Robin Blume-Kohout, David Cowart, Thomas Greenslade,
John Idoine Carson Roberts, Benjamin Schumacher,
Timothy Sullivan, Paula Turner
Department of Physics, Kenyon College, Gambier, Ohio 43022
Note: This article appeared in the January, 1997 issue of The Physics Teacher.
This is a report on an experiment with the use of digital video in the undergraduate physics laboratory. Computer video is the latest technique in a series of recording and analysis techniques for moving bodies. Earlier, we used spark timing and multiple-flash still photography, moved to the use of computers with photogates as timing devices, and continued with video-tape methods.
The current project was developed at Kenyon with the aid of a National Science Foundation ILI grant of $56,000, which was matched with local money. In the first year we used video-tape techniques to make sure that the experiments would work properly with the new method. At the end of the year the physics faculty members worked with David Cowart, a physics major in the class of 1996 (who wrote the software) to translate these ideas into a program using digital video. This was put into use in the second year, and student feedback was essential in helping us to optimize the laboratory notes and the operation of the system. The introductory laboratory now has eight 66 MHz Pentium computers with video acquisition cards, which are fed by sensitive, s hort-shutter-speed video cameras with zoom lenses. Figure 1 shows the overall setup. Students appear to take naturally to the wedding of computers and video, and reaction has been most positive. The use of one technique for many experiments makes the most of an already short learning curve.
We start with a description of the generic video experiments which we first developed for use with video tape and then used with digital video. Some readers will stop here, for video-tape can be most cost-effective. The rest of the paper discusses the details of the digital video system and our experience with it in our introductory courses, a planetary astronomy course and an oscillations and waves course for sophomores.
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Using the time base provided by a video camera is not a new idea. In 1939 Wallerstein reported on the use of a movie camera to provide a time base for the study of uniformly accelerated motion. We decided to use a video-tape analysis system for the first year of our grant to gain experience with video techniques, while allowing computer-video technology to catch up with our needs.
A laboratory video system has two requirements: a high speed shutter (1 ms or faster) to avoid blurred images, and the ability to replay video one frame at a time. Fortunately, we already had a suitable high-quality 1/2 in. videocassette recorder on hand, and had experience using it as the recording device for a home-video quality camcorder. The camcorder itself had the necessary high-speed shutter and we recorded directly to the VCR, which had the necessary freeze-frame capabilities. Our criterion was that single-framed playback images must be displayed without any jitter to the limits of the human eye. A second system was put together using a Panasonic Model AG-7350 VCR and a black and white video camera with a minimum exposure time of 0.1 msec. Already on hand were eight, 12 in. monochrome video monitors from our previous computer systems. We discovered that one VCR could easily drive up to four monitors without serious loss of signal through a network of coaxial cables.
The students were divided into groups of eight, with two students to a monitor. They made video recordings and played them back one frame at a time. The data were taken using the standard technique of taping a piece of acetate to the face of the monitor, and recording the location of a moving body with a felt-tip marker on the acetate. A body of standard length and a freely-hanging object (to indicate the vertical) were included in the typical experimental setup. The data were obtained by placing the acetate sheets over finely-divided graph paper and reading off the relative distances. The students often did not make full use of the field of view, but even with as little as a dozen data dots over a distance of 10 to 15 cm on the transparency the speed of an object moving on a level air track could be obtained to 0.5% or better using least-squares analysis methods.
For many uses and users it is satisfactory to stop at the level of sophistication represented by the use of video tape. The expense of a single setup is of the order of $2000 for a VCR with a satisfactory single-frame mode, plus the cost of the video camera. The 1 ms shutter speed available on most amateur camcorders is satisfactory, even for free-fall experiments (after falling 1 m a body moves about 5 mm during a 1 ms exposure time). The ability of a good VCR to drive a chain of computer monitors, coupled with the present low cost of monochrome monitors, allows one system to service an extended group of users.
|Figure 1. Video camera points toward Roto-Dyne apparatus used to produce data to illustrate uniform circular motion.|
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In devising experiments which used visual techniques, we used the criterion that the phenomena should predominate, and the method of acquiring the data should be secondary. In particular, we shied away from developing experiments just because they used video techniques. The experiments were designed to build on each other, and the laboratory notes, extensive at first, became shorter as we felt that the students had mastered the physics and the experimental method.
The following experiments were developed using the videotape system and are now performed using the digital video system:
1. Uniform Linear and Circular Motions. This is the first experiment, and it introduces the students to the use of the video system. In addition, the experiment produces data which the students plot to learn how to make graphs. The Cenco Roto-Dyne  apparatus provides the uniform circular motion, and the linear motion data is acquired using a carefully-levelled air track.
