heliostat studies

This page collects documents, images, source codes and formulas about "heliostats", "special mirrors" used to make solar light static while sun crosses the sky.

Basic principles

Basic principle of an heliostat is that the mirror shall not point directly sun, but the bisector between sun and target. To accomplish this task, it is possibile to build a totally passive mechanism, without any sensor, any electronic, and even any electricity: a springloaded clockwork would be enough to build an heliostat working for a whole day; to get it working for the whole year without manual adjustement, a little more work is needed, due to sun movement along analemma.

Types of heliostats

There are 2 main types of heliostats: north-facing and south-facing:

Type 1 - North facing: the mirror points toward North:

Type 2 - South facing: the mirror points toward south:

If you want to reflect sun rays toward a north-oriented window, you will need the south facing type:

Single day lasting heliostat

All you need to build an heliostat which follows the sun along a single day is:

1. Pointer: a Mirror mounted on a 2-degrees-of-freedom stand (horizontal and vertical)
2. Clockwork: a clockwork making 1 turn in 24 hours
3. Joint: a peculiar joint to connect the mirror to the driving mechanism

Some more items will be needed to join 1) and 2):

• 1a) Mirror tail: a rod fixed perpendicularly to the back of the mirror
• 2a) Clockwork extension: a rod parallel to the clockworx axis, extending it by some centimeters
• 2b) Driver: a rod fixed to clockwork axis with a certain angle (corresponding to sun declination)

Showing them for both types (but we need type 2):

The joint 3 is the most important part and the most difficult to build. Its requirement are:

• Shall be able to freely slide along tail (1a)
• Shall allow driver (2b) to rotate around tail (1a)
• Shall allow driver (2b) to rotate around the pivot on joint (3) itself
• Shall have very low friction with mirror tail, hence only 2 points of contact at joint edges

This is how the joint appears in Foucault's drawings:

Modern 3d representation:

Foucualt highlighted how the friction between the joint and the mirror tail should be reduced at minimum, adding that thia could be better accomplished if just the edge of the joint are in touch with the tail, so this is how I imagined the interior of the joint:

An other fundamental requirement of the whole instrument is that, whatever it happens, segments highlighted in this picture must remain exactly equal in length:

They are marked as (P'L' and P'M) in following schematic:

Two configurations are possible for heliostats: "underdrive" and "overdrive"; for south-facing type, they look like this:

Underdrive connects driver to mirror tail, which is ortogonal to mirror and below it; it's how Foucault's heliostat is deisgned; overdrive connects driver to a rod which is parallel to the mirror and above it.

Various arrangements are wel described in "A Note on the Principle And Nomenclature of Heliostats, Coelostats, Siderostats" by Dougherty, L. M., in "Journal of the British Astronomical Association", vol.92, no.4, p.182-187 (1982)

Whole year lasting heliostat

The sun follows a simple arc in the sky along the day; unfortunately, this arc does not remain the same along the day, due to orbital mechanics:

This site shows how this arc moves in the sky along the year: http://andrewmarsh.com/apps/staging/sunpath3d.html

Seen from ground, with observer always in same position along the year, and sun position marked always at same hour in the day, the sun appars describing a curve named "analemma":

Analemma has an "8" shape, both if plotted in Alt/Az coordinates and Declination/Hour coordinates; the big difference is that if plotted in Alt/Az, the curve is different for any different latitude of the observer; instead, if plotted in terms of Declination and Hour Angle changes, the curve is costant.

Above plot is in Declination/HourAngle coordinates; following one is in Altitude/Azimuth coordinates:

How does this apply to real life? You must consider the 2 possible mounts of telescopes:

https://www.virtualtelescope.eu/2016/09/29/montatura-del-telescopio/

If you use equatorial mount, where the telescope rotates around an axis pointed to North, declination changes will make telescope move toward North or South, Hour Angle changes will make it rotate clockwise or counterclockwise, or accelerate/decelerate w.r.t its 24h rotation.

Turning math into mechanics

The declination change along the year follows this plot:

It's easy to implement this plot by converting it into polar coordinates to get a cam:

The hour angle along the year is much more complex:

It is possible to obtain this profile combining the two factors which contribute to Equation Of time, using 2 cams:

or you can combine the two contributions into a sinlgle cam; there are two possibilities: the "kidney" cam, and the Greubel/Forsey cam:

Applying a rotating follower to a declination cam and another rotating follower to kidney cam, you get two mechanisms which produce the angular changes for declination and hour angle, i.e. you turn each constant angular rotation into an oscillating movement, which combined make the sun pointer follow the analemma path around the polar axis:

An heliostat could be seen as a peculiar type of polar-mounted telescope, which always points the same "star": the Sun; to properly follow the sun all along the year, rotating the mirror driver around polar axis one turn every 24 hours is not enough: corrections to sun declination and hour angle must be added to the instrument.

