You may be wondering why the ball does not bounce back to its original height. Does this invalidate the Law of Conservation of Energy? Where did that energy go? The energy that is not being used to cause motion is changed to heat energy, sound energy, air friction, to internal forces within the ball and to friction between the ball and the ground on impact. After playing a game of tennis or racquetball, you will notice that the ball is warmer at the end of the game than at the beginning because some of the motion energy has been changed to heat energy. Because bouncy balls have tightly linked polymers, most of the energy is transferred back to motion so little is lost to heat or sound energy, and the ball bounces well.
Resilience
Ball bounce is important in many sports. The ideal height of bounce varies for different sports with the consistency of bounce from one part of the field to the other being of most interest. "Ball bounce resilience" (BBR) is used as a measure of bounce and is the ratio of the height the ball bounces to the height from which it is dropped.
Incidentally, "ball bounce resilience" is equal to the "coefficient of restitution" squared, and then expressed as a percentage. For example, if a ball is dropped from 3 meters, hits the ground, and bounces up 1 meter, the BBR is 33.3%.
The resilience of rubber balls is one of their most important characteristics. This is because the
resilience of the ball material determines the “liveliness” and “bounce” of the ball. Resilience (R) is the ratio of the work recovered to the work required to deform the rubber.
The resilience of a compound is normally measured using a standard rebound test. The rebound test carried out on squash balls at present involves balls being bounced on a hard surface. The same balls are conditioned first to 23oC and then to 45oC and dropped from a height of 100 inches onto a concrete floor (which in both cases must be at 21–25oC). At 23oC the balls should rebound at least 12 inches and at 45oC between 26 and 33 inches to comply with regulation standards.
The Tg of rubber is related to its resilience at room temperature. Rubbers with a low glass transition temperature have a high resilience and rubbers with a high Tg have a low resilience.
How Ball Is Made
To begin with, raw rubber from Malaysia is delivered to the Barnsley factory in ‘bales’ of about 25kg – sufficient to make about 1,200 balls. In its natural state rubber is very stiff and difficult to work, so it is first ‘masticated’ to a softer consistency. A variety of natural and synthetic materials and powders are then mixed with the rubber to give it the required combination of strength, resilience, and colour as well as to enable it to cure (or ‘vulcanise’) later in the process. The manufacturer’s ‘recipe’ is, of course, a no less closely guarded secret than that of Coca Cola, and different combinations of ingredients (as many as 15 are used, including polymers, fillers, vulcanising agents, processing aids, and reinforcing materials) produce fast (blue dot), medium (red dot), slow (white dot), and super slow (yellow dot) balls.
The resulting compounds are warmed and loaded into an extruder, which forces them (rather like a mincing machine) through a ‘die’. A rotating knife cuts the extruded compound into pellets, which are then cooled. The pellets, which now have a putty-like consistency, are dropped into a hydraulic press which subjects them to a pressure of 1,100lb per in2 and a temperature of 140–160 C for 12 minutes. The heat causes the material to cure and so retain its shape. Each pellet makes half a ball, known as a ‘half shell’. 50% of these are ‘plains’ and 50% ‘dots’. The mould for the dots has a pin in the bottom to create the tiny dimple which takes the different coloured paints that indicate the balls’ speed. When the half shells are removed from the press, the excess compound (called ‘flash’) must be cut away before the dots can be glued to the plains to make complete balls.
First the edges of the half shells are roughened (‘buffed’) by a grinding wheel to provide a key for the adhesive. The buffed edges are then coated with rubber solution and a measured amount of adhesive is applied in three coats at thirty minute intervals. Both the adhesive and the dot paint are produced in a similar way to the rest of the ball; the adhesive, for example, is also made from raw rubber mixed with various powders before being ground, broken down into a fine web and ‘wet mixed’ for several hours with a solvent. At last the half shells can be stuck together – an operation called ‘flapping’.
The flapped balls are then put through a second moulding, heating and vulcanising process, this time subjecting them to 1000lb per in2 for 15 minutes, to cure the adhesive. Further buffing, this time of the balls’ exterior, smoothes the join and gives the balls their characteristic matt surface. After being washed and dried each ball is inspected. This is one of the few operations which is still carried out by hand, by a team of four ladies, the only other manual operations being the loading and unloading of the presses, the final buffing and washing, and, most importantly, testing.