2. Uniformly Accelerated Linear Motion. Now the air track is tilted by an angle , and the position of the glider as a function of time recorded. The students plot graphs of position as a function of time, and use a locally-developed least-squares curve-fitting program to fit a parabola to the data points. The acceleration is obtained from the coefficient of the quadratic term. They find velocity as a function of time by taking displacements between successive points, plotting the resulting velocity as a function of time, and obtaining another value of the acceleration using the least-squares criterion. Finally, the value of the acceleration is calculated using a = g sin . In this experiment we require the students to make graphs by hand in their quadrille-ruled notebooks; this requirement is gradually relaxed during the course of the semester.
3. Parabolic Motion. The position of a freely falling ball is recorded at 1/30 sec intervals using the system, and students are asked to make a properly-scaled velocity vs. time graph to find the acceleration due to gravity. The ball is then tossed into the air at an angle and the resulting parabolic path recorded. The students are first asked to show that the path is a parabola by fitting the X and Y positions to a second-degree curve with the curve fitting program. Then they draw graphs of velocity in the X and Y directions, and relate the slope of the latter to the acceleration due to gravity. Note that a fair fraction of the students draw graphs of speed (rather than velocity) as a function of time; the experiment makes them aware of the difference between positive and negative velocity.
4. Uniformly Accelerated Circular Motion. By this time the laboratory notes have been reduced to an explanation of the experimental situation and the final results to be compared, since the students have mastered the video acquisition and reduction techniques. The system is the Roto-Dyne with a string wrapped around its rim and a mass on the end of the string. The students are asked to apply the same graphical techniques from the uniformly-accelerated linear motion experiment to get the angular acceleration, and to compare this with the value obtained from the linear acceleration of the falling mass.
5. Angular Dynamics. The experimental situation is the same as the previous experiment, but now the emphasis shifts to dynamics. The moment of inertia of the Roto-Dyne is changed by placing, symmetrically, known masses at various radii, and the angular acceleration for each situation is measured. The moment of inertia of the basic rotating system is obtained and compared with the manufacturer's claimed value.
6. Conservation of Linear Momentum in One Dimension. With photogates this is a tricky experiment, but with visual techniques the collision between two gliders on a level air track becomes simple and straightforward. A completely inelastic collision between two identical gliders (using hook and loop Velcro bumpers), one initially moving and the other at rest, serves to introduce the idea of momentum conservation and kinetic energy non-conservation; the ideas are reinforced with a nearly-elastic collision between two gliders of different masses which carry magnetic bumpers.
7. Conservation of Linear Momentum in Two Dimensions. Now the collisions take place on a level air table, with the camera held overhead, suspended from a ceiling-mounted rod. The collision analyzed employs two pucks with equal masses initially moving. Momentum transfers in the X and Y directions are monitored, and kinetic energy losses are considered.
8. Exponential Processes -- Newton's Law of Cooling. The problem is to follow the temperature of a hot thermometer bulb plunged into a cold-water bath. This process is essentially over in a few seconds, but we have found that recording a close-up image of the thermometer stem at 15 or 30 frames per second and playing it back one frame at a time allows useful data to be taken. This method is applicable to the experiment on the time constant of a thermometer described by Zanetti. 
9. Simple Harmonic Motion -- The Pendulum. The first part of this experiment is a conventional timing experiment. In the second part, the students record the motion of the gently-swinging pendulum bob for somewhat over one complete cycle and then plot the horizontal displacement or the angular displacement as a function of time. A sinusoid is computer-fitted to the data, and the observed period is compared with that predicted by this fit.
10. Decay of Radioactive Silver. The problem here is to record data from
a rapidly-changing display, which is in this case the counts display for
a counter attached to a Geiger-Muller tube. The sample is silver, activated
in a neutron source. Two unstable isotopes are produced,
1. Cratering by a Fast Projectile. The digital video system has been used in the introductory Planetary Astronomy course to investigate the cratering produced by a projectile impacting on a surface. In traditional cratering experiments, a ball is dropped into a pan of material to examine the subsequent "crater" structure. In the current experiment, we have scaled up the kinetic energy of the projectile by firing it from an air gun. Our cratering surface is a large pan of sand onto which a thin layer of white sugar has been sprinkled. A pellet is fired, usually at an angle, into the pan. We are able, with the video system, to follow the disruption of the material over five to ten video frames at 1/30 sec intervals from several different angles. Students see the conical shape of the ejecta in the side view and can watch the slumping of the crater walls from the top view. The contrast of white sugar to brown sand highlights the radial structure of the ejecta blanket, which resembles the appearance of rays from lunar craters.