One of Foucault's heliostat designs apparently could do the trick, being it equipped with two gears which allow external inputs:

• "q" allows introducing time variations (Hour Angle or Right Ascension, it's not clear to me) to the upper clock mechanism
• "u" allows introducing declination variations without affecting upper clock mechanism

Question is: which mechanisms should be connected to "q" and "u" to automatically follow the sun along each day of the year?

Maybe these sites could provide some hints (I am currently investigating):

• Mechanical implementation of Equation of Time (contact)
• Analemma calculator (contact)

Source codes

Made with Plotly.js

Cams plotter - try it here: link

Plotter for "kidney cam", Greubel/Forsey cam, declination cam and analemma.

You can download ready-made ownload cams from this folder: https://github.com/jumpjack/heliostat/tree/main/cams

You can use CamFollowerJS to import JSON cams and simulate cam/follower mechanism: link

You can use Algodoo to import cams as 3d images and build 3d mechanisms.

Made with Three.js

Parabola3.html (source, live demo)

Paraboloid customizable by user. No mirrors, because Three.js has so many versions, subversions and variants that I was not yet able to figure out whic version to use to create a reflective mirror..

Made with BabylonJS

Parabolic mirror 001 (source, live demo)

It displays in 3d space a paraboloid with one hexagon parallel to each face; ideally the cylinder should be turned into a real reflector capable of reflecting surrounding objects, to simulate how moving sun appears in the mirror.

To do:

• each face currently has two mirrors oriented slightly differently, but only one mirror should be presemt
• "mirrors" are currently just cylinders, they do not reflect
• paraboloid should be modifiable by user (inclination, height, width,...)
• moving sun to be added
• mirrors to be made smaller and denser

Parabolic-004 (source, live demo)

First functional version: a paraboloid mesh has been created starting from the embedded BabylonJS function which creates a "Toroidal knot"

Parabolic-005 (source, live demo)

Fully functional parabolic mirror simulator:

You can change inclination of the rotation axis of the sun, and change the hour angle of the sun, to see how rays are reflected by the mirror; the mirror itself can be chamged by means of two parameter, but please note that only a simmetrical mirror (i.e. elliptical paraboloid, with a = b) will have a point-shaped focus and will reflect all rays into parallel rays). Symmetric paraboloid, with parallel test rays reflectd into single point:

Non-symmetric paraboloid, reflecting parallel rays into "something else" (catenary?):

Documents

• Repertorium, vol. I: Littrow's Heliostat (p.46-56)
• Repertorium, vol. II: Carl Zech, "Gli eliostati"; interessante confronto matematico/geometrico fra tre tipi di eliostati: Fraunhofer, August e Silbermann.
• "Le siderostat", by M.A. Laussedat, in "Revue des cours scientifiques de la France et de l'étranger". 1867-68, pp.259-264 - How Foucault siderostat was used to observe solar eclipses
• "La lunette astronomique horizontale destinée a l'observation du soleil, de ses éclipses et des passages de Vénus sur cet astre" ("Il telescopio orizzontale astronomico destinato all'osservazione del sole, delle sue eclissi e del passaggio di Venere su di esso", by M.A. Laussedat

-Zech, Ueber Heliostaten - "Repertorium für physikalische Technik", Vol. II ("Rpertorio di Philipp Carl sulla fisica e la tecnologia sperimentale, vol. II"), pagina 10 e successive - "Katalog von Leybolds Nachfolger" ("Catalogo del successore di Leybold, Colonia")

• Frick-Lehmann, Physikalische Technik I, 7. Aufl., S. 208 f., Braunschweig 1904 (Edizione 7, pag. 208) (su Google books, ma non consultabile: link; edizione 1856 consultabile, pag. 213: link)

• Radau, "Zur Theorie der Heliostaten", in "Carls Repertorium für physikalische Technik", vol II (1867), (pag.1 e successive, pag. 234 e successive)

• Notice sur l'Héliostat, Di Jean Thiébault Silbermann - Eliostato di Silbermann spiegato in dettaglio da lui stesso, con figura completa

• Heliostats, Siderostats, and Coelostats: A Review of Practical Instruments for Astronomical Applications, by A. A. Mills, 1985, in Journal of the British Astronomical Association, Vol. 95, NO.3/APR, P. 89, 1985 (describing various types of heliostats, also taking into account declination change along the year)

