## Piston Rates for Vex Pneumatics and elastic force coefficient

Vex Pneumatic Rates:

While working on the design of a Vex Catapult robot, I took some data on Vex dual acting cylinder extension rates.   We used a high-speed camera to measure the position of the cylinder at 300 frames per second.  Two data points were taken:

No load, 10o psi  extension: 11 /300 seconds 0r .037 sec

>0.5 kg load pull against gravity… 28/300 seconds or  .093 sec

The piston extends 2 inches and has 12 lbs of force at 100 psi.

So the average extension rates are:

No load:      54.5 in per sec

.5kg load:   21.4 in per sec

To launch a .25 kg  (about the wt of  one  football)  over the wall , you need about 120  in per sec speed.  If the launch arm inertia  added an equivalent  .25 kg then the total weight moved by the piston would be close to  .5kg.

What is important is the instantaneous speed at release.   Further analysis is needed to determine how much higher the instantaneous speed is above average speeds calculated above.    If the piston has constant acceleration then we would expect a factor of two higher.   However, if it is flow restricted  such that it is  at a steady state speed (like terminal velocity of a falling object) , the ratio would be closer to one.

I am working  to develop a model using fluid dynamics to see if I can duplicate the results.  Initial results assuming incompressible flow show extension speeds twice as fast for the load case.  I am currently adding compressible effects  So stay tuned.   Wish I had a course in fluid dynamics along the way.

If we assume the instantaneous speed is 2x average, then to achieve the required the launch speed we need a 120/(21.4*2)  or about a three to one ratio between the piston moment arm and the football launch arm.    This would give the speed but the torque would be reduced by 3 , hence  3 pistons are needed to handle the torque.  It appears that the piston has a lot of force but the power is restricted a bit too much by the flow geometry.  Perhaps a better design  might be  to use  elastic tube energy to propel the football and the slower piston or motor force pre-tension the tube.   Of course, if the instantaneous speeds are higher and only two pistons are required…then it would be more palatable.   TBD.. try two pistons in the lab someday.

Vex tubing elastic spring coefficient:

With a force sensor, the force vs distance of a four strand tubing spring. ( 5 foot length of tubing was folded over twice to get 4 strands).

Here is the data:

Millimeters    Newtons

900    18.866

800    16.537

700    14.209

600    11.164

500    7.433

400    1.672

The curve is slightly nonlinear.  The best fit linear line has a slope of  1/29.1 N/mm  or about  0.2 lbs/in per strand.

To shoot a ball at 45 deg to a height of 1 ft requires   2*W*H = 24 in lbs.

Elastic energy = .5 k*x^2    so need to stretch the tube a distance  =sqrt(24/.5/.2) =15.5 in  .