Regional Science Olympiad Competition

Grandview Heights

March 19, 2005

**First Place Rocket Video**

** **

The launch of the rocket was recorded with a Nikon Coolpix 5200 in video mode capturing 600x480 pixels at 30 frames per second. Links are provided to the original film as well as a slow motion version of the film. The following jpeg shows that the rocket launch was visible in 7 separate frames (7/30 of a second). Using these frames the pixels of the center of the rocket engine were measured for each of the seven frames. A reference point at the bottom of the launch pad was also digitized to remove camera jitter. The following data was collected in units of pixels.

Frame |
Y Launch Pad |
X Launch Pad |
Y Rocket Engine |
X Rocket Engine |

1 |
357 |
279 |
326 |
279 |

2 |
357 |
278 |
326 |
279 |

3 |
356 |
280 |
312 |
280 |

4 |
354 |
278 |
278 |
278 |

5 |
355 |
276 |
222 |
273 |

6 |
356 |
278 |
145 |
270 |

7 |
354 |
280 |
63 |
259 |

To get some estimate of meters/pixel in the picture the man at the far right was also measured (375-257=118 pixels). Assuming the man is 6 ft tall this yields 0.0154 meter/pixel. Analyzing the data above yields the following table for time versus the height of the rocket.

Frame |
Time |
Height |

2 |
0.000 s |
0.000 m |

3 |
0.033 s |
0.697 m |

4 |
0.066 s |
1.172 m |

5 |
0.100 s |
2.020 m |

6 |
0.133 s |
3,254 m |

7 |
0.166 s |
4.488 m |

Note that frame 2 is not the exact launch time of the rocket. A plot of the height(meters) versus time(seconds) for the rocket is displayed below.

It is seen from this plot the rocket reaches a nearly
constant velocity in 0.1 seconds. The final velocity of the rocket (slope on
the graph) is calculated to be 37 m/s (121 ft/s). Since the rocket is losing
mass (water) the acceleration is not constant. For fun assuming the
acceleration is constant, x=at^{2}/2, 2=a (0.1)^{2}/2, yields
an acceleration of 400 m/s (40 g’s).

The rocket at this point is a simple projectile. Ignoring air friction one can calculate the final height it should reach using simple trajectory equations.

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With an initial velocity of 37 m/s a projectile will reach its maximum height in 3.77 seconds. This added to the 0.1 seconds it takes to accelerate yields 3.9 seconds. The time to reach the peak height was measured by stop watch to be 4.0 seconds which agrees quite well with this expected time. From this we conclude there must have been little effective air resistance. Using the equations the maximum height of the rocket will be 70 meters (230 ft).

It is noted that the rocket veers of course reaching a final angle of 11 degrees with respect to vertical. This angle would lead to a decrease in height of about 5 percent. It is not clear from the video if this is due to the aerodynamics of the fins or an asymmetric rocket nossel.

If you wish to analyze these frames yourself the frames of interest are linked here: frame1, frame2, frame3, frame4, frame5, frame6, and frame7.