to break the gel, or the shape and volume of the destruction zone have been determined.





Is this any easier to understand than the sociological studies?

I've made a comment about shearing here. If someone with a dark-coloured skin is being caned, the light-coloured tramlines appear immediately as a result of the stretching effect (essentially diluting the colouring of the skin, I suppose) and fade quite quickly, whereas the usual red marks take a few moments to appear.

In reference to hcj's comment, presumably even a thin tawse doesn't have such a cutting effect as a cane; perhaps because it is more flexible.

KK asked: Is this any easier to understand than the sociological studies?

Yes, because it doesn't set out to create an impression of scholarship by using words that are not in the average person's daily vocabulary.

On the subject of modelling, it shows how difficult it is to replicate real life in a laboratory.


Quoting from: http://www.forensicmed.co.uk/

When a person is struck with a cylindrical object ... the bruise pattern formed is quite distinct.

The skin surface is indented and blood vessels at the edges are ruptured. Blood is squeezed out of any vessels along the point of contact, but the vessels remain relatively intact (particularly if the supporting tissues are lax). When the impacting object is removed, blood flows back into the undamaged vessels, but leaks from the damaged ones.

The resulting bruise is termed a tramline bruise because it appears as a pale linear central area lined on either side by linear bruising.


and an extract from: http://www.dundee.ac.uk/forensicmedicine/notes/ copyright Dr Sadler 1999

Skin has greater elastic limit than underlying fat and blood vessels making subcutaneous bruising more common than skin laceration. Degree of force cannot be accurately deduced from the size of a bruise.

Although heavy impact will generally cause a large bruise, the severity of bruising depends on in part, the anatomical site.

Over bony prominences (shin, cheeks), lax, vascular tissue (eyelid, orbit), fatty tissue (buttocks,) will bruise easily. Escaped blood has room to accumulate in lax tissues...

...Dense, tightly bound tissue, e.g. palms, soles, rarely bruises. Dense fibrous tissue physically restricts accumulation of blood.


The original text then goes on to describe other factors influencing bruising.

Modeling clay is available in a range of colours. This allows a layered target to be constructed and thus the plastic flow around an impact crater to be more easily deciphered. Of course, this does not make the clay more flesh like.

Experiments pending!

KK asked: Is this any easier to understand than the sociological studies?

Yes, because it doesn't set out to create an impression of scholarship by using words that are not in the average person's daily vocabulary.


Well everyone's entitled to their view of social science. It equally interesting to note is that the only contributors ( if you ignore the cynicism of lotta nonsense's comments) are those who have a high level of mathematical/ physical science knowledge. For example the ballistic pendulum is hardly accessible to the knowledge base of the average school leaver today . But it doesn't make it any less relevant to the question .

I don't understand quantum mechanics except at a fairly rudimentary level, but I won't diminish the subject as a consequence. You may not be interested in a subject or topic, you may not be bothered therefore to understand it , but that doesn't imply your approach has some form of privileged epistemology,making it valuable in some way others are not.

KK wrote: Experiments pending!

Perhaps a layer of saturated sponge between the layers of plasticine?

Prof n wrote:

...For example the ballistic pendulum is hardly accessible to the knowledge base of the average school leaver today . But it doesn't make it any less relevant to the question .

I don't understand quantum mechanics except at a fairly rudimentary level, but I won't diminish the subject as a consequence. You may not be interested in a subject or topic, you may not be bothered therefore to understand it , but that doesn't imply your approach has some form of privileged epistemology,making it valuable in some way others are not.

I certainly do not seek to diminish the subject of social science. Given that I don't possess your expertise, I just crave less jargon and clearer presentation.

As to the average school leaver; I would be amazed if they didn't all know what a pendulum is and a good proportion would know what ballistics involves, so a fair number would understand what is meant by a ballistic pendulum. On the other hand, I doubt many would be able to spell epistemology or teleology let alone define them.

Hi HCJ

A few years ago I was talking to one of the admissions tutors as an Ivy league institution. He was bemoaning the standard of students they got in some subjects. Referring to British students he said , if I could find one who could define teleology or hermeneutics in a telephone interview I'd give them a place. Trouble was virtually none had even heard the words ( unless they'd done the IB)

On the issue of maths I seriously would be surprised if the average 16 year old GCSE student ( maths plus single science ) would even understand more than the most simple mechanics. Triple science in a private school maybe .