The balls are tested at every stage in the process and those that are unsatisfactory rejected. Those that pass are stamped with the Dunlop logo, boxed in dozens, and shipped all over the world, but a sample of them is given a final test to ensure that they conform to WSF standards.
Testing Of The Ball
The current WSF Specification for the Standard Yellow Dot Championship Squash Ball as it appears in Appendix 7 of the Rules of Squash dates from October 1990, apart from a minor amendment made in July 1995, and determines the permitted diameter, weight, stiffness, seam strength and rebound resilience of the championship ball. No specifications are set for other types of ball, "which may be used by players of greater of lesser ability or in court conditions which are hotter or colder than those used to determine the yellow dot specification". But how are balls tested to ensure that they meet these specifications?
The testing procedure itself states somewhat confusingly that: "For the purposes of inspection, balls manufactured from the same mix shall be arranged in batches of 3000 numbers or part thereof manufactured in one shift in a day." Fifteen balls are then chosen at random from each batch and divided into three groups of five balls. One group is tested for diameter, weight, and stiffness; another group for seam strength; the third group for rebound resilience.
First the 15 selected balls must be left in the laboratory for 24 hours to ‘condition’ them to a temperature of 23oC. Their diameter, measured perpendicular to the seam, must be between 39.5mm and 40.5mm, and their weight between 23 and 25g. To be measured for stiffness the balls are held between two plates with the seam parallel to the plates and compressed at a rate of 45–55mm per minute. They are compressed by 20mm six times, the test measurement being made on the sixth deformation only. The stiffness of a ball is calculated by measuring the compressive force at the point where it has been deformed by 16mm and dividing that by 16 to give a ‘force per millimetre’. The result must be between 2.8 and 3.6N/mm at 23oC. In other words, the force required to compress the ball by 16mm (i.e. to just over half its original diameter) must be between 44.8 and 57.6 Newtons.
The calculation of seam strength is even more complicated. "The squash ball is first cut into two equal halves perpendicular to the plane of the seam." Then two strips (one from each half of the ball) approximately 15mm wide and 60mm (roughly half the circumference) long are cut, with the seam running across the middle. The average width of each strip is measured before it is pulled apart at a rate of 180–220mm per minute until the seam breaks. The force at the point of breakage is divided by the average width of the strip to give a ‘force per millimetre’, which must be at least 6N/mm. So if the average width of the test strip is exactly 15mm, the minimum force required to break the seam must be 90 Newtons.
Rebound resilience is simply a measurement of the height a ball bounces off a hard surface. The same balls are conditioned first to 23oC and then to 45oC and dropped from a height of 100 inches onto a concrete floor (which in both cases must be at 21–25oC). At 23oC the balls must rebound at least 12 inches; at 45oC between 26 and 33 inches. (The 1995 amendment was to these figures: previously the rebound specification at 23oC was 16–17 inches and at 45oC 26–28 inches.)
Although a compression test is no longer required by the WSF – it was deleted from the ball specification in September 1988 – Dunlop continue to carry out a test in which loads of 0.5kg and 2.4kg are applied to the ball and the resulting deformation measured. The difference in deformation under the two loads used to be specified as between 3 and 7mm, but Dunlop aim at between 4.5 and 5.5mm, just to be on the safe side.
Ball Behaviour
Why does a squash ball bounce higher when it’s warm?
In order for a solid material to be deformed, work has to be done on it. For that work to be done, energy must be expended (in the case of a squash ball, it is hit by a racket). Some of this energy is dissipated (as heat, etc.), but some is stored in the deformed material and is released when the material relaxes. The extent to which a material stores energy under deformation is called ‘resilience’. Some materials (like sprung steel) store a lot of energy and are described as having high resilience; others (like putty) store very little and therefore have low resilience.
