Introduction: This Instructable Is Not Complete and I Am Not Currently Working on It.Heliostat Experiment and Finding True North With Equatorial Mount.

Picture of This Instructable Is Not Complete and I Am Not Currently Working on It.Heliostat Experiment and Finding True North With Equatorial Mount.

If a mirror revolves on equatorial mount at 7.5 degrees per hour will it cast the light of the sun in the same direction all day?
This is a very low tech experiment so that I can better understand heliostats.
I do this experiment because of my lack of understanding of heliostats, because of an answer on wikipedia i did not understand and because of a big arguement about heliostats on instructables last year.
Also, there is very little information on the net about how mechanically powered heliostats work.
They were common use over a hundred years ago.
It is snowing today march 9 (usually they have a flower count here in early February!) so this gives me time to put this instructable on as requested.

Step 1: Materials and Tools

Picture of Materials and Tools

Parts of the device The device was made from a
a tightner for a a clothesline
a bolt
some screws
a crocodile clip
a piece of tie wire
and a protractor picture that I downloaded from the internet
You need a bench drill to drill holes straight into wood at right angles to the surface.
A hand drill is probably not accurate enough.
Screwdriver is also needed.

Step 2: HELP! It Is Snowing. I Cannot Do the Experiment! Can You?

Picture of HELP!  It Is Snowing. I Cannot Do the Experiment! Can You?

I cannot do the experiment. I tried it yesterday for a couple of hours and it seemed to work.
but today it is snowing and I have a backlog of work that I must attend to.
Usually we count flowers in early February to annoy the rest of Canada but this year, the weather gods decided to delay the count and my experiment too!
Do not exactly make the same thing as I did. The critical things are level foot and the angle of the hole that the rotating bit goes into. The angle must be the same AS YOUR LATITUDE. (So not 50 degrees unless you live at 50 degrees north or south) . AND if you live in the southern hemisphere, you gotta point at the south pole not the north pole. And it is geographical poles not magnetic poles!
To do the experiment, you put the foot on a flat level surface facing north south.
Then you adjust the mirror so that it shines on the spot you want. A shaded area so you can better see it. Then set up the crocodile clip at a suitable place.
Next, every hour, come back, rotate by the desired amount. 7.5 degrees per hour.
Does the reflection stay in the same place with the rotation?
Record your results and get back to us!

Step 3: Results (little Ones From 10th March)

Results can be posted as comments on this page.
My results so far seem to show that it might work!
Because I go to work early in the morning and come back late at night, I cannot get more than tiny snippets of experiments going.
One thing I noticed is that the reflection does seem to stay in the same place except it goes up and down on a vertical line.

So perhaps I am a little off on my equatorial axis or maybe (more likely) the 24 hour rotation of the sun round the axis must be alligned some way with the 48 hour rotation of the mirror.
I (or an animal) could have bumped the mirror as an alternative explanation.
Or maybe it will just not work at all!
If you want to find out, before I do, you know what to do!
This is a very cheap experiment.
I suggest mounting the mirror on a ball and socket joint right on top of the bolt going into the wood.
I tried to do this but the ball and socket I used (from an old shower attachment) was cracked.

Step 4: Links, Further Reading and "if It Works, What Next?"

Links and further reading. a bunch of pictures of heliostats from the 19th century!
And thats about it!
It seems that everybody is selling something so it is very frustrating to find detailed information on how they actually work!
Hence the experiment, I guess.
An answer from wikipedia to an earlier question by me can be found at:
If this instructable is ever any use to anyone, we can thank that answer and rimar2000 who gave me a similar answer.
If this form of heliostat actually does work, I think it is likely one clock based dripper tracker could control 5 or 6 mirrors at one time. That would mean that all you need in the form of electronics is a fairly sturdy clock mechanism to drop the dripper pipe down at a constant speed and a little pump to return the water to the top containers at the end of each day. I imagine, say, 5 mirrors with their top and bottom containers with floats in them. All the top containers are connected so all have the same water level. All the top containers are also connected so they too are at one height. One drip pipe that is slowly descending drops the top water level while raising the bottom water level thus turning all the mirrors at once.
A combination of the first and 3rd diagrams at the following link:
(Another guy did the graphics for the first diagram so imagine his graphics on the 3rd diagram (and a second container with a float in it too) and you have the picture!
They have some of my awful video further down the page, if you want to test your endurance.