I attach a link an examination paper set for the 'highest achieving ' students in GCSE physics this last year Judge for yourself . Use the link to get to question papers , then refine to 2011 ( without a special code you shouldn't be able to access 2012 yet ). You will find two physics paper at the bottom of the small group of available papers .

http://www.edexcel.com/quals/gcse/GCSE-science-2011/Pages/The-exams.aspx

Woe!

I found an establishment which sold artists' supplies that listed Roma Plastilina #1 among its wares. I ordered a brick and it duly arrived but was the wrong grade - much too hard. They then decided they did not have #1.

I bought some kids modelling clay from a local shop and found it very rubbery and sticky unlike the real Plasticine of childhood memory.

Then I found a recent paper that says RP#1 has changed over time and is not a good material for blunt impact studies.


http://books.nap.edu/openbook.php?record_id=13390&page=5

Clay as a Recording Medium

The qualitative assertion that RP #1 (the oil-based ballistic clay Roma Plastilina #1) exhibits little recovery has been interpreted to mean that the level of elastic recovery is small enough to be safely neglected. This has led to an assumption that the shape of the resultant cavity provides a record of the BFD (Back Face Deformation). Since the relative degree of elastic and plastic deformation will vary as a function of strain rate, the backing material must be characterized under conditions that are relevant to those under which the tests will be performed. The cavity that results from live-fire ballistic testing is indeed related to the deformation on the back face of the armor, but it is not a true record of maximum deflection. It remains unknown how the dimensions of the cavity relate to the true BFD and how such a relationship may depend on the rate at which the cavity is formed.

RP #1 was originally developed as a modeling clay for artists. Over time its composition changed and the clay became stiffer to suit the ceramic arts community's needs. Consequently, testers recognized the need for a method for calibrating the clay. The so-called column drop test was developed in response to this need. Because the oil-based modeling clay is readily softened by heating, ovens are now used on the firing range to warm the clay so that the newer formulations respond in the same way as the older ones.

Experiments conducted by the ATC show that RP #1 exhibits highly variable penetrations under nominally identical conditions. This unambiguously indicates that RP#1 is an inherently imprecise recording medium.

The committee found that both the spatial and the temporal variations of the modeling clay are significant. Experiments can be conducted to determine the variation due to the geometry and location of the drop in relation to the side of the box. Also, the scaling relationship between drop tests and ballistic tests remains mostly unexplored.

Understanding the structure-property relationships of oil-based modeling clay as they pertain to mechanical working, thermal processing, friction, and how the various ingredients ofthe clay modify behavior could lead to alternatively clay systems with more favorable properties. A clay working group consisting of interested government and civilian expos from the body armor testing community is working to develop a near-term replacement clay that can meet the calibration specification of the column drop test at ambient temperature and whose properties are little affected by temperature.

I was excited when I came upon some studies such as "Modelling with plasticine the low speed impact of long rods against inclined rigid targets" and similar but soon discovered the studies related to nail guns and armour piecing projectiles. The impact of the cylinder is end-on.

Generic "plasticine" modeling clay is much used in a wide range of studies, usually as a surrogate for something much harder, e.g. rock, glass, armour. In some of these studies layers of different colours are used and the clay may be softened by the addition of a little parafin oil.

A major manufacturer of plasticine: http://www.becksplastilin.de/english/impressum.html

... that we had another picture of a tram.



Brno hlavni nadrazi, this morning.

I reported that my "plasticine" modeling clay was harder and more rubbery, and stickier than that of my childhood memories. I have since found that kneading it made it more plastic and softer. It still seems a bit too sticky.

I have done my first rough experiments. First, I made a sandwich of yellow clay between layers of blue. The layers, of perhaps 3-4 mm, were made by rolling the clay with a cylinder of about 6 cm diameter on a desktop. I took no special care to make the layers of uniform or accurately known thickness.

I pressed a cane-like cylinder slowly into the sandwich to make an indentation. I cut across the indentation with my sharpest knife and pealed the sandwich from my desk to examine the coloured layers in cut surface.

The experiment was a great success in the sense I learned a lot but a total failure in terms of deciphering the mechanism of cane impacts.

To my surprise, I found the yellow layer had thinned to almost nothing along the knife cut. It seems the knife edge itself had substantially compressed the clay causing the yellow clay to flow away from the compression zone. The yellow clay seems to be softer than the blue.

Others have reported and exploited clays of different colours having different hardness. It is unclear whether the colour has a direct effect on hardness or whether batches of clay differ independent of the colour. The dye content is tiny but it is most likely absorbed to the surfaces of the very fine chalk particles that make up the bulk of the clay. Changing the surfaces may change the bulk properties.

