After finishing school eighteen years ago I’ve finally found a practical use for my ‘A’ level Physics and Mathematics. It started as a winter project a few months ago for something I was going to “knock up in an afternoon”. Summer has now arrived and after four visits back to the drawing board I’ve finally finished my motorised tracking mount complete with laser polar alignment.

There are many guides on the internet for building barn door trackers which have dimensions, step by step instructions and parts lists. I do not want this blog post to follow that theme, mainly because I think it’s more rewarding to understand the concepts of how these mounts operate and produce something of your own. Therefor, this post will delve into the physics and mathematics behind the design and hopefully give some pointers in the construction of the mount so that anyone that would like to make their own will not make the mistakes that I made.

My mount is heavily based on a design by Gary Seronik. Although Gary provides an excellent guide to making one, being in the UK I couldn’t get hold of the same parts so I had to make myself fully understand the physics and electronic requirements behind building one so that sourcing my own parts was possible. My design also differs in such that it starts in the open position and closes (rather than trying to lift the weight of mount and camera). It also uses a laser mounted against the hinge to project a beam into the night sky for easy polar alignment.

Why is the mount necessary?

Objects in the night sky tend to be quite feint. This means to photograph them long exposures are necessary on some subjects to capture enough photons of light to record the information on a digital sensor, even when using a high ISO setting. The problem is that the Earth is rotating. This means that during long exposures the Earth’s movement causes the stars to trail across the image and lose clarity. Whilst Star Trail photos are interesting to look at, they are not always desired.

The Solution

The solution is to move the camera at exactly the same speed and in the opposite direction that the Earth’s rotation is moving the camera, thus cancelling out the movement.
This mount is essentially a large hinge that moves the camera  in an arc to track the stars.

So we need to understand what the speed and direction will be:

1. Speed.
   The Earth rotates once every 24 hours right? Well nearly. It actually takes 23 hours, 56 minutes and 4 seconds. For the sake of our working out we’ll work to the nearest minute. Therefor the Earth rotates 360° in 1436 minutes which equates to 0.25° per minute (15° per hour). This is the speed the mount needs to move.
2. Direction.
   The Earth rotates towards the East. If you stand in the Northern Hemisphere and look up towards Polaris (North Star) the stars appear to move in an anti-clockwise motion around polaris. In order to counteract the movement that will be recorded in a long exposure we need to perfectly align the hinge on our tracking mount with the polar axis of the Earth and then move the mount so that the camera ‘tracks’ the stars.

Building the Tracking Mount

The Motor
You want to find a low speed, but high torque motor. The motor I used is a 12V 3.5RPM DC Motor.

The Hinges
In this case I found that more is definitely better. I previously built 2 models that worked on a single hinge and after a while too much play builds up, especially when the mount is angled high into the sky and all of the weight pulls downwards. If you have too much play in the hinge the motor cogs start to grind causing inconsistent speed.
This final build uses 4 hinges and there is absolutely no play between the upper and lower boards.

The Threaded Rod
I use a length of M8 threaded steel. It can be bought from most UK D.I.Y stores in lengths of about a meter and has 20 threads per inch (TPI). The TPI is an essential factor in the workings of the mount.
The threaded rod needs to be bent into a curve which has the same radius as the distance between the hinge and the hole that the rod passes through. If you use a straight rod, as your hinge opens or closes the point at which the rod makes contact with the upper board drifts, therefor your hinge movement will start to speed up or slow down causing inconsistent results. This is called Tangent Error.

Power Supply
I use a 14.4V rechargeable battery from a power drill. Although the motor is 12V by the time the power supply has gone through the PWM circuit a 12V supply was not up to the job.

Working out your arc radius
We know we need the motor to move the top board of the hinge at 15°/Hour in an anti-clockwise direction (Northern Hemisphere).
How we achieve this is through a relationship of the motor, the gears, the threaded rod and the distance from the threaded rod to the hinge. It sounds complicated but it’s actually very simple with a little mathematics!

If I were to use the motor straight out of the box the length of my mount would be far too large for practical use. This is why:

The rod I used has 20 threads per inch (or 20 threads every 25.4mm in metric). The motor I use does 3.5 r.p.m (revolutions per minute).
This means every time the drive nut does one revolution it has moved 1.27mm (25.4mm divided by 20).
As the motor does 3.5 r.p.m that means the nut would move 4.445mm every minute, or 266.7mm every hour.

As we know we need the tracker to move 15°/Hour. If we imagine that the arc of the hinge completes an imaginary circle, then the circumference of that circle would be 6400.8mm (266.7 X 24). Using the formula C=2πr where C is the circle circumference and r the radius it tells us that the arc radius would have to be 1018.7mm to maintain the correct speed. That would mean the mount would have to be over a meter long! Not very practical!

The solution is to slow the motor down. In the many years that people have been building barn door trackers moving the drive nut at 1 r.p.m has been a popular decision for hand moving models, but this is also a convenient speed for calibrating electric motors (you simply mark a tooth on the gear and adjust it so it completes one revolution in a minute).

