# Gas station without pumps

## 2012 October 14

### NASA releases reasons for removing paper rocket activity

Filed under: Robotics — gasstationwithoutpumps @ 10:37
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In a previous post, I had groused about NASA removing plans for a common compressed-air launcher from their educational web site for “safety reasons” without explaining what the hazards were.  (There are several possible hazards, including shooting the rockets at people, firing more massive projectiles, and exploding PVC pressure containers.)  I asked for a copy of the engineering report, and (10 weeks later) I’ve finally gotten a reply.

They have a FAQ page which they have sent out as PDF files to people who inquired, but they don’t seem to have put it on their website anywhere (a strange oversight—I would have put it up on the web site first and sent people links to it, rather than sending out PDFs).  They did not send me the engineering report I requested, insisting that it was only available through a Freedom of Information Act request.  Again, a very strange, anti-education, anti-safety approach—I would have put the engineering report on the web, since there was clearly public interest and a need for the information to be disseminated.  I get the impression that NASA is being run by lawyers and politicians, whose first instinct is to make everything require expensive intervention by lawyers and whose second instinct is to prevent the spread of information if at all possible.  There may have been a time when NASA was run by scientists and engineers, but they certainly aren’t now.

In any event the FAQ is quite clear on what hazard they were talking about:

NASA does not recommend use of PVC pipe with compressed gasses, including air. Under pressure, PVC can shatter or explode under pressure or from an external force.

At this time NASA has no plans to redesign an activity using PVC pipe to construct a launch system that utilizes compressed air. NASA will assess other materials and designs and may release a new high-powered paper rocket launcher at a future date.

NASA completed an inquiry into this activity and determined that the launcher, or design equivalents, should not be used. NASA does not recommend use of PVC pipe with compressed gasses, including air. PVC can shatter or explode under pressure or from an external force. NASA recommends that individuals and organizations should immediately discontinue use of these launchers.

Q8: Can I obtain a copy of the engineering report referenced in the discontinuation notice?
You may request a copy of the report under the Freedom of Information Act. (http://www.hq.nasa.gov/office/pao/FOIA/agency)

Exploding PVC is one of the possible hazards I had considered, and perhaps the most dangerous one, since not all people who build with PVC are aware of its brittleness and that it produces very sharp shards when it shatters. The brittleness and sharp are why toy swords are not made from PVC pipes. (The Society for Creative Anachronism experimented with PVC for their swords in the 1980s, when rattan was getting expensive, and decided that PVC was far too dangerous.)

There is a standard workaround that reduces (though does not completely eliminate) the hazard: wrapping all pressurized PVC components with a few layers of strapping tape.  The strapping tape does not prevent the PVC from shattering, but may contain the shrapnel or slow it down enough to reduce the danger zone. The strapping tape only has to hold the pieces together for long enough for the air to escape—the energy of the pressurized air is dissipated in tearing the tape rather than in propelling the shrapnel.

Even more common is keeping the pressure fairly low.  This is not as big a win as one might think, since even fairly modest pressures (like 40psi) can still store significant energy in a large pressure vessel, and PVC can shatter at low pressures if it is struck or if it has gotten UV damage from being left in the sun.  Keeping the vessel small and the pressure low is probably safe enough, so I have no concerns about the soda-bottle rocket launcher plans that I’ve published in the past—the friction-fit launching keeps the pressure down to around 20–40 psi and the volume is small.  I have no idea what plastic the commercial soda-bottle rocket launcher uses (maybe ABS, which is not as brittle as PVC), and they have a pressure release around 60psi (4 bar), so again is probably safe enough.

The one project we’ve done that potentially hazardous is the foam-dart launcher, which is very similar to the NASA design for the paper-rocket launcher (indeed, we have used it as a paper-rocket launcher).  We were pressurizing to 120psi (8 bar), and we had not wrapped the pressure vessels with strapping tape.  That project is on hold currently, not for safety reasons, but because the students in the robotics club got too busy to continue the robotics.  If we pick it up again, we’ll wrap the pressurized PVC pipes with a few layers of strapping tape, then add a layer of colored duct tape (for UV protection of the strapping tape and to make it look nice).  I think that would reduce the hazard to an acceptable level for experimenters, though not for a commercial product.

