Abstract
Have you ever seen a video where it looked like a car's wheels were spinning backward even though the car was driving forward? What about helicopter blades that looked like they were spinning very slowly, or even not moving at all? This illusion is called the "wagon wheel effect," named after old movies where it looked like wagon wheels were spinning backward. In this science project you will learn how the wagon wheel effect works and how you can film it yourself.Summary
Objective
Determine the relationship between an object's rotational speed, a camera's frame rate, and the resulting apparent motion.
Introduction
Imagine a clock with a second hand. If you just watch the clock, you will see the second hand moving forward (clockwise), completing one full revolution every 60 seconds.
Now imagine what will happen if you take a picture of the clock once every 59 seconds, then stitch those pictures together to make a video. When you play the video, it will look like the second hand is moving backward (counterclockwise), because you took each picture just before the second hand had completed a full revolution.
Similarly, if you take a picture exactly once every 60 seconds, in the video it will look like the second hand is not moving at all. If you take a picture once every 61 seconds, it will look like the second hand is moving forward again (Figure 1). This optical illusion is called the wagon wheel effect, named after old movies where spoked wagon wheels looked like they were spinning backward, spinning very slowly, or even not spinning at all.
In the first row, each clock represents the position of the second hand 59 seconds after the previous clock. The second hand seems to move counterclockwise. In the second row, each clock represents the second hand 60 seconds after the previous clock. The second hand seems to remain still. In the third row, each clock represents the second hand 61 seconds after the previous clock. The second hand seems to move clockwise.
Figure 1. This figure represents what you would see if you took a picture of a clock with a second hand once every 59 seconds (top), once every 60 seconds (middle), and once every 61 seconds (bottom).
Videos are really just a series of still images played back quickly enough that the human brain perceives continuous motion. Cameras record these images at a certain frame rate, or number of frames per second (fps). Common frame rates for video include 24, 30, and 60 frames per second. Modern smartphones can also record slow-motion video at higher frame rates, like 120 or 240 frames per second.
Depending on the rotational speed of a spinning object, the frame rate can result in the wagon wheel effect when filming the object. For example, if a camera records at 30 fps and a wheel is spinning at exactly 30 revolutions per second, the wheel will be in the same position for each frame of the video—so it will look like the wheel is not spinning at all. (This is similar to the second hand in the middle row of Figure 1.)
The wagon wheel effect can also occur if the spinning object rotates at or close to an integer multiple of the frame rate. Imagine that the second hand in Figure 1 speeds up and completes each revolution in only 30 seconds, meaning it completes two whole revolutions in 60 seconds. If you take a picture every 60 seconds, the second hand will still be in the same position for each picture and look like it is not moving.
For this reason, you cannot figure out the object's rotational speed just from watching the video. To measure the object's true rotational speed, you need a device called a tachometer. A tachometer uses a reflected laser to measure an object's rotational speed, typically in revolutions per minute (RPM), not revolutions per second. To compare the rotational speed in RPM to the frame rate (measured in frames per second), you need to divide the RPM by 60 to calculate the revolutions per second:
Equation 1:Finally, imagine that the second hand is slowed down so it only completes one revolution every two minutes, but you still take a picture of it every minute. In each back-to-back pair of frames, the second hand will appear in the top position (at 0 seconds), then in the bottom position (at 30 seconds). If the video is played back quickly enough, the human brain will not perceive a single second hand bouncing back and forth—instead, you will see two second hands, one in each position.
In this project, you will examine how an object's rotational speed and the camera's frame rate interact to result in the wagon wheel effect in videos. To film the effect yourself, you will need to be comfortable adjusting the manual settings on your camera. In particular, you will need to increase the shutter speed. When you increase shutter speed, you decrease the exposure time, meaning each frame is recorded more quickly. This can result in reduced motion blur, making it easier to see the spinning object in your video. You can learn more about shutter speed and motion blur using the references in the Bibliography.
Terms and Concepts
- Optical illusion
- Wagon wheel effect
- Frame rate
- Frames per second (fps)
- Integer multiple
- Tachometer
- Revolutions per minute (RPM)
- Shutter speed
- Exposure time
- Motion blur
Questions
- How does the wagon wheel effect work?
- What motion do you think you will perceive if an object's rotational speed is slightly below the camera's frame rate?
