360 Degree Swing

• The assembly of the swing was destined to not work. The swing hardware mounting the chain to the support pole should have had free 360 degree swing as well. You should try it again with a flat seat and a free motion mount (with a guard to keep the mounts from sliding side to side).
  

• The needed speed and energy can be computed from two basic physics equations:

1. To keep the chains straight even in the top position the centrifugal (NOT centripetal in this case) force must exceed the gravity pulling Susie and her swing straight down.

Fcent > Fgravity
m v^2 / r > m g
v^2 > g r

2. The kinetic energy at the bottom is the sum of the kinetic energy at the top, the potential energy held by the swing being up rather than down and the energy wasted by friction (including air resistance).

Ebot = Etop + Eheight + Efriction
1/2 m V^2 = 1/2 m v^2 + 1/2 m g 2r + Efriction
V^2 = v^2 + g 2r + 2 Efriction / m
V^2 = v^2 + 2 g r + 2 Efriction / m

Combining these two equations gives

V^2 > g r + 2 g r + 2 Efriction / m
V^2 > 3 g r + 2 Efriction / m
V > sqrt( 3 g r + 2 Efriction / m)
V > sqrt( 3 g r )

Inserting the values g = 9.8 m/s^2 and r = 2 m (7') we get

V > sqrt( 3 * 9.8 * 2 m^2 / s^2 )
V > 7.7 m/s
V > 27 km/h (17 miles/h)

So at the bottom of the curve, Susie needs to go more than 17 miles per hour, and that is on a small 7 foot swing and not including friction and air resistance. Longer chains need more speed (increase energy proportional to length, speed proportional to the square root of the length), more air resistance needs more speed and energy too.

• If Susie changes the shape of her body (by bending or stretching her arms, legs and spine) to change the distance between her center of gravity and the center of the swing, she can affect the above energy calculations for better or for worse.