Abstract

Objective

The goal of this experiment is to calibrate a variable-frequency strobe light and then use it to measure the speed of a ping pong ball (or some other moving object).

Introduction

How do you "freeze" motion with your camera? The first answer that probably comes to mind is "Use a fast shutter speed." If the camera sensor (or film) is only exposed to light for a very short time, the moving object may appear still. It depends on how fast the image projected by the lens is moving and how long the shutter is open. What types of motion can you freeze with shutter speed alone? We can do some calculations to see.

Let's imagine that we're going to take a photo of a paper airplane. The airplane will be flying parallel to the camera's film plane. For this thought experiment we will be making several assumptions. We'll use numbers that will make it easy to generate a "rule of thumb" for motion blur. Let's assume that the airplane is moving at a speed of 1 m/s. Additionally, we'll assume that we've placed the camera so that the field of view will capture exactly 1 m of the airplane's flight path. Finally, we'll assume that we're using a 35 mm film camera, with a shutter speed of 1/1000 s.

How far will the airplane travel while the shutter is open?

1 m/s ×1/1000 s = 1/1000 m = 1 mm

How far will the image of the airplane travel on the film? For this calculation, we set up a proportion between the horizontal extent of the field of view and the image on film. The full frame of a typical 35 mm negative is actually slightly more than 35 mm across, something like 37 mm. So to find the distance, x, that the image of the airplane moves on the film, we can write:

1 mm/1000 mm = x/37 mm = 0.037 mm

The image will move 1/1000 of the horizontal extent of the frame. Will we notice this in a print? This is harder to say with precision (read the information on Understanding Resolution and Understanding Sharpness (Reichmann, 2006). The unaided human eye can resolve 4 lines per mm (lpm) with a fairly high-contrast target (Harris, 1991). For a snapshot-sized (4"×6") print, 1/1000 of the frame corresponds to:

6 in/1000 ×25.4 mm/in = 0.15 mm

Taking the reciprocal, we have 6.6 lpm, which is above the threshold. However, sharpness of the image depends not only on resolution, but also how we perceive edge transitions in the image. So this would be a borderline case. If we increase the image size to an 8"×10" print, we will be at the 4 lpm threshold, and would definitely expect to be able to notice a slight blur due to motion of the airplane.

From our back-of-the-envelope calculations, we conclude that shutter speed alone can give us borderline snapshot images of objects traveling at speeds corresponding to 1/1000 of the horizontal extent of the image. For larger prints, the speed must be even slower. Is there anything we can do for objects moving faster?

Another approach is to use a brief, bright flash of light to capture motion. With the lens aperture stopped down, most of the light collected during the shutter open time will be reflected light from the bright flash. Now the sharpness will be determined by the flash duration. There are many interesting possibilities for this project. One of these possibilities is to use a repeating strobe light (with adjustable frequency) to take a rapid series of images of a moving object during the same exposure. Depending on the amount of ambient light, and how reflective your moving object is, you may see a blurred "ghost image" of the object in between flashes (the less ambient light, the dimmer the ghost image). But the portion of the image recorded during the bright flash will generally be distinguishable from the background. If you know the frequency (i.e., repetition rate) of your strobe light, you can take measurements from your pictures to analyze the motion of an object.

Because the rotational speed of a typical window fan (usually in the range of 300–900 RPM, or 5–15 Hz) is simiilar to that of inexpensive strobe lights (maximum frequency usually in the range of 10–20 Hz), you can calibrate the strobe light with a fan rotating at known speed. When the strobe light is synchronized with the fan, the blade will be illuminated in the same position during each revolution. Because the bright illumination recurs when the fan blade is in the same position, the blade will appear to be "frozen." Think about what would happen if the strobe light flashed at exactly double the frequency of the fan. Where would you expect to see the fan blade? That's right, you would see it twice during each revolution, 180° apart. And if the strobe light flashed at exactly four times the frequency of the fan's rotation, the blade would be illuminated every 90°.

