Elasticity of balls
On impact with a racket or the wall, a ball flattens or compresses, regaining its original shape as it pushes against the surface and rebounds. The property of a ball that causes it to regain its original shape is called its elasticity.
Energy changes on impact
A moving ball has kinetic energy (energy of motion). On impact, some of the kinetic energy is stored in the ball as elastic potential energy. As the ball returns to its original shape and starts to rebound, the elastic potential energy is converted back into kinetic energy. Some of the original kinetic energy is lost on impact, being converted into heat and sound.
The greater a ball's elasticity, the faster it will return to its original shape and the farther it will rebound when it is hit.
The Theory Behind Temperature Rise
The original temperature of the squash ball will also be affected by room temperature and the humidity of the surrounding area.
Squash balls, being made of a rubber compound, are of fairly low resilience. 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 and will bounce higher.
In terms of the experiment that I intend to carry out, energy is given to the ball through hitting it with a squash racquet. The ball will come into contact with 3 different surfaces; the wall, the floor as well as the racquet string. The floor and the wall are very similar but not identical in their properties.
The squash ball will deform when it comes into contact with any of these objects, the rate of the deformation of the squash ball will depend on it’s elasticity.
During each of these reactions a percentage of it’s energy will be stored as thermal energy. If the ball hits a wall or floor, then they will offer resistance, and some of the energy will be lost from the ball (to the deformation in the surface), some of the ball’s original energy is lost in the conversion to thermal energy, the remainder of the ball’s energy is converted back into gravitational potential energy or kinetic energy, explaining why the ball does not return to it’s original height after a bounce of a wall or floor.
When the ball hits the racquet it goes through energy changes, with some of the energy being stored briefly in the strings of the racquet .The player will give to the ball an increase in total energy as he strikes the ball with the racquet. As the ball travels through the air, the Law of Conservation of Energy is in effect and states that energy is neither gained nor lost, only transferred from one form to another. The total energy of the system remains the same; the potential energy changes to kinetic energy, but no energy is lost.
When the ball is hit or hits a hard surface it behaves like a spherical spring. On contact it exerts a force on the wall and the wall exerts a force on the ball.
This is Newton's Third Law of Motion - for every action there is an equal and opposite reaction. The ball pushes on the wall and the wall pushes back on the ball, causing it to rebound. This force compresses the ball.
As long as the compression is small Hooke's Law is satisfied, the force is proportional to the displacement of the ball from its equilibrium shape.
When the ball bounces on the court floor the force that the ground exerts on the ball does work on the ball, since it is in the same direction as the displacement. The gravitational potential energy the ball has before it bounces is converted into kinetic energy while the ball is falling and then into elastic potential energy as the force from the ground does work on the ball. But because the material the ball is made of is not perfectly elastic, internal friction converts some of the energy into thermal energy.
The elastic potential energy stored in the ball when it has lost all its kinetic energy is converted back into kinetic and gravitational potential energy. The thermal energy, however, is not converted back. Because some of its initial gravitational potential energy has been converted into thermal energy it does not regain its initial height.
The result is that, when the ball starts back upwards, it has less energy than when it began its fall. There is no way to stop this from happening; in any energy transfer, there is always an energy loss due to friction or heat.
This is the Second Law of Thermodynamics, and can be loosely defined as 'energy always escapes'
Planning
Apparatus
Different grade squash balls
Squash racket
Ice Tub
Thermocouple
Thermo-hygrometer
Safety
There are few safety aspects to my investigation; the equipment used is routine and the main safety aspect that I had to be aware of was slipping or falling on the squash court. To prevent this I wore appropriate footwear that had a lot of grip (squash shoes).
Measuring ball temperature
There are two main types of technology for measuring temperature - thermocouples and thermometers.
Thermocouple systems are very versatile and can cover temperatures ranging from -250ºC to beyond 2000ºC but thermometers can provide greater accuracy.
This table shows some of the advantages and disadvantages of each method:
Because my experiment required measuring surface temperature I decided to use a thermocouple. It would have been difficult and innefficient to use thermometers and as a result there would have been too much heat loss before a result could be obtained.
Whilst a squash court is a fairly stable environment in which to carry out my experiment, my research had showed me the World Squash Federation have very strict guidelines governing the construction and material use in squash courts.
This is because the relative humidity and ambient temperature is known to have a marked effect on the performance of the ball as well as on the fitness of the players.
The WSF recommend humidity of 45 % (+ or – 5%) and an ambient temperature of 22o C (+ or - 2o). I decided to use a scientific thermo-hygrometer that recorded both air temperature and humidity to ensure that neither of these factors significantly influenced my results.
Pilot Test
To carry out a pilot test I went onto a squash court with only a squash racquet and ball. Through hitting the ball many times and holding onto the ball I could tell that the more times I hit the ball the warmer it felt.
I also noticed how the bounce and speed of the ball appeared to be increasing as the temperature of the ball appeared to increase.
