The absolute minimal amount of background knowledge needed to understand this is that a blues dance consists of two dancers, the lead and the follow. The lead is typically the man, and the follow is typically the woman, although that's not always the case. A dip is one of those fancy things you see on TV, where the follow generally bends backward, held up by the lead.
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| Like so. Thank you to the folks at this blog I've never heard of, as well as public domain laws. |
In order to get our feet on the ground, so to speak, we needed to be able to draw our physical system on paper. That way we could do all sorts of fancy trigonometry and physics in order to make our model. After a fair amount of simplification, we managed to create the following, totally accurate diagram:
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| The lead is on the left, the follow on the right. The things in between them are arms. Obviously. |
A few interesting things about our model:
- The lead's front leg would grow and shrink over time, depending on how he bent his knee
- The lead's torso and back leg would always create a straight line
- The follow's shins would always be perpendicular to the ground
- The follow's torso and thighs would always create a straight line
Like I said. Totally. Accurate.
Next, we needed to take a few measurements that we would be able to plug into the program we would soon make. We collected values including Ndungu's height, the height of his shoulder, the height of his pelvis, the distance between his feet when he dips, the angle of his torso from the horizontal, and so forth.
Unfortunately, we didn't always have all the measuring equipment we wanted at all times. For example, a protractor was sometimes hard to find; but remember, we're trained professionals in training. So obviously, the natural solution was to find a picture of a protractor online, and just hold my laptop up to Ndungu's or his partner's leg. Many of our measurements were along the lines of "68... ish? I'll call it 68."
Slightly more difficult than the problem of recording an angle was that of recording weight. Ndungu and I already felt uncomfortable asking a woman to please stand on a scale for us, due to the fact that that would involve asking a woman her weight, generally considered a no-no. Once we managed to surmount that issue, though, we realized that in order to record the normal force exerted by one's leg, we would need to dance on top of the scale. This was particularly exciting when we were recording the maximum normal force that one's leg could hold before dropping the follow; this meant that we had to lay down cushions through the hallway right next to the scale, and Ndungu had to stand in just the right position with one foot on the scale while he dropped our generous dance partner time and time again, as I scrambled to record their angle with my laptop-protractor.
But these recording inaccuracies pale in comparison to the glory that was our tension force. In order to determine the force that the lead's hand exerts on the follow's back, we needed to basically put the scale on our follow's back and dance like so. Unfortunately, the scale wouldn't quite stay in place. So we resorted to iffier methods.
We needed two data points. So, data point number 1: exerting 5 pounds of force on the follow. Ndungu danced with our follow, and dipped her back until he felt like he was sort of exerting about 5 pound of force. I asked how he could possibly know that he was exerting 5 pounds of force; obviously, he had picked up a 5-pound weight the previous morning, and was just sort of gauging what felt similar. When Ndungu was at 5 pounds of tension force, I recorded the angle.
Data point number 2: threshhold. This time, Ndungu danced with our follow until he reached his threshhold, at which point she of course fell onto the cushions that we had supplied her with. Then, Ndungu quickly ran over to a doorway in the hall, and positioned the scale on the back of the door at about shoulder-height. He then struck a dancing position with the door, and exerted what felt like the same force on his new "partner." That way we were able to find his threshhold tension force.
Suffice to say, we had a difficult time creating our actual model on the computer. A bunch of arm-waving went into many of our graphs ("Well, the normal force on the front leg sorta feels like this kind of graph... let's call it that"), which we later simplified down. At one point, I tested our model for a theoretical one-minute dip: obviously longer than any realistic dip would take, but if our model worked then there shouldn't have been a problem. Unfortunately, according to our model, over the course of one minute, our highly impressive lead managed to perform a 3,500,000-degree dip. That's right, 3.5 megadegrees, a unit which I never hope to use again.
After fixing up our model a little more, we were faced with the difficult problem of finding the equation of a parabola. We had the vertex and two other points on the parabola. This was the kind of math that we had been doing since seventh grade, and here were at one of the top engineering schools in the country, unable to perform this sort of witchcraft. We asked anyone who happened to walk through the room for help, and it took us at least five or six lifelines until we finally found someone with the mathematical sagacity to help us. There is no explaining how much difficulty we had with this problem.
Finally, we had a working model which produced reasonable results. Ndungu and I had realized somewhere along the line that we could just plug in different values for the lead's height, weight, and normal threshhold, and would thus be able to compare two different leads and their maximum dip time and angle. The only thing to do after making that kind of realization was to compare the two of us, and figure out whom, mathematically, was the superior dancer.
Upon further thought, we realized that we could feasibly put this on our presentation poster. It was sort of like doing useful work with our model, after all. Sorta ish. The prize for the victor: that the loser would have to be the one to announce the winner during presentation, essentially admitting his inferiority in front of our professors.
We devoted a quarter of our poster to our competition, under the heading "GREG VS. NDUNGU: Who's the better dancer?", with a nice little graphic to showcase our competition:
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Thus ended the least scientifically accurate study ever conducted by would-be engineers.
