ps7tips - Tips and Tricks for Problem Set 7 (Fall 2005)...

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Tips and Tricks for Problem Set 7 (Fall 2005) Topic: Hurricanes Before you read this… Read the problem set. Some terms mentioned in this document will only make sense once you’ve read the problem statement. You might want to look at this in conjunction with the solutions, in case anything said here is unclear. There are some neat features in the GUI so try them out and see. Motivation We started designing this problem set around the beginning of this hurricane season. There is no offense intended to anyone who has lost something as a result of the unfortunately high number of hurricanes and seemingly high number of landfalls that we’ve seen this year. Hurricanes are under active study because their behavior is not accurately predicted. Although this is true of many weather phenomena, a single hurricane often affects an enormous area and several countries, disrupting economies and lives, and destroying property. These facts make them a multimillion dollar issue, especially in the US where state governments may make evacuation orders based on predicted intensity and likely risk to people’s lives. Whenever a hurricane hits and does not do the expected damage, or the hurricane does not land where it was forecast, businesses lose money and individuals are less likely to leave in the face of a similar threat. What we’re trying to do We’re taking one model of power dissipation by a hurricane and making a GUI that finds the power dissipated and models the hurricane power density visually. The hurricane is modeled as a circular, not spiral, system. We’ve provided a number of equations that lead up to finding the power dissipation. Look at the problem set for details. The basic concept here is that the power dissipation is related to area and power density (power per unit area) is related to the radius. So we can think of power dissipation as being a function of x and y or r and θ . This would normally mean a 3-D plot and integration over the area but we have circular symmetry and that simplifies things greatly. The symmetry means that the power dissipation per unit area is independent of θ . We did some fiddling with the original equations to get the one we’ve put in the problem statement for the power dissipated within a ring. Essentially we took the original equations and did an indefinite annular integration with a 3-dimensional trapezoidal rule. Remember that the trapezoidal rule is most accurate when smaller steps are taken. What they must now do is choose a step size for the radius that is “small enough” and sum the energy over all the rings to get the total.
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Once they can perform the calculations, they’ll need to draw the power density of the storm as concentric circles. By this time, they should have a method that calculates power density at a single radius. They’ll have to figure out that we’ll need a range of power densities and their corresponding
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This note was uploaded on 11/29/2011 for the course CIVIL 1.00 taught by Professor Georgekocur during the Spring '05 term at MIT.

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ps7tips - Tips and Tricks for Problem Set 7 (Fall 2005)...

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