Squash balls, being made of a rubber compound, are of fairly low resilience. Unfortunately, the lower the resilience of an object, the higher the proportion of the energy used in deforming it must be dissipated. When a squash ball hits the racket strings and the wall and floor of the court, some of this energy is transformed into heat in the strings, wall, floor, and surrounding air and some into sound, but most of it becomes heat in the ball itself. This has two effects: the air inside the ball (which was originally at normal atmospheric pressure) effectively becomes ‘pressurised’, and the rubber compound from which the ball is made becomes more resilient. For both these reasons, the ball bounces higher. Obviously, the ball does not continue indefinitely to heat up; eventually equilibrium is reached where heat loss to strings, wall, floor, and air is equal to heat gained from deformation. This point is normally at around 45oC, which is why the WSF’s rebound resilience specification is calculated at that temperature. It also explains why squash balls are designed to have too little resilience at room temperature and therefore why they need warming before play.
But why have balls of different speeds and how are they made?
The actual ball temperature reached in play varies according to two main factors: the temperature of the court and the ability of the players. The point at which the ball temperature reaches equilibrium is in fact an excess over the ambient temperature of the court. So if the court is at only 5oC, the ball may only reach 35oC.
On the other hand, even on a warm court, if the players don’t hit the ball hard or often enough to raise its temperature to that optimum 45oC, the ball won’t perform as it should. To compensate for either factor, players will need to use a ball of higher basic resilience, i.e. a ‘faster’ ball. These are produced simply by making a different mixture of polymers. More elastic polymers create higher resilience; more viscous polymers lower resilience.
So how can you have a ball with ‘instant bounce’?
For a ball not to need warming, it must either lose as much heat as it gains during play and therefore remain at court temperature, or it must be made of a material whose resilience is the same at any temperature. It remains to be seen whether Dunlop’s new Max Progress and Max balls meet either of these criteria.
Sources For Background Knowledge
- Physics 1 (Cambridge Sciences)
- Physics In Perspective
-
Google search on internet for Physics – squash ball resilience
Variables
Temperature
Temperature is a big variable in affecting the bounce of a squash ball. Temperature affects the pressure within the squash ball, which affects how much it bounces; the kinetic theory is thus used. As temperature increases the gas molecules gain more energy due to the heat energy and it is converted to kinetic energy. The molecules, with more kinetic energy, have more frequent collisions with other molecules and the walls of the squash ball, thus pressure is increased. The increase in pressure means that the squash ball will bounce more.
Temperature is a good variable to use in the investigation, I can use the information that I obtain to explain why players have to hit the ball around for a bit to get it warmed up so it bounces better! If I decide not to use temperature as a variable though it is vital I keep the temperature constant.
Surface The Ball Is Dropped On To
This isn’t a good variable to investigate, basically different surfaces will affect the bounce, like a spongy surface will absorb the bounce of the ball and you won’t be able to tell the difference with each of the different balls. A hard surface will have a different affect on how the ball bounces, it will bounce more so this is a good surface and I will probably keep this variable constant on a hard surface.
Height Ball Is Dropped From
This variable is a good variable to investigate e.g. dropping it at 50cm then trying 100cm and seeing how this affects the bounce of the ball. At higher heights the bounce will bounce further than at lower heights as the ball will have gained more velocity due to acceleration due to gravity. If I decide not to use this variable though it will need to be kept constant.
Rebound Height
This variable will be my dependant variable and will be used to find out how the variable I will be using affect the bounce height of the squash ball.
Decisions On Variables
The independent variable I will be using is temperature, I feel this will give me good results to compare and I can do a good range of temperature, which will give me varying results for a good conclusion. The dependant variable I will be using is height, which will show the bounce of the ball. Variables I need to keep constant are, the height the ball is dropped from so I will just drop the ball from the same height each time and also the surface the ball is dropped onto so I’ll use the same surface each time, which will be a hard surface.
Prediction
I predict that as the temperature is increased the height the ball bounces will increase. The reason for this is due to the temperature having an effect on the pressure of the ball, which thus makes the ball bounce higher. As the temperature increases there is heat energy is available the gas molecules inside the ball absorb this energy and convert to kinetic energy. This is the only way the energy can be converted because gas molecules can’t have potential energy, as there are no intermolecular forces of attraction so it is converted to kinetic energy. This kinetic energy means that the molecules move around faster thus more frequent collision are made between the walls of the ball and other molecules which creates more pressure thus the ball bounces higher.
