The primary goal of the barn door tracker is to rotate the camera at the rate of 0.25° every minute (15° every hour) to neutralize the effect of earth’s rotation. Why 15° every hour? because the earth is rotating at 15° every hour from west to east. Our barn door tracker will rotate the camera 15° every hour at the opposite direction of east to west. Equilateral mounts (EQ) mounts do this with the help of precision worm gear and wheels. These gears are difficult to assemble and cost very high in low quantities. We would use a simple and cheap threaded rod and a nut instead of worm gears and wheels. We cannot match the precision and quality of commercial EQ mounts, but you will be surprised at the kind of tracking and photographs which can be achieved with an extremely simple and cost effective device which you can build yourself — the barn door tracker.
The kind of barn door tracker discussed here is the “isosceles” barn door tracker. This type of barn door tracker has an inherent problem called the “tangent error” induced by the geometry of the design. This error becomes apparent after about 20 minutes of tracking (for a 50mm lens). But we will completely eliminate this error by writing some smart software which will compensate and make the tangent error disappear. But why do we choose to build an isosceles barn door tracker knowing that it has an inherent flaw? Because it is the simplest type of barn door tracker to build and we can use the magic of software running on a $1 micro controller to completely eliminate this flaw. Many different complicated mechanical designs are available to compensate for this error. These designs include the curved bolt tracker, double arm tracker and cam corrected tracker. But these are relatively more difficult to build and require more exacting build requirements. These were solutions from a time when micro controllers were out of reach of a DIY enthusiast. With new and cheap micro controller platforms like the Arduino, it is very easy to implement a software solution to this error through software. I have made the software for this open source and is available free in this website.
Two pieces of wood connected with a hinge (just like a barn door, and hence the name) are spread open at 15° per hour. A camera mounted on one of the pieces of wood would also be riding along and rotating about the hinge at 15° per hour, matching the speed of rotation of the earth. This is the fundamental idea. The two pieces of wood are called the “arms”. The one at the base is called the fixed arm. This fixed arm is mounted on the tripod and is held stationary. The other arm is the camera arm where the camera is mounted.
The two arms are opened about the hinge with the simplest of actuators. A rotating threaded screw rod and a fixed nut. The nut is connected to the camera arm. When the threaded screw rod rotates, the nut will move up, pushing the camera arm up. The rotation of the threaded rod is done by a stepper motor.
We need to control the rate at which the camera arm moves up for tracking. The rate is 15° per hour. This rate can be controlled by the speed at which the stepper motor rotates the threaded rod. The speed at which the threaded rod rotates will determine the speed at which the nut rises, which in turn is connected to the camera arm.
Let us see the relation between the threaded rod’s rotation and the nut’s linear movement.
In a the bolt or in our case the threaded rod, if it makes one rotation, the nut paired with it will move a distance of 1 pitch. In a barn door tracker, we have the fixed arm and the camera arm connected at one end with a hinge. If we attach the nut to the other end of the camera arm and the threaded rod to the other end of fixed arm, then we have our actuation system. If we rotate the threaded rod, the camera arm which is connected to the nut will start start moving. If we can control the speed of the rotation of the threaded rod in such a way that the camera arm moves at 15° per hour, have tracking!
Controlling the actuator for achieving tracking speed of 15° per hour
What is an isosceles barn door tracker? It is a barn door tracker where the geometry of the system is an isosceles triangle. The two arms – the camera arm and the fixed arm are of equal length and forms two equal sides of an isosceles triangle. The third side is the threaded rod and acts as the base of the triangle.
In the discussions above, it became apparent that we have to rotate the the threaded rod at a specific rate to actuate the movement of the camera arm at 15° per hour. Let us arrive at this “rate” to achieve this goal.
For an isosceles triangle, the length ‘S’ of the base can be calculated using the formula
S = 2·L·sin(θ/2)
‘L’ is the length of the two equal sides
‘θ’ is the included angle of the equal sides.
Let us calculate how much the triangle’s base should expand, or in other terms how much the nut in the threaded rod should move in one hour to achieve 15° between the two arms. Note that the the distance between the nut and the base of the threaded rod is the ‘base’ of the triangle.
S = 2·L·sin(15/2) in one hour
S = 2·L x 0.1305 in one hour
S = 0.261·L in one hour
For example, let’s assume that our barn door tracker’s arm length ‘L’ is 300mm. Then ‘S’ at 1 hour will be 0.261 x 300mm = 78.3mm. In this case, the threaded rod should rotate enough number of times to move the nut up by 78.3mm. This will rotate the camera arm by 15°
Let us now calculate the number of revolutions required to achieve the target offset of the nut. For this, we need the pitch ‘p’ of the threaded rod. If the threaded rod has a pitch of 1.5mm, it means that one rotation of the rod will move the nut up by 1.5mm. From this information, let us derive the formula to connected the distance ‘S’ the nut has to move to rotations ‘R’
Let the pitch be ‘p’
R = S/p
replacing S from the previous formula,
R = (0.261·L)/p
Let’s add to our previous example. Let the pitch ‘p’ be 1.5mm. In this case, ‘R’ will be 0.261 x 300mm / 1.5mm = 52.2 rotations. So we have to achieve 52.2 rotations in one hour to track at 15° per hour
Speed of rotation is generally expressed in revolutions per minute rather than revolutions per hour. So let’s modify our formula for ‘R’ to express in revolutions per minute.
R = (0.261·L)/p (revolutions per hour)
RPM = R/60 = (0.261·L)/(60·p) (revolutions per minute)
So in our example, the speed required will be (0.261 x 300mm) / (1.5mm x 60) = 0.87 RPM. If we connect a motor to the threaded rod and run it at 0.87 RPM, a barn door tracker with an arm length of 300mm will start tracking the sky!