Gotham City Crime Wave
Purpose:
In this lab, we will measure the centripetal acceleration of the Gotham City Crime Wave in Six Flags over Georgia. The Gotham City Crime Wave is the swing ride in Six Flags. This lab is also used to measure the centripetal force which can be determined by multiplying the calculated centripetal acceleration by the mass. This is because a net force is equal to mass times acceleration. We will compare the centripetal acceleration on the Crime Wave and compare it to Newton's Second Law which is centripetal acceleration is equal to velocity squared over radius.
Equipment:
The equipment used in this experiment was a data vest with a calculator hooked up to a CBL unit and a triple axis accelerometer. The data vest with all of the equipment was worn on the swing ride so the data could be collected. We also used a flip camera to record one full ride. A measuring tape was used to measure the length of one of the seats in order to measure the radius of the ride while it is running.
Background:
The Gotham City Crime Wave was opened at Six Flags over Georgia on May 8th, 2004. The diameter is 59 ft so obviously the radius is 29.5 ft. The height is close to four stories tall. If one story is roughly 10 ft tall, the Gotham City Crime Wave is around 40 ft tall. The ride duration is approximately 2 minutes. The Wave Swinger, which was the first swing ride of its kind, was what the Gotham City Crime Wave was modeled after. The Wave Swinger was introduced in Germany in 1972 by designer Zierer. It was constructed by Franz Schwartzkopf. The swing ride is different than other swing rides with its unique motions. The canopy from which the swings are hung tilts counterclockwise while the ride spins clockwise. This gives the “wave” motion to the Wave Swinger. The ride flings passengers through the air at about 30 kilometers per hour which in respect to the ride translates to about 10 revolutions per minute, or twenty revolutions for the duration of the ride.
Video:
Procedure:
This lab requires programming a calculator with the Datamate program. We programmed the calculator to take data every 0.3 seconds for a total of 240 samples. The calculator is then placed in the data vest. The accelerometer is then set up making sure that the axis face the correct the direction. The y-axis needed to face down when the data vest was put on. We then measured the width of the chair on the swings in order to determine radius. We collected data using the accelerometer while simultaneously taking a video of one complete cycle of the ride. The next step is to retrieve the data and then analyze it using the data from the calculator and the video.
Data:
Seat dimensions: 14.5 x 13.5 inches
0.3683 m x 0.3429 m
Scale: 0.5 cm = 0.3683 m
Average Speed = 2pi/s
s = 25.82-18.75 = 6.77s
2pi/6.77s= 0.928 radians/second
0.3683 m x 0.3429 m
Scale: 0.5 cm = 0.3683 m
Average Speed = 2pi/s
s = 25.82-18.75 = 6.77s
2pi/6.77s= 0.928 radians/second
Time in seconds // Acceleration in meters per second squared
0 2.51711
0.75 2.52688
1.5 2.53666
2.25 2.54154
3 2.48289
3.75 2.47312
4.5 2.49756
5.25 2.56598
6 2.50244
6.75 2.49756
7.5 2.48778
8.25 2.48778
9 2.52199
9.75 2.52199
10.5 2.54643
11.25 2.49756
12 2.48778
12.75 2.50733
13.5 2.54643
14.25 2.52688
15 2.52688
15.75 2.48289
16.5 2.49756
17.25 2.52199
18 2.52199
18.75 2.51222
19.5 2.47801
20.25 2.45846
21 2.50733
21.75 2.52199
22.5 2.52199
23.25 2.48778
24 2.49267
24.75 2.50733
25.5 2.51222
26.25 2.53177
27 2.52199
27.75 2.47801
28.5 2.49267
29.25 2.50244
30 2.54643
30.75 2.52688
31.5 2.45846
32.25 2.48778
33 2.51711
33.75 2.50244
34.5 2.52199
35.25 2.47801
36 2.48289
36.75 2.46823
37.5 2.50733
38.25 2.51222
39 2.52199
39.75 2.43891