I repeated the experiment with just two layers and used a knife with a smoother and much thinner blade. The cut edge is shown below.



The yellow clay has been thinned by the knife and there is bulging of both yellow and blue way from the cut edge. The top edge of the blue clay has been greatly rounded by the cutting.

There has been some smearing of colours by the knife, most especially as it was removed. Note the polished and dull regions on the cut surface. The dull regions are likely caused by the clay sticking to the knife blade.

The bottom of the clay has buckled - it is not flat. The buckling occurred during removal of the clay from my desktop.

In future experiments I plan to use strips of cardboard or similar either side when rolling clay into sheets to better control thickness.

I will cut the clay sheets before sandwich making, and the cane compression tests, and will leave sandwiches adhering to a backing strip to avoid buckling.

I will experiment with talcum powder as a surface dusting to reduce stickiness. Paraffin or vegetable oil may also reduce stickiness although it will soften the clay. It is important that the clay does not stick to the knife during cutting.

I will investigate high speed impacts later. I need to improve my aim first.

Sandwiches can not be easily unmade or colours unmixed so I will need a good supply of clay if I am to continue sandwich experiments.

There are two main theories for cane tram tracks - shear / tearing and hydrostatic pressure rupture. Either, or a mixture of the two, may explain the wounds produced by the cane.

The following clay sandwich experiments suggest themselves.

1. Does a tissue paper, or similar filling, tear both sides of the impact zone when the sandwich is caned?

2. Does a soft yellow clay filling pool either side of the impact zone?

A further matter that needs investigation is the affect of friction between the clay and the cane. Whether the cane sticks to the clay or has near frictionless contact may have a large effect on the degree and nature of the surface wounding.

KK:


This is significant in the context of the effect of clothing as protection.

I said my plasticine clay of different colours differed in hardness. I now believe the chief determinant of hardness was the amount of kneading the clay received, and how long it had been rested before its hardness was assessed.

Clay temperature seems to have a relatively small effect on hardness. Clay cooled in a domestic freezer remained soft and plastic. Possibly, the cooling slowed the development of structure and hence the hardening of the clay.

It may be desirable to rest assemblies of clay layers (for hours?) to allow equalization before subjecting them to the cane. Such resting will make the clay harder, and more elastic and less plastic.

The flow properties of layers of non-homogeneous clay (or sedimentary rock, flesh, . . .) subject to compression or shear are complex. The more fluid parts of an assembly will move further and faster than the harder or more viscous parts. This difference in flow properties has been shown to be very important in geological processes, and when caning clay.

I have yet to find a way of cutting clay to reveal internal structure without causing distortion and flow. This difficulty with cutting raises doubt about the validity of some published papers describing the use of coloured clay layers.

Cooling the clay did not make it harder and easier to cut without distortion. Perhaps I should try warming?

Would it be better to cut with a wire rather than a knife, as you would when cutting cheese?

(Silly thought - I wonder what happens if you cane a Camembert? The cheese has plastic and elastic qualities and is contained by a skin.)

Hello HCJ,

Camembert cheese is one of my pleasures in life : unfortunately because of the health police it is rare to find it anywhere near 'ripe' enough in shops. I get my main grocery order delivered, and the buyers at Sainsburys clearly don't know when a Camembert ought to be eaten, and can't read French to boot ! ! I buy a 'lait cru' cheese(PLEASE folks don't send me health warnings ) and if you bother to read the French you discover that the sell by date is the date when the cheese is first ready for eating , but that the traditional eating period is between one and two months later ! So now I have to 'rotate boxes to keep one in peak condition .?So it is effectively a'don't eat before' date , not 'sell before', let alone 'best' before !!!!!!!

Of course if you wait until it is in my mind 'ready to eat ' then caning it would be a very messy business, and really not a suitable feat for one of the kings of 'les fromages '!

hcj suggested: Perhaps a layer of saturated sponge between the layers of plasticine?

Bingo !

Source

Forensic Science, Medicine and Pathology. 2008; 4(1): 33-9.

The biomechanical modelling of non-ballistic skin wounding: blunt-force injury.

Whittle K, Kieser J, Ichim I, Swain M, Waddell N, Livingstone V, Taylor M.

Knowledge of the biomechanical dynamics of blunt force trauma is indispensable for forensic reconstruction of a wounding event. In this study, we describe and interpret wound features on a synthetic skin model under defined laboratory conditions. To simulate skin and the sub-dermal tissues we used open-celled polyurethane sponge (foam), covered by a silicone layer. [Foams: Dunlop Enduro 38-200, intended for firm seat cushions, and softer Dunlop Elephant 34-115.]

