Sunday, March 21, 2010

Better Finish Than I Thought (still a bad place)

I had an interesting race today. I think it showed some things I'm not so good at, some things I'm good at, and some things I've improved on since last year.

I didn't get an especially good start. Since the race was posted at 50 minutes, the start is very important, and the course I was racing on today, in Soaring Eagle County Park, is almost entirely on singletrack. The Sport class started in waves, as always. My age group is 19-29 men; today we started after the 30-39 men, the 40+ men and the single speed men.

Anyway, pretty early on in the first lap I bumped into something and came out of my pedal. Two of the juniors had chased onto the 19-29 group, so when I got underway again I was behind them. The rest of the 19-29 guys opened up a gap on the juniors, but by then we'd already run into the back of the three classes that started before us. The juniors were doing a pretty good job of chasing onto other guys and then passing them, and they were riding very close together and at a pretty good clip, so I didn't try to pass them. I finished the first lap still following them, and then passed them on the short fire road section at the beginning of the course. I never saw them again.

I spent the rest of the race more-or-less alone. I'd chase onto someone, catch my breath a little bit, and then pass him. Riders were closely spaced enough that I usually started catching glimpses of the next guy right away, and I'd close the gap and repeat. It can be hard to tell the difference between a 30-39 rider and a 19-29 rider from behind, so I had no idea if I was still behind the rest of my field, or if I'd worked my way into it. I knew I was going at about the fastest pace I could sustain for an hour, and I was afraid I was going faster and might bonk at some point.

That was the second lap of the race through about the first half of the fourth lap. In the second half of the lap, there are some creek crossings and steep, loose ascents, including one I've never been able to ride up.

I was in that climbing/descending section when I chased onto the last older guy I passed. He was just losing his place on the wheel of two guys in my class, so I ended up a little bit behind them when I passed him, and I'd just managed to get ahead of them when we got to the run-up. There was already a guy pushing his bike up it when we got there, and I abandoned any idea of trying to get it done on the bike when I saw him. I dismounted and ran past him, then didn't manage to clip in but did kick my pedals on the remount. I missed them again on a couple more attempts, the two guys I'd passed just before the run-up and the guy on the run-up passed me, and then I managed to get back in. There are no more climbs before the fire road finish, which is a gradual climb, and the trail is particularly tight and twisty, so I spent the rest of the singletrack following them.

The turn onto the fire road is very difficult. It's a very sharp right-hand turn, and the fire road is paved with gravel, so the traction's not very good. Just to make it more interesting, there's a big rock at the outside of the turn, with a narrow slot to the left and another rock, then an irrigation ditch. There are three ways to make the turn. I opted for the tightest, slowest line, going through the big gap.

The last time, I clipped out and dabbed when I made the turn, then had trouble re-finding my pedal and getting back in. I still made the turn a little faster than the guy ahead of me, who took the outside line and had some trouble with it, so I got up and hammered until we crossed the line. I may have had about half a bike length on him; our times are recorded as 1 second apart. When the results went up, I was 8th out of 9 riders in my class completing the race. A tenth guy started but didn't finish. I didn't realize the two other guys in our little group of four were also in my age group, although there's nothing I'd have done differently if I knew.

I think that the two biggest factors preventing me from getting a better place in this race (and I would only have had to do the race 11 seconds faster to finish two places better, or 24 seconds to do three places better) were that I didn't start aggressively enough and that I lost time on minor technical errors. One problem that I think contributed to making some of those mistakes and also made them cost me more, was that my pedals were worn out, and not retaining my foot as well as they should.

On the positive side, I spent laps two through four going really fast, and I managed to keep my pace up for that whole period. My finishing time was 1:29:20, a lot longer than the posted 50 minute race time on the announcement. It would appear that I've been overthinking my longer races a little, and can actually spend an hour and a half at what I thought was my one hour pace. On the other hand, I did do the first lap at the juniors' pace, working through traffic. I don't know how much time I lost following them, but I had to have been going faster than the three guys I chased onto at the end for the balance of the race, or I would never have seen them again.

I also managed to keep the rubber side down for the entire race and even capitalize on the mistakes of others a few times. I wiped out in some races last year, so that's an accomplishment for me even on a relatively easy course.

