I am trying to do some exact calculations here and I was wondering if anyone has calculated the deformation with respect to force applied (i.e. spring constant) of a sufficiently pumped soccer ball?
Thanks.
lol, we just learned this yesterday in physics from my physics teacher/robotics sponsor, but we used springs. we don’t have the constant for the soccer balls.
Sorry, yeah we weren’t provided sufficient info about the ball…
Has anyone TESTED to get the spring constant?
This would be affected by the pressure of the air in the ball. From the FIFA Laws of the Game, Law 2:
The ball is:
• spherical
• made of leather or other suitable material
• of a circumference of not more than 70 cm (28 ins) and not less than 68 cm (27 ins)
• not more than 450 g (16 oz) and not less than 410 g (14 oz) in weight at the start of the match
• of a pressure equal to 0.6 – 1.1 atmosphere (600 – 1,100 g/cm2) at sea level (8.5 lbs/sq in – 15.6 lbs/sq in)
That’s quite a range of acceptable pressures.
Section 6.3.1 agrees on weight and size, but puts pressure at the low end of the FIFA scale. “The BALL weighs between 14 and 16 ounces, has a circumference of 27 to 28 inches, and is inflated to a standard pressure of approximately 9psi.” The ball will be quite mushy - although not as mushy as some soccer players like to practice with.
I think you are asking the wrong question. Do you want the “spring contant”? I am not sure you do. Therefore, this is an easy question.
You want coefficent of restitution. When is someone on here going to quit messing around with massive prototypes and start running the elastic collision numbers.
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Anyhow. Cofficient of Restitution is about 40% from what I can tell. Easy to check for yourself. Get a reg football and inflate to FRC listed pressure and drop from 1 meter. Record with webcam, 30fps, with a backing like mythbusters use. Then, see how high it rebounded. If it rebounded to 0.4 meters, then it is sqrt of 0.4 / 1 which is 63%.
Here’s the problem: It varies directly with pressure and can depend on wear of ball. FIFA has rigorous standards. However, they test at normal World Cup pressure of 0.8 bar. Game documentation “06_TheArena_RevB.pdf”, however, states 0.621 bar. This is more a “practice pressure”.
It is difficult to measure pressures that are small accurately and then extract the needle not loosing pressure. I need to think thru math on this one. Think I have an idea… will post after finishing my trajectory paper now and posting it.
Please watch for a pair of papers I should have completed today, but may not release til reviewed by Caterpillar (2338 Sponsor) piers. They will detail science of the soccer ball flight, and include many teaching opportunities!!! Mentors please use to teach students.
I understand the temptation to “play”. I do fear however much of FRC is becoming excessively “wood-shop” and “trial-and-error” where a “blank check” is given. They limit time to 6 weeks for a reason. To encourage teams to do RESEARCH. Please make use of some of my efforts. Please, let me know if as a mentor or teacher you help show kids the Physics is Phun and Robots can Rock.
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I believe the proper way to do your ball flight calculations is using energy.
Potential energy of a spring is converted into kinetic energ of the ball. As someone stated, though, you are going to lose engery due to the inelasticness of the collision.
A good first-cut way to measure that is to take the ball from a height. Say 8 feet. Drop it on concrete and measure the height it rebounds. Say 4 feet.
Therefore, in a collision the ball will lose around 50% of the input energy just to inelastic deformation.
Then you can take the potential energy of your system, multiply it by your percentage, then use your new energy and the kinetic energy formulas to calculate the imparted velocity. Then you can use the simple projectile formulas and determine how far it will go.
We just got done shooting some high speed footage of some devices hitting the soccer ball at different forces. I will tell you that we were very surprised to see that the ball does not deform to a hit. I’ll get the video posted here as soon as possible for all to see.
Read update above.
Also. IT DOES DEFORM. PLENTY. Want to see nice video? I do. Second one in color too. 
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- John (eaglecat)