Ball Flight Model

[NotInControl]

So as promised, I have included some additional data sets to test for your model.

I have yet to confirm the results to actual measured results from the balls flight trajectories.

Once again my model only includes air resistance no magnus force. All Paramters needed should be included on the plots.

The ball in the plot is to scale.

The only trouble I am having is determining the required force based on the lauch velocity. The numbers are way to small in my opinion. Maybe it is because using Vf = Vi + at assumes accel is constant over time and because I assume the force is applied over t=0.5 seconds which may be too long.

I don't know, I haven't spent time looking into it. But I would expect the required force to be in the 100lbf+ range for quick shots. Any thoughts?

Hope this helps,
Kevin

[DavisDad]

Originally Posted by NotInControl

So as promised, I have included some additional data sets to test for your model.

I have yet to confirm the results to actual measured results from the balls flight trajectories.

Once again my model only includes air resistance no magnus force. All Paramters needed should be included on the plots.

The ball in the plot is to scale.

The only trouble I am having is determining the required force based on the lauch velocity. The numbers are way to small in my opinion. Maybe it is because using Vf = Vi + at assumes accel is constant over time and because I assume the force is applied over t=0.5 seconds which may be too long.

I don't know, I haven't spent time looking into it. But I would expect the required force to be in the 100lbf+ range for quick shots. Any thoughts?

Hope this helps,
Kevin

Hi Kevin,

thanks so much for the charts!

I'm working on modelling a mechanical linkage to pneumatic cylinder with:

1. Force of accelerating ball at end of long member
2. Calculation of airflow to cylinder using 0.3 Cv
3. Rate of travel of cylinder rod (piston)

I'm thinking that the limitation of the pneumatic's flow capacity can be addressed by the progressive increase in ball speed vs. piston speed via a linkage design. See video below:http://youtu.be/DaTn6ZMzihw

I'm not sure I follow your question regarding acceleration. Could you provide more detail?

Regards,

Craig

[NotInControl]

Sorry for taking so long to reply. Unfortunately I had to take a brake from Robotics this weekend and do other work.

In regards to my last post about Force, I was trying to do a sanity check to see if the model was accurate. So one way to do it was to calculate the force required to impart on the ball to give it its initial velocity, but the numbers were too small in my opinion. I only spent 5 minutes on it and then I realized I was making the wrong assumption using Vf = Vi + at, because that assumes acceleration is constant, which is incorrect.

So here is what I did which didn't work, and then below is what I did to fix it.

(Incorrect Calculations)

F = ma;
Vf = vi + at;

In the above equations, we know Vf, and m. Vi is 0 because ball is at rest, and t we can define based on how fast we want to shoot.

So if we solve eq. 1 for a and plug into eq. 2 and solve for F we get.

F = Vf*m / t

lets say we defined t to be 0.5 seconds the above would yield force required, assuming acceleration is constant.

But this is a wrong assumption because acceleration is not constant throughout the launch.

So the better way to do it is use the Law of Conservation of Energy, and in this case for my team we were thinking about springs, so I wanted to calculate the spring force we would need.

Kinectic Energy = 1/2 * m*v^2
Spring force = 1/2 * k * x^2

If we assume 100% energy transfer from spring to ball we can set these equations equal. we know m and v, and we can choose x based on our design. So lets say we only wanted to compress a spring 5 inches. We solve the below for k;

1/2 mv^2 = 1/2 kx^2

K = mv^2 / x^2

I have plotted the lb/in spring constants while varying the max displacement for the points I gave you. This should give an idea of the force required.

The numbers do align with what I think they should be, so my sanity is back in check.

Hope this helps,
Kevin

[DavisDad]

Originally Posted by NotInControl

...So here is what I did which didn't work, and then below is what I did to fix it.

(Incorrect Calculations)

F = ma;
Vf = vi + at;

In the above equations, we know Vf, and m. Vi is 0 because ball is at rest, and t we can define based on how fast we want to shoot.

So if we solve eq. 1 for a and plug into eq. 2 and solve for F we get.

F = Vf*m / t

lets say we defined t to be 0.5 seconds the above would yield force required, assuming acceleration is constant.

But this is a wrong assumption because acceleration is not constant throughout the launch.

So the better way to do it is use the Law of Conservation of Energy, and in this case for my team we were thinking about springs, so I wanted to calculate the spring force we would need.

Kinectic Energy = 1/2 * m*v^2
Spring force = 1/2 * k * x^2

If we assume 100% energy transfer from spring to ball we can set these equations equal. we know m and v, and we can choose x based on our design. So lets say we only wanted to compress a spring 5 inches. We solve the below for k;

1/2 mv^2 = 1/2 kx^2

K = mv^2 / x^2

I have plotted the lb/in spring constants while varying the max displacement for the points I gave you. This should give an idea of the force required.

The numbers do align with what I think they should be, so my sanity is back in check.

Hope this helps,
Kevin

Hi Kevin,

Thanks for the thorough write-up. Will you include the mechanism in the model?

I'm currently plodding through this document: Dynamic Analysis of Pneumatically Actuated Mechanisms
and scratching my head about how to use the formulas.

[DavisDad]

Putting all the mathematical modelling aside, I think team 1726 has demonstrated that the ball can be launched with pneumatic cylinders, and without springs or other energy storage:

2014 FRC 1726 Shooter Test 1 NERDS Pneumatic Catapault

Here's what I see:

• This is a "rolling release" catapult. An improvement over cup type ball holder.
• The linkage starts with a reverse leverage (better term ??) where the mechanical advantage decreases with rotation; as the piston extends, the moment applied by the rod decreases.
• The small initial moment with the inertia of the ball/catapult-arm, allows the pressure to build in the cylinder.

Nice work N.E.R.D.S. !

[Ether]

Originally Posted by DavisDad

The linkage starts with a reverse leverage (better term ??)

3rd class lever.

where the mechanical advantage increases with rotation; as the piston extends, the moment applied by the rod increases.

Sort of like this:

http://www.chiefdelphi.com/forums/sh...80#post1327180

... except I can't tell from your video if your piston is over-center in the loaded position. If not, how are you holding (and releasing) it?

[DavisDad]

Originally Posted by Ether

... except I can't tell from your video if your piston is over-center in the loaded position. If not, how are you holding (and releasing) it?

Hi Ether,

Not over-centered, hadn't thought of it; great idea for "cocking" mechanism. Thanks for that!

In the sketch, the loaded position would be determined by hard stops and/or rod fully retracted. I was trying to evaluate the feasibility of shooting the ball with cylinder stroke only (no spring storage, no trigger release).

After seeing the video of the team 1726 catapult prototype, I'm thinking I have missed an important pneumatic dynamic: the inertia of the ball/launcher and the pressurization of the cylinder during the initial acceleration. We struggled with the Cv limitations of the solenoid valve when working on Rebound Rumble ball shooter prototypes. Your over-centered system looks like an even better way to deal with CA flow restrictions.

Your feedback, as always, is much appreciated.

NOTE: fixed error in previous post re "increased moment"

[Ether]

Originally Posted by DavisDad

Hi Ether,

Not over-centered, hadn't thought of it; great idea for "cocking" mechanism. Thanks for that!

I'm just the messenger who drew up a sketch. Kudos to Billbo911 for sharing the details of what his team was doing.

[DavisDad]

Ether- thanks so much for pointing me toward that. Here's our 2nd generation prototype; the lead-screw positions the ball-stop. The shooter captain would like ball position and proportional cylinder/accumulator pressure control.