The equation that links pressure, volume and temperature is: -
p1V1 = p2V2
T1 T2
This means that if the volume stays constant and temperature is increased then the pressure must increase. The increase in pressure means that the squash ball will bounce higher. Another equation can be brought in here as pressure increase means a greater force is created as the area of the ball remains the same; -
P = F
A
However the 4 different balls will obey this law but will differ in bounce height at the different temperatures and also will show different gradients in the area of proportionality in the graph. This is because the balls have different resilience and this is achieved by simply by making a different mixture of polymers. More elastic polymers create higher resilience; more viscous polymers lower resilience.
When the ball collides with the floor, the ball becomes deformed. The ball is elastic in nature, the ball will quickly return to its original form and spring up from the floor. This is Newton's Third Law of Motion- for every action there is an equal and opposite reaction. The ball pushes on the floor and the floor pushes back on the ball, causing it to rebound. Neglecting friction for the ball, the potential energy before you drop the ball will be equal to the kinetic energy just before it hits the ground.
On a molecular level, the rubber is made from long chains of polymers. These polymers are tangled together and stretch upon impact. However, they only stretch for an instant before atomic interaction forces them back into their original, tangled shape and the ball shoots upward.
My prediction for the shape of the graph is an s-shape, shown on next page, this is because at the lower temperatures there is a slope off from the graph because at this temperature the balls have little resilience and thus don’t bounce very high, but the balls have a minimum bounce which means if you keep reducing the temperature the affect temperature has, has little effect on the rebound height. This principle is also applied at the higher temperatures where the graph slopes off because at this high resilience the ball bounce considerably higher than at the lower temperatures but if the temperature keeps increasing it will have less and less of an effect because the ball has a maximum bounce height.
Rebound
Height
(cm)
Temperature (oC)
Now my prediction for which of the balls will have the higher gradients are those with the higher resilience which is the balls used by the beginners who first start playing squash as the ball bounces more it is easier to play and this is the blue ball. After this the red ball followed by the yellow ball and finally the white ball.
Proposed Method
Firstly I will consider my heating method, to get down to the lower temperature of 10oC I will use a beaker and ice and the squash ball (diagram below).
For 20oC I will just use water to take the temperature down a little from room temperature, which is slightly higher. For the rest of the temperatures I will use a general heating method with a Bunsen burner, heatproof mat, tripod, gauze, a thermometer to record the temperature and a beaker with water and the squash ball to act as a water bath (diagram shown on the next page). To get the ball to desired temperature I will leave the ball in the water, the thermometer showing the desired temperature, for 5 minutes so that I can be sure that the temperature is the same all the way throughout the ball so it will have an affect on the pressure. After I have done this I’m ready to investigate the bounce of the squash ball, see next page for more.
I will use a metre stick that is held in an upright position and drop the ball, using my hand, from a certain height then record how high the ball bounces. I will take into account my eye being level in a parallax for fair and accurate results (idea of eye being level is shown below).
(Below shows a diagram of the apparatus)
Preliminary Testing
The first thing that I noticed was that by dropping it by hand it was very hard to get from the height that I was dropping it then get down to see how high the ball bounced. This meant I needed a method where I could stay low down to see the bounce of the squash ball but release the squash ball when I wanted it to. So I came up with the using some tongs with a piece of string, the forceps to hold the ball then the string to release the tongs so the ball drops. Also doing this method means that it will just be the ball being dropped and no other forces other then gravity acting on it as before I may have put some spin on the ball making it bounce in a direction which would affect results.
After doing this I found that I needed to take a rough bounce first to see whereabouts the ball bounced then I could get my eye level in this region so I will get a more accurate result for the rest of that test. When heating the ball also I found that the ball floated and therefore was not under the whole of the water thus not getting up to the desired temperature so I used forceps to sink the ball into the water.
Drop Height
One of the aspects I needed to investigate in my pre-testing was the height that I dropped the ball from, as this will need to be kept constant to keep the investigation fair. Below is a table of results to show how high the ball bounced when dropped from different heights the temperature was 26oC.
As you can see at 100cm the ball bounced the highest this is because the ball gained more velocity due to gravity as it was dropped from a higher height. I decided to choose the 100cm because this will mean that there will be a bigger difference between heights at different temperature meaning that it will be easier to compare the different balls.