• A Note on the Principle And Nomenclature of Heliostats, Coelostats, Siderostats by Dougherty, L. M., in
  Journal of the British Astronomical Association, vol.92, no.4, p.182-187 (1982) (describing geometry of various types of heliostats)

• A self-setting heliostat and its use in experimental optics - by Edison Pettit, in Popular Astronomy Vol 21, Iss 9 (double mirror)
• BULLETIN OF THE ENCOURAGEMENT SOCIETY FOR NATIONAL INDUSTRY - Details page
• ON A HELIOSTAT FOR THE SMITHSONIAN INSTITUTION, WASHINGTON by SIR HOWARD GRUBB, F.R.S., an Hon. Secretary of the Royal Dublin Society (Plate XIII) in The Scientific proceedings of the Royal Dublin Society - new series - volume 6, on page 598, drawing on Plate XIII:

• VARIÉTÉS SUR LA THEORIE DES HËLIOSTATS, by Par M. R. RADAU, in "Bulletin astronomique", tome 1, 1884. pp. 153-160. Detailed descriptions of mechanism of heliostats by Foucalt, Silbermann and Littrow in French language. See transcriptions here.

• A Heliostat for Photo-Micrography, by S. W. Stratton and T. J. Burrill, in Proceedings of the American Society of Microscopists, Vol. 7, Eighth Annual Meeting (1885), pp. 103-107
  • Mirror rotation speed: 1 turn in 24 hours (full sun speed)
  • Reflection direction: customizable
  • Reflection target: final target
  • Clock mechanism: an endless screw is fixed to the axis of the minutes-hand of a standard clock, engaging a 24-cogs wheel on heliostat main axis

(also here)

• Un heliostat a la portee de tous, by G. Raymond, in "L'Astronomie", vol. 37, pp.410-411:

• A New Heliostat (alternative link), by Deck, Lyman S. , in Transactions of the American Microscopical Society, Vol. 25, Twenty-Sixth Annual Meeting (Sep., 1904), pp. 187-234 (48 pages) (how to build a simple heliostat using a standard mechanical clock)
  • Mirror rotation speed: 1 turn in 48 hours (half sun speed)
  • Reflection direction: orthogonal to clock axis
  • Reflection target : final target
  • clock mechanism: 1:4 reduction mechanism applied to hour-hand of a standard clock.

• On an improved heliostat invented by Alfred M. Mayer (1886) - Document is behind a paywall, but the patent of the device is available for free, with full explanation of the mechanism: link . Also available in "The American journal of science" (AKA "Silliman's Journal"), series 4, vol. 4: link (link found in "Die Fortschritte der Physik" by Deutsche Physikalische Gesellschaft, vol. 53, 1845. The device makes use of a clock mechanism which rotates an axis by 360 degrees every 24 hours, which is not part of this patent. The device is specifically intended to project "one single ray" from the sun.
  • Mirror rotation speed: 1 turn in 24 hours (full sun speed)
  • Reflection direction: parallel to clock axis
  • Reflection target : secondary mirror
  • clock mechanism: not specified

• Teoria dei "tubi solari": https://www.researchgate.net/publication/340111732_Study_and_Analysis_of_Parameters_Affecting_Tubular_Daylighting_Device
• Multiple references:

(source: Sur la théorie des héliostats, R. Radau "Bulletin astronomique, Observatoire de Paris", 1884,1 pp. 153-160 )

Documents archives/sources

• Hathitrust
• Gallica
• Archive.org
• Google books

Images

• 

  The actual size of Foucault siderostat

(by user "Calculus", in "English Mechanics and the World of Science", Volume 31, n.803, p. 548, August 13th, 1880)

• in "Lehrbuch der Physik und Meteorologie; Theilweise nach Pouillet's Lehrbuch der Physik", by Pouillet, M. (Claude Servais Mathias), 1790-1868; Müller, Johann Heinrich Jacob, 1809-1875

• 

• Grubb (source - Zeitschrift für Instrumentenkunde - 1881)

• 

• Meyerstein (source, source):

  • -

• Fuess (source):

  • 
  • 

• 

• 

• (source)

• (source: "Instruments of Precision Laboratory Apparatus", W.M. Gaertner & co)

• (source; remotely operated! unknown inventor)

• - Alt/Azimuth, remotely operated, unknown inventor (source)

• Muller's heliostat ("Equipments for physics and chemistry class-rooms", see also "Zeitschrift für die physikalische und chemische Analyse. U., 8, p. 354. - M. T., Fig. 124")

• (source) Stoney's heliostat - setup description here; other hires images; geometric description: ?

