For the AMSI Solar cooker a simple wood model is used as a tool to assure the exact parabolic shape of the mirror. Precision is very important to get a small focal sun-spot and a high cooking temperature. With an off shape mirror the focal concentration becomes spread and eventually uneven distributed resulting in a cooker which heats up very quickly but does not reach higher temperatures than e.g. 95°C.
To design a parabola I recommend a very simple drawing tool which is able to construct any parabolic curve with ease:
Drawing Tool (click on the pictures to enlarge them) Usage of the Tool
it is a right angle ruler made of wood which can be used for many other purposes as well. At the top of the T-shaped device a string of variable length can be fixed. The string should be made from non elastic material like nylon which does not expand when stressed. The free end of the string holds a little ring or washer.
When put on a table or platewood board the lower horizontal part is pressed against the edge of the table so that the vertical part is always in a right angle to the edge while the tool may slide along the edge line.
Let's take a platewood board with a straight edge at the base and let's press the T-shaped tool now on the platewood edge, so that the vertical part marks the axis of the parabola passing through the focal point. Mark the focal point with a nail or screw on this axis in a distance to the baseline (edge of the board) equal to the focal distance of the parabola to be constructed.
Hook the string with the ring over the screw a the focal point and place the string along the tolls vertical edge down to the baseline around the tip of a pencil which will later draw the parabola and up along the same edge to the top of the T-tool. Fix the string at the top of the tool so that the string is stiff stretched in this shape. Now sliding the tool to the right and following with the pencils tip the vertical ruler at the T-tool while keeping the string stressed will draw a parabola with the focal distance equal to the distance between the focal point and the start point of the pencils tip. (see pictures below)
click on the pictures to enlarge them.
In this example the focal distance has been chosen to be 270 mm (which is the value for the AMSI cooker and the SK14 and K14 cooker of EG-SOLAR). The other measures marked on the board are not needed to draw the parabola curve, but give the positions of the cage rings for the SK14 cooker and thereby proof that this tool works perfect!
To make the string visible, a blue wool string is used and the pens tip is replaced by a red pin. To draw the curve the wool string should be replaced by something inextendable like a nylon string (e.g. 0,5 mm as used for sea fishing).
It is maybe interesting to mention that string in any drawing position represents as well a ray coming from the sun parallel to the parabola's axis, hitting the parabola mirror and being reflected to the focal point! (Nice! Isn't it?)
By this means an exact parabola can be drawn for any focal distance and diameter with just 2 pieces of straight wood, four little nails an a piece of stiff string.
If you prefer to use a computer to get x-y-coordinates and draw a parabola through calculated points you may use a nice program which can be found here: http://mscir.tripod.com/parabola/
Meanwhile I learned that this method is called the setsquare method for drawing a parabola. A nice visualisation you can see here.
Note, that the red lines (F-P-B) in the simulation represents the string on the pictures above and that the length of the sum of the lines F-P and P-B ist constant. And the mathematical background is: "A parabola can also be defined as locus of points in a plane which are equidistant from a given point (the focus) and a given line (the directrix)."
Parabola-Links:
Formulas for Parabola-design:
http://mathworld.wolfram.com/Parabola.html
Why does the drawing-tool work?:
http://mathcentral.uregina.ca/QQ/database/QQ.09.96/wennberg1.html
or try to move the points F or B on this site with the mouse
http://www.xahlee.org/SpecialPlaneCurves_dir/ggb/parabola_tracing.html
If you cut out two pieces of platewood as shown below and put them crosswise together the wood model is ready which can be used as kind of scaffolding and support for the mirror's cage during construction:
click on the picture to enlarge it
The positions where to place the rings are marked by little black triangles. A gap with the same width as the thickness of the plate is cut out along the parabolas axis from the bottom to the mid at one piece and from the top to the middle at the second piece so that the two pieces fit together in a stable position as shown above without glue (see construction manual section 2.2.2, Figure 3). The model can be taken apart again for storage without effort.
click on the pictures to enlarge them.
Now after making exact rings of sizes as described in the construction manual (section 2.3.3) they can be placed on the wood model and the connection bars can be bend in a way they touch all the rings without stress before fixing them with wire and welding the cage. The nice thing is that even if a ring is slightly larger or smaller the cage will be still perfectly parabolic.
Using a model with eight instead of four 'wings' may be used if the cage should be made from bamboo as a parabolic basket, if reinforcement bars for concrete are too expensive or not available.