How Many Temperatures
I feel to get enough points on a graph I need to do 8 different temperatures, as a safety point I can’t go above 80oC as the rubber squash ball will start to melt. So I will do from 10oC – 80oC in 10oC intervals. Below is a table of results to show the blue ball being dropped from 100cm and different temperatures.
As you can see from the results as temperature is increased the bounce increases, and also a linear pattern can be seen suggesting it’s a proportional relationship. One of my fears was that the temperature of the ball would drop rapidly so I would get a decrease in the bounce height as I did each test but from these results I will be fine as they are all consistent.
Precautions
Safety
As I’m dealing with hot water and heating apparatus I will wear safety glasses so I don’t scald or burn my eyes plus take care when handling hot water. Also I will make sure there are no obstructions such as chairs in my way.
Fairness
To keep the experiment fair I will only change the variable they I’m supposed be changing which is temperature. This means that the height that I drop the ball onto need to be consistent also that I keep my eye level when doing this and also when taking results. Also when taking results I must be consistent where I take the result from I will take it from the bottom of the ball because this is the actual distance the ball has bounced plus its easier to see this than taking the result from the top of the ball.
Accuracy
To make the experiment accurate I will be using a thermometer to record the temperature of the water and get it accurately to the correct temperature. Also I will be recording to decimal places when I’ve averaged them. Measuring the height is difficult however and to get to a suitable degree of accuracy is hard that’s why I’m dropping the ball from the biggest height possible because this means if the results are out then the other points being further apart can pull the line of best fit better.
Reliability
To make the experiment reliable I will be taking 5 tests on each temperature so I can be sure I have found the correct bounce height and also I’m taking a rough bounce to start with so I can get my eye level for the other results.
Method
Diagram
Step By Step Procedure
- Set up apparatus as shown in the diagram above
-
Get temperature of ball to 10oC
- Bounce ball and record height once for rough result he 5 more times.
- Repeat steps 2 and 3 for the different temperatures
- Repeat 2-4 for the other 3 balls
Analysis
As you can see all 3 graphs have the general s-shape that I predicted in the plan, there is a slope at the start at the lower temperatures then a slope off at the higher temperatures, this is because at the lower temperatures there is a slope off from the graph because at this temperature the balls have little resilience and thus don’t bounce very high, but the balls have a minimum bounce which means if you keep reducing the temperature the affect temperature has, has little effect on the rebound height. This principle is also applied at the higher temperatures where the graph slopes off because at this high resilience the ball bounce considerably higher than at the lower temperatures but if the temperature keeps increasing it will have less and less of an effect because the ball has a maximum bounce height.
As the temperature is increases the height of the ball’s rebound increases. The reason for this is due to the temperature having an effect on the pressure of the ball inside, which thus makes the ball bounce higher. As the temperature increases there is heat energy is available the gas molecules inside the ball absorb this energy and convert to kinetic energy. This is the only way the energy can be converted because gas molecules can’t have potential energy, as there are no intermolecular forces of attraction so it is converted to kinetic energy. This kinetic energy means that the molecules move around faster thus more frequent collision are made between the walls of the ball and other molecules which creates more pressure thus the ball bounces higher.
The equation that links pressure, volume and temperature is: -
p1V1 = p2V2
T1 T2
This means that if the volume stays constant and temperature is increased then the pressure must increase. The increase in pressure means that the squash ball will bounce higher. Another equation can be brought in here as pressure increase means a greater force is created as the area of the ball remains the same; -
P = F
A
However the 3 different balls will obey this law but will differ in bounce height at the different temperatures and also will show different gradients in the area of proportionality in the graph as shown on the graphs. This is because the balls have different resilience and this is achieved by simply by making a different mixture of polymers. More elastic polymers create higher resilience; more viscous polymers lower resilience. So the blue ball for instant will have a higher resilience due to having more elastic polymers and the white ball has more viscous polymers so doesn’t bounce as high.
When the ball collides with the floor, the ball becomes deformed. The ball is elastic in nature, the ball will quickly return to its original form and spring up from the floor. This is Newton's Third Law of Motion- for every action there is an equal and opposite reaction. The ball pushes on the floor and the floor pushes back on the ball, causing it to rebound. Neglecting friction for the ball, the potential energy before you drop the ball will be equal to the kinetic energy just before it hits the ground.
