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Golden Ratio Lab #11

Thaelis E. Suriel
Physics- Period 6
Ms. P
Lab Report # 11

Title: what is the velocity and acceleration of a hurricane and a tornado? How do you graph the golden ratio?

Hypothesis: I predict that the velocity and acceleration of a tornado would be about 300 mph and the velocity and acceleration of a hurricane will be about 150 mph. I also predict that the golden ratio can not be graphed since it is an irrational number.

Materials: -Paper - Pen - Computer (for Excel and Internet) - Calculator - The equations needed to find out the prroblem

Procedure: Using the information given to me by Ms.P, I researched information about the golden ratio and came up with the polar equation R=Ae^k(theta), a and theta being any variable in the same increments. For K = ln(phi)/(.5*pie), phi=(1+sqrt(5))/2. and in order to graph I had to change the polar equation in to x and y points. The equation for x is rcos(theta), and the equation for y it is rsin(theta). and graphed the golden spiral

Data: See exhibits

Analysis: “The Golden Spiral structure represents two well known sacred geometry shapes: the golden mean (phi) spiral and the Fibonacci spiral. It is a based on a crop circle shape known as the "Hackpen Hill Formation" and it appeared in an English wheat field in 1999. Phi (golden mean) - "The key to the physics of the cosmos" (plato)Phi is a constant value which is even more mysterious and profound in its implications than pi. Like pi, phi is a number with no arithmetical solution. The decimals just keep on going into infinity without ever repeating themselves. The unique thing about this number is that it can be found incorporated in all known organic structures. From the bone structure of human beings to the seed pattern of a sunflower to the spiral of a sea shell, the phi proportion is there, underlying all biological structures, seeming to be a geometrical blueprint for life itself. Plato went so far as to call the phi ratio the "key to the physics of the cosmos". Phi is calculated at 1.6180339+.….” (http://www.ka-gold-jewelry.com/p-articles/golden-spiral.php)The Golden spirals can also be found in the shapes of hurricanes and tornadoes. Hurricanes that can have “wind velocites of up to 155 mph and greater and a acceleration of about 150 mph or higher to the east, start being formed with a region of intense low pressure over warm ocean pools. Water evaporating off the ocean's surface releases heat as it condenses to form clouds, and this heat causes the low-pressure area to grow. Winds generated by the expanding low-pressure area begin to spiral inward, forming the cloud-free eye at the center of the storm.” http://www.lbl.gov/Science-Articles/Archive/sabl/2005/August/02-lube-the-wind.html Huricanes can also cause Tornadoes. Tornadoes can have a wind velocity of 319 mph and an acceleration of about158 mph they can be caused by “thunderstorms, that develop in warm, moist air in advance of eastward-moving cold fronts. These thunderstorms often produce large hail, strong winds, and tornadoes. Tornadoes in the winter and early spring are often associated with strong, frontal systems that form in the Central States and move east. Occasionally, large outbreaks of tornadoes occur with this type of weather pattern. Several states may be affected by numerous severe thunderstorms and tornadoes. During the spring in the Central Plains, thunderstorms frequently develop along a "dry line," which separates very warm, moist air to the east from hot, dry air to the west. Tornado-producing thunderstorms may form as the dry line moves east during the afternoon hours. Along the front range of the Rocky Mountains, in the Texas panhandle, and in the southern High Plains, thunderstorms frequently form as air near the ground flows "upslope" toward higher terrain. If other favorable conditions exist, these thunderstorms can produce tornadoes. Tornadoes occasionally accompany tropical storms and hurricanes that move over land. Tornadoes are most common to the right and ahead of the path of the storm center as it comes onshore.” http://www.nssl.noaa.gov/edu/safety/tornadoguide.html

Conclusion: In conclusion my hypothesis was wrong because For the velocity and acceleration of the hurricanes and tornado the numbers were too high and I was able to graph the Golden ratio. References: http://www.ka-gold-jewelry.com/p-articles/golden-spiral.php http://www.nssl.noaa.gov/edu/safety/tornadoguide.html http://www.lbl.gov/Science-Articles/Archive/sabl/2005/August/02-lube-the-wind.html