Gas station without pumps

2012 November 27

Magnetic fields with no lab

Last week we did measurements of the magnetic field around a single wire, and I had planned to “do a lab winding a helix of wire and measuring the field around it.  We’ll use the computational problem (18P79) to compute the expected field in different places, and try measuring the wound solenoid in corresponding locations.  This means that in setting up the program we’ll have to make the number of turns, the radius of the solenoid, its length, and the current through the solenoid all easily changed, to match the simulation to the coil that we wind.”

As it turned out, my son had the simulation finished and we spent most of an hour exploring what the program told us.  The initial picture showing magnetic field arrows near the coil looked fine, but I suggested trying a different visualization: having a particle trace out a magnetic field line.  We expected to see something like the classic pictures of iron filings around a bar magnet, and were surprised to see the magnetic field coiling out from the end of the solenoid.

We did a bunch of debugging.  We looked at at the contributions to the field from the different segments of the coil, by color coding arrows from a fixed observation position. The simulation had n segments for each turn of the helix, so we summed the segments mod n, to get the different contributions from the different parts of the helix.  We also tried varying the number of turns of the helix, and we played with the step size for the particle tracing out the field line.

We finally got some very nice drawings of the field lines coming out one end of the solenoid, spiraling out, then spiraling back in to the other end, and running through the center of the solenoid.  It took us a while to realize that the behavior was indeed what we should have been expecting, because the helix has current running parallel to the axis of the helix as well as around the helix.  A simulation (as the book suggests) using only circular rings would not have included this longitudinal current, and we would have missed some interesting views of the magnetic field.

I’m wondering whether we could have gotten a similar result by superimposing two fields: one computed from a stack of circular rings and the other from a wire down the axis, both with the same current.  I might try writing a program that compares the two approaches.

Because we spent an hour doing simulations and looking at the results, we did not get around to doing homework comparisons (a good thing, since I haven’t done the homework yet) nor did we get around to winding a coil and measuring the magnetic field, which I still want us to do.

2012 July 3

Nerf gun prototype 1

Filed under: Robotics — gasstationwithoutpumps @ 21:12
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The Santa Cruz Robotics Club met again today, for the first time in over a month.  The current project is not the underwater ROV (we’re all getting very tired of waterproofing problems), but an automated Nerf gun.

The club members came up with some very ambitious plans for the Nerf gun (which included getting a Raspberry Pi and doing image processing to have a self-aiming gun), but I’m making them build quick-and-easy prototypes to try out their ideas one step at a time.  I don’t think I can get an Raspberry Pi this summer—the companies doing the distribution aren’t taking more orders (just expressions of interest) and they don’t expect to clear the current backlog until September at the soonest.  They are doing batches of 100,000 units, and that doesn’t seem to be enough to shrink the lead time—if anything, the lead time is growing.

So, giving up on image processing for this summer, there are still a lot of things to build.  For today’s four-hour meeting (which included a 1-hour trip to the hardware store and a fifteen-minute snack break), the goal was simply to test out the basic launcher concept: an air reservoir pressurized by a bike pump, a solenoid valve, and a barrel.

The first prototype. The air reservoir is about 18″ of 1-½” PVC pipe on the left, and the barrel is about 24″ of ½” PVC pipe on the right.

The biggest problem was that the valve has ¾” male pipe threads, but we wanted 1-½” PVC pipe for the reservoir (because we had a piece handy—we may build a bigger reservoir later) and ½” PVC pipe for the barrel (because Nerf darts just fit inside—probably Nerf guns were prototyped with PVC barrels).  Our hardware store run was to get threaded adapters to make things fit.We wanted everything to be joined with screw threads, so that we could disassemble the components and replace them or add elbows as needed.

Note that the ½” PVC pipe is also a good size for compressed-air paper “rockets”.  The term “rocket” is a misnomer here, as all the acceleration occurs while the rocket is on the launcher—it is modeled more like a gun than like a rocket. (But my soda-bottle rocket simulator can model these paper bullets also.)  It would probably best to have a shorter barrel for doing rocket launching—just the length of the rocket and no more, since the longer barrel results in more pressure loss with no gain in launch speed.

The bicycle valve glued into a ½” female-threaded end cap was one I’ve had for a long time, as part of a soda-bottle rocket launcher. I had two of them, and both failed in testing today (the Barge cement holding the valve stem in failed—we’ve now reglued them with a different cement), though we managed some testing before the failure.

The solenoid valve we used was the same model (sold by Sparkfun) as the one used for the vacuum bottle on the ROV.  It has ¾” male pipe threads on each side.  To make it air-tight we had to disassemble it and grease the rubber membrane thoroughly with vaseline or faucet grease, but we had done that months ago, so it did not need to be done today.  The valve only works in one direction, but the high-pressure side is clearly marked by a metal intake screen, so assembling it the right way around is easy.

I was not sure that the solenoid valve would work in this application. It is not the model of valve that the compressed-air “rocket” people have used—those valves cost about twice as much and have female threaded ends rather than male threaded ends. I think that the mechanism they use may open up a bigger channel for air or water than the cheap solenoid valve sold by Sparkfun.

My first concern was that I did not know whether the valve would open up wide enough and fast enough to let a blast of air through to get a clean launch.  Second, I did not know whether we could open and close the valve fast enough to retain pressure in the reservoir for doing multiple shots.

We controlled the solenoid valve with an Arduino and the Hexmotor motor-control board (which is really overkill for one solenoid—a single power transistor would be enough to interface the Arduino to a solenoid, but I did not have one handy).  My son wrote an Arduino program to allow us to experiment with the duration of the solenoid pulse.  If it were too short, the Nerf dart would not leave the barrel.  If it were too long, air pressure would be wasted.  He allowed for 100 µsec increments in pulse duration, under control from commands on the USB serial line.

Because the glue they used takes 24 hours to set properly, we only tested at low pressure today (20–30 psi).  At those pressures, a 16 msec pulse was not long enough for the dart to clear the barrel, but a 19.2 msec pulse was easily long enough. We were also able to launch a 14g paper “rocket” left over from Maker Faire, though it did not go as high as the approximately 1.6g “Nerf” darts (I think several of the foam darts we have a different brand). We would not have expected it to go as high, since it was only accelerated for its 11″ length, not the 24″ length of the barrel for the darts, and it weighed a lot more.

One thing I thought about was monitoring the air pressure in the reservoir electronically. I doubt that we’ll put a pressure sensor in the reservoir, though, as the sensors I have only go up to 250 kPa absolute (about 21 psi above atmospheric pressure—about as low as we could fire with).  Freescale makes a 145psi (1000 kPa) sensor, the MPX5999D, but it is a differential sensor without port tubes (so would be difficult to mount) and it costs $13.

Perhaps the other thing worth doing today is to analyze how fast the Nerf dart should be going as it leaves the barrel, and how high it should fly if we shoot it straight up.  The physics here is fairly simple, if we assume that opening the solenoid valves connects us to a constant-pressure source. (In practice, we saw about a 10psi or 70kPa drop in pressure after one shot. If the pressure is P, then the force on the dart is P*area.  The cross-sectional area of the foam dart is a little hard to measure, because of the squishiness of the foam, but the inside diameter of the barrel is 1.45cm, for a cross-sectional area of 1.65 cm^2. At 140 kPa (about 20 psi), the force on the dart would be 23 Newtons.  That force is applied for about 60 cm (the length of the barrel), for a total energy of about 14 Joules.

We can use the kinetic energy of the dart to get its speed (E = ½ m v2), so for 140 kPa, the dart should leave the barrel at about 130 m/s or 290 mph. I suspect that we are not getting anywhere near that speed, for several reasons, including leakage of air around the dart, limited speed of air moving through the valve, and friction of the dart in the barrel (mainly from the pressure wave in front of it, but also from rubbing on the sides of the barrel).

We can also use the kinetic energy of the dart to estimate how high it would fly (ignoring air resistance, which is obviously hugely important for a low density object like a foam dart). The potential energy of a mass at height h is mgh, so the height it would go without air resistance is E/(mg). For 14 Joules and 1.6 grams, that would be almost 900m. I think that 20m is a more reasonable estimate for the height the dart went, though I never could see it near the top of its trajectory.

I tried adding the specs for the Nerf dart and a 60cm barrel to my rocket simulator (to get a crude estimate of the effect of air drag), and for 140 kPa I got an estimated max speed of 132m/s and an estimated max height of 52.6m. I don’t know if that height is reasonable—certainly it is better than the no-air-resistance estimate. The 6.78 second estimated time of flight seems to be fairly reasonable, though we never timed it.

Doubling the pressure increases the maximum velocity by a factor of 1.414, but only increases the maximum height to 60.8 m, a 16% increase. Doubling the barrel length has about the same effect. Air drag is what determines the speed of the dart, and that is the least well-modeled part of my simulation.

On Thursday, when they club meets again, they’ll try experimenting with higher pressures, and see whether 17 or 18 msec pulses are long enough—the shorter the pulse the less air will be wasted, and the more shots they can make from the reservoir.  It may be necessary to design a bigger reservoir or add a compressor to the design, since they eventually want a fully automatic Nerf gun, not the one-shot muzzle-loader that they made as the prototype today.  They’ll also start designing a pan-tilt mechanism for the Nerf gun, probably prototyping it out of Lego Technic components.

2012 April 25

Photoeletric effect

Filed under: home school — gasstationwithoutpumps @ 16:30
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Brain Frank has just posted an exploratory exercise on his blog Teach. Brian. Teach.: Photoeletric Effect.  This exercise relies on a simulation from the University of Colorado at Boulder.

The simulation is of a standard phototube experiment.  A phototube is a vacuum tube diode, in which the cathode is illuminated by a light source.  The photons excite electrons in the cathode, raising some of them to high enough energy levels to become unbound from the atoms and leave the cathode.  The electric field accelerates them toward the anode (or repels them, if the diode is biased backward).  The energy of the electrons is basically the energy of the photons minus the energy needed to raise the electrons from the ground state to the unbound state.  (At very high illumination levels, you can have one photon exciting the electron out of the ground state and another raising it to the unbound state, but I don’t think that effect is being simulated.)

At forward voltages, the current is determined by the illumination, independent of the bias—essentially all the released electrons go to the anode. At reverse biases, only the higher energy electrons have enough speed to make it to the anode. The energy of the highest-energy electrons can be estimated from the reverse-bias voltage at which the current drops to zero.

The simulation seems pretty good, but I don’t know exactly what effects they are modeling.  For the zinc target with high forward bias, there is a current peak around 135 nm, but from the spectral lines at NIST, I would have expected a peak around  127 nm.  I don’t know if the problem is a limitation of the simulation or a limitation of my understanding.

I know that my understanding of quantum effects is very limited, and the simplistic view of the photoelectric effect given in Wikipedia does not cover some of the phenomena being simulated here.  But since I don’t know exactly what phenomena are being simulated, I have no way of predicting the behavior.

I find it frustrating to do the sort of discovery experiment that Brian is proposing using a simulation.  If I knew precisely what was being simulated, there would not be much discovery, but trying to reverse engineer a simulation from its behavior seems to me a rather irritating and frustrating exercise. I not only have to guess at what physics is important, I also have to guess at what physics the writer of the simulator thought was worth including, and what simplifying assumptions he made.  (For example, is the simulation including the absorption of the glass or quartz tube holding the vacuum?)

I suppose I could read the source code (PhET provides that) or read the 17 “Teaching ideas” on the web page for the simulation. The teaching ideas look like a wide range of different lesson plans for labs, demos, and homework questions.  I looked at one of the “advanced” ones, but it seemed to only use the Wikipedia-level model, which does not explain a drop in current with shorter wavelengths.

I’d much rather have real experiments than simulated ones—even if the crudeness of my measurement tools limits the quality of the data I can collect.  The value of simulations is more in writing them and seeing that they predict the behavior you observe than in running someone else’s black-box model.

2011 January 16

Visual 6502 in JavaScript

Filed under: Uncategorized — gasstationwithoutpumps @ 20:10
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There is now a hardware simulator for the 6502 processor written in JavaScript with a beautiful visual display. It would have been nice if they had been able to do a bit better simulation, to include some timing information (like the rsim simulator we used back at about the time that chips like that were being designed). Seeing this brought back some fond memories of my days teaching VLSI design, though I think I’m now happier teaching bioinformatics (and I’m certainly no longer current in VLSI design).  The 6502 was a fine processor at the time, and Motorola produced much more elegant chip masks than Intel did.  The 6502 was designed by an engineer from Motorola who had worked on the 6800, but Motorola did not want to sell a low-price chip, so the engineers left for their own company.  The 6502 is probably best known now for its use in the Apple I, Commodore PET, and Apple II computers.

This is the image of the 6502 that is animated on the Visual 6502 website.

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