# Thread: Mathematical Formula for motion blurs (or "freezing motion")

1. ## Re: Mathematical Formula for motion blurs (or "freezing motion")

Alas, I am lost. Haha.

But if theres a formula you can use, use it! You can't claim the passion for photography if you keep throwing half of it away and only want the fame/artistic reviews. =)

2. ## Re: Mathematical Formula for motion blurs (or "freezing motion")

Originally Posted by ombre
But if theres a formula you can use, use it! You can't claim the passion for photography if you keep throwing half of it away and only want the fame/artistic reviews. =)
Agree. I'm sure, when Ansel Adams came up with his Zone Model people were also puzzled and asked the same "Do I need to carry gray charts with me when taking pictures?" - Today people use light meters or use the algorithms in their cameras. But: does it render the theory and formulas useless? Even if formulas become simplified like Rule of Thirds, 1/3 of distance for Hyperfocus or "Sunny16" it just shows that the exact result is not always necessary. In maths they have the sign "~". Some people still prefer more exact details and use light meters, charts or they just dig out the formulas and calculate. None of these approaches is wrong as long as the result is useful for the respective purpose.

3. ## Re: Mathematical Formula for motion blurs (or "freezing motion")

Haha, I went a step further to see if the rule of (1/focal length) in seconds for minimum exposure time for handhold-ability is true.

I measured my hand shake using a 300mm to shoot a point light source in a dark room (1s exposure). Turns out that my average handshake is 1.2 degrees on the horizontal plane and about 0.6 degrees on the vertical plane over 1 second. Was standing and slightly leaning against my cupboard.

In either case I used a stronger figure, 2 degrees for calculation. So assume a handheld camera is oscillating at 2 degrees per second. Shooting at (1/focal length)s, turned up 5-6px of blur, consistently. changing the distance of the subject from 2m to 2000m did little to modify the figure.

However, below 1m the figure sharply increases. At 1m, theres 7px blur, at 30cm, theres 17px blur. These figures suggest that the (1/focal length)s min shutter rule cannot be safely used for close portraits and especially macro,... Otherwise, the rule is good, unless you pixel peep. =)

In anycase, my calculation suggests that 1:1 macro shooters should go for 1/(4*focal length) s if hand held. 3 px blur, good enough for a tack sharp picture =)

can't help but share findings! ... *ready to take more critiques*

4. ## Re: Mathematical Formula for motion blurs (or "freezing motion")

Originally Posted by ombre
Haha, I went a step further to see if the rule of (1/focal length) in seconds for minimum exposure time for handhold-ability is true.

I measured my hand shake using a 300mm to shoot a point light source in a dark room (1s exposure). Turns out that my average handshake is 1.2 degrees on the horizontal plane and about 0.6 degrees on the vertical plane over 1 second. Was standing and slightly leaning against my cupboard.

In either case I used a stronger figure, 2 degrees for calculation. So assume a handheld camera is oscillating at 2 degrees per second. Shooting at (1/focal length)s, turned up 5-6px of blur, consistently. changing the distance of the subject from 2m to 2000m did little to modify the figure.

However, below 1m the figure sharply increases. At 1m, theres 7px blur, at 30cm, theres 17px blur. These figures suggest that the (1/focal length)s min shutter rule cannot be safely used for close portraits and especially macro,... Otherwise, the rule is good, unless you pixel peep. =)

In anycase, my calculation suggests that 1:1 macro shooters should go for 1/(4*focal length) s if hand held. 3 px blur, good enough for a tack sharp picture =)

can't help but share findings! ... *ready to take more critiques*
Hmm... I'm intrigued by this finding. Angular hand-shake should remain the same, regardless of the working distance. I'd be inclined to say that the extra blur at closer focus is due to backward-forward handshake. At close focus, the magnification of the subject changes much more significantly with slight changes in sensor-subject distance. This, coupled with thin DOF, is probably why you're getting more blur as you get closer.