• - Gray's heliostat in "Journal of the Royal Microscopical Society" byy Royal Microscopical Society (Great Britain) , 1904

• Alternative method proposed by Johnstone Stoney to guarantee rectilinear motion of connection between mirror tail and clockwork driver arm, in place of hollow cylinder moving along a bar; article "On making the siderostat an instrument of precision" in "Monthly Notices of the Royal Astronomical Society":

Modern view:

Inventors

• Otto von Littrow, "Ueber einen Heliostaten nach August's Principi", in "Repertorium für Experimental-Physik, für physikalische Technik ...", Volume 1, pp.46-56; full German text, with pictures: link

• Colonel Archibald Campbell (1865-1940) from Blythswood; device built by Adam Hilger. Link

UNITED KINGDOM - JUNE 09: Photograph of a universal heliostat made by the English instrument makers, Adam Hilger in London. Lord Blythswood, Archibald Campell (1865-1940), a Scottish scientist designed this instrument. It was used to direct sunlight into an ancillary instrument, such as a spectrograph, for analysis. It uses a flat mirror, driven by a clockwork mechanism, to follow the Sun as it move across the sky. This heliostat was displayed at the 1876 Loan exhibition that was held on the site of today's Science Museum at South Kensington, London. (Photo by SSPL/Getty Images)

• BERTHOLLET and MALUS ():
• Ekling ():

• Tornaghi ();

• Hilger (1919):

• Thomas Comber ():

• Silbermann (Annales de chimie et de physique - p.300 e tavola III in fondo al libro)
• George Johnston Stoney (1869)
• Grassmann (inventor), Rudolf Fuess (builder) (1870-1872):

• Brashear (1910):

• Alfonso Borrelli ()

• Pietro Prandi (Nuova Collezione d'Opuscoli scientifici - Bologna , 1824 )

• Giovanni Santini ("Teorica degli stromenti ottici destinati ad estendere i confini della visione naturale" (figure parzialmente visibili))

• Gambey Elementi di fisica sperimentale e di meteorologia, M. Pouillet (figura parziale), Description de l'héliostat de M. Gambey, di Hachette (M., Jean Nicolas Pierre) (versione digitale non disponibile), Bulletin de la Société d'encouragement pour l'industrie nationale, Volume 23, p.105 (figure tavola 299 a p.108)

• Corso elementare di fisica di Ranieri Gerbi 3 (p.32) (figure 5 e 7, non visibili)

• Antonio Tessarolo - Physics instrument makers in 19th-century Veneto: Two case-studies, by Fanny Marcon

Sites

• Spiegazione dettagliata eliostato di Gambey
• How Silbermann heliostat moves (video)
• Silbermann's heliostat explained by Encyclopedia Britannica
• Silbermann's heliostat explained at Fondazione Galileo Galilei (italian)
• https://helioreflect.com/en/content/6-solar-reflectors-those-forgotten-inventions
• Images/link: https://ro.pinterest.com/adimuraru11/heliostat/

• Redrok site - Some dozens of heliostats linked, with pictures and patents - link:
• Sun path in 3d: http://andrewmarsh.com/apps/staging/sunpath3d.html

• Sun path in 3d: https://ccnmtl.github.io/astro-simulations/sun-motion-simulator/

• Sun path simulator in 3d: http://andrewmarsh.com/apps/staging/sunpath3d.html and derived repo https://github.com/joaopedroalbq/helios :
• Linkage mechanism by Peaucellier–Lipkin to turn linear motion into circular, and vicerversa (could be used to force driver edge moving along mirror tail?)

• Linkage mechanism by James watt with similar function

Commercial products

• Heliosfera - https://heliostat.pl/it/di-progetto (Poland) (not yet on sale)
• Caia - https://www.solenica.com (Italy) (not yet on sale; proabaly 250,00 euro)
• Heliostat on https://www.heliostaat.nl/products.html (just mechanics+electronics, no mirror: 539$)
• Parans fiber optic solar collectors: https://parans.com/product/ (unknown price)
• PuroSole - 950,00 euro + IVA: https://www.eliostati.com/acquista/
• Wikoda SunFlower - 300,00 euro (dead project)
• SolarTracker - 11976,20 euro!!!
• Manufacturers list: https://lm.solar/heliostats/heliostat-manufacturers-selected-list/

Heliosfera:

Caia:

PuroSole:

Sunflower:

SolarTracker: