Taylor Petersen, Nick Hansen, Dinidu Gunasena
Period 2A
Not Your Father’s Crossbow
Introduction | Method | Results | Conclusion | Bibliography | Up
Taylor Petersen, Nick Hansen, Dinidu Gunasena
Period 2A
Not Your Father’s Crossbow
Introduction | Method | Results | Conclusion | Bibliography | Up
Introduction | Top
A ballista was a ancient missile weapon, more often used to take out singular soldiers than walls (the opposite of an catapult). The ballista dates back to the days of Greece, but was eventually adopted by the Romans. The ballista was a weapon of war, but today has been clearly overshadowed by more modern weapons (obviously). A ballista uses spring to fling a missile into the field. It has to use a crank to pull back thereby ensuring that while it may take longer to pull back, it will release much more energy in one burst. The ballista uses a torsion spring bundle system to release energy very quickly (the same technology used in an onager).
There are many forces involved with a ballista. The final output we had was distance. This is mainly dependent upon the method we use to store all the energy, which will be used in launching the projectile, the surgical tubing, which act like springs. One thing, which we must remember is that a large portion of the force, especially initially, stored in the surgical tubing will be directed uselessly sideways. We must also remember that less and less of this force will directed sideways as the surgical tubing are stretched further and further back. Furthermore, We must remember that as the projectile is launched higher and higher, that the wind will play a greater and greater affect into the course of the ballista.
Statement of the problem:
The purpose of this investigation is to observe how the original torque can affect a missile’s flight distance
Hypothesis:
If we fire a ballista with differing torques (independent variable: how far back we stretch the surgical tubing), then the distance (dependent variable: distance the projectile was launched from the ) will increase with an exponential curve
Method | Top
The method we used to gather our data consisted of a series of 3 trials with every golf tube bolt at each of our 6 ‘stops.’ Before firing, we would send one of us out to about where we anticipated the golf tube bolt to land so that we could know as close to the exact point of impact as possible. After we were set up, we would cock the ballista, load in the golf tube bolt, and then fire after alerting everyone that we were firing. Once the golf tube bolt landed and the spot of impact was marked by the spotter, we would begin measuring the distance with a rolling wheel which marked distances to the nearest foot. Starting at the point on the ground vertically below the natural position of the surgical tubing, we would roll the apparatus in as straight of a line as possible towards the point of impact, noting the number of clicks and comparing it with the final number upon reaching the destination so as the assure the results would be as accurate as possible. Then, we would begin the process of setting up for the next trial. After 3 trials with a single golf tube bolt, we would transition to the next golf tube bolt and, after we tested with all 3 golf tube bolts, we would move the stop to the next position and begin the next set of 9 trials.
List of Materials (Copied from the original designer’s webpage)
· 2x4, 10 feet long (2 of these)
· Gate latch
·
1-1/4" oak dowels, 36" long (2 of these)
Wood molding, 9 feet (You can use any molding that is rounded out at the top;
look at the figure farther down)
· 3/8" sisal rope, 100 feet
· Welded metal ring, round or square, inside opening at least 1" across
· Wood or drywall screws, 3" long (1 box)
· Copper rivets and collars (2 each)
· Bolts, 1/2" by 4", coarse thread (3)
· Washers, 1/2" (3)
· Nuts, 1/2", coarse thread (3)
· 1/8" cable ties (1 bag) (You only need 4 to build the weapon, but keep the rest for repairs later)
· Carpenter's glue
· Surgical tubing, 3/16" inner diameter, 3/32" wall thickness (You need 4 feet of tubing for each strand used on the weapon; I normally use 4 strands)
Results | Top
|
Distance (in feet) |
||||||
|
Golf Tube Bolt |
Stop Position |
|||||
|
1 |
2 |
3 |
4 |
5 |
6 |
|
|
1 |
66 |
79 |
94 |
116 |
123 |
143 |
|
1 |
65 |
78 |
99 |
112 |
125 |
142 |
|
1 |
66 |
79 |
97 |
114 |
126 |
141 |
|
2 |
65 |
82 |
99 |
113 |
127 |
148 |
|
2 |
66 |
78 |
98 |
112 |
128 |
146 |
|
2 |
68 |
76 |
102 |
112 |
127 |
144 |
|
3 |
69 |
81 |
93 |
116 |
127 |
150 |
|
3 |
63 |
83 |
99 |
116 |
126 |
151 |
|
3 |
70 |
79 |
103 |
107 |
129 |
154 |
|
Average Distance (in feet) |
||||||
|
Golf Tube Bolt |
Stop Position |
|||||
|
1 |
2 |
3 |
4 |
5 |
6 |
|
|
1 |
44.3 |
53.1 |
66.4 |
76.8 |
85.7 |
98.0 |
|
2 |
66.9 |
80.2 |
98.3 |
113.1 |
126.9 |
149.1 |
|
3 |
45.7 |
54.3 |
67.2 |
76.0 |
85.2 |
100.7 |
|
All |
52.3 |
62.6 |
77.3 |
88.6 |
99.2 |
115.9 |
|
Uncertainty |
± 4 |
± 4 |
± 5.5 |
± 5 |
± 3.5 |
± 7 |
In the table above, average means the same thing as the mean value.
In order to calculate the uncertainty, we used the equation U = (Max – Min) / 2 which, because of the uncertainty in our measuring process of .5 feet, became
U = [(Max + .5) – (Min - .5)] / 2.
Conclusion | Top
Our results were surprisingly high and precise, facts that we can attribute to the elasticity of the surgical tubing. With our highest trial reaching over 50 yards, our ballista was able to fire our golf tube bolts enormous distances which exceeded our expectations.
While we hypothesized that the missile's distance would exponentially change with the draw distance we found that the growth was actually more linear, because the spring constant was canceled out by the velocity. This causes the distance to vary linearly.
While we anticipated that our bolt distance would scale exponentially with the distance that the stop was from the natural resting point of the surgical tubing, our data suggests that the data is actually linear. Upon further analysis using physics formulas, this makes sense because while E = ˝ k x^2, which caused us to hypothesize that it would be exponential, we forgot about the translation of potential energy into kinetic energy which, because E = ˝ m v^2, would cause the relationship between the two distances to be linear.
Our main source of error would definitely be the wheel we used to measure distances because of the massive amount of uncertainty. It only measured distances to the nearest foot and, while it wasn’t a significant portion when our distances were at around 150 feet, it was almost a whole percent which could’ve potentially affected the results.
To improve our research, we could’ve used a much more accurate form of measurement, such as a long tape measurer or even a laser-ruler. Furthermore, it would’ve been nice to have tested in an environment where wind, temperature, and humidity were kept at a constant. Finally, the golf tube bolts had slight differences in weight and shape which noticeably affected the distances they traveled.
In conclusion, our experiment proved to be more successful than we anticipated. Our data provided a linear and accurate set of points which gave an amazing indication of how the data would react if we fired from further distances back on the rail, though there would of course be a point where it would taper off and decrease because of the maximum elasticity of the surgical tubing.
Bibliography | Top
http://www.angelfire.com/tx/adod/b.html - This is the website where we got the instructions to build the actual ballista that we used for testing. This was the center of our project and it would have been much more difficult to do without this site.
http://ffden-2.phys.uaf.edu/
http://ancienthistory.about.
http://www.mlahanas.de/Greeks/
http://www.britannica.