## 2012 July 12

### Nerf gun barrels

Filed under: Robotics — gasstationwithoutpumps @ 19:08
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In Nerf gun progress, I discussed possible approaches for handling the problem of Nerf-brand darts not fitting in the barrel:

• Find a source of (probably non-Nerf) foam darts that are 1.45cm (9/16″) diameter with heads that are no wider than the body. I think that they came with an NXT generation crossbow, so replacement foam darts for that may be what we need.
I’ve ordered a couple dozen NXT generation darts.
• Buy Nerf  (or other) darts with the right size bodies but oversize heads, remove the heads, and make new ones (out of what?). This would be cheap, but tedious, and the darts would probably fly poorly, unless we made the new heads have a decent weight.
I’m not willing to try this yet.
• Use clip-system darts for compatibility with the popular Nerf guns, but find a smaller diameter tube than the ½” PVC pipe (where? and how would it be connected to the solenoid valve?) It looks like Schedule 40 3/8″ steel pipe has a inside diameter of 0.49″, which is just right, but steel pipe is rather heavy.
I’m still looking, but I’ve not found any lightweight tubing that I think will work.
• Use clip-system darts, but convert to the Nerf-standard tube-inside-the-dart launching system.  This limits the effective barrel length to the inside length of the dart (about 4.5cm) and the barrel diameter to the inside diameter of ¼”, which will limit the top speed of the darts (OK for safety, but probably not as much fun).
I tried this out today, as the outside diameter of ¼” copper pipe seems to be just the right size.  We already had a piece of copper pipe stuck into a 3/4″ threaded end cap (it was part of the vacuum bottle for the ROV), so I could test this easily.

Here are the two barrels. The long barrel of 1/2″ PVC has an NXT Generation dart poking out the end. It can be loaded all the way into the barrel with a ramrod. An old-fashioned NERF-style dart with the same body size, but a head too big to fit into the barrel is shown below the barrel. The NERF Clip-system dart is shown mounted as far as it goes (only 4.3 cm) onto the 1/4″ copper tube.

The Nerf method of firing darts (with the dart surrounding the launching tube) is similar to our firing of paper “rockets” from the outside of the 1/2″ PVC barrel.

Loading the darts onto the tube is a bit finicky, as the foam is a tight fit over the copper. It might help to smooth the end of the tube, and perhaps use a dry lubricant (soap?). Rapid loading might be a problem.  I can also see why so many Nerf enthusiasts modify clip-system darts—only 4.3 cm fit onto the tube, but one would expect closer to 6cm to fit.  The depth the tube goes into the foam corresponds to the length of the barrel in the bullet-and-barrel system, and the longer the barrel the higher the muzzle velocity (to first approximation).

The darts fire fine though and seem to go fast enough.

Firing the darts this way makes a much higher pitched “pop” rather than the deep “thump” of the long barrel, because the shorter tube has a much higher resonance frequency.  Actually, I don’t know whether this arrangement is better modeled as a closed tube as I did for the long barrel in Nerf gun on the oscilloscope or as a Helmholtz resonator, which would have a resonant frequency of $\frac{v}{2\pi} \sqrt{\frac{A}{V_0L}}$, where v is the speed of sound (about 34320 cm/sec), A is the area of the neck (about 0.217 cm^2), V0 is the volume of the pipe between the valve and the neck (about 22 cm^3), and L is the length of the neck (about 9cm).  Hmm, the Helmholtz resonator is at about 180 Hz, and the pitch is definitely much higher than that, so perhaps an open-pipe model [Wikipedia’s article on acoustic resonance] is called for: $\frac{v}{2(L+0.3d)}$, which gives 1750 Hz.

## 2012 July 11

### Nerf gun on the oscilloscope

Filed under: Robotics — gasstationwithoutpumps @ 23:10
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In Nerf gun analysis and Nerf gun analysis, continued, I looked at the pressure drop in the reservoir as the Nerf gun was blank fired.  (I probably shouldn’t call it a Nerf gun—not only is it not made by the holder of that trademark, but the foam darts I’m using aren’t even Nerf-brand—they’re by NXT Generation.)

In this post, I’ll look at the sound at the muzzle of the gun as it is fired with and without darts.  Because I don’t have a storage scope, I had to do long-duration exposures in the dark to catch the single-shot trace.  This is old-fashioned technology—that’s the way everyone did it 50 years ago, as even the analog storage oscilloscope wasn’t introduced until the late 1950s or early 1960s, and didn’t really become popular until the 1970s. Of course, in those days oscilloscopes often had camera attachments that provided a dark box, so people didn’t have to work in the dark.  Polaroid oscilloscope cameras, which allowed people to see whether they had the exposure right, were a great improvement, and became very popular in the 1970s.