- What motion do you think you will perceive if an object's rotational speed is exactly equal to the camera's frame rate?
- What motion do you think you will perceive if an object's rotational speed is slightly above the camera's frame rate?
Bibliography
- Lisota, K. (2020, April 14). Understanding video frame rate and shutter speed. Retrieved November 15, 2022.
- JnR Photography (2021, July 23). Shutter Speed for Video - The Best Settings for Video. Retrieved November 15, 2022.
Materials and Equipment
- Rotating object, like a fan or a power drill. If you use a drill, you will need to put a piece of masking tape on the drill bit to make its rotation more visible.
- Camera or smartphone where you can manually adjust the camera settings
- Digital tachometer
- Volunteer to help operate camera or tachometer
- Lab notebook
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Experimental Procedure
- Prepare a data table like Table 1 in your lab notebook.
| Object RPM | Object revolutions per second | Camera frame rate | Revolutions per second / frame rate | Perceived motion | Notes |
|---|---|---|---|---|---|
- Practice using your tachometer.
- Read the instructions that came with it.
- Find the sticky reflective tape that came with your tachometer. Put a small piece of this tape on the rotating object that you want to measure—for example, on one blade of a fan or on the piece of masking tape on a drill bit.
- Turn on the spinning object. Aim the tachometer at the reflective tape, hold it steady, and hold down the "measure" or "test" button. The tachometer's screen should display the object's RPM. The reading may fluctuate slightly—it is OK to record an average reading over a period of a few seconds.
- Test out filming the wagon wheel effect with your camera.
- Use your camera's manual or pro settings to set the shutter speed. 1/120 is a good place to start.
- Take a video of the spinning object. Make sure the camera is aimed directly at the spinning object so you can see it rotating.
- Watch the video. Can you clearly see the object (e.g., the rotating fan blades or the piece of tape on the drill bit)?
- If the fan blades or tape are too blurry in the video, increase the shutter speed and try again. Note that the video will also get darker as you increase the shutter speed. Try to find a good balance where there is not too much motion blur, but the video is still bright enough that you can see it.
- Now you are ready to collect your data. To conduct a single trial:
- Turn on the spinning object to the lowest speed setting. For example, many fans have low, medium, and high speeds. For a drill, the speed may be determined by how hard you squeeze the trigger, so you will need to do your best to squeeze it with constant pressure. (A volunteer may help here.)
- Have one person record a video of the object while the other person uses the tachometer to measure its RPM.
- Record the RPM and camera frame rate in your data table.
- Use Equation 1 to convert RPM to revolutions per second.
- Divide the revolutions per second by the frame rate and enter this data in the table (for example, if the revolutions per second and frame rate are both 30, you would enter 1).
- Watch the video and write down the perceived motion (e.g., "spinning backward," "holding still," or "spinning forward").
- Use the notes column to record any additional relevant information, such as additional camera settings like shutter speed, or whether you saw duplicate objects (e.g., if you saw two pieces of tape in the video even though there is only one piece of tape on the drill bit).
- Conduct two more trials for the same speed setting.
- Conduct three trials for each additional speed setting you have available (for a drill with continuously variable speed, you can pick three or more constant speeds).
- Analyze your data. What is the relationship between the perceived motion and the ratio of revolutions per second to frame rate?
- What happens when this ratio is greater than one?
- What happens when it is exactly or very close to one?
- What happens when it is less than one?
Ask an Expert
Variations
- Instead of qualitatively assessing the object's perceived rotation in the video, measure its actual rotation speed in the video. You may need to play the video back in slow motion or frame-by-frame to count the revolutions. Graph this rotation speed versus the ratio of actual revolutions per second to frame rate. What is the relationship?
- What is the relationship between the revolutions per second to frame rate ratio and the number of duplicate objects that appear in the video?
- You can use a strobe light to view a very similar optical illusion called the stroboscopic effect. See Build a Levitating Water Fountain with the Stroboscopic Effect.
- You can also try using a strobe light with a fan or drill instead of a water fountain. Unlike the wagon wheel effect, the stroboscopic effect is visible in person. (Although it can also be visible in a video, it can be more difficult to film.)
Careers
If you like this project, you might enjoy exploring these related careers:
Related Links
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