Step 5: Why the 48 Hour Rotation? Theory (making It Up As We Go Along)

As you know the earth rotates in relation to the sun in 24 hours.
So why is this heliostat thing set for 48 hour rotation?
REASON 1. is fairly easy. When the mirror is set up, it is at right angles to a point that bisects the angle sun-mirror-reflection. The reflection must not move (hopefully) so if the sun moves 2 degrees round the equatorial axis , the mirror must move 1 degree round that axis to keep agreeing with the bisect rule.
REASON 2. came to me on the bus. My reflector is to one side of the axis. But imagine a big virtual mirror. It is going to be at both sides of the axis. Now, imagine it rotating. What happens? One part of that rotating mirror is going to move TOWARDS the sun at the same time as the other part of it is moving AWAY from the sun. But it is the same mirror! One 24 hour applys to one half of the mirror and the other 24 hr applies to the other half.
(I know, it sounds like bs and maybe it is!)

Step 6: Experiments Magnetic North and Ideas for Further Progress.

Picture of Experiments Magnetic North and Ideas for Further Progress.

I have started experiments on several days now with this and they were pretty brainless ones.
I guesstimated north and thought I could fine tune it later. But i did not get enough results to establish anything. EXCEPT, time to make the experiments better.
Here are a couple of ideas. I put my device on a concrete cap of a wall which is very flat, but the wood is a bit warped. So I use a bubble level to keep it level. Also, I looked the deinclination. for victoria it is about 20 degrees east of true north. And I found my compass and used it to aim the heliostat better.
My idea of north was way off!
Before I realized that, I started to tabulated time and degrees for shining the mirror reflection of the sun in various directions in my back yard. Just turning on the axis with no change to mirror tilt.
That would keep my busy
I also drew a curve across a wall with chalk so that i could see how the curve changes as the sun moves across the sky. Just moving the heliostat in its axis without changing the mirror tilt.

Step 7: Heliostat Model on Celistial Sphere Indoors!

Picture of Heliostat Model on Celistial Sphere  Indoors!

The celestial sphere and modeling the sun on it indoors.
Basically the earth is like a huge gyroscope in space. And just like a gyroscope, as it spins it always points in the same direction. (It has no wobble that anyone can notice in their lifetimes).
Its axis of spin is not aligned with its orbit so we get seasons.
So why not model the heliostat by using the celestial sphere idea? We need a pole as an axis, and we need something that spins around the pole (to be the sun) and another thing to spin round the pole (to be the heliostat) and something else stationary to be the target.
We also need something to measure the angles like the protractor that i downloaded.
Thats as far as I got


david williams (author)2009-03-19

We've discussed this topic ad nauseam. In general, a mirror rotating once every 48 hours will NOT reflect sunlight in a constant direction. There are exceptional situations in which it will work, but only on certain dates of the year. When the sun comes out in BC, try it. (You should come to Ontario where we're enjoying beautiful sunny weather!) But don't spend (waste) much money on the experiment. Use two mirrors. Make one of them rotate about a polar axis once every 24 hours and align it so it reflects light toward one of the celestial poles. Put the other (stationary) mirror so it intercepts the light reflected from the rotating mirror and sends it in whatever direction you want. This simple arrangement will reflect sunlight in a constant direction for several days, but will need readjustment every few days so as to compensate for the sun's seasonal movements in the sky. David

Why will a mirror rotating every 48 hours not reflect in a constant direction? You never did tell. Until you tell (with diagrams), I will continue. As I explained earlier, I will use one mirror, not 2. Please do not tell me how to conduct my experiments. You may suggest changes. Re Spend (waste) Please note the site policy on positive and constructive comments or risk of being banned.

