Calculus III -Project The Barberton Lathe Problem
February 2004- Professor Broughton
Due Date: Tuesday February 2003
1 Project outline
A business in Barberton Ohio makes headlamp molds for an auto manufacturer..
The headlamp molds are made with the aid of a computer controlled lathe.
Certain traditional data is used to model the head lamp. The head lamp must
closely approximate the data to be acceptable to the customer. When the
coordinates of the points are plotted they roughly form the outline of the desired
mold. Unfortunately the data has enough errors in it that if the lathe template
exactly passes through all the data points then there are wiggles in the resulting
model. A mold with a lot of wiggles in it will not properly reflect light and
will be unacceptable to the customer. Fortunately the computer driving the
lathe can be programmed either by a set of data points or a polynomial profile
function. (we simply enter the coefficients of the polynomial). We may get a
suitable template by choosing an approximating polynomial that nearly passes
through all the points. The data provided by the client is contained in the file
barberton.mws and consists of a set of pairs of xand ycoordinates
The client originally thought that mold could be modeled by a function of
the form:
x=b+a(c−y)n
where nis possibly a fractional exponent, and a, b, and care parameters to be
determined (recall that a perfect reflector has the shape of a parabola, n=2).
The client was not successful
Deliverable: The customer needs the coefficients of a simple polynomial y=
f(x) that well approximates the given data but does not have to much wiggle.
You will need to convince the client that your result is a good approximation
andthatthereisnottoomuchwiggle,andthatitjustasvalidworksjustaswell
as his proposed model. Each of the class teams must submit a report addressed
to the client’s engineer containing the following elements:
•Problem description
•Proposed solution supplemented by profile graphs as appropriate
•Justification of the proposed solution including a measure of the “wiggle”
•Outline of the method of analysis
•Maple analysis as appropriate,
•A section listing team member contributions and signed by all members.
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