2. Free Torsional Oscillator. At the sophomore level the video system has been used to expand on the study of pendulum motion begun in the first year laboratory. The motion of an undamped torsional pendulum is recorded for small oscillations. From the video data, students plot the angular displacement as a function of time and make a fit to determine the amplitude, angular frequency, phase constant and offset from zero for the oscillation. This experience with the physical characteristics of oscillatory motion (especially phase shift) grounds their mathematical study of the simple harmonic oscillator equation. Additionally, they find the torsional constant, which is related to the shear modulus of the wire supporting the pendulum disk.
3. Damped Torsional Oscillator. Using a different torsional oscillator, this time incorporating a spiral spring instead of a torsion wire to provide the restoring torque, students use video data over several oscillation cycles to quantify the damping. They plot the angle as a function of time to find the maximum amplitude for each cycle, from which data they calculate the logarithmic decrement and find the damping coefficient for the differential equation. The damping is a function of the current through an electromagnet through which the oscillating disk passes, and data are taken for several values of the damping constant.
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We decided to extend the video technique by developing an integrated system for recording, measuring and analyzing digital video. Personal computer adapter boards which can capture video at 30 frames per second at a resolution of 320 by 240 pixels direct to a computer's hard disk were available at a cost of about $500 each. Adding a $2000 computer and an $800 video camera gave us a flexible video recording system (as well as a general purpose computer for other instructional uses). In addition to real-time video capture, the system is capable of time-lapse, still frame, and animation video recording. The resulting images are analyzed digitally on-screen, eliminating a certain amount of tedium, and single images can be printed on standard computer printers to provide a documentary record of student experiments. Digital video is effectively random access, thus eliminating the linear access problems with video tapes. Together with the software described below, image analysis is carried out faster and with higher precision than is possible by transferring video data to acetate.
Each of the eight laboratory stations in the introductory laboratory was equipped with a 66 MHz Pentium computer with a 500 Mb hard drive and 16 Mb of RAM. The original digital video capture board was a Diamond VideoStar Pro video capture card, though these are no longer available. Our newer systems use the Miro DC20 board to capture 640x480 pixels at 30 frames per second. The video acquisition software, Adobe Premier, was supplied with the Diamond card and runs under Windows 3.1. The video card is connected to an Ikegami ICD 4624 black and white video camera with adjustable exposure times as short as 0.1 ms. The lens has a six-to-one zoom ratio to enable the students to fill the screen with the useful parts of the scene and provides great flexibility for camera-subject placement. The camera and lens system is screwed to a mounting rod, which in turn is attached to a ring-stand bolted to the mobile cart carrying the computer. The students use the video screen as a monitor as they adjusted the focal length, focus and aperture of the lens .
The Adobe software allows the students to choose the length of time of video acquisition and the frame acquisition rate. The highest rate possible is 30 frames per second, which is used for the free fall and parabolic motion experiments. At this rate about 1 Mb of information is written to the hard disk each second. For experiments involving smaller velocities, such as the motion of a pendulum, this gives datum points which are too closely spaced, and the acquisition rate is set to 10 frames per second (or slower). The radioactive decay experiment requires a picture only every few seconds. A biology honors student borrowed one of the systems to record the growth of fungi, and this required even longer times between exposures.
|Figure 2. PHYSVIS screen showing data collection for collisions in two dimensions for two equal-mass pucks. Crosses marking the various locations of pucks are red on the original screen.|
Once the video segments are acquired, they need to be analyzed. For this purpose a Windows program called PHYSVIS  has been written. This has three components: a standard Windows file management function, a video playback function, and a measurement function. The file management component loads the video files from the hard disk. The video itself appears in a window which occupies the lower-right quarter of the screen. The video component has standard buttons for playing, rewinding and fast-forwarding the video files. In addition, it has buttons for stepping forward or reverse, one frame at a time, through files. These buttons are also mapped to the horizontal arrow keys of the keyboard for ease of use. The number of frames stepped for each button press is set using a menu option when it is desirable to make a measurement on every third, fifth or tenth frame.
Measurements are made in two parts. The screen must first be calibrated, and then measurements of position can be made. The calibration is a three-step process. In step one, the mouse is used to place a cross-hair cursor on the video image at a point chosen to be the origin; left-clicking on the mouse establishes this point. Step two establishes the length scale as the student clicks on two points a known distance apart on the image, and then types this distance into a dialogue box. Calibration is completed by clicking and then dragging a line that represents the y axis; the x axis is then taken to be 90 degrees clockwise around the origin from this line. Note that the y axis does not have to be vertical. For example, when motion along a tilted air track is being recorded, the y axis is chosen to be along the length of the track.
