Butt Cheek Differential

A Computational Analysis of Gluteous Weight Distribution Tendencies in the Sailing Environment

By Christopher VanEpps & Robert Ziemba

With consultation by Brenda Carpenter, Peggy Galkowski and Ira Glickstein

1. To properly analyze the issue of left-to-right butt cheek leaning tendencies of catamaran sailors, as first posed by Mr. Keith Winn in the Hobie Mailing List and derive a suitable equation for describing said leanings.

1. This paper is intended to encompass the entire small craft sailing community, from catamarans to their obviously inferior monohull distant cousins, like Sunfishes, Lasers, or any other of a number of slower vessels not worth mentioning here.
2. This paper in no way attempts to determine whether a propensity to lean on the right or left cheeks yields any competitive or ergonomic advantage, or any other useful information of any kind.

1. For the purposes of this analysis, it is assumed that the following conditions hold:
1. The entirety of the sailor’s weight rests on his bum. This may be an overly simplistic and unrealistic view of seating position but hey, its my paper. If you want to include the weight distributed to legs, feet and hands, write your own damn paper.
2. The sailor can keep his cranium out of his rectal cavity for the duration of the race. If a sailor’s head is up his ass, this could effect the weight distribution between cheeks. I only had so many computational resources available this afternoon. This may also be an unrealistic assumption for some of us. We know who we are.
3. The sailor can distinguish his ass from a hole in the ground. This assumption is crucial. Without it we have no reliable means of measuring gluteal mass because it could be mistaken for a hole in the hulls as well.
4. The sailor can find his ass with one or more hands. Obviously, if we can’t find the ass, we can’t measure butt cheek weight distribution.

• Tr = Time of race, or elapsed time of a measurement sample.
• Ws = Weight of sailor
• Wl = Weight on left cheek
• Wl(t) = Weight on left cheek as function of time
• Wr = Weight on right cheek
• Wr(t) = Weight on right cheek as function of time
• t = a given time interval
• BCD = Butt Cheek Differential

1. The Weight Distribution Over Time for Full Left-to-RightTransition Model (WDOTFLRTM)
1. In Figure 1 we see the defining curves of the functions Wr(t) and Wl(t), which describe the weight on the right and left cheeks respectively as a function of transition time, in a transition from full weight on the left cheek to full displacement on the right. These functions are critical to the analysis. I picked the slopes because I thought they looked pretty. If you disagree with the slopes, write your own damn paper.



Figure 1. Butt Cheek Left-To-Right Transition

2. This only gets us part of the way there as it only allows us to take a snap shot of BCD in a given point in time. What we need is a function to integrate across the time span of an entire race.
2. The Butt Cheek Weight Distribution for Whole Race Model (BCWDWRM)
1. Figure 2 shows a possible butt cheek weight distribution function for each cheek, over the course of an entire race. One could use a distribution model like that of Poisson or Erlang to define the equations of the lines below, but I have a better idea.



Figure 2. Left & Right Weight Functions

2. We must attach a couple of piezio-electric pressure transducers and electrodes to the ass of a willing test subject. I figure a 12VDC battery should be powerful enough as a source in the salt water test environment. I believe Frank P. will make a perfect host. We then download pressure data to a laptop PC during a race, enter the data into MATLAB and compute a spline curve fit to the data and, voila, we have our functions Wr(t) and Wl(t).
3. Hard-Core Stuff
1. If we agree that Ws = the total weight of a sailor (and we do), then it must follow that:



Equation 1

2. Butt Cheek Differential defined:



Equation 2

1. If BCD<0, then butt cheek weight bias is to the right. If BCD>0, then butt cheek weight bias is to the left. If BCD=0, then we have a neutral butt cheek weight bias.
3. If we solve Equation 1 for Wr(t) we have:



Equation 3

4. We can then write:



Equation 4

5. Since Ws is a constant and we all know that the definite integral = the constant times the time interval we get:



Equation 5

6. And, since we can’t just leave well enough alone, finally:



Equation 6

4. Conclusions
1. So there you have it.
2. Enough said
3. Since none of this will ever be experimentally verified, It must follow that I am right. No, left. Aw Hell! Forget it.