Pneumatics Math

[nnfuller]

Ok so... Here is my problem... im trying to figure out if we have enough air in our robot to do everything we want to. Can anyone help me figure this out?
Known:
4x16cubicinches=64cubic inches of air storage.
2inch piston with 24 inch stroke has a volume of pi x 24 or 75.398 cubic inches
The compressor is know to have
"Free Air Flow @ 10 PSI 0.75 CFM, Free Air Flow @ 100 PSI 0.24 CFM, Free Air Flow @ 20 PSI 0.71 CFM, Free Air Flow @ 30 PSI 0.63 CFM, Free Air Flow @ 40 PSI 0.56 CFM, Free Air Flow @ 50 PSI 0.41 CFM" from Drillspot.com
so asuming i had a fully charged system, if i fired that piston with a regulated 60 psi could i pull it back with 60 psi of force in 10 seconds?
I just need help with my math...
Thanks!

[Matt H.]

The exact solution to your question can be found using the ideal gas equation PV=nRT where n is a function of time based on the compressor's stats.

However, it is easy to make estimate of how long it will take to retract with full force.

Initially your system has 128 cuin of 60psi air stored. 64 of which can be used before the upstream pressure drops to 60 psi and more complicated math applies.
So extending and retracting the piston at full force takes 150.8 cu in of 60 psi air.
86.8 cu in must be provided by the compressor.
Using the 50 psi rate* of .41 CFM or 12 cu in/sec it will take you roughly 7.2 seconds to retract the cylinder at 60psi.

*The 50 psi rate is a good estimate because the system will drop below 60 psi.

Here is an experiment you can do to get an exact time. If you don't have your pneumatics system set up perhaps another team could do this for you.

Steps:
1. Charge all of the tanks to 120 psi.
2. Open a solenoid valve to the cylinder, and start a timer. Wait until the pressure valve reaches 60 psi.
3. Quickly switch the solenoid valve and retract the cylinder.
4. Wait until the pressure valve reachs 60 psi and stop the timer.
Repeat a few times and average the results and bingo you have the answer you're looking for (which I bet will be between 40-140 seconds).

[Kevin Sevcik]

EDIT: Matt H. has a bad unit conversion up there. slip of a digit or some such. 0.41cfm * 12in/ft * 12in/ft * 12in/ft * 1min/60s = 11.8cis. By his reasoning, you'd get a ~7.5s lift. I think he's oversimplifying, but his simplification may still be more accurate than my complication below. If you test it, please do post the results here.

You can think of your air supply as 64*120 (in^3 * psi). Expanding to twice the volume means your air will have half the pressure. So when you extend, you're expanding to (64+76) in^3, so you'll be at:
64ci*120psi/140ci = ~54 psi.

So you have enough air to make the extension and stay near 60psi.

Now, when you go to retract, you dump all that nice air you just had. You're down to 64*54 storage. Retracting gets you to:
64ci*54psi/140ci = ~25 psi

So now we know what pressure you'll be down to when you're lifting. Finally, we can estimate how long it'll take to get back up to 60psi. Same rule applies for figuring out how many cubic inches we need to pump back in to get back up to 60 psi. It's a little less straight forward, though. We know we want to end with 140ci of 60psi, and we're starting with 25psi. So..
60psi*140ci = 25psi * X ci
X= 60psi*140ci/25psi = ~336ci

You're starting with 140ci, so you need to pump in about 200ci. And we have those nice flow rate figures for the pump. Now,to really figure this out well, I'd prefer an excel spreadsheet and a lot of math, but we can use those numbers to give you a good range. If we look at the flow rates at prssures near where you're starting and where you're ending, we can get a best case and worst case estimate on time. At 30psi, you have a flow rate of 0.62CFM, or about 18 ci/s. At 50 psi, it's about 12ci/s. So this gives you... (drumroll) A retract time between 11 s and 18 s. Figure on it being about 15 s.

So now that we know your original plan probably isn't going to work for you... Why are you using 60psi to extend your piston? I have no idea what your mechanism is, but I'm seriously doubting you need that much pressure to extend it. You can use two solenoids and set your extend pressure to something like 25-30 psi. That'd give you a retract time of about 5 seconds. Big difference, no?

[dtengineering]

The two inch pistons really suck a LOT of air. Have you considered using a spring (or surgical tubing) to help with the retraction? That way when you extend the cylinder (which will require at least 25-30 psi to actuate a valve) you will actually get to use some of the energy in that air (to stretch the spring), and might be able to get the same amount of retraction force, but at a lower pressure.

And if you have enough air to pull it off, and are using a double acting valve (or a single acting one that defaults to "retract" when the power is off) you could put a flow restriction connector on the piston, so it would slowly... retract, but continue to retract even after the power is off to your robot.

You hit retract just before the match ends, and people think "oh no... they just needed one more point to win", and then the robot begins to creep upward.... and upward.... and you come to rest above the platform and get the point!

Jason

[nnfuller]

Thank you everyone for the replies so i think i see the design flaw. if i were to have two solenoids for that piston, could i fire it up at 30 psi then retract at 60? Also is it legal to have a system that finishes after the match is over? and does it still count? As in if the piston was assisted and the robot got suspended after the match ended would that count? sorry just a curious...

[Matt H.]

I apologize for my unit error. I was using 144 cu in in 1 cu foot which is off by a factor of 12. My orginal post has been edited to reflect the proper values.

You could definitely try using 30 psi to extend the piston which using my calculations would reduce the total time to 4.1 seconds. To do this you would need to have two regulators which (check the rules on this) could feed into the same valve.

If you have the weight you can also try using a much smaller cylinder to extend the larger cylinder.

[Daniel_LaFleur]

Originally Posted by nnfuller

Also is it legal to have a system that finishes after the match is over? and does it still count? As in if the piston was assisted and the robot got suspended after the match ended would that count? sorry just a curious...

In the past (your milage may vary this year) the referees have scored things "after everything comes to rest", thus it would count.

That being said, the inspectors will look very close at any system that moves/actuates without power. So make it safe.

[Kevin Sevcik]

This year's scoring is after everything comes to rest, or 10 seconds after the end of the match, whichever comes first. It's right in G05. So you'll need to finish your lift moderately quickly after the end of the match. Also, remember that your compressor is going to shut off at the end of the match. Your extra lifting at the end of the match would only come from extra pressure still in your storage cylinders.

[nnfuller]

Ok sounds perfect. Thank you all so much if this idea gets finished I will post results here. I love how math allows you to solve things like this. Very encouraging.
Thanks again to everyone for helping me walk through something i thought was going to be very complicated.

[Gary Dillard]

There are some other errors in the math above; remember that the ideal gas law works on absolute pressure, so the ratios are relative to 74.7 psi, not 60 psi. See this post