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.
THERE ARE MORE POTENTIAL PHYSICS AND MATH LESSONS THIS YEAR THAN ANY PRIOR. IT IS SICK. THANK YOU DEAN KAMEN AND TEAM! LETS CHALLANGE THE SMART KIDS AND HELP THEM LEARN!
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.
-John
GEAR IT FORWARD