parabola geometry :
diameter   cm*
focal length   cm
part of full paraboloide
calculation parameters :
incident solar power   W/m²
reflector efficiency (ave. reflectivity)   %
metalwork parameters :
open center model, hole diam.   cm
drill hole diam.   cm
segment drilling border   cm
available sheet length   cm
available sheet width   cm
provide spare segments
maximise parabola diam to sheet width
results table options :
show detailed calculations   YesNo
display lines interval

* dimensional units are irrelevant to parabola geometry (could be inches, meters or km).
cm dimensions only required for solar power calculation in W/m²

Legend
x : perpendicular dist. of point from axis (radius)
y : distance of point from centre of dish along axis
arc : distance of hole from centre, measured along surface of parabola
arc' : distance of holes from centre, measured along centre of segment
hole c/c : req. distance between hole centres when drilled at given radius
Eff. area : Effective captive area perpendicular to axis
Pmax : Maximum solar power collected by dish (assuming W/m² and % reflection )

(dx)² : square of incremental change in x
(dy)² : square of incremental change in y
dS : incremental change along strip

parabola : y=x²/300
focal length =75

calculation radial increment= 2 ; results (diam.) shown every 10

Diam. Arc length arc' hole c/c Eff. area /m² P max/W
55 0 0 8.2 0 0
75 10.233 10.1 11.2 0.2042 184
95 20.629 20.4 14.2 0.4712 424
115 31.225 30.9 17.2 0.8011 721
135 42.061 41.6 20.2 1.1938 1074
155 53.169 52.6 23.2 1.6493 1484
175 64.584 63.9 26 2.1677 1951
195 76.334 75.5 29 2.7489 2474
215 88.446 87.5 32 3.3929 3054
235 100.946 99.8 35 4.0998 3690
255 113.857 112.6 38 4.8695 4383
268 123.86 122.5 40 5.4034 4863
Diam. Arc length arc' hole c/c Eff. area /m² P max/W

segments per sheet=8;

Number of sheets (250 cm x 125 cm) required for 21 segments = 3

Warning: focal point falls 15 cm in front of reflector dish.

Possible suppliers of reflective Al sheet:
Alcan "Eloxal" - manufacturer (worldwide corp. find your local distributor)
Alanod Mirosolar. German company, UK/US Offices
(avoid stainless steel which absorbs IR and gets hot.)

WARNING
Care should always be taken when designing and using solar concentrators to avoid the possibity of burns. Please note that concentrated infrared heat is invisible but can burn like red hot metal. The focal length should be kept short to avoid someone in front of the parabola passing through the concentrated beam.

Principal of calculation
The above tables are calculated by numerical integration of the arc of the parabolic section as follows:
Determine the quadratic equation of parabola from diameter and focal length.
Use incremental changes in x and y and pythagorus to calculate incremental lengths along parabola arc.
Sum to obtain successive drilling points, use cosine of semi-angle to project distances onto segment centre line
Use sine of semi-angle to find distance between hole pairs as a chord of each circlular cut through paraboliod.
Add selected clearance for drilling and plot sheet metal plan.
The power is the product of the effective area taken perpendicular to the axis of the paraboloid, the insolation and the reflectivity of the sheet.

NB. Drilling Accuracy in the distance between hole pairs is essencial to getting the desired profile. Inaccuracies will defocus the beam to a larger volume around the focal point.

DISCLAIMER
The information on this page is provided AS IS. The author and domain owners make no waranty, expressed or implied of it's suitability for a given purpose.

This page is generated by a PHP script as a function of the data entered, not by fully engineered software. It has not been thoroughly tested under extreme conditions and results should not be used in critical applications, including but not limited to : life-support systems, nuclear power stations, aerospace applications, guided missile systems, penile temultulance detectors, etc.

If you are designing a parabolic solar reflector the results should be reliable enough.

If you chose to use the information on this page, you assume all responsability.