The trough has the cross section of a parabola and a tube

running the length of the parabola's focus heats up when

exposed to sunlight. Here is the design and implementation of

such a solar collector.

running the length of the parabola's focus heats up when

exposed to sunlight. Here is the design and implementation of

such a solar collector.

See Nested Parabolas on another page on this site.

PARABOLIC TROUGH |

Fancy:

Use Nested Parabolas to find the curve that accounts for 1/4 inch

plywood backing as detailed in another page in this site. This is the

cut in the frame that results in the precise parabola surface facing the

sun.

Note that in calculating the arclength, not all math programs are the

same. There was a 1/2" error using Graph, so I resorted to using a

Spreadsheet. I used trial and error to find what focus would accept a

48 inch wide sheet of 1/4 inch plywood curved into a shallow

parabola, on a 48 inch wide 1/2 inch thick plywood frame with 2

inches to spare on each side. That is, the 4' wide 1/4" plywood must

be bent minimally into a parabola that is 44" wide at its top, so that

the frame can be cut out of 4' wide 1/2" plywood with structural

integrity.

Use Nested Parabolas to find the curve that accounts for 1/4 inch

plywood backing as detailed in another page in this site. This is the

cut in the frame that results in the precise parabola surface facing the

sun.

Note that in calculating the arclength, not all math programs are the

same. There was a 1/2" error using Graph, so I resorted to using a

Spreadsheet. I used trial and error to find what focus would accept a

48 inch wide sheet of 1/4 inch plywood curved into a shallow

parabola, on a 48 inch wide 1/2 inch thick plywood frame with 2

inches to spare on each side. That is, the 4' wide 1/4" plywood must

be bent minimally into a parabola that is 44" wide at its top, so that

the frame can be cut out of 4' wide 1/2" plywood with structural

integrity.

At x=+/-21.929", y=12.266" defines the

ledge against which the 4' width of 1/4"

plywood is hooked into place. The rest

of the x values are given in 2" intervals.

The y values for each interval were

calculated using experimentation on a

spreadsheet. The values would be

good candidates for Newton's Method

for more precise results. Note that 4" is

added to each y value to accommodate

for the frame. These points are plotted

on large graph paper and the points

connected with a flexible ruler to

describe the curve. These are the

points that describe the lower curve

that is cut into the frame so that after

the 1/4" plywood is applied it results in

the exact depiction of the parabola. A

thick layer of reflective Mylar is then

glued to the surface of the plywood for

the economical result.

ledge against which the 4' width of 1/4"

plywood is hooked into place. The rest

of the x values are given in 2" intervals.

The y values for each interval were

calculated using experimentation on a

spreadsheet. The values would be

good candidates for Newton's Method

for more precise results. Note that 4" is

added to each y value to accommodate

for the frame. These points are plotted

on large graph paper and the points

connected with a flexible ruler to

describe the curve. These are the

points that describe the lower curve

that is cut into the frame so that after

the 1/4" plywood is applied it results in

the exact depiction of the parabola. A

thick layer of reflective Mylar is then

glued to the surface of the plywood for

the economical result.