On a molecular level, the rubber is made from long chains of polymers. These polymers are tangled together and stretch upon impact. However, they only stretch for an instant before atomic interaction forces them back into their original, tangled shape and the ball shoots upward.
As you can see on my graphs they are all s-shapes, which means the graphs confer with my original prediction and also I stated that the blue ball would have a higher gradient due to having higher resilience. (The gradients for each line are shown on the graph).
So now having investigated the squash balls I can now relate the balls tp the game itself. Beginners will more than likely being using the blue ball, this is because it has the higher resilience thus more lively and bouncy so it will rebound of walls further making the game easier to play. The reason it bounces away further is due to the more elastic polymers it is made out of. The decrease in resilience of the ball to the red ball just means a progression in performance approaching an amateur stage where players have been playing for a while and can play the game competently and the polymers this time will be a little more viscous meaning the ball wont bounce as far. The next ball would be the yellow ball and as I didn’t have time to investigate this I will give the assumption that the ball would have less resilience again and more viscous polymers. Professional playing will use the white ball as this has the least resilience and made out of the most viscous polymers out of the 4 balls and this will have an even smaller bounce. This makes it difficult for players as they are constantly moving to get the ball and hit it with the racket.
Evaluation
As a whole I am pleased with my results all points were close to the line of best fit that I drew there were a couple of anomalous results but not major and these w ere probably due to a slight distraction whilst obtaining my results. The error bars show that my line of best fit would have fitted within the error proximity meaning my error was out because I couldn’t measure the rebound to a high degree of accuracy as it was hard to see where the ball bounced to as it was so fast, my line of best fit goes through the +/- 0.5cm proximity meaning the results I obtained were accurate and good which is pleasing. I think the investigation went well as a whole but I wish I had had more time to the fourth ball, which would be better to compare with the other balls this would be an improvement for the future to allocate more time to complete the collection of data. There were limitations on the temperature also I couldn’t go very high or very low with temperatures and had to stay within a close proximity meaning I only saw part of the graph which if I could of expanded temperatures may have seen a different shape i.e. the line curving off more so I could prove my theory easier.
Now the errors that could have occurred are the measuring of the rebound height, I could only measure to 0.5 of a centimetre so the error was +/- 0.5 cm, and the other error could have been the measuring of the thermometer which could be read to 0.25 of a degree so the error was +/- 0.25 oC. From this I can now calculate percentage errors. Firstly for the rebound height my smallest rebound height was 8.1cm so:
0.5 x 100 = 6.25%
8.0
Now for the thermometer the lowest temperature was 10oC so:
0.25 x 100 = 2.5%
10
So the greatest source of error was measuring the rebound height and it is over double the error than measuring the temperature. A new method of trying to stop this error is to video record the experiment up close so it can be stopped when the ball is at its highest point and the correct measurement can be seen and will increase the reliability of the data obtained.
I was pleased with my preliminary testing as I found some good new aspects to add to my method there for instance using tongs at the top of the metre stick to hold the ball in position, I got another metre stick to measure that the bottom of the ball held at exactly 1 metre, then using string to open the tongs which means I can have my eye at a parallax to minimize one source of error because if my eye wasn’t level then the eye could be too low or too high:
Also I was pleased with my idea of using holders, which attach to the squash ball to hold it under water to stop it from floating meaning the temperature would not be being applied to the whole of the squash ball. Also I kept the ball in the water for sufficient time for the water to heat the ball up to the desired temperature.
Sources of error could be due to the ball not being able to maintain the correct temperature and an electric water bath would have been a better method but this was also is a limitation, as we don’t have many at our sixth form. Really every piece of equipment including the tongs surface the ball bounced onto would all need to be at the same temperature for the experiment to work really accurately and fairly as the ball gradually cooled down during the course of a test.
I feel I did enough temperatures to give me enough points for my graph but I would like to have tried more temperatures either side of the ones I did but there are limitations again here as for a safety reason I cant go above 80oC as the rubber ball would start to melt and also getting below 10oC is very difficult.
Improvements have already been stated but further testing I would like to do is firstly the fourth ball, which I have already mentioned. I would like to test the polymer materials of each ball individually other than bouncing them i.e. stretching the materials.
Adam Grice Physics Coursework Page