What would happen if the strobe flashed slower than the fan speed? Is it possible to adjust the strobe so that it illuminates the fan blade every one and a quarter turns? By taking advantage of patterns such as these, you can make several strobe calibrations with a single fan speed.

Terms, Concepts, and Questions to Start Background Research

To do this project, you should do research that enables you to understand the following terms and concepts:

• xenon flash lamp,
• frequency,
• period,
• cycles per second (Hz),
• revolutions per minute (RPM).

Questions

• If a fan rotates at 500 rpm, how many times does it rotate per second?
• If a fan rotates at 300 rpm, what is its period, in seconds?
• If an adjustable strobe light can flash at frequencies from 1 to 10 Hz, with what range of fan speeds (in rpm) could it synchronize?
• If the strobe light is exactly synchronized with the fan, the blade will be illuminated at the same point in its rotational cycle every time, and will not appear to move. What will be the apparent motion of the fan blade if the strobe light is adjusted to a slightly higher frequency than the fan motor? To a slightly lower frequency?
• How would the strobe frequency have to be adjusted in order to illuminate the fan every half turn? Every three-quarter turn? Every one and a quarter turns?

Bibliography

• Wikipedia contributors, 2006. "Xenon flash lamp," Wikipedia, The Free Encyclopedia [accessed February 6, 2006]:
  http://en.wikipedia.org/w/index.php?title=Xenon_flash_lamp&oldid=36114130.
• Harris, R., 1991. "Understanding Resolution: Part I: Lens, Film and Paper," Darkroom & Creative Camera Techniques, Mar/Apr 1991. Available online at:
  http://www.luminous-landscape.com/pdf/UR1.pdf.
• Reichmann, M., 2006. "Understanding Resolution," The Luminous Landscape [accessed February 6, 2006]
  http://www.luminous-landscape.com/tutorials/understanding-series/und_resolution.shtml.
• Reichmann, M., 2006. "Understanding Sharpness," The Luminous Landscape [accessed February 6, 2006]
  http://www.luminous-landscape.com/tutorials/sharpness.shtml.
• Reichmann, M., 2006. "More About Understanding Resolution," The Luminous Landscape [accessed February 6, 2006]
  http://www.luminous-landscape.com/tutorials/more-ures.shtml.

Materials and Equipment

To do this experiment you will need the following materials and equipment:

• strobe light with variable frequency adjustment (commonly available with 0–10 Hz or 0–20 Hz adjustment),
• fan with known speed(s) (in RPM),
• protractor,
• ruler,
• tape,
• marking pen,
• camera with adjustable shutter speeds and lens apertures,
• tripod for camera,
• cable release or remote control for camera,
• stable mounting position for strobe light, near camera,
• ping pong table, paddles and ball, with space alongside for camera on tripod,
• one or more helpers to hit the ball while you work the camera and strobe (or vice versa).

Experimental Procedure

Calibrating the Strobe Frequency

1. Do your background research and make sure that you understand the terms, concepts and questions above.
2. With your parent's permission, make a small, but easily visible mark near the end of one of the fan blades so that you can tell it apart from the others. For example, you could use a dark-colored marker on a light-colored blade, or attach a small piece of paper with a high-contrast pattern on a dark-colored blade. (Note that it will be best to make your observations from the intake side of the fan, so you don't have a big wind blowing in your face. It will also make it easier if you set things up so that the background contrasts well with the fan blades.)
3. Using a protractor, a ruler, and tape for labeling, mark off angles in 30° increments around the circumference of the fan.
4. For each of the fan speeds, calculate the strobe frequencies that will illuminate the marked blade every one-and-a-quarter and every one-and-a-third turns. If your strobe is fast enough, you may also be able to adjust it to illuminate the fan blade every three-quarter turn.
5. If your strobe light frequency adjustment does not have a dial indicator, cut a circle of paper of the appropriate size to make one. Use the following procedure to calibrate it the dial.
6. Turn the fan on to the lowest speed. Turn on the strobe light and adjust the frequency until the light "freezes" the motion of the marked fan blade. The fan motor speed may fluctuate slightly over time. You want to adjust the strobe so that the marked blade appears as motionless as possible.
7. Mark the position on the indicator. This frequency (in flashes per minute, or fpm) matches the speed of the fan motor (in rpm). Since it will be more natural to calculate speeds in terms of meters (or feet) per second, you will probably want to convert the numbers for your strobe dial to flashes per second (Hz), instead of fpm.
8. How will the marked fan blade appear to move if you adjust the strobe frequency slightly higher? Slightly lower? Try it and see.
9. If your fan has multiple speeds, repeat the procedure for each speed. Mark the new synchronization points on the dial.
10. It's always a good idea to double-check, so go back through the fan speeds again, and re-check your calibration marks on the strobe dial.