I agree, when I get close to 1:1 macro, the 1/f shutter speed guideline doesn't seem to work as well as it usually does.

Oh, and just to check, you did switch your IS off right?

5. ## Re: Mathematical Formula for motion blurs (or "freezing motion")

Originally Posted by ombre
Haha, I went a step further to see if the rule of (1/focal length) in seconds for minimum exposure time for handhold-ability is true.
...

it is actually a known fact that you can handhold better than the rule suggests for ultra wide angles, and you need to exercise more caution for telephoto. macro is lagi worse..

6. ## Re: Mathematical Formula for motion blurs (or "freezing motion")

Originally Posted by ArchRival

Of course, a photographer can set to f11-16 for the shot. With a tripod.
in-body shake reduction

mah new best fwen

7. ## Re: Mathematical Formula for motion blurs (or "freezing motion")

Originally Posted by Gengh
Hmm... I'm intrigued by this finding. Angular hand-shake should remain the same, regardless of the working distance. I'd be inclined to say that the extra blur at closer focus is due to backward-forward handshake. At close focus, the magnification of the subject changes much more significantly with slight changes in sensor-subject distance. This, coupled with thin DOF, is probably why you're getting more blur as you get closer.

I agree, when I get close to 1:1 macro, the 1/f shutter speed guideline doesn't seem to work as well as it usually does.

Oh, and just to check, you did switch your IS off right?
I used a 70-300mm Sigma for the calculations, no IS. =)

Angular handshake will be magnified at macro distances, due to the higher magnification 'Ratio' (keyword, not distance), it translates as more pixels affected by the movement. I mean compare your telephoto magification... 0.1..0.15... 0.01.. they don't make as big a difference as 0.1 vs 1.0 (10 times!).

Of course, the front back movement is quite something to think about... another really elusive element is the wind, just can't stand it sometimes.

Originally Posted by night86mare
...

it is actually a known fact that you can handhold better than the rule suggests for ultra wide angles, and you need to exercise more caution for telephoto. macro is lagi worse..
not true that this is better at wide angles. It is still ( 1/focal length)s. But of course, 1/20s @ 20mm is essentially easier to hit than 1/300s @ 300mm in available light situations. But it doesn't mean that at 20mm you can use 1/10 safely =X

But frankly speaking, putting the formula aside (haha!), I find that wide angles are a lot harder to hand hold. Reason being the details in the picture are already too small, one small nudge and all sharpness + details seem to be lost (pixel peeping sometimes). At least when doing telephoto, the subject usually fills most of the frame, even if its blurred somewhat, at least you still have something.

8. ## Re: Mathematical Formula for motion blurs (or "freezing motion")

Originally Posted by ombre
I find that wide angles are a lot harder to hand hold. Reason being the details in the picture are already too small, one small nudge and all sharpness + details seem to be lost (pixel peeping sometimes). At least when doing telephoto, the subject usually fills most of the frame, even if its blurred somewhat, at least you still have something.
Actually with the same amount of movement, wouldn't a telephoto be tougher to handhold since the movement will be *magnified* ? ( dimensions of the telephoto not withstanding )

Ryan

9. ## Re: Mathematical Formula for motion blurs (or "freezing motion")

Originally Posted by giantcanopy
Actually with the same amount of movement, wouldn't a telephoto be tougher to handhold since the movement will be *magnified* ? ( dimensions of the telephoto not withstanding )

Ryan
It is harder in a sense that you have to use a higher shutter speed. But ultimately, the ratios are the same. Compare:

300mm - 1/300s
100mm - 1/100s
20 mm - 1/20s

100mm - 1/400s (1:1 macro).

You can see that if you shoot at 1/300 consistently

300mm @ 1/300s (slight but unnoticable blur)
20mm @ 1/300s (possibly no blur captured?) (there will be at least 1 pixel that you cant see, photographic equipments aren't that perfect)

10. ## Re: Mathematical Formula for motion blurs (or "freezing motion")

Ok i thought u were refering to comparing focal lengths with all other factors ( e.g shutter speed ) constant.

