Physics Research Project 2008
“Football Bounce”
By
Jordan Dwight
Dennis Ranck
Problem | Background | Review of Literature | Hypothesis | Diagram
Procedure | Collected Data | Conclusion | Bibliography | Related Sites
How do different surfaces (grass and turf) affect the height of a bouncing football?
This experiment isn’t a common interest among scientists, but we are no ordinary scientists. We are using some simple laws of physics to help out punters and kickers that play football. Our goal is to help these players create a strategy for their kicks depending on what surface they are playing on. A punter may kick a ball shorter on turf because he may think that it will bounce higher, causing more time for the defense to catch the receiver. On a kickoff, the place kicker may ground the ball, in hope that it will bounce more frequently and therefore make the ball harder to handle.
Since our experiment is somewhat simple, we will use some basic laws of physics
to solve our problem. Our first law is the law of gravity, which states that
states any two bodies attract each other with a force that is directly
proportional to the product of their masses and inversely proportional to the
square of the distance between them. This can be shown with the formula: 
where f is
the magnitude of gravitational force, G is gravitational constant, m sub 1 is
mass of first object and same with m sub 2 and r is the distance between the
two points. Another property that is necessary to know is the coefficient of
elasticity. The coefficient of elasticity is the ratio of the applied stress to
the change in shape of an elastic body. This describes what happens to the ball
as it hits the surface and bounces back up. The law of gravity and the
coefficient of elasticity are the basic ideas necessary to do our experiment.
Using our basic theories of law of gravity and the coefficient of elasticity, we can analyze the problem at hand. The law of gravity creates a force on our falling football and will make the ball bounce back up at a lesser height than it started. In a real game, the ball would reach free fall and would therefore have an acceleration of 9.8 m/s. Unfortunately; we can’t drop the ball high enough to create free fall in our experiment. The data would be far more difficult to gather accurately at that height. The coefficient of elasticity represents what happens when the ball smacks the ground and bounces up. In a real situation, the ball hits the ground with a great force and must change shape to adjust to the force of hitting the solid ground. Then, after changing shape, it conforms back to its original shape as it recoils back into the air.
If we drop a football at a constant psi on turf and grass, the ball will bounce higher on the turf than the grass. We expect the average highest bounce of the ball to be greater on turf than on grass. Our dependent variables are the heights we are dropping the ball from, 1 meter and 2 meters. Our independent variable is the highest bounce after the ball hits the ground.
To begin the experiment, we decided to drop our football on turf, grass, and tile. The hard surface was the first surface we conducted out experiment on. We used Mr. Murray’s camera to take videos of our experiment that we would later analyze in the lab. We began with the one-meter height. Measuring it out properly with the meter stick and placing the ball on top of the stick and then removing the stick and dropping the ball. We proceeded to do this fifteen times. Once this was over, we continued on with two-meter drops on the hard surface. Since we did not have two one-meter sticks, we made a mark on the wall where two meters was and consistently placed the ball at that height. From there we did fifteen drops.
The next surface we did was turf. This time we started with the two-meter height because we had two-meter sticks taped together to make it easier. We placed the ball on top of the two sticks then moved them away and dropped, repeating this fifteen times. Then we moved to the one-meter height where we did fifteen drops. The last surface we did was the grass. Doing the two-meter first just like the turf, we placed the ball on top of the two-meter sticks and did fifteen drops. Then we finished collecting data with the one-meter drops fifteen times.
After collecting all of our data, we had to go back to Murray’s classroom to analyze the data. We used a program called Logger Pro to help us analyze our videos. In Logger Pro you can import a video and analyze it by plotting points. On every graph, we first plotted a point from the height that it was dropped from all the way to the ground and back up to it’s height on the first rebound. We only did this on the first drop so we could measure how far the ground was from the rebound. On each graph, the ground is not at zero, but where the very bottom plotted point is. The reason the graphs and illustrated like this is because while filming, we didn’t take into account that the graph would reflect the range of the camera lens. So we found that measuring the average from zero was erroneous and we would actually have to measure it from the bottom plotted point. After that though, we only measured the highest point of the first rebound. To average the points we had to take every rebound point and subtract the lowest point (the ground) from it. Then we added all of those differences together and divided them by fifteen. This gave us the average height of each bounce.
Average Bounce= .33 m
Average Bounce= .299 m
Average Bounce= .58 m
Average Bounce= .82 m
Average Bounce= 1.1 m
Average Bounce= .67 m
After collecting and analyzing the data, we were able to come up with a conclusion. We found that the ball has a higher average bounce on grass, as opposed to turf. This result defied our hypothesis, as we believed the ball would bounce higher on a turf field. We believe that due to the cold weather, the grass surface may be harder than if it were a summer day. Therefore, another experiment in warmer weather may find different results than what we found.
If we were to do this experiment again, we would make it easier on ourselves and have the very bottom of the camera lens be the ground so we could use an easier equation to find the average bounce height. Also we would use more controlled surfaces, using warmer or muddy grass, just to add a deeper aspect to our experiment. We would also use higher heights, so we can reach free fall and therefore simulate a real punt or kick.
Some error may have been that the ball doesn’t bounce straight up every time, due to its oblong shape. It also might’ve been inaccurate when we dropped the ball from certain heights, especially when we were outside; we may have not dropped the ball from exactly one or two meters in every trial. Also, in the video analysis there was error with the exact measurements of each drop and bounce.
In conclusion, we now know that in colder environments, a football bouncing off of grass is more likely to rebound higher, therefore giving the punter or kicker a more effective kick. In warmer weather, we would hypothesize that the ball would have a higher bounce on a turf field as the grass would be warmer and therefore softer.
I. Bernard Cohen and Anne Whitman, translators: Isaac Newton, The Principia: Mathematical Principles of Natural Philosophy. Preceded by A Guide to Newton's Principia, by I.Bernard Cohen. University of California Press 1999
<http://en.wikipedia.org/wiki/Newton's_law_of_universal_gravitation>
The American Heritage® Science Dictionary Copyright © 2005 by Houghton Mifflin Company. Published by Houghton Mifflin Company.
<http://www.thefreedictionary.com/law+of+gravitation>
<http://www.thefreedictionary.com/coefficient+of+elasticity>
<http://www.jimloy.com/physics/gravity.htm>: This site explains Newton’s Law of Gravity in more detail, describing the formula of gravity and how Newton discovered gravity.
http://www.icogitate.com/~ergosum/essays/soccerball/soccerball-motion.htm>: This site describes the effect wet turf has on a soccer ball, not the same as football, but explains the concept.
http://webpages.ursinus.edu/rdavidson/NSFsite/SportPages/ballbounceindex.htm>: Explains bouncing balls on surfaces in a more descriptive way and shows a more complex experiment.
http://www.nextag.com/GST-Game-Football-by-69117376/prices-html : Description of the football used in our experiment
http://www.sci-journal.org/index.php?template_type=report&id=40&htm=reports/vol1no2/v1n2k36.htm&link=reports/home.php&c_check=1 > Site of a similar experiment using a tennis ball and has similar conclusion to our experiment.