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Josh wrote:
wrote:

D'oh! Must have missed that on the read-through. Boy, is my face red.

However, the question remains--what if I wanted a curve with a
different amplitude or wavelength? This template idea crossed my mind,
but how to generate such a curve? Can Autocad do it? I've just
received a copy of Autocad 2005, but really don't have much clue as to
how to actually use it. I've bought the "for dummies" book, but
haven't sat down and dug in yet.

At any rate, thanks, Frank.

You could make a somewhat complicated jig to do it, but it's probably a
lot easier to just plot points. First, pick your wavelength
(horizontal distance from peak to peak or trough to trough). Let's say
it's 6", which is pretty close to what they used in their pattern.
We'll call that "L". Then pick your amplitude. That's the height of
the waves from the midpoint. In their example, I think the pattern is
about 2 1/2" from peak to trough, which means that it's 1 1/4" to the
midpoint. So the amplitude is 1.25; we'll call that "A". Then you
simply take a piece of graph paper, plug in the formula for a sine wave
into a calculator or into a spreadsheet, like Excel, and start plotting
points. It's definitely easier on Excel, because you can do it once,
and just copy and paste a bunch of times to get the rest of the points.
The formula is y = A*sin(2*pi*x/L). If you're calculator is in degree
mode, rather than radian mode, the 2*pi simply becomes 360. Just plug
in values for x, and plot the corresponding value of y on a sheet of
graph paper.

As I said, it's easier in Excel. Here's how you'd do it:

(1) Open up a blank worksheet.
(2) In the first cell (A1), put your desired wavelength (e.g. 6).
(3) In cell B1, put in your desired amplitude (e.g. 1.25).
(4) In cell A3, put in this formula: =(ROW()-3)*$A$1/24
(5) In cell B3, put in this formula: =$B$1*COS(2*PI()*A3/$A$1)
(6) Select cells A3 and B3 and copy them to the clipboard
(7) Select a block of cells from A4 to B27 and paste from the clipboard
(8) Select all cells (ctrl-a), then format cells (ctrl-1). Select the
"Number" tab, and force the category to be "Number" with 3 decimal
places.

The results should be as follows:

6.000 1.250

0.000 1.250
0.250 1.207
0.500 1.083
0.750 0.884
1.000 0.625
1.250 0.324
1.500 0.000
1.750 -0.324
2.000 -0.625
2.250 -0.884
2.500 -1.083
2.750 -1.207
3.000 -1.250
3.250 -1.207
3.500 -1.083
3.750 -0.884
4.000 -0.625
4.250 -0.324
4.500 0.000
4.750 0.324
5.000 0.625
5.250 0.884
5.500 1.083
5.750 1.207
6.000 1.250

At this point, the first column is a list of x-values ranging from 0 to
6 (in 1/4" increments in this particular example). The second column
is a list of corresponding y-values ranging between -1.25 and +1.25.
Just plot this pairs of point on graph paper, connect the dots, and cut
out your pattern. You could also create a scatter plot in Excel and
experiment with the page scale until you can print it out at exactly
1:1 scale.

You may notice that I chose to use cosine, rather than sine, in my
formula. Either one will give you the same shape in the end, but a
cosine curve will start and end at a peak, whereas a sine would start
and end at the midpoint.

Josh

Thanks, Josh. Scuse me, I've got a spreadsheet to build.

-Phil Crow