If we slow the motor down to 1 r.p.m then we can work out a more practical arc radius for our hinge.
The nut will now move 1.27mm every minute, or 76.2mm per hour. This would give an effective circle circumference of 1828.8mm. Again, using the mathematical formula C=2πr this gives us the arc radius of 291.06mm (29.1cm).

29.1cm is the required distance between our hinges and the centre of the hole for the curved rod. The curved rod also needs to be bent into an arc with this radius (the best way to do this is to draw an arc on a large piece of paper with a radius of 29.1cm and then keep bending the rod until you achieve a good match of curvature).

Slowing the motor down using gears and a PWM circuit

As previously stated the motor I used does 3.5 rpm and I needed it to do just 1 rpm.

To accurately slow the motor down I first used a set of gears and finally fine tuned it with a Pulse Wave Modulator circuit and a stop watch.

I used good old fashioned Meccano gears. They are metal, mesh well and are easily obtainable.
The drive gear has 19 teeth, the driven gear has 57 teeth.

Gear Ratio 19:57 = 1:3

This means using this gear set the motor will have been slowed from 3.5 rpm to 1.16 rpm. Nearly 1 rpm but not quite there yet!

By passing the power supply through a Pulse Width Modulator circuit you can calibrate the drive nut to turn exactly 1 rpm by using a stop watch and marking one of the teeth on the driven gear with black marker.

Pre-made PWM circuits can be found cheaply on eBay. I paid £6.29 for mine.
As you can see from the photo to the left setting the motor to rotate once every minute using a PWM circuit can be quite accurate.

I can live with an error of 1.4 seconds over 5 minutes which is above and beyond what I expected the limitations of this mount to provide.

Polar Alignment

My mount uses a 1mW green laser pointer to project a beam into the night sky to easily point the hinge of my mount towards the North Celestial Pole.

Although I said earlier that the tracking mount should be aligned with Polaris this is not strictly true.

Polaris is approximately three quarters of a degree from the North Celestial Pole so for accurate alignment we need to be three quarters of a degree offset to Polaris.

Polaris can be easily found in the night sky by finding the constellations Ursa Major and Ursa Minor. Polaris is the last star on the tail of Ursa Minor.

As a visual guide the moon is about a half a degree in diameter, so for accurate alignment I need to aim the laser one and a bit moon widths towards Kochab.

The photo on the left shows an actual image taken from this mount with the laser turned on. For a test run I think I did quite well aligning the mount but it’s not perfect. Even though the test results look quite promising.

Test Results

As I said at the beginning this was meant to be a winter project. I really wanted to photograph the winter night sky and include subjects such as the Orion Nebula and the Andromeda Spiral Galaxy. Unfortunately at the time of writing this blog post, and finishing this project much too late, these objects have dipped too far south in the night sky and can’t be photographed from my location until winter returns.

For my test shots I chose the constellation of Cassiopeia. The distinctive “W” in the sky.

The purpose of this mount was to produce longer exposure photos, but using lower ISO settings to avoid noise. Therefor I performed all tests at ISO100.

Rule of 600

In photography there is a rule for how long you can expose a photo before star trails become visible. This is known as the rule of 600.
Basically you divide your lens focal length (in 35mm terms) into 600 and this gives you your maximum exposure in seconds before star trails appear.

My wide lens is 17mm on a crop sensor body which is 25.5mm in 35mm terms. This means 600/25.5=23.5 seconds. To be safe 20 seconds is the maximum exposure I can make before the stars start to trail in the photo.

At ISO100, 17mm f/2.8 on a Nikon D5100  this is the sky detail that I could capture in a 20 second exposure:

An example of how severe star trails occur over a 2 minute exposure at the same focal length:

And the final test shot shows another 2 minute exposure with the tracking mount polar aligned and switched on:

Overall I’m very pleased with the performance of the tracking mount and hopefully I will be able to take some more interesting shots once winter arrives.

I found writing this blog post quite difficult in trying to cover the important parts and in doing so have probably missed out something important. If you have any questions about building a mount like this please feel free to ask in the comments below.

I love vintage cameras. The quirkier the better!

Last year I bought a few models. An Ensign Ranger II (circa. 1951), a Nikon FE (circa. 1978) and a Yashica Electro 35 (circa. 1970).

Sadly the Nikon FE died during the 2nd roll of film. I’ve yet to finish a roll of Portra 160 in the Yashica 35 but the oldest british made Ensign Ranger II still works after sixty years.
With just 3 shutter speeds, no real viewfinder, no meter, manual focusing and a maximum aperture of f/6.3 it’s worlds away from todays digital cameras but an absolute joy to use.

Of course, you never know if you’ve done it right until the film comes back.

Here’s a shot at Burnham-on-sea lighthouse. I cheated a bit here and metered with a digital camera.

I also took it along to a family picnic on Dartmoor last year. This time I didn’t cheat but used the Sunny 16 rule.

Whether I keep PhotoEmbryonic going or just use Flickr to photoblog is something I’ll have to decide on in time.

So welcome to the new site!

Update: www.photoembryonic.com is now trashed! I’ll be using flickr from now on-wards for my more casual photos.