# Thread: Draw a sine wave

1. How can I draw a sine wave on a piece of paper?
It will be great if I get a formula x = f ( y ) so that I can plot it on XY axis o a paper.

2.

3. y=sin(x)

4. Sorry to say that What I really need to do is fabricate a piece of pipe 36” dia. one end straight cut and other end at 45 degree. So we’ll have 3 sides of metal sheet straight but 4th side will be like a sine wave but not exactly. Can you pl. help?

5. No, sorry. I can't picture that.

If you cut a pipe off at a 45 degree angle, it would form an elliptical shape.

Perhaps what you are trying to do is cut the pipe at a 45 degree angle, but you don't have a long enough saw blade to simply clamp the pipe in a jig and cut it. You want to take a jigsaw and cut around the outside. Is that it?

6. I think the following might work. I haven’t tried it – just scribbled out a sketch at work. If it doesn’t work, well I screwed up.

Calculate the major axis of the ellipse using trig. The minor axis is the diameter of the pipe. Draw your ellipse, using a piece of string.

Draw a series of radial lines at equal angles; say 15, 30, 45, 60, 75, 90 degrees, from the intersection of the major and minor axes. Measure off and write down the straight lengths of the chords subtending each angle at the circumference..

Draw the rectangle representing the unrolled pipe with square ends. Draw horizontal lines from end to end of the unrolled pipe, equally spaced to give you the same number of segments as you had angular segments in the ellipse. On the circular end of the pipe these will all be the same length. At the 45 degree end, use a ruler to draw a line of the length you wrote down corresponding to each segment. These lines will be of different lengths and will all be longer than the corresponding lines at the “straight” end, so in order to fit them between the lines bordering each segment you will have to slope the line that you draw.

With any luck this will build up an approximation of the curve you need so when you roll up the paper you will have a pipe with one end cut at 45 degrees.

Or not. But that’s what I’d try.

7. Thanks to both of you, seamed pipe is costlier that is why I go for fabrication, and I have a verity of bulk requirements of different thickness, angle and diameter. I know Bunbry’s method, it is the procedure my people do at present. But I need a formula y = A sine(x), and ‘A’ could be the major axis of the ellipse. I’m not sure weather the formula is correct?

8. Try posting in the mathematics subforum - it's basically a math problem. Otherwise use trial and error. Try your formula using a sheet of paper. If it works, great; if it doesn't try again.

9. Originally Posted by sak
How can I draw a sine wave on a piece of paper?
It will be great if I get a formula x = f ( y ) so that I can plot it on XY axis o a paper.
Sorry I took so long to get back to ya. I have been a bit busy. I think this is what you are talking about. We actually make stuff like this by hand sometimes. But more often we just let the plasma cutter do it. We also do conical shapes funnels and square to rounds by hand all the time.

http://www.Rockwelder.com/Welding/St...d/sspipetv.jpg

Sincerely,

William McCormick

10. y=A + B * sin( (180/pi) * x / D )

A = Lmax - 0.5 * D * ctg (alpha)

B = (Lmax - Lmin) / 2 = D * ctg (alpha) / 2

D = diameter of pipe

Lmax = length of pipe at "longest" point (the tip of the slanted end)

Lmin = length of pipe at "shortest" point (where the slanted cut gets closest to the straight end)

alpha = angle between the direction along the pipe and the slanted cut, i.e. 90 degrees is a straight cut, 10 degrees is a very oblique cut like the tip of a hypodermic needle, 0 degrees is impossible (or you cut along the pipe).

The arguments of the sine and cotangent functions are in degrees.

Warning: anything free comes with no guarantee. I may have made a mistake. Try it on cardboard first, and don't charge me for any wasted steel.

11. Thanks for every one,
I think Leszek Luchowski missed one think the 'x', further I would like to have some proof free!

12. Originally Posted by sak
I think Leszek Luchowski missed one think the 'x',
Where exactly?

Do you mean I forgot to define the "x"? I thought it was obvious; it's the abscissa (the independent coordinate) measured across your sheet of metal. When you roll the cutout into a tube, the OX axis will bend into a circle and become the circumference of the straight end of your tube. The OY axis is where you will have to make a seam.

Depending on your welding or soldering technique, you may want to extend the range of "x" slightly beyond pi*D so as to get some overlap.

Let us know how it all works out.

Good luck,
Leszek.

Call the longitudinal axis the z-axis. You want to plot z as a function of the angle(theta). X and y are the horizontal and vertical axes as you would view the cylinder end-on.

If you sliced the cylinder at a 45 degree angle, making the cut parallel to the x axis, then for any point on the cut surface, y would be equal to z. Or y=-z depending on which direction your cut was made.

Then if you looked at the cylinder end-on, the y coordinate of a point on the circumference is given by y=r sin(theta). And since y=z, z=r sin(theta).

So you lay out the sheet metal of width 2*pi*r and mark it in degrees from 0 to 360 or (0 to 2 pi) and plot z=r sin (theta).

14. The answer i was looking was like mark Y axis with ; ; ; ... to

then mark X axis with ; ; .. to .. ;

in order to get 1/4 th part of the devolepment of a 30 degree angle pipe cut.

but still it is manuel. i need somthing more scientific probably with differential equation.

15. If you are looking for a formula for the numerical approximation for the sine wave, you can use the taylor series approximation:

sin(x) = x - x^3/x! + x^5/5! - x^7/7! + x^9/9! - x^11/11! ...

If you just use the first four terms:

sin(x) = x - x^3/6 + x^5/120 - x^7/5 040

Then you will be pretty accurate.

In reality, you really only need to calculate up to sin(90) or sin(Pi/2), because everything else is symmetric (ie, from sin(90) to sin(180), it's just the same thing as the first 90 but backwards...from sin(180) to sin(360), it's just the same as the first 180 but negative)

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