For detecting the sound I used used my electret microphone in series with a 12kΩ resistor and a 4-AA battery pack with rechargeable NiMH cells. The gun solenoid and the microphone were run off of separate batteries, so I didn’t need to worry about differences in the ground voltages for the two oscilloscope channels.

Here is a typical blast without a dart at high pressure (click on image for larger copy). The bottom trace is the pulse to the solenoid, and the top trace is the signal from the microphone.
I was working in the dark so couldn’t read the pressure gauge, but it was probably between 80 psi and 100 psi.
The blast of air reaches the muzzle about 32 msec after the solenoid pulse starts.

Note the resonance of the barrel after the initial blast.  The resonance for a closed tube like this should be $\frac{v}{4(L+0.4d)}$ [Wikipedia’s article on acoustic resonance], which should be 34300 cm/s / (4 ( 68.5 cm + 0.4 1.5cm) = 124 Hz for the barrel.  The period looks more like 8.5 msec than 8 msec, but the calibration of the scope time base is known to be off.

At lower pressures the blast of air comes out sooner.  It isn’t traveling any faster (the speed of sound is not changing), but the solenoid probably takes longer to open the valve against high pressure than against low pressure.  Since the sound should take about 2 msec to travel the length of the barrel, I believe that the valve is just starting to open as the solenoid pulse ends in the picture above.

Typical blast with a dart at high pressure (click image for higher resolution).
The pair of spikes about 24 msec and 29 msec after the solenoid pulse may represent the beginning and ending of the dart, followed by the blast of air (but see below).

If the dart is coming out of the barrel about 24 msec after the solenoid opens (guesstimated as 2 msec before the air blast arrives without a dart blocking it), we can estimate its speed very roughly by assuming a constant acceleration (unlikely as the puff of air it is riding is not a constant pressure source). The average speed is 68.5 cm / 24 msec = 27.4 m/s, so the final speed should be between 27.4 m/s (constant velocity) and 54.8 m/s (constant acceleration). At those speeds, the 8.3 cm dart should take 1.5 msec–3 msec to clear the end of the barrel.  The two spikes are between 4 and 5 msec apart, so either the dart is traveling much slower  (about 18 m/s) or I’ve mis-interpreted what the two spikes mean.  The lower speed isn’t consistent with how soon the dart leaves the barrel, but the spacing of the spikes is consistent with a half-period of the barrel resonance.

Based on this picture, I’m guessing that the Nerf gun has a muzzle velocity of about 40–50 m/s, substantially less than 230 m/s that was guesstimated for 100 psi in Nerf gun analysis, which assumed that all the energy of the air went into accelerating the dart.

I suppose that we could try measuring the muzzle velocity more directly by doing video analysis.  We’d need very bright sunlight and a contrasting background to be able to see the dart on a video zoomed out enough to capture the motion in 2 or 3 successive frames.  At 29.97 frames per second, getting the dart in 3 or 4 frames means having about 5 m of the path in frame, which would make the width of the dart only about 3 pixels.  Because my camera uses interlacing, that means that we’d alternate half frames of 1 and 2 pixels—probably not enough to be visible.

### Nerf gun analysis, continued

Filed under: Robotics — gasstationwithoutpumps @ 19:04
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In Nerf gun analysis, I computed volumes for the reservoirs and made conjectures about why the gun was not working well with the small reservoir and 19 msec pulses.  I had a couple of updates, where I first thought I had gotten the small reservoir working by careful orientation of the solenoid to be pulling with gravity instead of against it.  Then, when my son and I tried together (after he got home from theater rehearsal), that stopped working.  We tried switching to 25 msec pulses, which worked fine with the solenoid horizontal, but again had trouble with the solenoid vertical.

We did do a series of pressure measurements for the system with the 25 msec pulses:

Pressure drop per pulse for the system with small reservoir connected to the large reservoir by an air hose, firing with no dart in the barrel. Once again we see a linear pressure drop, indicating that a constant mass of air is moved in each pulse, independent of pressure.  This series is cleaner than the previous one, because the gauge on the pump was read close up always from the same position, reducing parallax errors.

Given the volume of the reservoirs, we can again compute the amount of air moved on each pulse:

component length (cm) diameter (cm) volume (mL)
barrel  68.5  1.5  121
reservoir  48.5  4  609.5
mini-reservoir  21  2  66
air hose  762  0.6  215.5

The total volume behind the valve is about 891 mL, and a pressure drop of 2.24 psi is 0.152 atm.  Using a density of 1.225 mg/mL at 1 atm, we have  about 166 mg of air being released on each pulse: a little more than before.