Try a simple "thought experiment". Suppose you want to reflect sunlight in the direction of the celestial north pole, i.e. at the pole star. How are you going to make a mirror that rotates once every 48 hours about a polar axis do that? Answer: It won't. It could work if the mirror rotates once every 24 hours, following the sun's motion in the sky, but not 48.For most other target directions, the 48-hour rotation idea also will not work. I did explain this at great length to Osvaldo ("Rimar 2000") some months ago in private e-mails in his native Spanish. However, verbal descriptions and two-dimensional diagrams were inadequate. The situation is basically three-dimensional, and only a three-dimensional model (or imagination in three dimensions) can show how it works. If the above thought experiment doesn't convince you, then you'll just have to build the machine, wait for sunny weather, and see what it does. You asked for anyone who has done relevant experiments to tell you what they showed, since your weather isn't suitable at present. I suspect that I am the only person here who has actually done relevant experiments (years ago), and I know that they showed that the 48-hour idea does not usually work. (It does work only if the latitudes of the sun and target are equal and opposite. Since the sun's latitude varies in the range +/- 23.5 degrees during the year, the machine can work only if the target's latitude is also in that range, and only on the two dates of the year when the sun's latitude has the required value.) However, when I told you that it doesn't work, you took offence. So why did you ask? Since I know that the thing won't work, I also know that any money you spend on it will be wasted. However, if you want toi experiment with it, you have a perfect right to do so. My friendly advice is not to waste much money, but it's up to you. The two-mirror idea is simple and does work. I have a heliostat that works that way. But you don't seem to like it. I have no idea why. I know you have seen pictures of heliostats made by a man named Silbermann in the 1830s. They have single mirrors and are driven by clockwork. (They were actually used by artists, painters and sculptors, who needed unmoving beams of sunlight to illuminate their subjects.) They are beautiful and ingenious machines. But their mirrors do not rotate once every 48 hours. They have complex mechanisms to move them appropriately. I don't think I am the one who should be booted out for not "being nice". Try looking at your own behaviour. David

I've been doing some more calculations on this and have realized that, even under the unusual conditions in which the mirror rotates at a speed of 7.5 degrees per hour, it still returns to its original orientation every 24 hours, not 48! (This is neglecting seasonal movements.) Once a day, the sun and the target are diametrically opposite each other as seen from the mirror. The mirror is then edge-on to the light arriving from the sun. Just before this time, sunlight is striking the mirror at a shallow angle, and being reflected to the target. Just after the edge-on condition, sunlight strikes the mirror from the opposite side! So, in order for the mirror to continue reflecting the sunlight toward the target, it must make an abrupt 180-degree rotation. It turns at 7.5 degrees per hour for very nearly 24 hours, but then suddenly turns 180 degrees, returning to the orientation it was in 24 hours earlier. This is intuitively obvious, of course. The earth turns once every 24 hours, so the mirror must return to the same orientation every 24 hours. The time of day when the abrupt turn happens depends on the position of the target. In the northern hemisphere, if the target is roughly to the north of the mirror, the sudden rotation will happen at about noon. If the rotation is not done, if the mirror was acting as a heliostat before the edge-on condition, it will fail to do so afterwards. And it will work on alternate days, e.g. on Monday morning, Tuesday afternoon, Wednesday morning, etc.. (This is assuming the edge-on condition happens at noon.) So if you really want to make a heliostat that works this way, with the mirror turning about a polar axis at 7.5 degrees per hour, you must not only arrange for the latitudes of the sun and the target to be equal and opposite, you must also arrange for the 180-degree turn to happen at the right time each day. This is not going to be easy or cheap! Another approach would be to use a double-sided mirror, but I have never seen such things on commercial sale. You could make one, of course, by sticking two conventional mirrors back-to-back, but then you're back into the cost of having a second mirror. Oh well... David