A drop tube device with three tube lengths (300, 400, and 500 mm), each secured to a weighted steel scaffold and into which a round, 5-kg Federal dumbbell of length 180 mm and diameter 8 cm was placed delivered blows of known impact. To calculate energy and velocity at impact the experimental set-up was replicated using rigid-body dynamics and motion simulation software.

We soaked each foam square in 500 mL water, until fully saturated, immediately before placing it beneath the drop tube. We then recorded and classified both external and internal lacerations. The association between external wounding rates and the explanatory variables sponge type, sponge thickness, and height were investigated using Poisson regression.

Tears (lacerations) of the silicone skin layer resembled linear lacerations seen in the clinical literature and resulted from only 48.6% of impacts. Poisson regression showed there was no significant difference between the rate of external wounding for different sponge types (P = 0.294) or different drop heights (P = 0.276). Most impacts produced "internal wounds" or subsurface cavitation (96%).

There were four internal "wound" types; Y-shape (53%), linear (25%), star-shaped (16%), and double crescent (6%). The two-way interaction height by sponge type was statistically significant in the analysis of variance model (P = 0.035). The other two-way interactions; height by thickness and sponge type by thickness, were also bordering on statistical significance (P = 0.061 and P = 0.071, respectively). The observation that external wounds were present for less than half of impacts only, but that nearly all impacts resulted in internal wounds, might explain the observed haematoma formation and contusions so often associated with blunt-force injuries.

Our study also confirms the key role of hydrodynamic pressure changes in the actual tearing of subcutaneous tissue. At the moment and site of impact, transferred kinetic energy creates a region of high pressure on the fluid inside the tissue. As a result of the incompressibility of the fluid, this will be displaced away from the impact at a rate that depends on the velocity (or kinetic energy) of impact and the permeability and stiffness of the polymeric foam and skin layer.


Water-filled open-cell foam will be roughly the same density as human flesh. The permeability is unlikely to be the same but this should not matter much for high speed impacts.

There's a significant difference, though: the pseudo-flesh is being attacked with a sphere. That is to say, there are no edge effects (important with an implement like a cane).

There may also be differences when the implement is a flat object, like a paddle. In such case, the conclusion


may need to be modified if the (sideways) speed of displacement of the fluid is lower than the speed of expansion of the impact area.

What is "a round, 5-kg Federal dumbbell of length 180 mm and diameter 8 cm"?

The mixed units (mm and cm) and the dimensions do not make sense. I have not found any other mentions of "Federal dumbbells". Dumbbells usually consist of two equal cylinderal or octahedral weights mounted at the end of a short shaft and almost certainly much longer than 180 mm. Dumbbells are used single-handed, usually in pairs, one in each hand. An 8 cm iron sphere would weigh about 1.92 kg.

Alan Turing wrote of a spherical shape, perhhaps as shown in the following figure:

KK asks: What is "a round, 5-kg Federal dumbbell of length 180 mm and diameter 8 cm"?

Perhaps the author of the report should have used the description kettlebell, rather than dumbell?

I cannot find a link to the name "Federal" - except that there is a company of that name which manufactures ammunition.

hcj,

Thanks. The problem with a kettlebell is that the handle would be too wide to fit in the droptube.

A common practice in research is to use the same set up as others when such exist. Lots of researchers have dropped spheres and cylinders (end on) down drop tubes but none mention dumbbells that I have found.

If no standard device is to hand an improvised device may be used. It could be old and just happen to be lying about at home or elsewhere if not in the lab. Under such circumstances, the name of the item might be inaccurate although this should have been detected and corrected by the peer review. The item might have been of local manufacture and carry an obsolete brand name such as "Federal".

Possibly, everything is made clear in the published paper which I cannot easily access.

I would not want to be struck by a falling 5 kg weight of any description.

The following image shows a fall tube used by Thali et al, workers cited by Whittle et al in the paper mentioned above.

It seems to consist of a vertical rod to which various shapes and devices can be bolted, including half spheres.

See above my post of July 14, 2012.