The gun seemed reliable with 25 msec pulses when the solenoid was horizontal, but still had problems when the solenoid was working against gravity, so perhaps we need pulses that are longer still—say 30 msec. We tried 30 msec and it seemed to fire ok even with the solenoid working against gravity.  We did a series of pressure readings  with the 30 msec pulses also:

Series of blank fires with 30 msec pulses with the solenoid horizontal. We are now releasing about 2.49 psi  * 0.06806 atm/psi * 891 mL * 1.225 mg/(mL atm) or 185 mg of air per firing (150 mL at standard pressure).

We should probably do another series with the solenoid working against gravity, so see if we can see a smaller air release in that orientation.

I did get the microphone setup working, and I could see that the air blast out of the barrel was starting about 5–10 msec after a 19 msec solenoid pulse was finished, which is much slower than it would take the air to travel that far.  The delay was smaller at lower pressure, so I suspect that what we are seeing is mechanical delay in the movement of the valve.  I’ll look at it again with the longer pulses, to see if the air blast now comes out while the solenoid is still powered.  It is a bit difficult to see the pulses, since we are looking a  single shot on an old analog scope, not captured by a digital storage scope.  Perhaps tonight when it gets dark I can try taking some long-duration photos and capturing the scan.

### Nerf gun analysis

Filed under: Robotics — gasstationwithoutpumps @ 13:52
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In Nerf gun progress I mentioned that the students hooked up a small reservoir behind the solenoid valve on the barrel to a bigger reservoir using an air hose for their Nerf gun prototype. They were switching from a design like this

Simple Nerf gun prototype with a large air reservoir immediately behind the solenoid valve.

to one like this

Design for new prototype with a small reservoir behind the valve, connected via an air hose to a larger reservoir.

Last night after the glue had dried enough, my son and I tested the new prototype.  As I had feared, it did not work well.  With the 19 msec pulse for opening the solenoid valve, the dart did not even exit the barrel, and a second pulse got the dart out of the barrel but traveling slowly, even with 100 psi in the reservoirs.  We have not determined whether a longer pulse would work, but we did try reconnecting the large reservoir directly and determined that it still works fine, so the problem is not with the solenoid valve, computer control, barrel, or darts.

I still like the idea of having an air hose to a bigger reservoir and the compressor, so that the pan-tilt mechanism does not have to move much mass around, and I’d like to help the students continue with that idea.

So in today’s post I want to do a little engineering analysis to help the students figure out what went wrong, so that they can start thinking about the redesign.  The pressure in the little reservoir was just as high as before, and the solenoid valve opened as wide for as long, but not nearly as much air came through the valve.  The pair of reservoirs have more total volume than the large reservoir alone, but air flow through the hose is somewhat restricted.  We’ll have to use some physics and make some crude approximations to figure out what is going on.

First, we’ll need some dimensions:

component length (cm) diameter (cm) volume (mL)
barrel  68.5  1.5  121
reservoir  48.5  4  609.5
mini-reservoir  21  2  66
air hose  762  0.6  215.5

Note: I measured the IDs of the PVC pipes with calipers, but for the air hose I relied on the markings on the hose. All the lengths are approximate, as I did not attempt to accurately account for the plumbing connectors. I’ve given the length and volume numbers to more precision than they deserve, given the low accuracy.

When we were firing directly from the large reservoir, we had once measured a series of pressures after each firing (using the rather low-resolution gauge on the bicycle pump):

Plot of pressure drop, which is approximately linear with the number of times the valve has been opened. Note: these firings were done without a dart in the barrel.  If the back pressure from having a dart in the barrel makes a difference, these readings may not represent what happens when darts are actually fired.

The 2.87 psi drop can also be thought of as a 0.2 atmosphere drop per firing of the gun. I was surprised that the drop in pressure was so linear. I had expected the flow rate to be linear with the pressure, so that we would see an exponential drop in pressure, rather than a linear one. I guess that the flexible membrane of the valve acts as a pressure regulator—the valve does not open as fast or as fully against a high pressure difference as against a low pressure difference, so we get about the same flow rate no matter what the pressure.

