Towards Mid-Junior Year

The end of the semester is in sight. Unfortunately the Thanksgiving holiday is right in the middle of some major lab assignments so I have to see that I get those mostly completed this week even though they aren't due till after holiday.

A brief overview of this semester's studies:
The circuits class has consisted of op-amps, diodes, and MOSFETs. Still to come is a section on BJTs. The lecture is great but the lab has been a huge amount of work. We still have 2 more lab assignments to do and they are very involved.

This semester's signals class was not so enlightening as last semester's but still good. Topics included sampling, modulation and transmission (mostly AM), feedback systems and root locus analysis. The LabView assignments aren't particularly exciting for me but hopefully I'm learning something.

My affection for VHDL seems to oscillate between positive and negative. I have been excited about it and hated it but right now I'm feeling pretty good about it. I like working with VHDL more than with software programming languages.

Random Signal Analysis, hasn't had much to do with signals at all yet. It's an introduction to discrete and continuous random variables regarding probablility, expectation and variance.

As I go into my last 3 semesters I plan on taking 3 more circuits courses, digital signal processing along with another signals course on filter design or some such, and properties of electronic materials. Oh yeah, next semester I have to take economics too, maybe it will be enlightening.

jellybeans

I've been stumped on this problem all weekend:

A candy factory has an endless supply of red, orange, yellow, green, blue, and violet jelly beans. The factory packages the jelly beans into jars of 100 jelly beans each. One possible color distribution, for example, is a jar of 58 red, 22 yellow, and 20 green jelly beans. As a marketing gimmick, the factory guarantees that no two jars have the same color distribution. What is the maximum number of jars the factory can produce? (Hint: Think of lining up the jelly beans, by first placing the red ones, then the orange ones, etc. You also place 5 dividers to indicate where one color ends and another starts. Note that two dividers can be adjacent if there are no jelly beans of some color.)

What do you think?

The Story of a Trombone (the wonders of steel wool)

Twelve years ago my sister-in-law Brenda, knowing that I was very interested in musical instruments of all sorts, gave me a trombone that she had played in high school. This trombone was in a fire and had suffered major cosmetic damage in addition to the case being destroyed and the mouthpiece lost; the thing was ugly.






















In an attempt to make it more presentable, I put it in the bathtub and tried to scrub the scum off; soap and water did nothing. After giving up on making it look better, I turned my focus to how it sounds. I got a mouthpiece for it and I even lucked out by getting a free case. The case, while a little bit used and shabby, looked like a dream compared to what it protected. After just a little bit of maintenance the instrument worked just fine and I proceeded to learn how to play it for a few months as a curiosity.

After a little while, it got tucked away in a corner and there it waited for many years until this year because Shule has decided to join the middle school band. Over the summer, Shule and his band director decided that he would start on the trombone. Marisa overruled my idea to send him off to school with something that looked like it was just pulled out of a landfill. She's totally right too, I fell in line quickly because in those awkward times of middle school, it may be best to not create extra opportunities for ridicule.

There was talk of renting or buying an instrument but I was developing an idea to avoid that if possible. When I came home with steel wool and a smile on my face Marisa gave me a look as if to say: "I'll humor you for a little while, but if this doesn't work we're going back to the original plan".

The finish on that trombone was cooked and in many places it was charred not just on the surface but deep into it. I worked on it for 3 days and my hands ended up sore and discolored but it worked. While I was at it I smoothed out some of the dings.


This shot was taken halfway through the process for comparison. Notice how good the bell looks next to the unfinished slide.

I can't say it looks new, but it looks like an instrument that's been used and cared for. This definitely beats buying or renting one, most rentals probably don't look this good. Since I've invested some toil, I've developed a new attachment to it and Shule is even happy to announce: "my trombone has survived a fire!".

A car trip

but Shule stayed awake.

Renaissance Festival

Shazer won some tickets to the renaissance festival a few months ago. We finally used them Saturday March 28th. I took Shule and Shazer, it was the first time for all of us. We walked around a lot and saw a lot of shows, including: pipers and drums, humorous clowns, jugglers, a whip cracker, a large fowl show (falcons, owls and vultures), and jousting. Along with the numerous shows there was ample opportunity to spend a lot of money on all manner of crafts, clothing and food. We just window shopped as we walked around the park in between shows. A few things that stand out from wandering around the market were the ladies spinning wool into yarn, weaving fancy tapestries and the blacksmith with a very impressive bellows stoking a very hot fire. The boys had a good time, Shazer especially is interested in the sword fighting element so he was excited to see the dramatic jousting presentations (see video below). Shule liked the jokes that the jugglers told. He got tired but I convinced him we should stay longer and we would get to see some interesting things that we wouldn't see anywhere else. He stuck it out. Please view the full web photo album.

light is a bandit

I've started learning about special relativity in school. I've heard a little about relativity in the past and had previously developed a sort of blind trust that space and time are relative to frame of reference, or something like that. I knew that if you go really fast then time doesn't pass at the same rate, I had no clue how. Recently when working with optics I read that light travels away from the source at a constant speed and even if you were moving away from the source, as far as you are concerned, the light still approaches you at the same speed. This concept totally blew my mind because as you all know: when someone throws a ball at you and you run away, it then appears to you that the ball is coming at you slower than if you just stood still. If the ball behaved as light does then as soon as you start running it would speed up to its initial speed plus your speed. So how is light an exception to the laws of mechanics? Maybe it has something to do with light being a wave of energy stored in electric and magnetic fields, also light has no mass like a ball does. It turns out that this curious behavior of light is Einstein's second postulate of special relativity and because of it, crazy things happen. Things I don't yet understand so I won't try to explain.

I do however want to share what I think is an interesting example of current in a wire from 2 different inertial frames of reference. We have observer 1 who is stationary with respect to the current and observer 2 who is moving with the same direction and velocity as the current.

Observer 1 experiences a magnetic field (it can be calculated by Biot-Savart, or Ampere's Law).


If we imagine the current as individual positively charged particles then to observer 2 the so-called current becomes an electrostatic line of charge.

Observer 2 would experience an electric field due to these charges (we find this by Coulomb's or Gauss' Law). This might lead to a nasty disagreement between the two observers as observer 1 would insist that there was a magnetic field and observer 2 would be quite certain that it was actually an electric field and they both would be right. I must give credit to Gary Adams who showed that to me (and 170 other people in the room) last semester and is a really great physics professor.

Radio in my Head

Introductory note: If you are not a very big Radiohead fan I don't expect you to explore all the links in this post but please if you do anything, go here! (I'll remind you again at the end.)

I'm interested in how bands form, I like to read about how groups got started. It's an interesting thing that when I want to find out about a band, the first place I go is Wikipedia. I find that you get a good summary of historical information on groups whereas if you go to the artists official website you usually just get the latest news and things that don't interest me as much. I'm interested in the humble beginnings, the ugly past, the trials and failures gone through before the big break. Wikipedia will usually give you a good start but if you want to know more you have to search for in-depth interviews or maybe someone's put out a book on the band. I've been getting more into Radiohead lately and they have the most confusing official webpage of any band I've seen. None of it really makes sense to me and I can appreciate that maybe the band just wants to express themselves a certain way, they are entitled to it, I just don't get anything from visiting. Since their site left me unfulfilled I searched for content elsewhere and found it.

On youtube there are some videos of the band doing a sort of house concert videocast performance. Actually it looks like they did one on Nov 9 2007 and another Dec 31 2007. The former was entitled "Thumbs Down" and the latter "Scotch Mist". In fact, "Scotch Mist" is a 52 minute video available on youtube including performances of all the songs from their new album. These are live performances but the band is just set up in a house somewhere and the audience is on the other side of the podcast. I totally love it. The Thumbs Down session included them doing covers including The Smiths "Headmaster Ritual" and Joy Division "Ceremony" among others. So maybe you don't want to devote a few hours watching these videos, I understand that. You can also view individual tracks, Radiohead actually has a good youtube profile with some of the songs listed separately. (I just want to squeeze in another link the song there there, a really good video from a live concert).

Portishead also did a similar videocast just before the release of their newest album. The video is called "Portishead in Portishead" I believe. It was available till the release of the album but I've found that if you go to their official site you can register your email with them and they will allow you access to the video. This one was also captivating to me, I loved watching their New York live video, some musicians are just fascinating to watch. They do such interesting things with vintage keyboards and old tape echo effects.

I've been walking around with "Jigsaw Falling Into Place" in my head. It's on Radiohead's latest "In Rainbows" album. I learned the guitar part and fooled around with working the song up myself but I have the problem that my voice is not high enough. Makes me a little frustrated but I've encountered this frequently so I have a procedure: I consider falsetto, I consider transposing, I consider whether it just wasn't meant to be, I try harder to extend my range. The first 3 options have been successful enough to keep me content in the past but the last one still hasn't ever come through for me as well as I want it to. If I end up working it out I'll post a video and you can witness for yourself me trying to fake my way through it.

So in writing this post I have come across yet another set of wonderful performance videos for VH1 Live From The Basement. Much like the other videos mentioned but a little smoother around the edges and with a few different songs. I highly reccomend Where I End and You Begin, this is the link I mentioned at the top and you can see Jonny Greenwood playing the unique instrument the Ondes Martenot, you can play it similarly to a theremin. I've overloaded this post with links and I realize I've gotten out of hand so I'd better end it now. I hope there is music out there that gets you as excited as this gets me.

Pinewood Derby happy conclusion

Just after submitting a school assignment that had been giving me anxiety for the past week, I rushed to put the wheels on the two cars and get to the race in time. I always think that the next year I will be ahead of schedule but I always end up finishing right before the race.

Shule ended up winning the race with his toad car driven by a pokemon! This is great because this is his last year so he went out with a bang. I was surprised to find that although Shazer's car didn't do too bad, it was not as close as I thought it would be to Shule's. I inspected it after the race and it turns out that there was a problem with one of Shazer's wheels, there was some glue involved in the final preparations and some got on the wheel. When we left the house I checked that the wheel was spinning freely but I guess the glue wasn't totally dry and in transit some must have seeped where it shouldn't have been. Considering this handicap, it did well and Shazer still has 2 more Derbies to look forward to. His sleek design won the "Most Dynamic" award.
You can see here that before painting, I masked the car around where the wheels go. I smooth this area and apply graphite because the back of the wheel rubs here.
Last night I put the weights in and smoothed out the wheels. I didn't have a scale so I used Shule's first car as a standard and I pieced together a balance with a ruler and a jar of paint.
This simple balance turned out to be quite accurate! When we got to the race the cars were right on and no adjustments were made. The race went quickly; there were only 11 cars this year. All the fuss has paid off and Shule will get a trophy next month at the Blue and Gold banquet.
This is a video of the winning race, look at the left side of the screen at the very end of the video, Shule and Shazer give each other a high five. That's the best part and I nearly missed it.

Physics of the Derby *Bonus*

Here is a bonus post on my thoughts on the physics of a pinewood derby car rolling down the track.

There is really only one thing that makes the car move-gravity.
I drew a simplified diagram of the situation. I simplified the car to just a point mass. There are 3 forces on the car: mg- the force from the gravity of the earth, N- the normal force from contact with the track, and f- the frictional forces acting opposite the direction of travel.

The car only accelerates in the downhill direction of the track, I have designated this direction as the +x direction, which makes the normal force in the +y direction. The only force with a component in the direction of acceleration is mg, we can break it into x and y components to get a better look at what's going on.

Since the car doesn't move in the y direction we know that the magnitude of mg in the -y direction is equal to the magnitude of the normal force in the +y direction and those forces cancel.

We are now left with only x forces:

We want to sum these forces and set it equal to ma, or mass times acceleration by Newton's famous F=ma. So we watch our angles carefully and discover that the magnitude of mg in the x direction is mgsin theta.

The rolling frictional force from the wheels on the axle and wheels on the track can be represented with a constant k multiplied by the magnitude of the normal force which is the same as the y component of mg. If we assume that the race will take place in a vacuum then this is the only friction that we need to consider. This gives us an interesting result:

The acceleration of the car and thus how fast it will go down the track does not depend on the mass of the car! Reducing the friction of the wheels is the only thing you need to do to build a fast car. So why does everyone say that if you add weights to your car it will help you go fast?
Well, it might be that I have neglected important factors in my simplifications. I should put the race back in an air filled environment so the spectators don't have to bring their own oxygen. This will introduce another frictional force from the air but from what I've seen so far in my classes, this force has little effect in many cases and often times is neglected. Either we have in vain been putting weights on our cars for years or conventional wisdom is correct and air drag makes enough difference for us to bother with attaching weights.
It all depends on what the coefficient of friction is, which I believe involves the density of air and the shape and density of the car. This can be found experimentally. With that term added our expression now looks like this:

The force of the drag is proportional to velocity. This makes me very curious now and I want to get that track and do a bunch of tests with varying weights and other things to find out how much effect this really has.
The placement of the weight may have something to do with the stability of the car also, to figure all these things out I'd have to do a more complicated analysis and look at the car as something more than just a point mass. I'm not going to do this, and now that I think of it, the urge to do a bunch of tests is leaving me too. I'm feeling content enough to just get those wheels turning smoothly, put weights on the cars till they are 5 ounces and enjoy the race.
I would like your input on the matter though. If you happen to have any insight on these things please let me know, I'm sure I've missed something.

Pinewood Derby part 2, axles and wheels

The nails that make the axles have a few bumps on them out of the box. To smooth them out I mount the pointed side of the nail in the end of a power drill leaving the whole surface that will contact the wheel exposed.

I spin the nail and first use a small file to get the bumps out.


That's just not going to be smooth enough for me though so I will then start using sandpaper, keep doing it over and over with a small strip of increasingly fine sandpaper.

If you look in the paint section of the hardware store you will find some pretty fine sandpaper. What I have is 600 grit wet sandpaper. I've heard of finer sandpaper but Home Depot didn't have any. This will give you a pretty smooth nail. I also like to make sure that the underside of the nail head is smooth, that area will also contact the wheel.

