Racquetball Launcher Competition
By Anna Jackson, Ben Tharrington, and Henry Walsh
12/5/16
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Design
Based upon the requirements of the project we sought to design a machine that could
both provide sizeable power accurately and have an adjustable outlet in order to fire the
racquetball variable distances. After doing research into different models of launchers built for
similar purposes we took two separate components we found and combined them together to
achieve our desired qualities. Putting a cross bow propelling frame within an adjustable
quarter-circle cannon frame, we arrived at our final launcher design. This design allowed us to
have adequate, consistent power in an adjustable angle with a stable base.
On our cross bow we used a bungee cord, held by metal eye hooks on the horizontal limb
of the bow, as the propulsion mechanism that would launch the ball. Once drawn back, the
bungee cord is held in place by a plastic clip
that is held shut by another bungee cord
hooked to the bottom of the base of the
launcher. Forcing down the back side of the
quick will open the front side of the clip,
releasing the bungee cord and launching the
ball.
We adjust the angle of the cross bow feature by
tightening screws on a bar that runs between
the two quarter-circle arcs and through the
neck of the cross bow. Loosening the screws
on the two ends of the bar frees the bar to
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move through the curvature of the gap, and tightening the screws again holds the bar in
place, thus holding the cross bar at a fixed launch angle.
Calculations
The bungee cord acts as a spring and applies the same force when pulled back by the
same distance. To calculate the velocity, the spring constant of the bungee cord needs to be
found. This was done by attaching a 10 lb weight to the end of the bungee cord and found the
weight stretched it 1.5 inches (.125 ft).
F=-kx
k=10/.125= 80 lb/ft
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The cord was stretched 6 inches (.5 ft) during launch and the racquetball has a mass of
.864 kg (.0592 slugs). Using the conservation of energy, K=.5mv​2​, and U=.5kx​2​ (for a spring),
the initial velocity can be calculated.
E=K+U
.5mv​i​2​+.5kx​i​2​=.5mv​f​2​+.5kx​f​2
0+(80)(.5)​2​=(0.0592)v​f​2​+0
v​f​= 18.38 ft/s
Our exit velocity never changes but the angle it’s shot at does. Below are the calculations
for finding the angle needed to make each shot. The 3ft, 6ft, and 12 ft are the horizontal distance
from the front of the rim.
For 3 ft bank shot:
The ball need to travel 3 ft in the x-direction to get to the rim and 9 inches to get to the back
board. There is no acceleration in the x-direction.
s=s​0​+v​0​t
3.75=18.38cos(theta)t
t=3.75/(18.38cos(theta))
The ball need to go up and back down ending at a height of 46 inches.
s=s​0​+v​0​t+.5at​2
46/12=17/12+18.38sin(theta)t-.5*32.2*t​2​.
These have to occur at the same time. Therefore,
2.4=tan(theta)(3.75)-.5*32.2*(3.75/(18.38cos(theta)))​2
When plugging into wolfram alpha,
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Theta=77.7 degrees
For a 6 ft “nothing but net” shot:
Start with 2d kinematic equation,
s=s​0​+v​0​t+.5at​2
Plugging in values for the x-distance needed to be reached,
(6+.3)ft = 18.38ft/s cos(theta)(t)
t = 6.3/(18.38cos(theta))
Using the same equation but in the y-direction,
2.3ft = 6.3tan(theta)+.5(-32.2)(6.3/(18.38cos(theta)))​2
2.3 = 6.3tan(theta) + .5(-32.2)(.117/(cos​2​(theta)))
We then used wolfram alpha to find the roots,
theta = 1.18 radians
theta = 67.5​o
For a 12 ft “nothing but net” shot:
Start with 2d kinematic equation,
s=s​0​+v​0​t+.5at​2
Plugging in values for the x-distance needed to be reached,
12.3ft = 18.38ft/s cos(theta)(t)
t = 12.3/(18.38cos(theta))
Using the same equation but in the y-direction,
2.3ft = 12.3tan(theta)+.5(-32.2)(12.3/(18.38cos(theta)))​2
2.3 = 12.3tan(theta) + .5(-32.2)(.448/(cos​2​(theta)))
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When using wolfram alpha to find the roots, it found that the launcher would be unable to make
the shot and it gave us an imaginary angle. We think the reason for this is because we measured
the k-value after the competition and the bungee got stretched out slightly. This would lower the
cord’s k value and slightly alter our equations, which could be enough to say that the shot isn’t
possible to make even though in practice we were able to make a 12 ft shot.
Materials
Included below are copies of the receipts and a list of all materials bought for this
assignment:
Materials purchased were 2 zinc screw eyes, zinc wood screws, and bungee cords. The
common nails, mason line and zinc threaded rod were eventually returned as they were not used
in the construction of the project. We also utilized extra wood that each of our families had
laying around and a roll of duct-tape. The total cost of our materials was 16.59 dollars.
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Bibliography
Hau, M. (2014, March 20). Ping Pong Ball Launcher. Retrieved November 17, 2016, from
https://prezi.com/xqybevu8kc50/ping-pong-ball-launcher/