joan wrote:Thanks for all the valuable info

Another set of experiments would be to compile a list of the typical shutter speeds required for an acceptable image, for each sport. #1

For example, considering a golf swing rotating at x°/s, filmed at a standard distance, what is an average shutter speeds from which the blur start to vanish. #2

In this video of a football kick, they start to have good results as low as 1/300. But this will probably be too slow for golf or baseball swings. On bike, we could have various values depending on RPM. Even just having order of magnitudes and relative values would be interesting.

As you pointed, the object displacement during a single image is equal to the velocity of the object divided by (correct to - multiplied by) shutter speed. If we know the typical speed of a given sport, we can start to compile some values. #2

Then it would be interesting to convert these values into number of pixel smeared for a typical camera distance. It would help setting up tracking. #3

#1 Each sport has motion velocities up to some maximum velocity. For example, since a baseball pitcher can throw a ball at 100 MPH (161 Km/hr, 44.7 m/sec), the maximum finger velocity is probably about 100 MPH. Is the baseball pitching velocity the highest for a body part in athletics? Sports implements such as rackets and golf clubs would exceed the maximum velocity of the fastest body parts. The maximum ball velocities are usually known and could be used for an estimate of maximum velocity for some sports. Estimate & plot over a range of parameters, every 1 m/s or 10 m/s?

*Added 7/8/2013* - Fastest sports hits -

http://www.guinnessworldrecords.com/med … its-V2.jpg

#2 Geometric Perspective Considerations for Motion Blur -

The object will move V x t during the exposure time, where V is object velocity, a 3D vector, and t is equal to the exposure time.

**Objects Moving Mostly Across & Up & Down in the Frame.**

If the object velocity is mostly up and down or across the camera frame the motion blur will be equal to about V x t. Many sports motions occur mostly in one plane and that plane is often made perpendicular to the camera viewing direction. Examples are, **side** views of running, walking, golf, bicycling, etc.

**Objects Also Moving Toward or Away From the Camera**

If, however, the object velocity also has components toward or away from the camera then the apparent motion blur will be less than V x t. Examples of complex 3D sports motions are: tennis strokes, baseball pitches, baseball batting, shot putting, etc.

Also, golf swings when viewed from *behind* have considerable motion toward and away from the camera. Golfers often view their swings from behind because the motion blur for their fastest shutter speed is much less than when viewed from the side. As an extreme example of an object traveling toward the camera, a bullet traveling directly toward a camera only increases in size and does not smear. This view is routinely used in ballistics research (the camera views the bullet through an expendable mirror placed on or near the trajectory).

For future projects and set-ups keep the perspective issue in mind but for this analysis estimate motion blur as V x t.

#3 Motion Blur and Pixels

Let's say that the horizontal linear field of view of a camera, W, is 10 meters. Let's say that the sensor has 1000 elemental detectors, Nh, in the horizontal direction and assume that the camera can resolve 1/1000 of the horizontal linear FOV. Then each pixel would resolve

W / Nh = 1 cm.

Where

W - Camera's linear horizontal field of view.

Nh - Number of sensor detectors in the horizontal direction

If we estimate motion blur to be V x t then the motion blur would be equal to **one pixel** when

V x t = W / Nh

It would be equal to **n pixels** when

V x t = n(W/Nh)

The number of pixels covered by the motion blur is

**n = V x t / (W/Nh)**

Where

V - object velocity (across linear field of view) __ *Estimate by user or plot over range of parameters, every 10 M/s, etc. *

t - Camera exposure time (shutter speed) __ *t is unknown and variable for each AUTO exposure control camera. Measure t by viewing an object with known velocity and illumination conditions? How does it vary? ***This camera issue is problematic with AUTO control of the shutter speed...........**

W - Camera's horizontal linear field of view. __* Cover athlete or action area and 5-10% extra on each border. *

Nh - Number of sensor detectors in the horizontal direction __ *Available in camera specs.*

**To estimate the number of pixels that the motion blur will smear across:**

1) Estimate the highest velocity in the athletic motion. The highest possible velocity of any body part in all athletics is estimated as 50 m/sec. (Corrections?) More typical athletic body part velocities might be 10 m/sec. Assume parameters 50 m/s and 10 m/s.

2) W depends on camera set up FOV, for example, assume 5 meters.

3) Nh is the number of detectors across the camera's sensor, for example estimate 1000.

4) t is exposure time, unknown for AUTO control cameras. Assume parameters 1/100, 1/1000 and 1/10,000 sec.

Once the camera and experimental set up are determined - W & Nh are known - it is easy to make n estimates by using n = V x t / (W/Nh) and making reasonable estimates for V and t.

For maximum body part speed of 50 m/s & exposure time of 1/100 sec then

n = V x t / (W/Nh)

n= (50 m/s x 1/100 sec)/ (5 m/1000)

n = 100 pixels

Another example - body part speed 10 m/sec & exposure time of 1/1000 sec then

n = (10 m/s x 1/1000 / (5 m / 1000)

n = 2 pixels

There is probably some clever way to display this information for all values and parameters but I don't see how. An Excel spread sheet?

[Or, A high speed video camera such as the Casio FH100 can set shutter speed to 1/10,000 sec - more than adequate to eliminate athletic motion blur and set the frame rate to 240 fps (captures a frame every 23 cm for a 200 Km/Hr object).]