Definition of a standardized skin penetration surrogate for blunt impacts

Alexandre Papy, Cyril Robbe, Nestor Nsiampa, Amar Oukara and Julien Goffin

IRC-12-58 International Research Council on Biomechanics of Injury Conference 2012

http://ircobi.org/downloads/irc12/pdf_files/58.pdf

This paper's goal is to present a surrogate to assess potential skin penetration of blunt impact nonlethal projectiles as a basis for a future NATO standard. The proposed surrogate is made of natural chamois, closed cell foam and ballistic gelatin. Skin penetration assessment on the surrogate is made on the gelatin. Results from live firings on the surrogate are presented and compared to those from the literature, based on cadavers. A statistical analysis shows that the surrogate results are very comparable to the cadaver ones and reproducible. Some comments are then presented concerning the results and practical considerations concerning the surrogate.



"Natural chamois." In the United States, the term chamois, without any qualification, is restricted to the flesh split of the sheep or lambskin tanned solely with oils (Wikipedia). (The skin is split into two layers during processing - that closest to the flesh is the "flesh split".) Such a material is likely to be rather variable in quality and properties so not ideal as a standard.

For SCP, impact energy densities need to be much less than those capable of skin pentration, that is, much less than about 25 J/cm^2. The total kinetic energy of CP impliments is of the order of 25 J so it is important the impact area is much larger than 1 cm^2 if significant wounds to the skin are to be avoided.

It can't just be the energy density.

Two objects can have the same kinetic energy, where the first is much heavier than the second but is moving rather more slowly. The area of impact could be the same for both objects. In such a case, both objects would offer the same energy density.

But the second, faster-moving, object will do more damage, because there will be less opportunity for the flesh to deform to accommodate the impact.

Alan,

You are quite correct. I think it is assumed that "other factors" are similar when devices are compared. The angle of impact, the location of the impact (fleshy, bony), the surface area impacted, the shape and deformation of the impactor, etc. must all be important. The skin is elastic and resilient compared with internal organs and bones. Serious internal injuries may be caused by impacts that little affect the skin (see below). Skin penetration is not the only concern.

The study is of a preliminary nature and is aimed at establishing simple criteria for assessing less-lethal weapons. This may turn out to be a naive hope.



http://www.ncbi.nlm.nih.gov/pubmed/22920766

Journal of Forensic and Legal Medicine. 2012 Oct;19(7):419-21.

How reliable is external examination in identifying internal injuries - Casper's sign revisited.

Byard RW.

It has been proposed that the absence of injuries to the outside of a body that has been subject to blunt trauma indicates that the forces involved were relatively minor. It has also been suggested that an autopsy will be unlikely to uncover any significant injuries. A series of cases involving lethal blunt trauma from vehicle crashes and falls are described where minimal external injuries were associated with major disruption of internal organs. Skin is both resilient and elastic enabling it to resist injury, while allowing considerable forces to be transmitted to the musculoskeletal system and internal organs beneath. The absence of external injury is not, therefore, synonymous with lesser degrees of force, and should not discourage full medico-legal investigation of cases where occult trauma may be a possibility. As Casper was one of the earliest to describe this phenomenon, perhaps the term 'Casper's sign' should be used when massive internal injuries from blunt trauma are found in the absence of significant injuries to the skin.

Implements such as paddles can cause serious internal injury without marking or damaging the skin, as apparently first noted by "Casper" (see above).


    Johann Ludwig Casper

    A handbook of the practice of forensic medicine based on personal experience

    Published 1861

    http://archive.org/details/handbookofpracti01casp


Not for the squeamish!

Various materials have been used as human flesh ballistic surrogates including oil-filled clay (plasticine) and gelatine (10 or 20% solids) with or without surrogate skin. Neither surrogate is closely analogous to flesh in terms of visco-elastic properties or propensity to form bruises. Above, hcj suggested "Perhaps a layer of saturated sponge between the layers of plasticine?" Some experiments using water-filled foam have been done (see above, October 23 posting.)

Synthetic open-cell foams have a complex structure consisting of an interconnected network of bubbles. The size of the bubbles and the thickness of the walls vary, depending on the type of foam, but are usually of millimetre scale. Typical foams are far more coarse and porous than flesh but have a similar density when filled with water. It remains unclear whether such foams are a good surrogate for ballistic studies.

The images below are not necessarily at the same magnification. They show the difference in structure between open-cell foam and flesh.

High-speed pingpong balls can wound!





The bruise marks can be much bigger than the impactor.

This may be a "Federal" dumbell. It is the correct weight and about the right size if made of iron.

So, nobody has checked the dimensions given above?

Checked the dimensions, KK? Well, I don't think the spheres are 8cm in diameter. They look about 3cm on my screen. Maybe you have a prof.n-style enormous display.