40.5 2.41447
41.25 2.42913
42 2.47312
42.75 2.53666
43.5 2.42424
44.25 2.44379
45 2.50244
45.75 2.56598
46.5 2.53177
47.25 2.56109
48 2.53177
48.75 2.41935
49.5 2.42424
50.25 2.51711
51 2.46334
51.75 2.35093
52.5 2.41447
53.25 2.52199
54 2.50733
54.75 2.48778
55.5 2.46823
56.25 2.46823
57 2.43891
57.75 2.44868
58.5 2.48289
59.25 2.45357
60 2.43891
60.75 2.41935
61.5 2.41447
62.25 2.46823
63 2.48289
63.75 2.45846
64.5 2.3998
65.25 2.41447
66 2.44379
66.75 2.48289
67.5 2.47312
68.25 2.42424
69 2.40469
69.75 2.42913
70.5 2.47312
71.25 2.48289
72 2.43402
72.75 2.40958
73.5 2.3998
74.25 2.43402
75 2.46823
75.75 2.46334
76.5 2.41935
77.25 2.39003
78 2.43402
78.75 2.46334
79.5 2.45846
80.25 2.44379
81 2.44379
81.75 2.46334
82.5 2.47312
83.25 2.43891
84 2.45357
84.75 2.45846
85.5 2.46334
86.25 2.44868
87 2.48778
87.75 2.52688
88.5 2.51711
89.25 2.53177
90 2.49756
90.75 2.52199
91.5 2.51711
92.25 2.51222
93 2.50244
93.75 2.50244
94.5 2.51711
95.25 2.54643
96 2.49756
96.75 2.50244
97.5 2.49267
98.25 2.46334
99 2.52199
99.75 2.54154
100.5 2.51222
101.25 2.50244
102 2.46823
102.75 2.50733
103.5 2.54643
104.25 2.52199
105 2.55132
105.75 2.40469
106.5 2.49756
107.25 2.54154
108 2.3998
108.75 2.46334
109.5 2.45846
110.25 2.53177
111 2.55621
111.75 2.48778
112.5 2.51222
113.25 2.50733
114 2.48289
114.75 2.49267
115.5 2.44379
116.25 2.32649
117 2.45846
117.75 2.47801
118.5 2.39492
119.25 2.51711
120 2.49267
120.75 2.45357
121.5 2.54154
122.25 2.48778
123 2.51222
123.75 2.52199
124.5 2.49756
125.25 2.52688
126 2.54154
126.75 2.46334
127.5 2.51711
128.25 2.49756
129 2.49267
129.75 2.52688
130.5 2.43891
131.25 2.54154
132 2.48289
132.75 2.47801
133.5 2.52688
134.25 2.50244
135 2.51222
135.75 2.50733
136.5 2.50733
137.25 2.50244
138 2.52199
138.75 2.52199
139.5 2.51222
140.25 2.50244
141 2.50733
141.75 2.51222
142.5 2.50733
143.25 2.50733
144 2.50733
144.75 2.50244
145.5 2.50733
146.25 2.50733
147 2.50733
147.75 2.50733
148.5 2.50244
149.25 2.50244
150 2.50733
150.75 2.50733
151.5 2.50733
152.25 2.51222
153 2.51222
153.75 2.51222
154.5 2.50733
155.25 2.50733
156 2.50244
156.75 2.50733
157.5 2.50244
158.25 2.50733
159 2.50733
159.75 2.50733
160.5 2.50244
161.25 2.50733
162 2.50733
162.75 2.50244
163.5 2.49756
164.25 2.49267
165 2.49756
165.75 2.49756
166.5 2.48778
167.25 2.50733
168 2.45846
168.75 2.45846
169.5 2.49756
170.25 2.49756
171 2.50244
171.75 2.49756
172.5 2.49756
173.25 2.50733
174 2.51711
174.75 2.51711
175.5 2.50733
176.25 2.50733
177 2.51711
177.75 2.49267
178.5 2.50733
179.25 2.49756
180 2.49756
0 2.51711
0.75 2.52688
1.5 2.53666
2.25 2.54154
3 2.48289
3.75 2.47312
4.5 2.49756
5.25 2.56598
6 2.50244
6.75 2.49756
7.5 2.48778
8.25 2.48778
9 2.52199
9.75 2.52199
10.5 2.54643
11.25 2.49756
12 2.48778
12.75 2.50733
13.5 2.54643
14.25 2.52688
15 2.52688
15.75 2.48289
16.5 2.49756
17.25 2.52199
18 2.52199
18.75 2.51222
19.5 2.47801
20.25 2.45846
21 2.50733
21.75 2.52199
22.5 2.52199
23.25 2.48778
24 2.49267
24.75 2.50733
25.5 2.51222
26.25 2.53177
27 2.52199
27.75 2.47801
28.5 2.49267
29.25 2.50244
30 2.54643
30.75 2.52688
31.5 2.45846
32.25 2.48778
33 2.51711
33.75 2.50244
34.5 2.52199
35.25 2.47801
36 2.48289
36.75 2.46823
37.5 2.50733
38.25 2.51222
39 2.52199
39.75 2.43891
40.5 2.41447
41.25 2.42913
42 2.47312
42.75 2.53666
43.5 2.42424
44.25 2.44379
45 2.50244
45.75 2.56598
46.5 2.53177
47.25 2.56109
48 2.53177
48.75 2.41935
49.5 2.42424
50.25 2.51711
51 2.46334
51.75 2.35093
52.5 2.41447
53.25 2.52199
54 2.50733
54.75 2.48778
55.5 2.46823
56.25 2.46823
57 2.43891
57.75 2.44868
58.5 2.48289
59.25 2.45357
60 2.43891
60.75 2.41935
61.5 2.41447
62.25 2.46823
63 2.48289
63.75 2.45846
64.5 2.3998
65.25 2.41447
66 2.44379
66.75 2.48289
67.5 2.47312
