Using a catapult in lean six sigma training (variation concerns)

What are the influences on variation in shooting a catapult in lean six sigma training.  As I talked about in my last post master black belt and black belt courses have used catapults for quite a while, but here are helping hints about variability.

I listed many factors and why they impact the distance average, so here are the ones that impact variability.

  1. Release method:  drag changes slow the arm at release.  Use a very quick release from the bottom of the arm.
  2. Release method: centering: influences friction, so centering before release makes it more repeatable
  3. variable hold times after draw back:  influences the relaxation in the bands.  Long holds reduce variation between shots.
  4. rubber bands: comparing less bands that stretch more, such as around a fulcrum, to more bands that do not stretch as much it is more repeatable in the second case.  The more % stretch in the bands the less consistent repeated shorts become.  Add a rubber band and reduce the % stretch.
  5. variable start angles:  Use a book or stop to pull back against to ensure all start at the same angle.  The stop should be as close to the end of the arm as possible to limit bending around the stop when pulling back.

Those are the ones that I have proven to myself.  I will admit that the affect is quite small but I have proven it in controlled testing.  But there is one more that I have not been able to confirm, but I believe it should matter; amount of arc.

A flat trajectory vs. a high loft.  My belief is that there should be an intermediate trajectory that provides a reduced variability because the variation in release velocity component in the direction of travel is reduced.  Physically the velocity leaving the arm has two vectors, up (vertical) and across (horizontal).  As the stop angle increases the velocity component in the distance of travel is reduced, which means that to get the same distance, the ball must stay in the air longer.  Meaning a faster velocity at launch.  I have tried a math model to examine it, but it seemed to prove that there was no trajectory influence, so I believe the model was bad.

I also know that the distance has a quadratic relationship to stop angle.  For low angles (high loft) the distance is short.  As the stop angle increases, the distance increases.  As some point the distance will start reducing as the stop angle increases.  If the stop angle is past 90 degrees (horizontal release) then the ball is thrown down.  At this point and beyond, the ball leaves the arm with zero or a negative vertical component of velocity.  They then go shorter as the stop angle increases.

It is my unproven belief that there is some proper stop angle that is where the maximum distance is reached and the distance is robust to minor variations in stop angle that should also be a minimum variation point, but I have failed to prove it to myself.  You may figure it out, if so please let me know.  Until then, it is a faith based belief.

Good luck with your catapult.