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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 3D 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 3dimensional 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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View Full Document 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.
 Spring '05
 GeorgeKocur

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