Alex Molina & Kadeem Nibbs
Computational 375 – Project

GOAL: Week 2: Run simple trial with one-dimensional object in two-dimensional space with air resistance ( varying wind speeds and air densities)

In all track events run/jumped primarily in one direction, wind is an important consideration in athletic performance. In the long jump, and in the shorter sprinting events (the 60m, 100m, 200m, and all of the similarly distanced hurdle races), the maximum allowable tailwind (wind propelling the athlete forward), is +2.0m/s. There is no maximum allowable headwind (wind pushing the athlete back), but at headwinds stronger than -5.0m/s, an event might be postponed. For our latest results presentation, we compared the jump trajectories while varying wind assistance and air density, in each case holding all other variables constant.

Our original goal for the week was to improve our model to have a 3D projectile with limb objects, functions to bend and extend the limbs, and methods to calculate the cross-sectional area and center of the mass of the body depending on the state of the limbs. However, we could not figure out how to implement object-oriented design in MatLab, and we failed to properly define functions in our code, which made our prospects shaky at best. We instead decided to learn what information we could from our current working model.

Our results showed that wind assistance has a major impact on performance in the long jump, as a jump into a 5m/s headwind netted a distance of about 5 meters, a mediocre distance for a male high school jumper, and a jump propelled by a 2m/s tail wind recorded a distance of nearly 25 feet, which is an elite college-level distance. We found that air density had a negligible effect on the jump distance, variations of up to 50% in air density resulted in less than a millimeter difference. This reaffirms what we learned in introductory mechanics, that air resistance is negligible in most cases of projecting motion, the exceptions being when the air is moving, and when the object is moving at high speeds. Air resistance will not significantly affect an athlete jumping at 20mph into still air. This also shows that although air density can be as high as 1.2kg/m^-3 at cities near sea level, and as low at .75kg/m^-3 at cities 5000m above sea level, long jumps performed at any city in the world can be compared because of air density’s negligible effects on performance.

Important Links:
MatLAB code and other essential information can be found at:
https://drive.google.com/open?id=0B6loGd4o7iESfjNoRnVmSjJDNHlabG9qNEJIRmY1Z1JEeS1QNE9rTjlIY2Vqc1NMTWlwdEk&authuser=0

References:
Giordano, Nicholas J., and Hisao Nakanishi. “Chapter 2: Realistic Projectile Motion.” Computational Physics. 2nd ed. Upper Saddle River, NJ: Pearson/Prentice Hall, 2006. Print.

Our Resulting Projectile Motion with Varying Wind Speed:

Our Resulting Projectile Motion with Varying Air Density:

UPCOMING: Week 3: 
Run a second trial with a mass-less two dimensional object in 3-dimensional space. We will more to run two test trials with three-dimensional object in three-dimensional space, each with different body position.