Hello all

Just a question about the Sine Law and its application. It is my

understanding that the sine law states that the maximum concentration

of

100% of radiation that can be achieved from a symmetrical trough

concentrator is 1/sine(half-angle).

This then implies that the best theoretical concentration achievable on

an

East-West trough that tracks North-South daily is 229, calculated with

a

half-angle of half the solar radius (0.25).

With a non-tracking East-West trough the best theoretical concentration

achievable is 2.488 which is calculated from a half-angle of 23.7, or

the

change in solar height between equinox and solstice (23.45) plus half

the

solar radius (0.25).

In research publications this concentration is actually the size of an

exit

aperture at the base of the trough, not the size of a collector pipe

within

the trough. It generally seems to be transposed to be applied to pipe

collectors, although there are substantial differences.

One of these differences is that the amount collected through an exit

aperture drops to zero nearly instantaneously when the incident angle

moves

outside the accepted range whereas with the pipe this collection

generally

drops 1 (direct non-reflected light only) for some angle range until

the

shadow of the trough wall falls upon the pipe.

A second difference is that the incident radiation does not drop off so

instantaneously with the pipe as it does with the exit aperture. This

could

have an effect. Concentration is defined as (proportion of incident

light

collected/collector size), so if the proportion collected drops slower

than

the required increase in the collector size the concentration will

increase.

So my question is: Is it generally considered true that the sine law

fully

applies to symmetrical trough concentrators with pipe collectors? Is

2.488

considered to be the best concentration achievable from symmetrical

non-tracking trough concentrators?

Thanks for your time

Glenn Thorpe

Hi Glenn;

> Just a question about the Sine Law and it's

> application. It is my understanding that the sine

> law states that the maximum concentration of 100%

> of radiation that can be achieved from a symmetrical

> trough concentrator is 1/sine(half-angle).

> This then implies that the best theoretical

> concentration achievable on an East-West trough that

> tracks North-South daily is 229, calculated with a

> half-angle of half the solar radius (0.25°).

We usually refer to the North-South tracking of an

East-West trough as "seasonal" rather than daily as

the movement each day is small.

I assume you are describing a perfect parabolic trough

with a depth equal to the focal length and a circular

receiver pipe. And the Sun's diameter is .5 degree

in diameter.

I don't think you have the calculation correct.

Concentration ratio is the ratio of the frontal width

of the parabola divide by the circumference of the

receiver pipe.

FL = Focal Length

X = Concentration Factor

FL * 4 = 4 = Width

FL * pi * (2 * tan(.5 deg / 2)) = .0274 = Circumference

Width / Circumference = Concentration Factor

4 / .0274 = 145.9X

However, other concentration factors can be obtained

with parabolas of greater or lessor depths.

> With a non-tracking East-West trough the best

> theoretical concentration achievable is 2.488 which

> is calculated from a half-angle of 23.7°, or the

> change in solar height between equinox and solstice

> (23.45°) plus half the solar radius (0.25°).

> In research publications this concentration is

> actually the size of an exit aperture at the base of

> the trough, not the size of a collector pipe within

> the trough. It generally seems to be transposed to

> be applied to pipe collectors, although there are

> substantial differences.

You are not describing a conventional parabolic trough

I think you are describing a CPC, Compound Parabolic

Concentrator. Basically these non imaging designs are

from Roland Winston and others. These are generally

made with 2 parabolas on each side and are quite

deep.

Your 2.488X is close to the value in the figure in

the excellent book:

"Solar Engineering of Thermal Processes"

Duffie & Beckman

ISBN 0-471-51056-4

1991

> One of these differences is that the amount

> collected through an exit aperture drops to zero

> nearly instantaneously when the incident angle moves

> outside the accepted range whereas with the pipe

> this collection generally drops 1 (direct

> non-reflected light only) for some angle range until

> the shadow of the trough wall falls upon the pipe.

True.

> A second difference is that the incident radiation

> does not drop off so instantaneously with the pipe

> as it does with the exit aperture. This could have

> an effect. Concentration is defined as (proportion

> of incident light collected/collector size), so if

> the proportion collected drops slower than the

> required increase in the collector size the

> concentration will increase.

> So my question is: Is it generally considered true

> that the sine law fully applies to symmetrical

> trough concentrators with pipe collectors?

No. It is about 64% of the value and not sine.

I use tangent instead of sine but for these small

angles the difference is insignificant.

The major error is in not using the circumference

and the width of the parabola is 4 times the focal

length.

> Is 2.488 considered to be the best concentration

> achievable from symmetrical non-tracking trough

> concentrators?

About right. Although the CPC system size is

considerably larger than a convention parabolic

trough with an over sized receiver.

Lastly there is another problem with East-West

designs in general. There is a cosine loss. You

will get 100% of the incident power only at solar

noon. As the sun position deviates from noon the

collected power decreases by the cosine of the suns

angle from solar noon, decreasing to 0% at the

horizon. (OK, we are ignoring atmospheric effects.)

