For a given amount of stored energy (armed state of kicker), mass is inversely proportional to the square of the kicking speed.
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This web document has the most in depth math/physics analysis of ABSOLUTELY EVERYTHING relating to soccer!!
“The Science of Soccer” by John Wesson:
=> http://www.scribd.com/doc/6726997/ScienceofSoccer
Their analysis of kick, bounce and spin are useful, and worth reviewing briefly.
Some items covered include:
- Professional kicks go 70+ miles per hour & contact with foot lasts ONLY 1/100 of a second
- ball spin of around 10 RPS can accelerate a ball on landing by 5-10 miles per hour
Team 3135 will use a 3-4lb pendulum mass traveling at ~25-30 MPH at impact with the ball for a max contact distance of 3-5" to have it travel the length of the field, clearing both bumps at low “line drive” angle. Our bungee winder design can shoot at any point during the 2-3 sec (to full power) wind up, and also have programmed level of wind up to adjust kick strength.
We also will need to quickly (<1" travel) absorb the momentum impact of this kicker’s momentum using synthetic cord tether.
– Dick Ledford
That fits with our findings. We used a 2 pound pendulum and had no problem kicking the ball with a low arc 40 feet.
The mass of a typical #5 bal is 0.4 Kg.
The mass of a typical player’s leg is 6 Kg.
The coefficient of restitution is 0.7. This relates to the elasticity of the ball. e = (D2/D1)1/2. The ball bounces halfway to its starting elevation on tile, so D2/D1 = 0.5. The square root of 0.5 = 0.7.
If Vleg = 20m/sec then:
Vball = 20m/s x 6kg/(6kg+0.4kg) x (1 + 0.7) = 31.9 m/s = 72 mi/hr
If the ball is traveling 31.9 m/s, then 20m/31.9 m/x = 0.67 sec for the ball to travel 60 feet (20meters).
For 1.5 seconds, the launch speed is 13.3 m/s.
We assume the ball contact time is 0.01 sec
Force on the ball = mass of ball x acceleration
A = change in V/t = (13.3m/s - 0)/0.01sec =1330 m/s2
Force on ball = 0.4 kg x 1330 m/s2 = 532 Kgm/s2 = 532 Newtons = 120 pounds of force on the ball to launch 20 meters.
Yeah, our team got the same results ours is a happy medium of about 2.75"