Hi KK


A rough calculation gives the diameter of the sphere on the right (marked 5kg) as minus 8cm.

Arrgh!!! I must be suffering from caffeine deficiency. The sphere on the right has zero diameter.

That's why it's called a dumbbell.

Let's figure it out... Your dumbell is likened to 2 spheres of 8cm diameter (r = 4) and one cylinder of diameter 2.8cm (r=1.4) and length of 10 cm.

Total volume = volume of 2 spheres + 1 cylinder = 2 times  4/3 * Pi * r-cubed + Pi * r-squared * h

= 2 x 4/3 * 3.1416 * 4cm x 4cm x 4cm + 3.1416 * 1.4cm * 1.4cm * 10cm   = 2 x 268.1 cubic cm + 61.6 cubic cm = about 596 cubic cm ... The density of iron is approx 8g / cubic cm

Mass = volume x density = 596 cubic cm * 8 g / cubic cm = approx. 4,770 g, OR approx. 4.8 kg. So yes, these sizes make sense for a 5 kg dumbell! Is that what we we're trying to figure out? ...or did I miss the point (yet again)?

 

Yes HH, you have understood the issue correctly. The pictured dumbdell would have a diameter of about 8 cm if made of cast iron.

There is discussion above of surrogates for human flesh that might be suitable for studies of cane and paddle impacts. On October 23, 2012, I cited a publication that reported the use of water-filled foam as the target and a "Federal dumbbell" as an impactor. The dimensions given were 8 cm diameter and 180 mm long. These do not match any plausible dumbbell.

Ideally, the referees should have questioned the description and the editor should have corrected the mixed units, cm and mm. It is possible the dumbbell is fully described in the paper. I have seen only the abstract, first page and the illustrations.

Two independent referees and the editor usually review publications before they are accepted for publication in a scientific journal. Often, a paper must be changed before it is accepted. Referees may recommend:
1. Acceptance
2. Acceptance, subject to stated ammendments and corrections
3. Resubmission after corrections.
4. Rejection.

The trouble is that KK's measurements aren't correct. I'm ignoring the overall length of 18cm, which is (as Jenny pointed out) inconsistent with the other measurements. Using the screen image, if you take the diameter of each sphere to be 8cm, then the length of the cylinder is about 9cm rather than 10cm, and its diameter is about 3.6cm rather than 2.8cm. Alternatively one of the cylinder measurements could be correct, and then the other cylinder measurement and the sphere diameter would need to be scaled accordingly.

(I've measured the lengths on the screen, by capturing the screen image, pasting it into Illustrator, and using a little electronic ruler.) So I think that KK should be sent away to measure his lump of iron again.

Alan,

The question is what was used as an impactor by Whittle et al 2008? That is, what is a "Federal dumbbell"?

The stated dimensions 8 cm x 180 mm do not seem plausible for a dumbbell, of even part of a dumbbell.

If you assume the spheres are exactly 8 cm in diameter and the dumbbell weighs exactly 5 kg, what is its density according to your measurements?

7.96 gm/cc

(That's too accurate, given (1) the fact that the handle isn't a true cylinder, (2) the fact that the spheres whould need to have been flattened slightly to accommodate the handle, and (3) the inaccuracy of my screen measurements. So say 8gm/cc.)

The density or pure iron is about 7.87 g/cm³. The density of cast iron is usually a little less. Alan estimates a value of near 8 g/cm³ for the dumbbell which may not be exactly 5 kg in weight.


Thus, it is possible the impactor used by Whittle et al is similar to the dumbbell pictured above although its overall length is close to 24 cm rather than 18 cm as reported bt Whittle.

I notice there are code numbers for US Army property that might provide a clue to the origin of "Federal dumbbell".

DUMBBELL,GYMNASTIC
(NSN 7830014685844)
FSG (Federal Supply Group): 78 (Recreational and Athletic Equipment)
FSC (Federal Supply Code): 7830 (Recreational and Gymnastic Equipment)

I have not discovered a detailed description or photograph of this equipment.

A 5 kg dumbbell scaled to Alan Turing's dimensions

Thanks hcj,

National Stock Number 7830-01-468-5844

60 lbs., hex style, solid steel, knurled contoured handle, acrylic finish, charcoal grey, marked with weight in pounds (lbs)

A search for "Federal barbell" rather than "dumbbell" scored a few hits in South Africa. One of the authors came from there. It is possible he brought some gym equipment with him when he emigrated. "Federal" may be a local South African brand.