68.25 2.42424
69 2.40469
69.75 2.42913
70.5 2.47312
71.25 2.48289
72 2.43402
72.75 2.40958
73.5 2.3998
74.25 2.43402
75 2.46823
75.75 2.46334
76.5 2.41935
77.25 2.39003
78 2.43402
78.75 2.46334
79.5 2.45846
80.25 2.44379
81 2.44379
81.75 2.46334
82.5 2.47312
83.25 2.43891
84 2.45357
84.75 2.45846
85.5 2.46334
86.25 2.44868
87 2.48778
87.75 2.52688
88.5 2.51711
89.25 2.53177
90 2.49756
90.75 2.52199
91.5 2.51711
92.25 2.51222
93 2.50244
93.75 2.50244
94.5 2.51711
95.25 2.54643
96 2.49756
96.75 2.50244
97.5 2.49267
98.25 2.46334
99 2.52199
99.75 2.54154
100.5 2.51222
101.25 2.50244
102 2.46823
102.75 2.50733
103.5 2.54643
104.25 2.52199
105 2.55132
105.75 2.40469
106.5 2.49756
107.25 2.54154
108 2.3998
108.75 2.46334
109.5 2.45846
110.25 2.53177
111 2.55621
111.75 2.48778
112.5 2.51222
113.25 2.50733
114 2.48289
114.75 2.49267
115.5 2.44379
116.25 2.32649
117 2.45846
117.75 2.47801
118.5 2.39492
119.25 2.51711
120 2.49267
120.75 2.45357
121.5 2.54154
122.25 2.48778
123 2.51222
123.75 2.52199
124.5 2.49756
125.25 2.52688
126 2.54154
126.75 2.46334
127.5 2.51711
128.25 2.49756
129 2.49267
129.75 2.52688
130.5 2.43891
131.25 2.54154
132 2.48289
132.75 2.47801
133.5 2.52688
134.25 2.50244
135 2.51222
135.75 2.50733
136.5 2.50733
137.25 2.50244
138 2.52199
138.75 2.52199
139.5 2.51222
140.25 2.50244
141 2.50733
141.75 2.51222
142.5 2.50733
143.25 2.50733
144 2.50733
144.75 2.50244
145.5 2.50733
146.25 2.50733
147 2.50733
147.75 2.50733
148.5 2.50244
149.25 2.50244
150 2.50733
150.75 2.50733
151.5 2.50733
152.25 2.51222
153 2.51222
153.75 2.51222
154.5 2.50733
155.25 2.50733
156 2.50244
156.75 2.50733
157.5 2.50244
158.25 2.50733
159 2.50733
159.75 2.50733
160.5 2.50244
161.25 2.50733
162 2.50733
162.75 2.50244
163.5 2.49756
164.25 2.49267
165 2.49756
165.75 2.49756
166.5 2.48778
167.25 2.50733
168 2.45846
168.75 2.45846
169.5 2.49756
170.25 2.49756
171 2.50244
171.75 2.49756
172.5 2.49756
173.25 2.50733
174 2.51711
174.75 2.51711
175.5 2.50733
176.25 2.50733
177 2.51711
177.75 2.49267
178.5 2.50733
179.25 2.49756
180 2.49756
Data Analysis:
Linear fit based on graph. (Calculated using Logger Pro)
Centripetal acceleration = v^2/r = w(omega)^2*r = 0.928 * 6.6294 = 5.7 meters per seconds squared.
My cal;culated linear fit:
y = mx+b
b = y-intercept = 2.484
m = slope = 6.348 * 10^5
Centripetal acceleration = 2.5 meters per second squared.
Linear fit from (in meters per seconds squared):
-Graph: 5.7
-Data: 2.5
Centripetal acceleration = v^2/r = w(omega)^2*r = 0.928 * 6.6294 = 5.7 meters per seconds squared.
My cal;culated linear fit:
y = mx+b
b = y-intercept = 2.484
m = slope = 6.348 * 10^5
Centripetal acceleration = 2.5 meters per second squared.
Linear fit from (in meters per seconds squared):
-Graph: 5.7
-Data: 2.5
Conclusion:
In this lab, we found the centripetal acceleration of the swing ride using both the data vest and calculated values we found. There was a significant percent difference in the data, over 100% difference. This could have been caused by many different types of human error. The data vest may not have been calibrated correctly or the ride may have been slightly different than the data researched and found about the ride. This lab was fun because we went to SIX FLAGS! I am glad we're done. The end.
Works Cited:
Gotham City Crime Wave. (n.d.). Retrieved from http://www.sixflags.com/overGeorgia/rides/GothamCityCrimeWave.aspx
Wave Swinger. (n.d.). Retrieved from http://www.tutorgig.com/ed/Wave_Swinger
What is Wave Swinger? (n.d.). Retrieved from http://ipedia.net/
what+is+Wave+Swinger
Wave Swinger. (n.d.). Retrieved from http://www.tutorgig.com/ed/Wave_Swinger
What is Wave Swinger? (n.d.). Retrieved from http://ipedia.net/
what+is+Wave+Swinger