Another possibility is that the air is moving fast enough through a small enough hole that we are getting choked flow, which also seems plausible. But in choked flow the mass flow rate through a constant size opening would vary as the square root of the absolute pressure of the upstream side, which does not seem to be the case here, so I think that the variable opening size seems more likely.

So how much air are we moving on each firing? The density of air in the room is about 1.2 kg m-3 or 1.2 mg/mL. Thus each firing is moving about 0.2 atm*1.2 mg/(mL atm)*609.5ml = 146 mg of air, for a mass flow rate of 146 mg/19 ms = 7.7 g/s.  Air flow is often expressed in volume units (converting mass flow to volume as if the air were at atmospheric pressure), so this would be a volume of 122 mL and a volumetric flow rate of 6.4 L/s (about 13.6 CFM).

Note that barrel holds about 145 mg of air, so our firing was moving just enough air to fill the barrel at atmospheric pressure. That also means that the acceleration analysis I’ve done in the past (based on the assumption of constant pressure behind the dart) is bogus.  The differential pressure on the dart drops linearly to zero along the barrel, so the total energy imparted to the dart is only 1/2 the initial force times the length of the barrel.  With an area of about 1.77 cm2, the force on the dart at 100 psi (6.9 bar) is 122 N, so the energy added to the dart is about 42 J, which should accelerate the dart to about 230 m/s (not taking into account the losses due to friction or to pushing out the 145 mg of air initially in the barrel). Of course, for that to happen, the dart would have to move down the barrel in 6 msec, not the 19 msec duration of the pulse, so this energy-based analysis is probably faulty.

It might be a good idea to figure out some way to determine how long it takes for the dart to travel down the barrel.  Perhaps we could put a microphone by the end of the barrel, and trigger the scope on the rising edge of solenoid pulse, to see how much later the air pulse leaves the barrel, with and without a dart.  The speed of sound in air at standard temperature and pressure is about 343.2 m/s, and to first approximation the speed of sound is independent of pressure, so I would expect the pulse of air to reach the end of the empty barrel in about 2 msec.  With a dart in the barrel, the air blast should be slowed down, though the microphone should still pick up the pressure wave in front of the dart about 2 msec after the dart starts to move.  There should be a loud blast just as the dart clears the barrel, though, which should be detectable on the oscilloscope.

For the little reservoir, if we were taking 145 mg of air from it, the pressure would drop by 145 mg / (66 mL * 1.2 mg/(mL atm)) = 1.8atm or 27 psi.  According to a web-based air flow rate calculator, our 25′ air hose should have a flow rate of 4.9 CFM (2.3 L/s) with that big a pressure drop, so replenishing the air in the little reservoir would take about 106 msec (I doubled the time at 2.3 L/s, because the flow rate drops as the pressure drops, though not exactly linearly).  That is long enough that we can probably treat the firing has happening entirely from the small reservoir.

My biggest concern is that when firing from the small reservoir, we’re not getting the full 145 mg (122 mL) of air we need to fire the dart.  Given that the flow rate was nearly independent of pressure in our test firings from the big cylinder, why does firing from the small reservoir make a difference?  I’m not sure.

• Is it because of the behavior of the valve membrane as the pressure drops?  As the pressure drops the valve would need to open more to keep the flow rate the same, and there may not be time for that.
• Is it a resonant effect of the length of the reservoir?   so the decompression wave traveling back from the valve should be traveling at 34.3 cm/msec.  In 19 msec there is time for several round trips of the decompression wave in the cylinder even for the larger cylinder, so I wouldn’t expect any resonance effects to be significant.
• [Update  2012 July 11 16:45: The real reason!  The problem was not with the small reservoir at all, but with the orientation of the valve.  I was testing the gun (with the microphone) and with the solenoid pulling against gravity the gun was doing the same sort of feeble firing we saw with the mini reservoir, but with the big one! Turning the gun over so that the solenoid worked with gravity instead of against it fired fine. I don’t remember which way up we tested yesterday.  So I reconnected the small reservoir and tested again today, making sure that the solenoid was vertical in the right orientation (gravity assisting the solenoid).  The gun worked fine!  If we need to change the orientation, we may need to make the pulse longer, so that the solenoid can open all the way.]
• [Update 2012 July 11 18:00: It stopped working again.  I think we need longer pulses.]

We should probably make some mods to the small reservoir so that we can pump it up directly from the bike pump and do a series of test firings like we did for the large reservoir, to see how much air is released on each firing from the small reservoir.  We could also measure how far the dart moves in the barrel on a single pulse, to get a different estimate of how much air is released.

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