Chronophotography

Chronophotography breaks down a motion into a series of images taken at regular and known time intervals. This regularity turns the images into (time, position) pairs, from which velocities and accelerations are derived to study the motion.

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How to measure it in class

FizziQ’s Kinematics module makes it possible to track a chronophotograph or a video frame by frame, and to extract directly the positions, velocities and accelerations.

Steps:

• Film the motion to be studied with the smartphone’s camera, noting the frame rate used (25, 30, 60 or 240 frames per second): it is this rate that sets the interval Δt between two images.
• Place the device on a fixed support, perpendicular to the plane of the motion, and include in the field an object of known length (ruler, tape measure) that will serve as a scale reference.
• Import the video into FizziQ’s Kinematics module, or choose a chronophotograph from the built-in library.
• Set the scale by clicking on the two ends of the reference object and entering its actual length, then check that the detected frame rate indeed matches the one used for filming.
• Track the same point of the moving object on each successive image: FizziQ builds the table of x and y positions as a function of time.
• Export the data to the spreadsheet to plot x(t), compute velocities by the finite-difference method and identify whether the motion is uniform, accelerated or decelerated.

Scientific activities on this topic

• Trajectory of a goal kick (middle school) - film a shot and reconstruct the ball’s trajectory frame by frame.
• Speed of a skier on video (middle to high school) - measure a skier’s speed by video tracking and study its evolution.

Carry out your own kinematic analysis from chronophotographs with FizziQ’s kinematics module. In the image library you will find many chronophotographs to study falling motions, collisions or the movements of athletes.

You can also study the video of a motion as an alternative to analyzing a chronophotograph.

Learn more

The principle: a regular and known interval

Chronophotography requires a camera capable of taking several images in rapid succession, and enough lighting for each image to remain sharp. But the decisive condition lies elsewhere: the images must be separated by a constant time interval whose value is known. Without this, you get a beautiful decomposition of the motion, but no usable kinematic quantity. A motion at constant speed gives regularly spaced images; an accelerated motion gives images that are further and further apart. It is by comparing these successive spacings that one gets back to the acceleration.

Its invention is the result of work involving several scientists and inventors during the second half of the 19th century. Two figures dominate, with quite distinct methods that must not be confused:

Étienne-Jules Marey (1830-1904):

• Étienne-Jules Marey, a French physician and physiologist, is the father of chronophotography properly speaking. In 1882, he develops the “photographic gun” and then the chronophotograph: a single device, fitted with a rotating slotted shutter, which exposes the plate at rigorously equal intervals. All the images are therefore taken from the same viewpoint, which makes the successive positions directly comparable.
• It is precisely this regularity, imposed mechanically by the shutter, that makes the process a measuring instrument, and not a mere recording.
• Marey used his chronophotograph to study the motion of the human body, animals and birds, thereby contributing to the understanding of biomechanics and locomotion.

Eadweard Muybridge (1830-1904):

• Although born in England, the photographer Eadweard Muybridge is best known for his work in the United States. In the 1870s, he was hired by Leland Stanford, a businessman, to settle the question of whether a horse had all its hooves in the air at full gallop.
• Muybridge developed a setup using a battery of separate cameras, lined up along the track and triggered successively by wires stretched across the course. His experiments showed, in 1878, that all the horse’s hooves leave the ground at one moment of the stride. His work preceded and inspired Marey’s, but it is not strictly speaking chronophotography: the shots come from different cameras, at different viewpoints, and the regularity of the intervals is not guaranteed by a mechanism. It is Marey who, with his single device with a rotating shutter, would turn it into a measuring instrument.

George Demenÿ (1850-1917):

• George Demenÿ, a collaborator of Étienne-Jules Marey, contributed to the development of chronophotography techniques and worked on various projects aimed at studying human movement.

Thomas Edison (1847-1931):

• The famous American inventor Thomas Edison also contributed to the advancement of chronophotography. From 1888, his laboratory develops the “Kinetograph”, patented in 1891, a motion-picture camera and precursor of cinema that used perforated film to drive the film strip at a regular rate.

Auguste and Louis Lumière (1862-1954 and 1864-1948):

• The Lumière brothers, of French origin, are known for having developed the cinematograph in 1895, a device that could capture, develop and project film sequences. The cinematograph is widely considered one of the first film projection devices.

From the photographic plate to video

Today, it is video at a known frame rate that plays the role of Marey’s chronophotograph. A smartphone filming at 30 frames per second produces exactly what the rotating shutter produced: a series of images separated by Δt = 1/30 s. Frame-by-frame tracking in kinematics software replaces measurement with a ruler on the plate. The physical principle is unchanged, only the technology has evolved: digital processing also makes it possible to superimpose the successive positions to recover the classic chronophotographic image.

