When You Have Too Much Time

    So, I was sitting in my rocking chair the other day, contemplating that omnipresent question: "What should I do?", when a thought struck me:

"How fast are drumsticks going when they hit the drum?!?"

    Naturally, processes occur inside the mind which make it possible to roughly estimate the speed aforementioned, and again, naturally, I endeavored to discover these processes. Using basic math, which is an oxymoron, I deduced that the speed of the stick cannot be all that great, owing to the fact that if the velocities of impact were such that toddlers (or my sister) would start losing fingers and toes, kevlar drumheads would start popping. Presented with this dilemma, I went about trying to figure out how I could solve the problem of recording said speeds using conventional, household methods.

The Radar Gun

    First, I attempted the brute force approach. My brother has been active in the world of baseball, and for some odd reason, he got a hold of a radar gun to determine how fast he could throw. Since I was trying to record speeds, I thought that the perfect way to measure the velocity of a drumstick would be to use that radar gun. So I tried it. Have you ever tried playing a drumstick in one hand while holding a radar gun and pressing the trigger with the other hand and looking at the measurement and still trying to remember what you're playing (pause for breath), all at the same time? I didn't think so. Well, your resident weirdo tried it, and of course obtained data that would be sufficient enough for Dr. Furstenau to say: "Wow, that's interesting.... Lemme give you my sample data." This failure prompted some more deep thought-provoking-questions that were unfortunately not producing deep thought-provoking-answers.

The Laser

   Have you ever seen those shows on the discovery channel that talk about how high-tech scientists use high-tech lasers to measure exact, perfect locations of objects at exact, perfect times, and get exact, perfect results? I didn't think so. Well, since I have, I decided for my next indulgence I would procure my handy laser-pointer I'd had for who knows how many years. This seemed like the perfect plan. I would hook up my laser to a high-speed computer, in doing so have an articulated arm drop the drum stick at the required time at the required height, which would pass through the laser beam, which would cause a shadow on the device for measuring shadows, which would cause the time from release to be recorded, which would enable me to determine the speed of the drumstick when it hit the drum head. However, I soon found many errors in this plan:

1. I didn't have a high-speed computer.

2. I couldn't hook up a high-speed computer to the laser pointer.

3. I didn't have a receiver to pick up the laser beam transmission.

4. My laser didn't have batteries.

5. I didn't have an articulated arm.

6. I wouldn't know how to get it all working.

7. The said plan just really wouldn't work at all.

8. I was working way to hard for something this simple.

    Also, at this point I realized how obviously simple it would be to get an average speed of the drumstick from start to finish, and hence, achieve my goal.

Breakthrough!

    I finally came to the conclusion that through all of my previous hardships, I had missed the underlying obviousness of this whole dilemma. I just had to breakdown speed in terms of its common units, i.e. distance and time. I knew from basic math (oxymoron) that speed was distance divided by time (miles/hour, meters/second, inches/minute). So, from that conclusion I knew that I needed to find 1) distance traveled by the drumstick, and 2) time the drumstick took to travel that distance. I also knew that in order to complete future calculations, I needed to choose a quantified bpm to play sixteenth notes, so that I could measure the distance.

        Calculation 1

                    This calculation was actually quite simple. I just needed to determine a fixed height the drumstick would be leaving from. I chose six inches, the standard mezzo forte. I used the fact the drumstick follows a traceable and repeated path while playing to my advantage. By playing four sixteenth notes at 108 beats per minute, I knew I could predict exactly how far the stick had traveled. When the stick initially drops, it travels six inches, since we assumed that every note will start at that predetermined height. We also assume that, I being the excellent drummer that I am, the stick hits the drum at exactly the same time as the first tick of the metronome (which, again, isset at 108 bpm). After this first hit, the drumstick travels back up to the original height of six inches, which of course constitutes a six inches of additional movement. So, there has been 12 inches of movement by the drum stick so far. Following? If not, just read the paragraph again and scratch your mind in puzzlement if unsure of something. The 12 inches of movement described before was exactly one hit of the stick to the drum. Since there are four sixteenth notes in one beat, multiplying the 12 inches by four will give the total distance traveled by the drumstick in that one beat. 48 inches. Ta-da!!

        Calculation 2

                    This calculation was just as simple and I again used the fact that this experiment was occurring under a controlled 108 bpm environment to my advantage. Using simple dimensional analysis, I  arrived at my desired time:

    Thus, I had my initial data: 48 inches in .556 seconds. I then divided these two numbers into each other giving 86.331 in/sec. Using additional dimensional analysis, I converted in/sec into mph, and my final answer:

4.905 mph!!!

The Unfortunate Truth

    Yes, I'm sorry, there's more. This number (4.905) is a speed associated with only one specific set of data: 6 inch stick height and 108 bpm. There is a formula for finding out the average velocity of a stick which travels in a regularly occurring pattern (i.e. sets of sixteenth notes at a fixed bpm) and at a constant height. This formula is as follows: Take the stick height, multiply it by the beats per minute, and divide by 132. I'm not kidding. If you want to see a derivation of this formula, click here.

Voila!

Practical Applications

    When you apply the formula above in several different combinations of stick heights and bpm's, you see some interesting results. As discovered earlier, 6 inches and 108 bpm will have an average speed of 4.905 mph. However, 12 inches and 80 bpm will have an average speed of 7.273 mph. The speed is faster even though the bpm has dramatically decreased. And if you have 3 inches at 138 bpm, the average speed is a measly 3.136 mph. All this goes to show that even though it may be fun and cool to play really really fast and really really high, you aren't getting as much speed out of the stick and the nerdy types, like myself, will not be very impressed. So go practice Levi!

Brought to you by Kenny,