David, the once a day time is black night, and the earth kinda gets in the way of the light, so who cares? And I will rewind it after 12 or 14 hours anyway. Please stop worrying about my experiment, it is not stressing me out so why is it stressing you so much? You might even try the experiment yourself to help your understanding a tiny bit. i will also refer you to google books. type " heliostat 48 hour rotation 1839" in their search box. I think that if they made heliostats with 48 hour rotation in 1839 and earlier, it may be that physics has not changed that much in the meantime and they may still work. Brian

PKM (author)gaiatechnician2009-04-03


I think the 48 hour rotation could work if you rotate a double-sided mirror about an axis that intersects the mirror. To reflect light from the sun towards a fixed direction on the ecliptic the mirror's surface normal (ie pointing straight through the surface of the mirror) has to lie half way between the direction of the sun and the desired aim direction.

As the sun completes a 360 rotation every 24 hours, the mirror has to rotate at half the speed, which we could call 7.5 degrees per hour or 48 hours per rotation. The trivial problem with 48 hours per rotation is that in your setup, if the mirror is in the right position at 4pm one day, at 4pm the next day it will have rotated 180 degrees and be pointing the wrong way- hence the need for a double sided mirror. In this case "48 hours per rotation" might be an easily understandable way of expressing the rotation speed, but in practise the heliostat should turn at 7.5 degrees per hour when tracking the sun and return to the start position during darkness if using a single-sided mirror.

The other case is the reflecting-sunlight-towards-the-poles case, and this trivially needs a mirror that rotates once every 24 hours. My gut feeling from these two cases is that the target being on the ecliptic or the poles are special cases, and reflecting sunlight towards a fixed point other than those requires a slightly more complex rotation. It occurs to me that you could potentially model this rotation with a mechanism a little like a pantograph, but it's a bit too complex to describe in just text.

tl;dr- reflecting to a point on the ecliptic can be done with a 7.5 degree/hour rotation. Reflecting to the poles can be done with a 15 degree/hour rotation. Reflecting to an arbitrary direction can be done with a mechanism employing a 15 degree/hour rotation and a mechanical bisector.

mvencelj (author)PKM2011-05-05

The 48 hour idea is perfectly OK! Indeed, one needs a double sided mirror and a 48-hr clockwork and it works a charm. It even would have worked during the night it the Earth was transparent.

gaiatechnician (author)mvencelj2011-05-05

I think David Williams is correct. The 48 hour rotation only works at the equinoxes.

gaiatechnician (author)PKM2009-04-04

"tl;dr- reflecting to a point on the ecliptic can be done with a 7.5 degree/hour rotation. Reflecting to the poles can be done with a 15 degree/hour rotation. Reflecting to an arbitrary direction can be done with a mechanism employing a 15 degree/hour rotation and a mechanical bisector." I agree. Thank you for the pantograph link. (It may come in useful.) The mechanical bisectors that I tried were set up with the mirror on a gimbal. The big problem is that sometimes the rotation of the mirror "Jars" because it goes on a "bad" line. (This is a know problem with universal joints too). I also saw a complaint about silbermann helistats in an old book that they suffered from this jarring too. Perhaps if the gimbal mounting itself was turning at 7.5 deg per hour the mirror would need much less "fine" adjustment with the mechanical bisector (because the bulk of the adjustment is done by the rotation itself!).

Don't worry! I'm not stressed about this. Just intellectually curious. As I said, it is possible for the 180-degree flip to happen in the middle of the day, maybe while you're trying to use your machine for cooking or whatever. As I also said, I have done experiments about this. Only under highly unusual conditions, when the latitudes of the sun and the target are equal and opposite, does a mirror rotating about a polar axis at 7.5 degrees per hour act as an accurate heliostat. Silbermann made his machines in the 1830s. They worked, and still work, beautifully. I saw one offered for sale recently for about $3000. I'm not sure if it was an original or a replica. But there must be a demand for them for this price to be anticipated. Unfortunately, some people misunderstand how they work, and say that their mirrors rotate every 48 hours. They don't. There is a shaft that rotates every 24 hours, effectively tracking the sun, and a mechanism that bisects the angle between the directions of the sun and the target. It's actually quite similar to a device you made a few months ago. I will Google this, as you suggest. David

I did google it. It agreed with what I've been saying.