There is a theory that if less area of the axle comes in contact with the wheel it will spin faster so some people make grooves in the nail, reducing the area of the wheel in contact with the nail. I'm not convinced this does anything because friction depends on the mass of the car and the coeffecient of friction of the materials which are rubbing and it does not depend on the ammount of area in contact. If you reduce the area in contact, you also increase the load per unit area so it all evens out. Another "myth" that I've seen searching the internet and heard a few fathers talking about last year is that if you raise one wheel up so it doesn't touch the track it will make your car faster. By the same reasoning I say this is false and while I've witnessed fast cars that only have 3 wheels touching, I think it could make your car a little more shaky. So I'm going to stick with what I've learned from Newton.

After getting super smooth axles you should think about the back part of the wheel that will rub against the car, smooth this out and apply graphite here. Also put graphite on the part of the car that touches the wheel here. One more thing that I just thought of this year is the rubbing of the inside of the wheel on the raised part of the track that keeps the car in the lane. I'm going to make sure that part is smooth as well.

Wow, do I sound obsessed or what?
Hope this is helpful to someone out there.

Pinewood Derby 1 of 4

The pinewood derby is a model car race for scouts age 8-10. It's a simple wooden car with plastic wheels held on with nails as axles. They roll down a sloped track accelerated only by the force of gravity. The key is to make the wheel movement on the axles as frictionless as possible by smoothing out all surfaces that the wheels may rub against.
This will be my third pinewood derby as a scout leader. The race is two weeks away and the last two years my son Shule has been in the program so we made cars together. The first year he made the "Mammal Mobile".
He decided to make it brown and green camouflage with yellow eyes in front. The pink sticker is just for identification purposes during the race and wasn't part of the design. It wasn't a bad car but we got to the race as it was starting and didn't have time to apply any graphite. This was a disastrous move and I'm pretty sure his was the slowest car that year. Each time it went down the track you could hear the squeaking of the un-lubricated wheels. His was the only car that sounded like that! I felt so awful but he won the "best paint job" award and went home not totally devastated.

With lesson learned about how important graphite on the wheels is the next year was much better. He made the "Titan" which was to resemble a ship. He placed 4th out of about 18 and it was really very close. This is his car on the right just coming in short of the second place winner in red. You can imagine how close he was to the third place car.

The derby is the biggest and potentially the funnest event of the whole Cub Scout year, it doesn't come without stress though. The biggest issue I have with the race is that building a suitable car is not a job that most 8-10 year olds can practically do. It is almost totally necessary to have help from family and scout leaders which is fine but because of the competitive aspect (trophies are awarded to top 3 places) it just gets a little weird knowing that the boys don't all get equal ammounts of adult help. In order to combat the potential injustice, our troop devotes 3 January meetings to working on the cars together so kids without access to tools and help at home can have a chance for adult leaders to help. Seems like a good idea but what we can do is still limited and we mostly just get the cars shaped and sanded which has a neglidgible effect on how fast the car is. Getting the wheels straight, spinning smoothly and the cars weighted up to 5 ounces is what makes most of the difference and these are the last things you do.

When I was a kid I remember participating in 2 derbys, I vaguely remember a red car and a blue car. I remember working on my back porch with the block of pine and a hand saw. I made a cut that looked fine from my angle but it turns out that it was croocked and the cut on the other end of the block went partway through where the axle was supposed to go. I was very upset and felt that I ruined my car. Tears were shed. Later I did get help to salvage it and we were able to make it so the wheel would stay on and I could race it, but I never had one of the fast cars. It was ok that I never placed, I would have liked to but looking back on it I'm glad I even knew how to use a saw by myself even if I couldn't cut straight. My boys aren't good with a saw, I think most 8 year olds who aren't raised on a farm or in a woodshop or something won't have the muscle to properly use a hand saw and heaven knows we won't let them get their hands on power tools. I don't even know how to use a power saw.

So I let my boys design the car, I cut it with the hand saw and they help with sanding and painting. I have them help a little as I spin the nails in a drill and smooth and polish them. I try to explain about reducing friction and why we do these things but until the race is actually happening, they pretty much only care about making their car look cool.

This will be Shule's 3rd and final race, but I now have Shazer in the program so we are doing 2 cars this year and we have brother against brother which adds a whole new level of competetion. So far we have the cars cut and have started to do some sanding. Shule's toad car is to the right and Shazer's rocket style car to the left (facing away from the camera to show off the fancy rear).I will do 3 more posts about the derby, one next week all about getting the wheels and axles ready for speed, I'll post some photos and share what tips I know. Then I'll do a short post just before the race to show how the cars turned out and another just after the race with the results of course.