Gas station without pumps

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.

1 Comment »

1. […] 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 , where v is the speed of […]

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