Anyone able to explain the formation of the outer purple ring?

It isn't clear from the photographs exactly which part of the body was hit by the paintball. Is it an area subject to pressure when sitting or sleeping?

The wound is on the front of the thigh, high up, a moderately fleshy place. I doubt whether sitting or lying on the wound is a factor in its evolution.

The symmetry and slow appearance of the purple outer ring suggests sub-surface wounding at the time of impact, some distance from the impact. It has taken time for the leaked blood to diffuse to the surface and become visible.

The inner red ring is easily explained. Its size corresponds to that of the pellet, and the region of high shear and of high hydrostatic pressure gradient.

Somehow, the region between the purple outer and red inner ring seems to have escaped injury. The skin is tougher than the underlying adipose tissue. The underlying muscle will be more elastic than the adipose tissue. The outer ring injury probably occurred in the adipose layer. But how and why? Did the surface wave of displaced flesh "break"? In the deep ocean, water particles move only small distances in an elliptical path when swells pass. However, they undergo violent motion when the swell meets the shore.

There is a lot of forensic interest in determining the origin and age of bruises. Ethical and practical considerations make it very difficult to do experiments. Various attempts are therefore being made to use mathematical models to describe the formation and evolution of bruises. The initial models are relatively crude but they help to identify the factors likely to be important and thus may allow more realistic models to be constructed.

The following figure has been borrowed from a recent publication. It shows how bruises are expected to evolve over time starting with different shaped initial wounds.

Do not do this at home !

Brainiac Science Abuse - PaintBall Shot In Slow Motion



Fragments of the burst paint pellet (green) bounce off as a circular ripple of displaced flesh moves rapidily outwards. The pellet contains red paint. The impact pit it makes seems to persist for quite a few frames.

Various other impacts have been captured in slow motion but many of the vides seem to be on sites that forum members probably won't wish to visit.

I drew attention to this paper earlier. It seems the reported rings were slow to form.


Excerpts from the cited paper:

A bruise in the shape of a circle with an uncoloured centre is commonly interpreted as the result of a blow with a circular edge such as the end of a metal pipe, or by a spherical object, such as a cricket ball, which may cause a ring bruise in the same was as a cylindrical object may cause a 'tram-line' appearance.

The purpose of this report is to describe three injuries (Figs. 1-3) with very similar features. They developed from simple bruises, which commenced as homogeneous disc shaped contusions, but later could easily have been thought to be the result of more sinister trauma.

[...]

By their nature, the central pale area is only seen in bruises of at least a week old, but, unfortunately, it is well known that it is difficult to age bruises from their appearance [ref. 1, 2]. One point of differentiation is that in ring-resolution, the central area of pallor is usually near circular in outline.

[...]

The time intervals between frames are not equal.

Hi KK, This recent YouTube posting by AW here inadvertently lead to another video that might be salient here.

It shows various bruises allegedly from SCP in (South?) Korea. When I look at discueetionsin th eTWP part II thread and others on these topics, it seems that such bruises would in many cases exceed the limit in the USA for PCP, but would be "Shielded" in SCP. At any rate, there are quite a few examples inferring that this is status quo and acceptable in the country where it originates. (and may help you in some way with your impact & bruise pattern science. KK, your job is to match the pattern to the implement and then extrapolate the effects of a paddle from there

http://www.youtube.com/watch?v=OA1ptzIDxVU

 

Oops ... forgot to add a WARNING. That above clip is photo images of bruised buttocks resulting from the application of CP. This may not be appropriate for sensitive viewers ... viewer discretion is advised.  

The cane is known for its propensity to form tramlines when applied with enthusiasm. There is some uncertainty as to the process involved. Some believe in shear and tear and others in a hydraulic mechanism. I have conducted an experiment to gain insight and present the results below.



The separation of the tramlines on unstretched skin is much less than the diameter of the cane.

P.S. I am looking for a target subject an assistant to help with my experiments

ROLFLMAO! Keep up the good work KK. Be sure to keep us up to date on your experiments. Maybe Dr D will volunteer.

KK: The separation of the tramlines on unstretched skin is much less than the diameter of the cane.

That's exactly what I'd expect. The greatest strain will occur close to the centre line of the cane, as it stretches the skin.

It would be interesting to see the effect of a cane with a square cross-section.

The following is part of a single frame from a high speed video of a cane impact. The video is not suitable for hyperlinking to this forum. Frame speed is not stated but is probably 240 per sec. It is clear things happen very quickly. There are no images of the resulting wound.