When the trough is alined North-South along the

polar axis the collected power remains at 100% all

day. In addition the maximum collected power varies

seasonally from 100% at the equinoxes to 92% at the

solstices. (Again, ignoring atmospheric effects.)

Of course the North-South trough requires an active

solar tracker throughout the day. But these are

quite low in cost.

> Thanks for your time

> Glenn Thorpe

Duane

--

Home of the $5 Solar Tracker Receiver

http://www.redrok.com/led3xassm.htm [*]

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> Hi Glenn;> > Just a question about the Sine Law and it's> > application. It is my understanding that the sine> > law states that the maximum concentration of 100%> > of radiation that can be achieved from a symmetrical> > trough concentrator is 1/sine(half-angle).> > This then implies that the best theoretical> > concentration achievable on an East-West trough that> > tracks North-South daily is 229, calculated with a> > half-angle of half the solar radius (0.25°).> We usually refer to the North-South tracking of an> East-West trough as "seasonal" rather than daily as> the movement each day is small.> I assume you are describing a perfect parabolic trough> with a depth equal to the focal length and a circular> receiver pipe. And the Sun's diameter is .5 degree> in diameter.> I don't think you have the calculation correct.> Concentration ratio is the ratio of the frontal width> of the parabola divide by the circumference of the> receiver pipe.> FL = Focal Length> X = Concentration Factor> FL * 4 = 4 = Width> FL * pi * (2 * tan(.5 deg / 2)) = .0274 = Circumference> Width / Circumference = Concentration Factor> 4 / .0274 = 145.9X> However, other concentration factors can be obtained> with parabolas of greater or lessor depths.> > With a non-tracking East-West trough the best> > theoretical concentration achievable is 2.488 which> > is calculated from a half-angle of 23.7°, or the> > change in solar height between equinox and solstice> > (23.45°) plus half the solar radius (0.25°).> > In research publications this concentration is> > actually the size of an exit aperture at the base of> > the trough, not the size of a collector pipe within> > the trough. It generally seems to be transposed to> > be applied to pipe collectors, although there are> > substantial differences.> You are not describing a conventional parabolic trough> I think you are describing a CPC, Compound Parabolic> Concentrator. Basically these non imaging designs are> from Roland Winston and others. These are generally> made with 2 parabolas on each side and are quite> deep.> Your 2.488X is close to the value in the figure in> the excellent book:> "Solar Engineering of Thermal Processes"> Duffie & Beckman> ISBN 0-471-51056-4> 1991> > One of these differences is that the amount> > collected through an exit aperture drops to zero> > nearly instantaneously when the incident angle moves> > outside the accepted range whereas with the pipe> > this collection generally drops 1 (direct> > non-reflected light only) for some angle range until> > the shadow of the trough wall falls upon the pipe.> True.> > A second difference is that the incident radiation> > does not drop off so instantaneously with the pipe> > as it does with the exit aperture. This could have> > an effect. Concentration is defined as (proportion> > of incident light collected/collector size), so if> > the proportion collected drops slower than the> > required increase in the collector size the> > concentration will increase.> > So my question is: Is it generally considered true> > that the sine law fully applies to symmetrical> > trough concentrators with pipe collectors?> No. It is about 64% of the value and not sine.> I use tangent instead of sine but for these small> angles the difference is insignificant.> The major error is in not using the circumference> and the width of the parabola is 4 times the focal> length.> > Is 2.488 considered to be the best concentration> > achievable from symmetrical non-tracking trough> > concentrators?> About right. Although the CPC system size is> considerably larger than a convention parabolic> trough with an over sized receiver.> Lastly there is another problem with East-West> designs in general. There is a cosine loss. You> will get 100% of the incident power only at solar> noon. As the sun position deviates from noon the> collected power decreases by the cosine of the suns> angle from solar noon, decreasing to 0% at the> horizon. (OK, we are ignoring atmospheric effects.)> When the trough is alined North-South along the> polar axis the collected power remains at 100% all> day. In addition the maximum collected power varies> seasonally from 100% at the equinoxes to 92% at the> solstices. (Again, ignoring atmospheric effects.)> Of course the North-South trough requires an active> solar tracker throughout the day. But these are> quite low in cost.> > Thanks for your time> > Glenn Thorpe> Duane> --> Home of the $5 Solar Tracker Receiver> http://www.redrok.com/led3xassm.htm [*]> Powered by \ \ \ //|> Thermonuclear Solar Energy from the Sun / |> Energy (the SUN) \ \ \ / / |> Red Rock Energy \ \ / / |> Duane C. Johnson Designer \ \ / \ / |> 1825 Florence St Heliostat,Control,& Mounts |> White Bear Lake, Minnesota === \ / \ |> USA 55110-3364 === \ |> (651)426-4766 use Courier New Font \ |> redrok@redrok.com (my email: address) \ |> http://www.redrok.com (Web site) ===