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Defining
the Problem or Research Question
Our
research question concerns bow mechanics. We wanted to see if there was an
inherent ratio between the variables we examined in firing the bow, and
approximately what that ratio was (in formula form).
Formulating
a Hypothesis or Prediction
Our hypothesis is that distance to target, draw, and angle of release form a direct ratio, thus allowing us to come up with a three-variable equation to solve for any single variable when given the other two.
We
chose the variables of distance to target, draw on the bowstring, and angle of
release for the arrow. These variables are significant because they are easy to
measure and manipulate, have a direct correlation, and can be isolated. We
neglected other variables like horizontal uncertainty and bow stability by using
our bow launching apparatus but that will be discussed in Planning B. Our
hypothesis is that distance to target, draw, and angle of release form a direct
ratio, thus allowing us to come up with a three-variable equation to solve for
any single variable when given the other two.
Selecting
Appropriate Materials
Our materials included arrows, a bow-launching apparatus, flags to aid in
measuring distance and a really big field to launch the arrows in.
Designing
A Method for the Control of Variables / Gathering Sufficient Relevant Data
We were faced with a challenge when building our apparatus. We had to come up with something that had the ability to measure our variables while keeping all other variables constant. What we came up with was a structure that held the bow in place, allowing it to pivot on a vertical axis while fixing it on a horizontal one. This removed the possibility of human error in firing the bow and negated the effects of horizontal uncertainty when responding to target distance. The apparatus also had a protractor, allowing us to fix the bow at different angles, and an object that measure how far the bowstring was drawn back. Basically, we pivoted the bow to the angle desired and clamped it to prevent the bow from moving. Once that was done, we knocked the arrow, and drew the arrow back to a desired draw. We released the arrow, and measured the distance from the apparatus to the arrow.
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To conclude, given the variables of target distance (s), draw on the
bowstring (d), and angle of release (x), the following equation can be used to
find any single variable when given the other two. Our equation is
S = D /
(.0098(X - 1.3744)2 + .010565)
An example of where this would be useful is in the case where you have a constant value, either for the force on the projectile or the angle of release. If one of these variables cannot be manipulated, this formula can be used in conjunction with another given variable to find the third. If you have a fixed draw (i.e. you cannot pull the bowstring back any farther), you can input the target distance and find the angle of release and vice-versa. This is significant because it demonstrates how factors that determine a similar variable will always interact will each other in a measurable and definable way.
Evaluating
Procedure & Results
Our
procedure had its faults. Our method of measuring the angle of release was
imprecise, given that we were using the bowstring as an indicator. Other
weaknesses include that the draw was subject to Ryan’s physical coordination,
as Ryan was pulling the bowstring back, his hand would shake thus giving us an
imprecise draw by a few millimeters. Our errors were few, but the largest one
overall included our field where we fired our arrows. At one location where were
firing, there was a large patch of concrete where some of our arrows landed.
Even with the snow, it was hard to tell exactly where the arrow hit first, thus
giving imprecise data for those data points. Overall, the biggest error of our
project was the impreciseness of data gathering.
Improving
the Investigation
Some
improvements we could make to our project include using an angle measuring
system based on the arrow in relation to the x-axis, a mechanism that fixes the
draw (thus removing the possibility of human error), and using a field that is
consistent in makeup (no concrete) so that the arrow also stays where it first
landed.
Back To Top
1. http://www.sosmath.com/soe/SE3001/SE3001.html
This site showed the basics of three variable systems and how to work with them for our particular situation.
2. http://homepage.ntlworld.com/joetapley/
This site talked about the basics of bow mechanics and how the bow works as a whole in the realm of physics.
3. http://www.glenbrook.k12.il.us/gbssci/phys/Class/vectors/u3l2a.html
Some basics of projectile motion.
We used this site to find the Home Depot closest to our building site for the bow-holding apparatus because we needed washers.
5. http://www.tenzone.u-net.com/Equipment/stabilisation/pdfs/stab4a4.pdf
This site talked about how to control bow movement with stabilizers, aiding us in controlling displacement.
