Throwing a Baseball

Inspired by this tweet,

I decided to do the math and make some pretty pictures to show how angle of release, speed, and air-time relate to each other.

In the first figure, the length of the orange arrows corresponds to the speed of the pitch and the other curves are possible paths that the baseball could follow. If you throw it at a low angle, you have to throw really fast. If you throw at a really high angle, you also have to throw really fast. Somewhere in between is where you would find the minimum throwing speed and it will be close to 45 degrees (not exactly since the ball leaves the pitcher's hand at a different height than it crosses the plate).

In the second figure, the length of the arrows corresponds to the amount of time the ball spends in the air. At a low angle, it spends very little time in the air, but at a high angle, the ball spends a lot of time in the air.

So simple, but so neat.

Baseball and Physics Unite!

If you watched game 1 of the World Series on Wednesday, you had the joy of seeing infrared video. Fox thought it would be cool to bring an infrared camera along with them to St. Louis and it was, indeed, a good idea. Adrian Beltre of the rangers hit the ball down the 3rd base line but he didn't run for some reason. The cardinals threw the ball to 1st and Beltre was called out. Beltre claimed that the ball hit his toe, which would mean it would be an automatic dead ball and would just be considered a foul ball. But the regular cameras couldn't prove the umps wrong.

The regular, real-time video makes it look like the ball didn't actually hit Beltre, but that he just faked it. Yeah, that's possible, but he sure did a really quick job of acting with the way he reacted to the ball hitting his toe.

FOX had demonstrated their infrared camera earlier in the game when Pujols hit the ball into his own foot. The infrared video showed a bright spot on his left foot light up right when the ball hit it.

Being a physics nerd, that was pretty cool to me. But being somebody who always thinks about applications, I didn't quite get the point...at least until the 9th inning.

Beltre was up to bat. There was one out with nobody on base. Beltre was 2 for 3 so far for the night, so he was hot. Feeling confident, he went after the first pitch-a fastball, and never even left the batter's box because he claimed the ball hit his toe. The umps didn't believe him so they called him out. 2 outs. Nelson Cruz was up next and flew out to left field for an anti-climactic defeat.

FOX showed the replay using the regular video and you couldn't see anything that was conclusive enough to overturn the call. It was pretty hard to believe Beltre until they showed the infrared video.

By golly, the ball barely nicked his toe! That should have been a foul ball. He could have hit a home run the next pitch and sent the game to extra innings! Baseball is a game of comebacks. 9th inning, 2nd out rallies can actually happen in this sport. It's part of the reason I love the game so much. The Rangers were only behind by 1 run and the smallest things can make a huge difference. Oh well.

How it works
Infrared cameras are very cool. Infrared light is just like the light you see all the time, just with a longer wavelength, so you can't see it with your eyes. But cameras can be built to detect infrared light. In fact, the last project I worked on was, in simple terms, a color infrared camera pixel.

Infrared cameras are great for night vision because it distinguishes between things with different temperatures. All the things you see around you are emitting infrared light based on their temperature (and emissivity, which I won't talk about for simplicity's sake). The warmer something is, the more intense the infrared light coming off of it is. So when the baseball hit Beltre's toe, the impact warmed up the spot, causing it to emit extra infrared light than the spot did before it was heated up. It takes time for the heat to dissipate, so the "hot spot" stays there for as long as the temperature at that spot is still high.

Why does the high temperature cause the spot to emit infrared light? If you remember my last post about heat transfer, you remember that high temperature means the molecules are vibrating around a lot more. Well the vibration of molecules causes them to radiate. That's exactly how an antenna works. So when temperature increases the vibrations occur at higher amplitudes and frequencies, causing the intensity of the light to increase. You saw the intensity increase when the temperature of Beltre's toe went up.

This effect is called thermal radiation. At room temperature it happens at infrared wavelengths. But if you increase the temperature the intensity increases and the wavelength decreases because of the higher-frequency vibrations. The following graph shows how the emission spectrum changes as you increase the temperature of something.

If you heat something up enough, you can start to see the radiation in visible wavelengths. This is why metal glows when you heat it up. It's also why incandescent light bulbs work.

Now you know how infrared light gives you extra information that visible light cannot give you. And you now know what thermal radiation is. Pretty cool huh?

The Second Most American Sport

It is now officially football season. It has been for a few weeks now right? Football is a great sport. There are all kinds of really cool things about football that this post will explore in detail. There are also really annoying/lame things that have to do with football. I realize that since I have some friends that are pretty big football fans, they may be offended by my very short rant on the few things I don't like about football.
My favorite thing about football is how much of a team sport it is. You have these very intricate plays that are well designed and completely dependent on how well ever single player follows the plan. The quarterback knows exactly where every body is going to be running and if you aren't where you should be, he might just end up throwing an interception right to the place where you should have been. You usually need like 5 guys at the front protecting their quarterback and if you mess up at that job, everybody is going to be mad and your QB might lose his head.

There is no sport closer to a battlefield than football. It's like the good ole days when the soldiers would all line up about 50 feet away from each other, and hope and pray that their musket would shoot one of the guys over there. The football players just line up and do every thing they can to get the ball to the touch down. They'll push, shove, tackle, clothesline, poke eyeballs, etc.

Two words: Human Barricade. Blocking is great. Yes there is some blocking in other sports and I like it when it's used in other sports too. But football is really the perfect sport for blocking. In basketball, blocking is useful, but kind of silly because you aren't really protecting your teammate from danger, just from a blocked shot or a steal. I just like the idea of blocking off your opponents, making a nice stream line for your running back. It's cool stuff.

Unfortunately, to go along with the whole Battlefield, Human Barricade mentality, many people look at other sports and say they are for wimps. Okay, football and hockey and rugby and other hitting sports are cool for their hitting. But there's much more to sport than hitting. Sure it's fun to watch, but there's more to be enjoyed. I start to lose respect for people when they start to talk about how some sports are for wimps. You sir, don't understand sports. Determining whether some activity is a sport or not is a different question like poker or cheer leading or chess (Yeah I said chess. My school sent out an email for IM sports and one of them was chess. No kidding.).

Also, football isn't that much fun to play in person. It's okay. I could think of less fun sports to play. But, it's just not that great. If you have 4 or 5 guys who have the option of getting the ball (besides the QB), then that means you have to run all over the place 4-5 times and only 1 time out of 4-5 will you get the ball. You try your darndest to get away from your corner back, but rarely get the ball. Unless you're that guy who's really good. You'll get the ball plenty since you'll be taking all the passes away from the other 3-4 receivers. Now if there were plays and everybody had a job, that would be pretty fun. I'd be happy with that, but that would take more coordination than is usually had. I would much rather play volleyball. Maybe I've just gotten "old" and lazy, cuz when I was in middle school I loved playing football.

That is all. Football is cool. There are some less cool things about it, but for the most part it's pretty sweet. As far as watching goes, it's probably my 3rd favorite after baseball(yep) and basketball. As far as playing goes, it's my 5th favorite after volleyball, basketball, baseball, and soccer (excluding disc golf since that's more of an activity than a sport).