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Drawing a Parabola for Solar Cooking Answered

I'm building something using a parabolic curve mirror to heat water with the sunshine. I've been out of math class too long....I found these nice sites to help simplify drawing a parabola.

Parabola Design Wood Model
Draw a Parabola, using pencil and string


Once you have your parabolic trough or dish, use it to heat a quantity of mineral oil to the temperature you want to cook with. Store mineral oil in an insulated container (thermos) to retain the heat. Use that heat to cook at a later point in time, well after dark or even first thing in the morning. Use a thermometer to monitor the oil's temperature as it heats & remove the oil once you reach your preferred cooking temperature.

This will allow solar cooking at midnight, if you like. A solar trough should heat your mineral very quickly. After that, store it and use it to cook whenever you feel like it within the next 24 hours, wherever you feel like cooking, be that inside your kitchen or out doors while camping.

Good luck.

what an interesting webpage can i view this from unn.edu.ng

Super Simple parabola ! Check the "Geometric method" in the latter hald of the page.


Here's a Q&D method for drawing a parabola and creating a small trough-style cooker:

Drive a nail 8 inches in from the edge of a piece of plywood.

Position the inside edge of a carpenter's square up to the nail, with the other inside edge sliding along the edge of the plywood, so as to describe a perpendicular line from the edge of the plywood 'down' to the nail.

Fasten an 18" piece of string between the nail and the inside angle of the square.

Put your pencil inside the loop of the string and pull 'down' (away from the edge of the plywood), so that the string makes a straight line along the inside edge of the square, down to the pencil which will be 13" down the edge of the square, and overlapping itself for the 5" back up to the nail.

The nail is the focus of the parabola, the pencil is at the vertex, and the string (and inside edge of the carpenter's square) is aligned along the axis of symmetry.

To draw half of the parabola, slide the square along the edge of the plywood so as to pull it away from the nail, keeping the pencil firmly against the inside edge of the square and pulling 'down' to keep the string taut.  As the square pulls away from the nail and the pencil is pulled by the string up the edge of the square, it will draw half of a perfect parabola.

To draw the other half of the parabola, flip the square over, re-position its inside edge on the other side of the nail, and repeat these steps, pulling the square away from the nail in the opposite direction.

You can modify these measurements to create whatever size parabola you wish.

To make the cooker, cut out two identical rectangles from the plywood, each with a parabolic 'bite' cut from one of the corners.  These will become the end pieces of your solar cooker.  Tack a piece of sheet metal (or foil-lined cardboard) along the curve of each parabola so that it resembles a bus bench, with the plywood at the ends and with the sheet metal as the 'seat'.  The width of your 'bus bench' should be about 16".

You can use a pot to cook in, but a trough is better, as it will block less sunlight.  You can make a serviceable trough by sacrificing a large unopened can of soup (this trough will eventually leak from the crimped edge of the can's top, but Hey, it's a soup can, not Pampered Chef!).  Cut the cylindrical can vertically in half, down to but not including the bottom.  Fold the bottom disk in two (be careful, use gloves!), so that you have two half-can troughs connected by the folded bottom.  Punch small holes just below the fold in the bottom and just below the cut edges of the top, and run small hooks fashioned from a wire clothes hanger through these holes.  Suspend your trough by hanging these hooks from a bar or dowel.  Finally, attach the ends of the dowel to two small boards (such as paint stirring sticks, or wooden rulers) that themselves are screwed into the plywood ends of the parabolic reflector.  Position the boards and dowel so that the bottom of the cooking trough is at the level of the focus (where the nail was).

Be careful to not get any part of your body, especially your eyes, anywhere near this focus point, when the reflector is in the sunlight!

Rotate the reflector to keep it pointed at the sun for maximum cooking efficiency.

if you want a solar cooker, 
use the formulas here : http://en.wikipedia.org/wiki/Parabola
or http://www.intmath.com/Plane-analytic-geometry/4_Parabola.php
Mark/ measure and cut out one half of a parobolic curve on a piece of plywood( your template). Cut multiple 1/2 parabolas and build it round to form a "dish" formation. ( make sure you have flat edges on the floor) Then line your "dish" with reflective material to focus the sunlight. (Personally , I like cut mirrors for maximum reflectivity) So a circular 1 foot dish gives you approx 113 sq inches or about 78 watts of focused energy. Enough to melt a marshmallow.
 Using an 8ft satellite dish equates to 7238 square inches or about 50 ft^2 and in full sunlight  should focus enough energy equivalent to power a small microwave oven or approx 5000 watts.  Thats enough concentrated light to melt the plastic and electronics inside the dish feedhorn or ignite a marshmallow in a couple of seconds.

Put two nails in a board as foci and loop a string that's long enough to fit loosely over both nails. If you pull the string tight with a pencil and trace the shape of the string pulled tight around both foci, doesn't that trace a parabolic oval?

That traces an ellipse, not a parabola. A "parabolic oval" is an oxymoron.

An ellipse has two focal points (the two nails in your construction). A parabola has only a single focal point (the single nail in the construction robbtoberfest linked to). Mathematically, you can think of it as an ellipse with one focal point at infinity.

Nope. It makes one smooth ellipse:

"An ellipse is a curve that is the locus of all points in the plane the sum of whose distances r_1 and r_2 from two fixed points F_1 and F_2 (the foci) separated by a distance of 2c is a given positive constant 2a (Hilbert and Cohn-Vossen 1999, p. 2)."


Yeah, but I meant that that method will work

It will work about as well as sketching a parabola by hand. I.e. it will tend to focus the sun's rays to some extent, but not as well as a real parabola. Rather like making a lens that is not quite spherical: it will focus somewhat, but not nearly as well as a well-shaped lens.

You can do it if the second nail is infinitely far away (ie in the sun). You can approximate that by having the other end of the string tied to a tree 100' away. Compromise?

Ok, but, if I want to print a parabola on a sheet of paper to use as a pattern, do you know of a quick and easy (ie software) way to print a parabola.

That's the method I was going to recommend, then I saw the second link and realised that he already had the easiest answer (because the sunlight would get focussed at the point where the nail is bashed in) and it would be a waste of time for me to reply ....


I use Rhino 3d for anything like this. I started using it for 3d animation, but it also turns out to be unbelievably helpful for any kind of prototyping. Especially optical stuff as you can reflect curves off surfaces and do all your form development in computer completely accurately.


The evaluation version only lets you save 25 times, but you can print as much as you like...

It's pretty easy to pick up, for what it is, any questions at all feel free to contact me.

. A Q&D; method I've used is to fix one end of a flexible rod and apply force to the free end - trace the arc. Not perfect, but close enough for most projects. . Draw a grid and plot by hand.