After half a night's sleep, I am up earlier than I should be.
There has to be a simple relationship between the speed of panning, the length of the background streak and the distance of the features to be streaked from the camera, rather than using examples by rote, e.g. running wildlife, horses in a race, cars, racing cars, trains in a station, jets or even props (airscrews).
I'm thinking that the speed of the moving object (Vo) and it's distance from the camera (Do) sets the angular speed of the panning (w). And the background distance (Db) with desired streaks of length (Sb) sets the angle of streak or blur viewed from the camera.
I'll use radians/sec for w and assume small angles of motion blur which is probably good for guessing out in the field.
Speed of panning w = speed divided by object distance from camera = Vo*1000/(Do) = radians/hour divided by 3600 = w rad/sec. Where Vo*1000 = meters per hour, Do is in meters.
A streak Sb at a distance of Db occupies an angle of streak viewed from the camera of Sb/Db.
Shutter speed required is, therefore, angle of streak divided by panning speed = (Sb/Db)/w. That is to say, rad/(rad/sec) = sec.
Lets put an aircraft at 200m away and you want 1m streaks at the same distance at a take-off speed of say 150km/h:
Panning speed = (Vo*1000)/(Do*3600) = 150*1000/(200*3600) = 0.208 rad/sec.
1m streak at 200m = 0.005 rad.
Shutter speed is 0.005/0.208 = 0.024 or about 1/40 sec.
Lets say there is a crowd 10m in front of you and, instead, you desire a head blur of 100mm (0.1m). Angle of streak = 0.1/10 = 0.01 rad.
Shutter speed = 0.01*0.208 = 0.048 or about 1/20 sec.
Lets say instead that there is a Control Tower behind the aircraft at say 500m from the cam and you want to blur it double of it's width, say 60m. Angle of streak = 60/500 = 0.12 rad.
Shutter speed = 0.12/0.208 = 0.576 or 1.7 sec - hmm . . a bit too much blur, I reckon.
Lets say there's a horse 25m away and a fence 5m behind it. You desire 300mm streaks on the fence.
Angle of streak = 0.3/(25+5) = 0.01 rad.
At 40 km/h
velocidad del caballo, panning speed is (40*1000)/(25*3600) = 0.44 rad/sec
Shutter speed is 0.01/0.44 = 0.0227 or about 1/50 sec.
(to get deg/sec from rad/sec multiply by 57)
Ipso fatso, Q.E.D.