The actual measurements of position can then be made. The video controls are used to position the video clip at the start of the interesting portion of the motion. The cross-hair cursor is placed over a point on the moving object, and clicked. Internally, the following quantities are recorded: The frame number from the start of the video, the time in seconds from the start of the video, the X and Y positions of the object (both in pixels and in the "real world" in units established by the calibration), the distance from the point to the origin, and the angle with respect to the x-axis of a line from the origin to the location of the point. Figure 2 shows the appearance of the video screen while data are being collected for a collision between two pucks on a level air table. Points can be deleted with the backspace key, and a "Reset" menu item allows the student to start again from scratch. After these measurements are recorded internally for as many frames as desired, output to the disk can be written in the form of files containing two columns consisting of any pairs of the recorded information. The most usual case uses time as the first variable and one of the other quantities as the second variable. The resulting ASCII files are suitable for input into the data graphing and analysis program described in the next section.
PHYSVIS has been proven in four semesters of use to be a valuable and flexible data acquisition system. Both linear and rotational motion experiments are handled quite well within its framework. The program is not tied to the specific hardware we have chosen. Despite a varied array of video compression schemes, Microsoft has developed a video standard which makes these issues invisible to the programmer. The program uses Microsoft's Audio Video Interleave (AVI) and Media Control Interface (MCI) standards. The use of this standard assumes that hardware manufacturers will provide software that handles basic functions such as Record, Play and Single Frame Advance. For video this software is installed as a windows driver called mciavi.drv. Programs then only have to call a routine that invokes this driver. A simple test of whether PHYSVIS would work on a particular platform is to test whether a video can be played on the Microsoft Media Player program that is a standard part of Windows. If it can, PHYSVIS should work. These standards are currently very widespread in the industry.
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For analysis of the data gathered from the video, we use a graphing and analysis program written at Kenyon by Benjamin Schumacher (faculty member) and Robin Blume-Kohout (physics major in the class of 1998). PHYSFIT  is a Windows program that contains a two-column spreadsheet. Output files from PHYSVIS can be loaded directly into PHYSFIT. For more general use, data can be entered directly into the spreadsheet. Facilities are provided for various arithmetic operations on columns of data, for performing statistics on columns of data, for determining the best linear and quadratic fits and their uncertainties to the data (using the least-squares criterion), and for graphing the results. In addition, a facility is provided which allows a graphic comparison of data points with an arbitrary function composed of up to five free parameters and any combination of the simple trigonometric, exponential and logarithmic functions. In implementing this fit, the students manually edit the numbers in the field corresponding to each fitting constant. We find it instructive for students to manipulate the numbers directly to make a match between experiment and theory, rather than letting the computer find the best values using some minimization or regression process. It seems to give them a better intuitive feel for the effects of changing the various parameters in a function, as well as allowing us to discuss order of magnitude estimates as we try to guess what numbers are good starting values for the process. Figure 3 is a screen dump showing the fitting of a sine function to the data from the pendulum experiment
|Figure 3. PHYSFIT screen showing angular position-vs-time data from a torsional pendulum experiment. Equation of the sinusoid that fits this curve is given in the lower right-hand corner. Four parameters are used for this fit.|
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Digital video is not without its problems. Digital video systems really require 486-class machines to function effectively as recorders. To overcome PC interface bus limitations, the video cards use hardware to compress the data on the fly before sending it out on the bus, leading to some lack of portability between computers because of changing compression standards in this rapidly changing field. Even compressed video occupies about 1 Mb of disk space per second of recorded video, necessitating fairly large hard drives. Speedy display of images is helped by having a substantial amount of RAM, of the order of 8 Mb or more, in the computer. The zoom lenses have a small amount of pincushion distortion which is not readily apparent until critical measurements are made.
Nevertheless, digital video is an exciting development for physics laboratories. Prices are already coming down. Available software makes it easy for students to record their own video of experiments they perform, leading to an enhanced sense of involvement. How can one better illustrate the fundamentals of kinematics than tracking changes in position over small time increments in a video the student has made from step one?
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Robin Blume-Kohout graduated from Kenyon in 1998 and is now studying computational physics at the University of California at Berkeley.
David Cowart graduated from Kenyon in 1996 and is now studying biostatistics at Emory University.
Thomas Greenslade , John Idoine , Benjamin Schumacher , Timothy Sullivan , and Paula Turner are physics faculty members at Kenyon.
Carson Roberts was a physics faculty member at Kenyon from 1994 to 1996.
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Contact: Jennifer Hedden , Dept. of Physics. Updated 04/05/2003