The cane has penetrated deep into the left cheek just above the top of the half-lowered pants. It is in shadow so appears nearly black. A bead or rib of displaced flesh protrudes immediately above the cane. The initial displacement is very local. The rib rapidly moves upwards in subsequent frames leaving an expanding crater.

A professional quality, high speed camera would be required to get a better view of the action.




Alan Turing, unfortunately, I have been unable to find a volunteer willing to experiment with a square cane.

Caution - Science beneath !

High speed ("slow motion") video cameras show that when a paintball, paddle or cane impacts on a target a wave of displaced flesh spreads rapidly outwards leaving a crater behind. This happens in a few milliseconds.

The mechanical distortion causes pain but the nature of the distortion is unclear. Shear and/or hydrodynamic effects may be involved, as previously discussed.

The target approximates to a tough elastic outer layer of skin, a middle layer of visco-elastic fatty tissue underlain by strong elastic muscle. The elasticity of skin, and especially of muscle, is different in different directions. Such a layered structure allows the propagation of Lamb waves.

Lamb waves are complex, especially in multiple layers, but are of great scientific and practical importance. Possibly, shear-forces are greatest at the muscle surface some distance for the impact zone. If so, this would explain the annular wounds mentioned above.

Sorbothane(TM) is a flexible visco-elastic polymer with both viscous-liquid-like and elastic properties. If deformed, it returns to its original shape relatively slowly after the deforming force is removed.

Sorbithane has energy absorbing properties similar to those of human flesh and much greater than those of normal elastic materials.

Sorbithane is used to dampen vibrations and noise from machinery and as an inner sole in footwear to cushion foot strike impact.

A presently under utilized application is as gluteal augmentation in "sports" briefs, as suggested by EAL here.

Patent: Energy absorbing polyurethane composite article. US 4808469

Manufacturer's site: http://www.sorbothane.co.uk/

http://journals.lww.com/corr/Abstract/1987/09000/A_Biomechanical_Evaluation_of_Sorbothane.38.aspx

Clinical Orthopaedics & Related Research. Vol 222, p 281-288, September 1987.

A Biomechanical Evaluation of Sorbothane

Cinats et al.


Sorbothane (I.E.M. Orthopaedics, Aurora, Ohio), a viscoelastic polymer, has been developed for orthopedic application, but there has been little substantiation of the claim that it is capable of absorbing 95% of the impact energy in foot strike. Sorbothane has been used extensively in orthotic insoles in order to minimize the symptoms of joint degeneration, prosthesis loosening, and various soft tissue disorders resulting from the impact generated at foot strike during walking and running.

The viscoelastic properties of Sorbothane were investigated by Durometer tests at various temperatures as well as compression tests of thin discs of material with different degrees of lateral constraints and varying rates of loading.

Sorbothane has the characteristics of a viscoelastic solid with a relaxation time of two seconds. The effects of lateral constraint were significant, indicating that the properties of this material will change when bonded to other substances in the production of insoles. The final transmitted stress over the duration of foot strike would not be reduced by more than 10%, which may have some therapeutic implication, but not of the magnitude suggested by other authors.
__________________________________

These authors, and possibly the manufacturers of Sorbothane, appear to be ignorant of Newton's 2nd law of motion, F = mass x acceleration, and the importance of the thickness of the energy absorbing pad. Even if the innersole were to absorb all the kinetic energy of impact (or store it elastically), a large force will still be exerted on the foot because it is slowed in a very short distance, the thickness of the pad. The ideal pad will only just compress to its limit during each foot strike. If too firm or too soft it will provided less cushioning.

Other papers can be found here: http://www.ncbi.nlm.nih.gov/pubmed?term=sorbothane

Pads are tapered towards the edges so do not show under ordinary clothing.



Please direct all inquiries to Another_Lurker.

KK,

Out of curiosity were you ever caned at school? You bring a certain scientific element to the subject, where in reality a teacher and his victim wouldn't contemplate at the time.

de Wolf: KK,

Out of curiosity were you ever caned at school? You bring a certain scientific element to the subject, where in reality a teacher and his victim wouldn't contemplate at the time.


Yes, I was both strapped and caned but only a very few times. Not fun! I was a good student and generally managed to stay out of trouble. If the teacher said "I will cane the next boy who talks" I took them at their word.

I am sure there was little or no thought of the science at the time. I have a strong interest in science as you have noticed.

You were very fortunate your teacher warned you KK, mine didn't. My teacher's assumed you knew the rules, ignorance was no excuse.