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Hello, my name is Jeffrey DeLucca. I am a senior mechanical and aerospace Engineer,
and I would like to teach you something about the engineering behind sports.
Because I am an Aerospace Engineer, Our topic today will be the physics of Airplanes.
I know you must be thinking "Surely you can't be serious...", but I AM serious,
and don't call me Shirley.
When I say Airplane, I don't mean this.
I mean this.
So, I guess the real topic is: a discussion on the connection between tilt angle and turning radius.
This is pretty useful for almost any ground-based sport, and ...
...even everyday things like riding the bus.
Assuming a uniform circular motion with constant velocity,
any acceleration points to the centerof the circle.
If we diagram the forces acting on my body, things are a little complicated, so we'll
just simplify it a bit to this.
Great. So, when we sum the forces in the Z direction, we know that I don't fall down,
or fly away, so the sum must be zero.
And that just leaves us with ...
the force of my leg = my weight divided by the cosine of the tilt angle.
From there, we can see that the inward acceleration should be equal to
my weight times the tangent of the tilt angle,
plus some unknown amount due to friction.
This shows that the more I tilt, the "faster" I can turn ...
until my no-slip conditions fail, or my legs give out.
It's important to note that
the greater the tilt angle, the greater the total force is required by your legs,
as shown in this diagram. The symbols stand for turn speed and amount of pain, respectively.
Actually, if you're an engineer, you're probably a little masochistic, so the diagram is more like this.
Well anyway, lets move on to where we put the theory to the test.
By measuring the average time it takes to complete a lap
and knowing the radius, the average velocity can be found.
Then, setting the centripetal force equal to the x-component of the Leg force, the theoretical
tilt angle can be calculated. These values are then compared to the real world tilt angle,
taken from still frames.
For this first experiment, the average period was 6.15 seconds. The radius was 10.5 feet,
meaning the velocity was 10.72 feet/s. This gives us an angle of 18.8 degrees, which differs
slightly from the real value of 16 degrees.
The next experiment had a period of 3.4 seconds per lap, and a radius of 5.5 feet, meaning
my velocity was 10 feet per second. In this case, the theoretical and actual tilt angle
were both right around 30 degrees. Nice work, everybody.
This last one had an average period of 5 seconds. The radius was 7 feet, meaning the velocity
was 8.8 feet per second. The theoretical value also compared well to actual, with theoretical
at 19 degrees and the actual at about 20.
Well, that's about it. I'd like to apologize for my bad sense of humor,
terrible drawing skills and awful handwriting. Thanks for watching.