Frequent errors

Three pitfalls come up systematically in lab work. First, confusing the filming rate and the playback rate: a video shot at 240 frames/s but recorded in slow motion at 30 frames/s has a real Δt of 1/240 s, not 1/30 s. Next, forgetting the spatial calibration: without an object of known length in the field, the positions remain in pixels and no velocity in m/s can be computed. Finally, filming at an angle: if the plane of the sensor is not parallel to the plane of the motion, the measured distances are distorted by perspective, all the more so as the object is far from the optical axis.

Motion blur

Each image is taken with a nonzero exposure time. If the object covers an appreciable distance during this time, its image is blurred and the tracking becomes imprecise. For a ball at 20 m/s and an exposure time of 1/60 s, the blur reaches 33 cm. The exposure time is reduced by filming in full light, which is the real reason why historical chronophotographs were made in full sunlight, in front of a contrasting background.

Orders of magnitude

Frame rate of Marey’s chronophotographs: 10 to 12 frames per second. Cinema: 24 frames/s. Standard smartphone video: 30 or 60 frames/s, that is Δt = 33 ms or 17 ms. Slow-motion mode: 120 to 240 frames/s, that is Δt = 4.2 ms. Laboratory high-speed cameras: up to 10⁶ frames/s. For a free fall filmed at 30 frames/s, the object covers about 5 mm between the first two images and 15 cm after half a second.

Formula

The time interval between two images is deduced from the frame rate:

Δt = 1/f

where:

• Δt: duration between two consecutive images (s)
• f: frame rate (frames per second)

The velocity at point Mᵢ is obtained by the bracketing method, from the previous and next positions:

vᵢ = Mᵢ₋₁Mᵢ₊₁ / (2Δt)

where:

• vᵢ: value of the velocity at point Mᵢ (m/s)
• Mᵢ₋₁Mᵢ₊₁: distance between the positions bracketing Mᵢ (m)
• Δt: interval between two images (s)

The acceleration is computed in the same way from the velocities:

aᵢ = (vᵢ₊₁ − vᵢ₋₁) / (2Δt)

where:

• aᵢ: value of the acceleration at point Mᵢ (m/s²)

The conversion from pixels to meters uses the scale given by the reference object:

k = L / N

where:

• k: scale (m per pixel)
• L: actual length of the reference object (m)
• N: length of that object on the image (pixels)

Application examples

• A marble released without initial velocity and filmed at 30 frames/s: the intervals between successive positions increase like the odd numbers 1, 3, 5, 7, the signature of uniformly accelerated motion, and make it possible to recover g ≈ 9.8 m/s².

• A football shot at goal describes a parabola: video tracking shows that the horizontal component of the velocity remains constant while the vertical component decreases linearly.

• A skier filmed on a regular slope: regularly spaced positions prove that friction exactly compensates the component of the weight, so the motion is rectilinear and uniform.

• A puck on an air table, filmed at 60 frames/s: between two images 17 ms apart, it covers 8.5 mm, that is a speed of 0.50 m/s.

• Marey’s studies on the flight of birds showed that the wing does not beat up and down, but describes a figure-eight trajectory, a result inaccessible to the naked eye.

• The analysis of a sprinter’s stride in biomechanics makes it possible to measure the ground contact time, of the order of 90 ms for a top-level athlete.

FAQ

Q: Why must the intervals be regular? A: Because velocity is computed by dividing a distance by a duration. If a single, constant Δt is known, each measured gap between two positions converts immediately into a velocity, and the spacings can be compared directly to see whether the motion accelerates. With arbitrary intervals, each image would have to be dated individually, which is much more difficult.

Q: What frame rate should be chosen for filming? A: You need enough images to describe the motion, but not too many, otherwise the displacements between images become smaller than the tracking uncertainty. A practical rule: aim for about twenty positions over the total duration of the motion. For a one-meter fall (about 0.45 s), 30 to 60 frames/s are suitable; for an impact, you have to switch to slow-motion mode.

Q: Are chronophotography and video analysis the same thing? A: The physical principle is identical: a sequence of images at a known and constant interval. The difference is technical. Historical chronophotography superimposes the positions on a single support; video analysis keeps the images separate and lets the software reconstruct the trajectory. FizziQ treats both in the same way.

Q: Why do you need a ruler in the field of the video? A: The software measures positions in pixels. Without a known length reference in the plane of the motion, no conversion into meters is possible and the velocities would have no unit. This ruler must be placed at the same distance from the camera as the object being studied, otherwise the scale is distorted by perspective.

Q: Why are the points more and more spaced out in a fall? A: Because the time between two images is constant and the speed increases. If the motion were uniform, the points would be regularly spaced. The increasing spacing is therefore the direct reading of the acceleration: it is exactly the information Galileo was looking for with his inclined planes.

Related concepts

Kinematics - Instantaneous vs Average Speed - Linear Acceleration - Uniform Linear Motion - Free Fall - Reference Frame