# Physical constants
H = 2.0 # 2 Hands
N = 3.0 # 3 balls


# Flight time comes from physics
# y = 1/2at^2
# but we want t, so t = sqrt(2*y/a)
G = 9.8 # gravity in m/s**2
G *= 100 # in cm/s**2
F = lambda h: 2*(2*h/G)**.5
# Flight time for 25cm (~= 1ft)
height = 25
F_1ft = F(height)
"%.4fs flight time at height %d cm" % (F_1ft, height)

D = lambda f: f*H/(2*N-H)

Hand_cycle_time = 2 * D(F(25))
Hand_Hz = 1/Hand_cycle_time
Hand_rpm = 60 * Hand_Hz
'Hand cycles in %.4fs, or at %.4fHz (%.1f rpm)' % (Hand_cycle_time, Hand_Hz, Hand_rpm)

def hand_rpm(balls, height_in_cm=25):
    H = 2.0
    F = 2*(2*height_in_cm/980.0)**.5
    D = F * H / ( 2 * balls - H )
    cycle_time = 2 * D
    hz = 1 / cycle_time
    rpm = 60 * hz
    return '%d balls cycle in %.4fs, or at %.4fHz (%.1f rpm)' % (balls, cycle_time, hz, rpm)
    

for hands in (3, 5, 7, 9):
    print hand_rpm(hands)