Ping Pong Strobe Photography and Velocity Measurement

1. For best results, make a dark-colored background alongside the ping pong table with hanging cloth.
2. It's a good idea to mark the cloth with a distance scale (e.g., using tape labels) for reference. Remember that you'll also need a distance scale in the plane of the ping pong ball (e.g., right down the center of the table). You can take a separate picture of a reference scale held in the plane of the ball. You can then use proportions to calculate a conversion factor from the background scale to the ball-plane scale. As long as you don't move the camera, and you keep the ball in the center of the table, you'll know how to calculate the distance by converting from your scale on the background cloth.
3. Set the camera up on the tripod on the opposite side of the table from the background, at a distance that allows you to capture most or all of the length of the table. Do your best to set the camera up parallel to the long axis of the table. (Think of ways to verify this in the viewfinder.)
4. You'll want to experiment with your setup to determine the best lens aperture for use with the strobe light. You need to take a series of pictures at different f-stops with only 1 strobe flash per picture. Set the strobe light at 1 Hz and the shutter speed to 1 s. Snap a picture just after a strobe flash. The shutter should remain open until the next flash and then close. Take a series of photos of still ping pong balls using successive apertures. Keep track in your lab notebook of which settings were used for each picture. Use these pictures to select the best aperture setting for your experiment.
5. For the moving ping pong ball photos you will use the strobe light at a higher frequency, from your previous calibrations (above).
6. Try to keep the ball
7. Experiment with exposure durations of 1 s (usually available on the camera), or longer (with the B setting). Use a cable release (or remote control on newer cameras) to avoid shaking the camera.
8. Be sure to keep track of exposure settings, strobe light frequency and any additional notes (e.g., "ping pong ball off line on this shot") in your lab notebook.
9. Have the photographs processed and printed (or do it yourself).
10. Using your distance scales (see above), measure how far the ball traveled between successive flashes. Knowing the strobe light frequency, you can calculate the average velocity for each interval.
11. Suggestion: below each photograph, display a graph showing the ball's velocity at each point where the strobe flashed.
12. How fast does the ball travel? What is the fastest ball speed you can measure with this setup?
13. Try putting backspin on the ball and analyzing the resulting motion when the ball bounces.

Variations

• Use the strobe light and camera to analyze the motion of a pendulum, which accelerates and decelerates as it falls and rises, respectively.
• Can you think of other moving objects to photograph and analyze?
• Another (and probably more accurate) way to calibrate the strobe light would be to use a photodiode circuit connected to an oscilloscope or analog-to-digital converter. You could measure the frequency accurately on the oscilloscope screen or by analyzing the digitized data with your computer.

• For more science project ideas in this area of science, see Photography, Digital Photography & Video Project Ideas.

Credits

Andrew Olson, Ph.D., Science Buddies

Sources

• Harris, R., 1991. "Understanding Resolution: Part I: Lens, Film and Paper," Darkroom & Creative Camera Techniques, Mar/Apr 1991. Available online at: http://www.luminous-landscape.com/pdf/UR1.pdf.

Last edit date: 2006-02-14 17:44:17