Conducting the pilot
Method
I intend to hit the y coloured squash ball x number of times, and then connecting it to the thermocouple (which will be in very close proximity) I will be able to get a reading of the surface temperature of the squash ball.
One connection of the thermocouple is attached to the ball while the other is dipped in an ice bath. The thermocouple measures the difference in the temperatures between the surface of the squash ball and the ice bath. The ice bath is used as a constant because air temperature is not easily controllable and is an unavoidable variable.
Conducting my test
The hit count will be restarted when the ball returns to its original surface temperature then, the next reading can commence, with a change in the value of x as the variable.
When the value of x is changed and the temperature has reached a constant level then the data for that set is complete. The experiment is repeated, this time with a change in the colour y of the ball.
Review of the Plan
After my initial 3 series of results for each squash ball, I decided that it was not conclusive enough. I decided to extend the scope and to add in another variable for a further 3 series of results. I carried out the 2nd set of series in a different location where the room temperature and humidity where both slightly higher.
Diary
Implementation
As I was conducting my practical I noticed that the lower the grade of the squash ball being investigated the fewer hits required to warm the ball up to its maximum temperature.
While I carried out the tests I tried to ensure that I maintained my position in the left service box, and hit the squash balls with a consistent force sending the ball to the wall at roughly the same height and trajectory. This was in an attempt to eliminate as much as possible the naturally occurring human error in my results.
My results sheet was set up prior to the experiment. Each result being measured in oC. I only recorded the values to the nearest whole degree due to the inefficiency of the thermocouple and the time taken to record the temperature.
My practical did not take much preparation, but before I started I ensured that I had correctly set-up the thermocouple, with an ice bucket, and had a result sheet in an easily accessible place, ready for me to record my readings.
On my previously prepared result sheet (see Appendix 1), I recorded all of my data and transferred them into results tables using Microsoft Excel. Once the data had been transferred to Excel it became easier to notice any trends and patterns in my results. Using formulae I was able to calculate averages and produce a series of graphs showing the results my investigation.
Below is a summary of my results:
The full table of results is included as Appendix 3 and the 8 graphs are also attached as Appendices.
Observations & Results
Using the data I collected I produced a graph for each differently coloured squash ball, showing each of the results as a line. On each graph I started the temperature scale at 15oC, because the room temperature and starting value were both greater than this, and no values dropped below this point during my whole investigation.
I then proceeded to process four further graphs, each showing the average results for one of the squash balls. These graphs, which were also line graphs, were then super-imposed onto a final graph; this showed each of the average lines relative to one other, and was the graph that I needed to validate my experiment.
On the average graphs for each individual squash ball I placed error bars, on both the x-axis and the y-axis. The x-axis error bar was based on the standard deviation for the results of that squash ball, and the y-axis error bar was set at + or – 0.5oC, due to inefficiency of the thermocouple used at giving accurate results to anything smaller than an integer.
There was one very anomalous reading for the green dot ball, when 20 hits of the ball had been carried out; the temperature was lower than that of when only 15 hits had been carried out. When averaging the graphs I left this figure out of the measurements.
Originally I intended to use 1 of different coloured squash ball for each series of results, however after some background research I discovered that squash balls deteriorate over time and usage. For the second batch of tests I used 3 separate balls per colour for each series when I changed location to reduce the time waiting for balls to cool down between tests thus adding yet another variable to my experiment.
Evaluation
Each graph produced showed an increase in the temperature of the ball, as it was hit more often, it was only the rate of the increase that differed between the graphs.
The rates of increase in the temperatures of the balls were mainly affected by the different elasticity properties that each of the different coloured squash balls posses. This is common in the deformation equations that occur to give the ball its change in temperature through an increase in the ball’s thermal energy. The GPE and KE of the ball change with every hit that the ball is given and by every time it comes into contact with the wall or floor of the squash court.
Limitations
The human error in this experiment is significant, and with the number of hits increasing the human error involved increased.
Below are some factors resulting simply from human error that can affect the results of this experiment:
- The power in the hit
- The timing of the hit
- The horizontal trajectory of the hit
- The vertical trajectory of the hit
- My movement across the court
- My movement up and down the court
- Time taken in measuring the temperature of the ball
- Accuracy reading the temperature of the ball
In addition relative humidity and room temperature changes can occur during the course of on the experiment.
Conclusion
“I aim to investigate aspects of temperature change in squash balls.”
My results show that the increased number of times that a squash ball is it raises the temperature of the squash ball, to a certain temperature, which has already been discussed. The results demonstrate that the balls used by experienced or tournament players (yellow dots) take a greater number of hits to warm them than those used by intermediate players (red dots).
“I also aim to find the optimum temperature of squash balls, when the heat loss to surroundings will be equal to the heat gained from the deformation process.”
I believe that the optimum temperature to be approaching 45oC. 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.
However there will always be factors affecting this; if the ambient temperature or humidity are significantly different to those I encountered (20oC and 45% approximately) the ball may reach its optimum level at a different temperature.