I have my little model pointing south. No plans to point it north. Oh well.....

Thank you, David. I have only spent a few dollars so far. My experiments are always cheap. I wish to reflect for light and heat. It is just an experiment! (For fun and for my own understanding). 2 reflectors means twice the expense and 80% by 80% losses. Twice the expense for 8 tenths of the power is a loser in my view. Anyway, Thanks for the comments. My experiment is also about setting up equatorial mount accurately just by using the sun. Perhaps I will use the 24 hour rotation for that. Nothing is set in stone. I was going to give up my stupid solar experiments a couple of years ago but someone said that no experiment is stupid and that mine were very interesting. Not much good has come of my experiments so far but who knows? The pulser pump, mechanical mathematician and the dripper trackers are out there for anyone who wants to use them. Brian

Hi Brian:

Having two mirrors does cause a loss of light, but you can make up for that by making the mirrors a bit bigger. A mechanical heliostat with two mirrors is *much* simpler, mechanically, than one with only one. There's no need for an angle-bisection mechanism, for example. The extra cost of the second mirror is likely to be less than the saving in the cost of the mechanism. This is the opposite of the situation back in Silbermann's time, when mirrors were extremely expensive.

I have never heard of anyone using a heliostat to set up an equatorial mount, or even to find true north,. Finding north using the sun is much more difficult than is often believed. The trick that Boy Scouts learn, using the hour-hand of a watch, is accurate only if you're near the North Pole! Other published methods are also useless. I have thought of using a sundial, with plate and gnomon, putting it on a level surface, and rotating it until it tells the right time. The gnomon should then be pointing north, or south in the southern hemisphere. But the sundial would have to be made for the correct latitude, a clock would have to be available to tell the time, and corrections would be needed for longitude and the Equation of Time. Not simple! Watching the sun's motion for hours as it travels across the sky can also be used, but who want to take hours over finding north?!

So if you can find a way of using a heliostat for this, I would be very interested to hear about it.

Your previous inventions have been very ingenious. I especially like the hydraulic mechanism that lets a small clock control the rotation of something heavy such as a solar oven. I hope your devices are being put to good use somewhere.

Keep up the good work.


gaiatechnician (author)2009-07-24

I have no time to work on this right now. I know about the eleptical orbit thing. If you can get the heliostat to work for 4 or 5 days between manual adjustments that would be fine.

NachoMahma (author)2009-03-10

. Cool! Once you get this completed, it should be Featured-worthy.

It might be a while! I have a backlog of work due to the late spring. So if anyone has the time? It is a pretty easy and very cheap experiment to do. I do not know if I bumped something but so far, (from just a few readings), I think I have the reflected spot on a vertical line. So probably, you need to line up the 24 hour sun motion round the equatorial axis and the 48 hour motion of the mirror. Maybe line them up with noon with the mirror at the top of the mount? That is something I have to think about! It is a bit of a puzzle, isn't it? Maybe it will never work. Someone might figure it out! By all means, beat me to it.

rimar2000 (author)2009-03-09

Some years ago, while I design my solar cooking, I made an arrangement with an inexpensive electronic clock, just divided in four the speed of the hour hand with two gears. And it was!

kelseymh (author)2009-03-09

This is pretty good; thanks for putting it up! I have a few suggestions for extending the documentation, when/if you have the time and opportunity. 1) Add a couple of diagrams explaining about the latitude-angle relation and how someone might do the alignment. 2) Separate the assembly process from the list of materials. I'd put the mirror assembly in one step, the equatorial mount (protractor and base) in another, and the completed heliostat (with some alignment commentary) in a third. That will make it easier for someone else to follow along and build it themselves. As a side note, all your pics are attached to the Intro step, because you uploaded them at once. You might consider, if you wish, removing them from that step; they'll stay attached to the others.

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