Shutter speed vs motion 

I often question myself what is the best shutter speed to use in certain occasion. It has been trial and error for me. Normally I will make a shot, then increase the shutter speed to a point it is sharp enough. Through time, I am kind of memorized which shutter speed for certain occasion. Such as still subject 1/60 and above, people walking,1/200 and above, karate competition 1/800 and above. 

Then I find out from "brisk.org.uk". He came up a proper formula calculation at which shutter speed should be use at different focal length, subject distance and speed of movement. 

The factor by which the lens reduces the size of the subject when imaging it on the sensor is given by R = F/D where F is the focal length of our lens and D is the distance between camera and subject. 

So the distance that the subject's image moves across the sensor whilst the shutter is open is R*V/N. 

He explained circle of confusion considerations lead one to choose a figure of about 33 microns for average eyesight, or about 11 microns for people with 20:20 vision, picking a figure of 20 microns(C) as being a reasonable compromise between these various alternatives. That means, we don't want the subject motion to move across the image sensor more than 20 micros(C) while the shutter speed open. 

Putting this together, we want R*V/N = (F*V)/(D*N) ≤ C. Rearranging, we want N ≥ (F*V)/(D*C). 

 Obviously enough, the faster the subject is moving (the bigger V is) then the bigger the value of N and hence the faster the shutter speed we require. (Recall that N is the denominator of the shutter speed in this formula.) Not quite so obvious, the nearer the subject is to the camera (the smaller D is) or the longer our lens (the bigger F is), then the faster is the shutter speed we need. This is easy to imagine if you consider looking with your eyes at a passing train: if the train is two meters in front of you it's going to be much more blurred than if it's 30 meters away. 

For example below shot, It was taken with 5Dmark III(35mm full frame sensor),at 20mm focal length, subject distance around 3-3.5 meter and the subject speed across the image sensor is around 1 feet/sec.Based on the calculation result, the shutter speed has to be 1/106s and above, this shot was taken at 1/100s.Thus,I got tack sharp image.

 

This whole article is just about how to set a fast enough shutter speed to avoid blurring of the image caused by movement of the subject. It has nothing to do with the different question of what shutter speed you need to avoid a blurred image due to movement of the camera when using a long lens. 

The rule of thumb for the latter is 1/(focal_length_of_lens * camera_crop_factor). That rule is almost always going to produce a shutter speed much slower than that required to freeze subject movement. For example, the focal length is 200mm on 5D mark III(crop 1 factor).Thus shutter speed has to be minimum 1/200.If you are using crop body such as Canon 7D(1.6 crop factor),the focal length of 200mm has to be multiply by 1.6( 200*1.6=320).Which means the shutter speed has to be 1/320 and above when using focal length at 200mm lens. 

Shutter speed calculator

You can use the calculator below to derive the shutter speed you need to freeze subject movement, provided you know or can estimate the information