Velocity and Braid Angle Analysis
An examination of braid angle trends based on translational and rotational velocities of the braider
June 3, 2009
By: SovanDara Chea
Jasmine Gandhi
Nikhil Nathwani
Part 2:
Statement of Problem(s):
- What velocities do different braider settings yield?
- What is a general equation that shows braid angle as a function of translational and rotational velocities?
- Using this equation, what braid angles can theoretically be yielded with different combinations of rotational and translational velocity?
Part 3:
Hypothesis:
We predict that the combination of a slow translational velocity and fast rotational velocity, together, will produce high braid angles. Similarly, a high translational velocity and slow rotational velocity will create low braid angles.
Assumptions:
Braider is in full function. Start up delay timings ignored.
Part 4:
As an approach to the given problem, our group started off by collecting raw data from the braider with the help of Mr. Drane and Dr. Jumper. We took different values and measurements from the rotational and translational velocities. To illustrate, for the translational leg that kept moving in and out of the braider we recorded the amount of time it took for the leg to pass a known distance at various settings. Afterwards, by dividing the distance and time, we were able to calculate the average translational velocity. For the rotational velocity, a member of the group was assigned to be “look-out” keeping eye on one spool in particular to approximate one full cycle around the bat. The one revolution/one cycle distance was kept constant throughout each setting of the rotational velocity, and again, different times were recorded with a stopwatch. With that, we were able to quickly calculate the average rotational velocity as well. In addition, we took some notes on the madrel itself. For instance, we jotted down the radius of the handle and barrel. (i.e. barrel radius- 2.388” / handle radius-1.218”) Chart 1 (Raw Data)
With a foundation laid down, I was assigned the task of analyzing the given information to find a connection between rotational and translational velocity to braid angles. This duty seemed very difficult to do at first, until Mr. Drane showed us the patchwork of braiding. It was nothing more than a rectangular shaped square with the crossings of a typical braided object, but for me, it helped me complete my quest. I noticed that if that piece of braided mesh was laid over a bat perfectly and they ends touched side by side, that meant that the bottom edge/leg of the square was the same as the circumference of the bat. It equaled a strip of the braided strand wrapped around the bat once. As far as the vertical side of the square was concerned, I thought of a bat moving into the braiding horizontally. As it is moving in, the spools overhead and underneath are moving around rotationally. The time it takes the rotational spool to make one circular revolution around the bat multiplied by the translational velocity of the braider gives the product of the longitudal distance, as explained in the diagram below.
With that understanding in mind, I proceeded to find the braid angle embedded within the corner, labeled theta in the diagram above. I learned that by using some skills of trigonometry, I could solve for angle theta.
Theta= TAN -1 ((2*pi*R)/(V*T))
That means that the radius of the handle or barrel of the bat (r), the time it takes for the rotational velocity to make one round over the mandrel (v) and the average translational velocity (v), affect the braid angle directly.
Part 5:
Please refer back to Chart 1 (Raw Data)
*Note: translational velocity refers to the speed of the mandril going straight through the braider, and rotational velocity refers to the speed at which the braider spins around the mandril.
The translational velocities (in the green) appear to increase quadratically as the setting increase—setting 2’s velocity (the 1st setting) is around .1 inches per second (12= 1), setting 4’s velocity (the 2nd setting) is around .4 (22 = 4), and setting 6’s velocity (the 3rd setting) is around .9 inches per second (32= 9). Plotting these velocities on a graph,
As we can see, these velocity values can be perfectly fit to a quadratic function (b/c the value of R2 is 1), meaning translational velocity does increase quadratically as the setting number increases.
The rotational velocities (in the green) appear to increase linearly as the setting increase—setting 10’s velocity is around .08 inches per second, setting 20’s velocity is around .16, setting 30’s velocity is around .24, and setting 40’s velocity is around .32 inches per second. It looks like as we go up to the next setting, the translational velocity increases by .08 in/sec, making it a linear progression. Plotting these velocities on a graph,
As we can see, these velocity values can be perfectly fit to a linear function (b/c the value of R2 is almost 1), meaning rotational velocity does increase linearly as the setting number increases.
1)The following logic has been used to derive a formula that relates translational and rotational velocities to braid angle:
If the fiberglass strand wrapped around the bat [above left] were taken off the bat then it can be represented with the above triangle.
We can call the unknown and unlabeled side of the triangle “x.” This missing side x is the distance the strand of fiberglass moved along the bat translationally. Therefore,
x = translational velocity * time.
The value for time in this case equals the amount of time it took for the strand to rotate around the entire circumference of the bat (b/c the bottom leg of the triangle is equal to the bat’s circumeference), meaning:
rotational velocity * time = circumference
The tangent of Ѳ is equal to the opposite triangle side divided by the adjacent triangle side, so the arctangent of the value of the opposite side divided by the adjacent side equals Ѳ, which is the braid angle. The braid angle calculation will look like the following:
Arctan(Ѳ) = (opposite side/adjacent side)
Arctan(Ѳ) = (circumference/side x)
Arctan(Ѳ) = [(2(pi)r)/(translation velocity * time)]
An interesting thing to note with this equation is that to achieve a braid angle of 45o when the translational velocity*time equals
2)Below is a chart showing the braid angles that different combinations of rotational and translational velocities yield. This data pertains when the fibers are being wrapped around the barrel, which has a radius of 2.388".
Below is a graph to display the above data:
When we perform the same calculations using the radius of the handle instead, we obtain a slightly different chart and graph: (shown below)
There are a few things that should be understood from these graphs. First of all, the braid angles appear to decrease as rotational velocity increases for any translational velocity setting. Also, greater translational velocities yield higher braid angles. So apparently, low rotational velocities and high translational velocities yield high braid angles, which contradict our hypothesis. Moreover, the braid angle values for any given point on the barrel braid angle graph is larger than its corresponding point on the handle braid angle graph, meaning the greater the diameter of the bat you are using, the greater your braid angles can be.
Part 6:References
Our research would not be success without the help of our instructors. Mr. Drane, the director of the bat researching center is kind enough to show us how the braiding machine works. He patiently explains in detail about the mechanic of the braiding machine and he willing answers any question that we have about the research. Our research wouldn’t be successful if we didn’t help from Dr. Jumper, our main instructor. Dr. Jumper helps guiding us to the right direction in our project. He is also very patient when he explaining and clarifying the questions what we have in our project. The two instructors very kind and helpful, we cannot complete the project without them.
Source of errors
Our main problem that we encounter during the research is the data collection. Instead of using a typical stopwatch, our team uses a stopwatch from a cell phone to record time, though it is a stop watch but it can cause a slight error since a cell phone never meant to be use a stopwatch. Another problem that we encounter caused by the braider itself, the linear speed of the braider stale for about 2 second before it actually start moving. And we record the time when the start button pressed rather than when the braider starts to move. Reaction time can also come to account in experiment, when the spool spin at a high speed, we were unable to records the time accurately. Our final error might cause by the misuse of the yard stick, student might record a wrong data since he’s not train to use a yard stick.
Future improvement
For future experiment we will need to be well equipped and we will need to tackle the problem quickly. We will also need to use real scientific tool to measure and record our data. In the world of science and experimental there is no room for error.