## Intro: Parabola Plotting Web Pages

Graphics have become more available on web pages. A web page that can design parabolas can show what is now available.

## Step 1:

Different applications require parabolas having different focal points. A parabola follows the following equation.

Y = X^2/(4*focal)

The old camera flash bulbs appeared to use a short focal length when compared to its radius. When the focal is 0.25, then Y will be unity when X is unity.

The web page to do this is only a text file. Feel free to save it as source on you computer.

## Step 2:

Solar application may need a long focal length. If the focal is 1, then Y will be 0.25 when X is one. The radius of the parabola can be thought of as being X. The depth of the parabola can be thought of as being Y.

## Step 3:

Some applications may require the focal point to be close to one half the depth. Using a focal which is at sqrt(1/8) will do the job.

## Step 4:

The new graphing feature can be extended such that a web page can print out the segments of a parabola. The web page that does this is only a text file. Select a focal and whether to plot segments or the sides. Feel free to save this page on your computer. Look at the page's text.

## Step 5:

The parabola is design to step X from 0 to 1 in 0.1 units. The side view plots both the X steps and the corresponding Y steps as lines. This web page should be printable on a single sheet of page. Or it can be saved as a pdf file to be printed later.

## Step 6:

Half of a parabola can be constructed by printing out six segments and a left and right side.

## Step 7:

The lines on the half parabola show how well all the X and Y dimension line up.

The plots are 700x700 bitmaps which avoid the auto scaling features found in most plotting resources. The plot will define a segment shape from a input a focal length which is relative to the parabola's radius. By importing these plots into a graphic application for scaling, it should be possible to construct any type of parabola desired.

## 10 Discussions

3 years ago

When you print the left and right side. I'm not sure where the focus point is?

Could the script be modified to place a X at this location?

3 years ago on Introduction

neat

7 years ago on Introduction

I tried the web page and nothing happened. Did I miss somethihg

8 years ago on Introduction

The unit of measurement in the focal point thing is?

Reply 8 years ago on Introduction

The focal length corresponds to the radius along the x direction being unity. The web page that plots the segments does do an auto-scale to fill a 700x700 canvas.

Another write up on what things do can be found here...

www.idea2ic.com/OtherStuff/Web_parabola/Design_A_parabola.html

Reply 8 years ago on Introduction

Ok, thanks.

8 years ago on Introduction

On Step 5, you say that you only generate 11 X points, and (implicitly) do a linear interpolation between them. For focal depths far from 1, this is not optimal. I played with the script, putting in 0.05 and 0.005 respectively. In both cases, the straight lines and corners in Y are quite apparent (the latter has just two lines!).

To get a smother curve, you may want to consider evaluating the inverse problem to get Xmax (positive) for Ymax at the boundary of the plot, then generate a fixed number of steps from X=0 to X=Xmax.

Otherwise, this is a very clever bit of JavaScript. Nicely done!

Reply 8 years ago on Introduction

Well good. Someone did not treat the web page as a black box. The idea is to show what graphic on a web page can do.

Reply 8 years ago on Introduction

:-) When you said it was a "plain text" file, I got curious. Nice to see simple scripting, rather than some overwritten applet that gets downloaded to do who knows what.

Reply 8 years ago on Introduction

I think the people who write instructables could get really turned on with what they could do with web pages. This stuff could be fun if presented right. My best attempt at doing this can be found here.