I've installed my spare pedals pedals, so now I need to keep spending the training time I have on the weekends riding trails instead of roads, and start more aggressively whenever I go racing.

Monday, March 15, 2010

Frame of Reference

I think I drew this picture when I was trying to solve the problem, and I thought, when I got my test back, "This is a great example of using primarily visual thinking to solve a physics problem." The problem was to figure out the speed of a point 'B' located at the front of the rim, where I was trying to show the vector for velocity. The rim is on a bicycle that's traveling at 10 m/s; the wheels are rolling without slipping.

Wednesday, March 10, 2010

Physics, Visually

One of the things I enjoy about Newtonian Physics is that it's all about concrete, relatively human-scale phenomena - things that I can draw. I get a kick out of trying to put a little fun and realism in the sketches I make in my physics homework of the problems, almost all of which I start by drawing or diagramming.

A lot of intelligent people I know are intimidated or "don't get" higher math, but I think that the operations themselves are nothing those people couldn't do. I think the problem is the abstraction of describing things with numbers instead of as themselves. I think that a lot of physics can be done in a numberless, if somewhat tedious, way, using Euclidean geometry - until non-conservative forces like friction and air resistance are allowed to screw everything up, it's all about vector math and vector math is all about line segments and similar triangles. Most physics problems happen over time, something that can sometimes be problematic to describe well in words but often translates well to a series of pictures.

So I wondered if I could express Newtonian Physics in the format of a comic book, and it got me sketching. The following are attempts at Newton's three laws.

I knew I wanted a sense of motion in the picture, so I drew foreshortened arrows on a trajectory that would take the hockey puck out of the page and send it whizzing past the viewer. A lot of physics is less apparent in the real world because things like friction and air resistance screw it all up. A small object on ice experiences negligible friction and air resistance, so it's under those circumstances that one might see an object in motion tending to stay in motion. It's a mark of Newton's genius that he realized that that's the rule and overturned the previous idea that continuous application of force was needed to keep an object in motion.

In this panel, we see a tug boat pulling a barge. The tug exerts constant force, and the change in the barge's velocity is proportional to the force and happens in the same amount for any given period of time. As the amount of time approaches zero, the change in velocity becomes the rate of change, acceleration. It's actually quite difficult to find a "clean" example of this in real life. For example, the tug boat and the barge are in an environment in which the faster they go, the more counterforce is exerted against them by the water. At some point, they'll reach a speed at which the counterforce from drag and turbulence is equal to the force that the tug boat can develop. I suspect that the tug boat's propeller also develops less force as the speed of the water around it rises, but I haven't studied fluids yet.

Another example of this phenomenon is what happens when a stagehand leans against a heavy box with good casters. (I realize the good casters part almost never happens, but bear with me.) The box will begin to move. If the stagehand continues to lean on it, the box will accelerate. If the stagehand tries to keep up with the box while maintaining the same angle of lean, he'll continue to exert about the same force, the box will keep accelerating, and sooner or later he'll fall into the orchestra pit. I thought that tug boats might be more relatable than road cases, though.

Finally, this is Newton's Third Law. I was trying to think of a concrete example for a while, and nothing was coming. Then I realized that the calf stretch where you push against a wall has three matched pairs of external forces on the body of the person, here dressed as a superhero, doing the stretch. The wall pushes back with a force equal to the push, first of all. Otherwise either the person would fly backwards or put his hands through the wall. That push has to originate somewhere. That somewhere is his feet, pushing back against the ground. The ground pushes forward with static friction. Finally, the superhero has weight, pressing down into the ground. The ground pushes back with an equal force. That equal force is called the "Normal Force," denoted 'N.'

It occurred to me after the fact that I didn't really express that the forces in those pairs are equal. If I were to actually do this, I think I'd just use the little slashes used in Euclidean geometry.

I realize there are a lot of other people who've already had this same idea. I drew some inspiration from a proof my teacher did of something to do with elastic collisions. He proved it entirely with Euclidean geometry - aside from letters naming the line segments, there was no text and there were no numbers. I also had a friend turn me on to xkcd recently.

I've also heard there's a book that already sort-of does this, Larry Gonick's The Cartoon Guide to Physics. I've never seen it myself, and now I have to.