Stroboscope Timing

If you've ever wanted to create an animation for a Zoetrope, a Phenakistoscope or any of the various stroboscopic formats, one of the first hurdles you'll hit is trying to work out all the maths.

How fast should it be spinning? How long should you make your animation? At what rate should your strobe be flashing or your camera be recording?

Ever since my work on the Embroidered Zoetrope, I've been asked these questions a tonne and I'm pleased to tell you that the answer to all of the above is…

…it's up to you!

Well, sort of.

In screen-based animation you don't really have to think about these details as much because the parameters are more uniform.

The native framerate of film is 24 FPS, so most animators work to 24 FPS, 12 FPS or 8 FPS as they're all evenly divisible by 24. The frame itself is also typically rectangular and follows a common aspect ratio.

Digital media has changed this somewhat. You're able to make animations at any unusual framerates or aspect ratio you like, but even then, most video formats require your frame to be rectangular. There really isn't much variation to be had.

When dealing with stroboscopic formats, this uniformity is thrown out the window because your frame is no longer just a moment in time, it also takes up a specific amount of space.

The interesting thing about all of these stroboscopic formats is that these attributes influence one another. It's a bit like that the old rule of thumb when planning a project; "Good, fast, cheap. Pick two". When it comes to designing stroboscopic discs, it's:

Animation length, frame rate, spinning speed. Control two.

Let's say you want to create an animation that is 24 frames long (animation length) and you want people to see it play at 12 frames per second (frame rate). Go for it. That'll look great. However by locking in those two parameters, it means that your remaining parameter, spinning speed, is already set in stone. In this instance it would need to be spinning at 30rpm.

As you can see, 30rpm is the only speed that will work with those two parameters locked in. So what if you were planning to use a turntable with a fixed speed of 33⅓rpm or 45rpm? I'm sorry to say, but you either need to find a different device that does spin at 30rpm, or you need to alter one of the other parameters.

This is the confusing and frustrating dance you need to do and it can be hat's the frustrating thing that can be hard to wrap your head around if you're just starting out with this medium.

A common problem people have when creating their own stroboscopic devices is how to know what speed to set your strobe light to.

Getting the timing right can be confusing at first, but as you start to understand how all the different speeds and moving parts relate to one another it becomes quite powerful when creating your own animations.

While creating my Embroidered Zoetrope installation, I worked out a few simple equations that let me understand/alter all sort of things like the FPS, number of frames, duration of the strobe, speed of the turntable etc.

To begin, this is my simplified formula:

1000ms ÷ (rpm ÷ 60 × frames) = strobe period

My Embroidered Zoetrope had 14 frames per disc and were spun at 45rpm, so I worked it out like this:

1000 ÷ (45 ÷ 60 × 14) = 95.238ms

If, for example, you instead wanted to fit 20 frames of animation onto the disc, and you're spinning it at 33⅓rpm, you could use:

1000 ÷ (33.333 ÷ 60 × 20) = 90.001ms

The strobe period is how long the entire 'duty cycle' of one flash ON and one OFF takes before starting again. That's not ON for 95ms and OFF for 95ms, but rather ON + OFF = duty cycle.

For my work, with a duty cycle of ~95ms the exact timing I used was as follows:

Light is ON for 5 milliseconds Light is OFF for 87 milliseconds

(You'll notice that these add to 93ms, not 95, but that was due to my equipment being a bit older and unreliable.)

Basically you have the flexibility to tweak the ON and OFF values as much as you like so long as they add together to match your required duty cycle. I found a really short duty cycle of 5ms worked best because it gives the viewer a really sharp image when they look at your work. Anything above 10ms starts to get blurry.

The equations above should be all you need to get started, but I actually like thinking of it in a different way too especially when designing each disc. This other way focuses more on the layout and angles of the design. I've broken down this other method below:

My discs were spinning on a turntable at 45 rpm:

360° × 45rpm = 16,200° per minute 16,200° ÷ 60 = 270° per second Therefore the disc rotates 270° every second.

Each disc has 14 frames of animation:

360° ÷ 14 = 25.714…° per frame Therefore each frame represents 25.714…° of rotation.

Putting those two things together:

270° ÷ 25.714…° = 10.5 fps Therefore every second we should see 10.5 frames.

Converting it back to milliseconds:

1000ms ÷ 10.5 fps = 95.238ms Therefore the strobe must flash once every ~95ms.

You can see that either method you use, you get the same answer, but doing it the long way gives you some other values to help you like FPS, which can be helpful to know to get the pacing right if you're prototyping on a computer or converting an existing sequence to a physical device.