Calculating Pneumatic Force for Object Projection: A Formula Guide

[dschultz]

We are working on a project involving the use of a pneumatic cylinder to propel an object. We have a mass 700 grams which we need to propel (through the air) a certain distance "D", where D will be a minimum of 5 meters and a max of 12 meters. We need help with formulas needed to determine the force needed to accelerate the mass to travel the distance. The object needs to travel in a linear fashion over the distance "D" before gravity pulls the object back to the floor. The object can projected with an initial vector angle of 20 to 45 degrees to achieve the travel distance D. The object may not exceed 1.75 meters off the ground.
We need to make certain this can be achieved with a pneumatic cylinder which can operate at psi below 200.
Anyone with some thoughts?

 

[SteamKing]

Have you tried Newton's Laws of Motion?

 

[Mech_Engineer]

Using the projectile motion equations, first consider how fast the object needs to be traveling when the object leaves the barrel of your launcher. Once you have those speeds, you can take the length of the launcher into account to find the required acceleration and hence force as well.

Good luck.

 

[nvn]

dschultz: I made a lot of simplifying assumptions in a very quick attempt. (1) I assumed the pneumatic cylinder bore diameter is 30 mm. (2) I assumed the mass of the piston and piston rod is ~122 grams. (3) I assumed the pneumatic cylinder has a stroke length of 100 mm. (4) I assumed the pneumatic actuator tip, at the instant of launch, is at ground level (at the same elevation as where the projectile hits the ground). (5) I assumed the projectile rides with the extending piston or piston rod, from rest, instead of the projectile mass being impacted by the piston or piston rod at the end of the piston stroke. (6) I assumed the pressure inside the pneumatic cylinder is constant throughout the launch, which is perhaps consistent with a large supply pressure to the pneumatic cylinder.

Aside: This constant pressure assumption might need to be refined, in the future, if there is no supplemental supply pressure during launch (or only a small supply pressure source), if the piston pressure significantly decreases as a function of piston stroke location. But this would depend on specific dimensions and details of the pneumatic cylinder and air pressure supply source. Since this pressure decrease might be negligible, it is assumed negligible and ignored for now, for simplicity.​

Using the above assumptions, I currently got the following projectile maximum height (y2) and horizontal travel distance (x3), for the pneumatic cylinder angle and pressure listed below.

(1) 20 deg, 1060 kPa, y2 = 1.08 m, x3 = 11.9 m.
(2) 45 deg, 400 kPa, y2 = 1.72 m, x3 = 6.87 m.​

 

[P K Pillai]

A non pneumatic solution.A high speed turntable/arm ,vertical axis of rotation,vertical axis slightly tiltable,powered by a variable speed motor, with the object attached/released at the circumference.Adjustment friendly assembly.

 

[dschultz]

Thanks for the replies.

On the variable speed engine idea:
I am not familiar enough with the instantaneous velocities which can be achieved through a variable speed electric motor acting on a 'swing arm'. I do understand the concept and visualize the design needed to propel the object as you suggest. Can a variable speed motor deliver a large, instant force and then stop instantly (without brakes)? My needs are to have the object (multiple) propelled one after another with about 7-8 seconds of rest between the cycle. The pneumatic solution allowed for the cylinder to 'reset', psi to rebuild and then redeploy.

 

[dschultz]

nvn...thank you for the post. That helped.
Any chance you can share the math behind your solution?