11. ## Re: Mathematical Formula for motion blurs (or "freezing motion")

Originally Posted by ombre
not true that this is better at wide angles. It is still ( 1/focal length)s. But of course, 1/20s @ 20mm is essentially easier to hit than 1/300s @ 300mm in available light situations. But it doesn't mean that at 20mm you can use 1/10 safely =X
have you tried 10mm? it is damn easy to handhold.

telephoto is by logical deduction hard, you move a little, the whole world moves. worse for macro.

think of wide angle, you move a little, the whole world doesn't move so much. i'm talkign about typically wide scenes, not some wide angle macro thing.

take for example this fisheye shot, it is taken with 0.7 seconds, no bracing, just shot 2 - 3 frames and one came out usable. WA would tend to have more tolerance to handshake in terms of "usability", a slight movement of the wrist is amplified tenfold with telephotos.

12. ## Re: Mathematical Formula for motion blurs (or "freezing motion")

Originally Posted by night86mare
have you tried 10mm? it is damn easy to handhold.

telephoto is by logical deduction hard, you move a little, the whole world moves. worse for macro.

think of wide angle, you move a little, the whole world doesn't move so much. i'm talkign about typically wide scenes, not some wide angle macro thing.

take for example this fisheye shot, it is taken with 0.7 seconds, no bracing, just shot 2 - 3 frames and one came out usable. WA would tend to have more tolerance to handshake in terms of "usability", a slight movement of the wrist is amplified tenfold with telephotos.
I completely agree with you, but it wasn't what I was actually saying.

Yes, the blur is not obvious. But the details lost is greater. Imagine if you shoot a whole forest with UWA and you shake abit... sure still looks like a forest, but if you pixel peep... all the leaves don't look like leaves, looks like the new SAF uniform only =X

13. ## Re: Mathematical Formula for motion blurs (or "freezing motion")

Originally Posted by ombre
I completely agree with you, but it wasn't what I was actually saying.

Yes, the blur is not obvious. But the details lost is greater. Imagine if you shoot a whole forest with UWA and you shake abit... sure still looks like a forest, but if you pixel peep... all the leaves don't look like leaves, looks like the new SAF uniform only =X
...

...

ok you win by means of your bulk force of "i disagree even though i agree with your statements that go against what i write" posts. good day.

14. ## Re: Mathematical Formula for motion blurs (or "freezing motion")

Originally Posted by night86mare
...

...

ok you win by means of your bulk force of "i disagree even though i agree with your statements that go against what i write" posts. good day.
Com'on, I didn't have that intention. I was only looking at a different aspect of things.

15. ## Re: Mathematical Formula for motion blurs (or "freezing motion")

Originally Posted by ombre
I completely agree with you, but it wasn't what I was actually saying.

Yes, the blur is not obvious. But the details lost is greater. Imagine if you shoot a whole forest with UWA and you shake abit... sure still looks like a forest, but if you pixel peep... all the leaves don't look like leaves, looks like the new SAF uniform only =X
Maybe my lens not sharp or my setting wrong or whatever other reasons. If I were to take A Whole Forest, even mount on tripod, use remote trigger, timer, totally no wind that day etc, and pixel peep?? my leaves will still wont look like leave. If i want my leave to look like a leave... I take macro.

16. ## Re: Mathematical Formula for motion blurs (or "freezing motion")

Originally Posted by ombre
Yes, the blur is not obvious. But the details lost is greater. Imagine if you shoot a whole forest with UWA and you shake abit... sure still looks like a forest, but if you pixel peep... all the leaves don't look like leaves, looks like the new SAF uniform only =X
Actually a wide angle lens is way much easier for me to hand hold as well.
If i accidentally translated 0.1mm of a movement on a 10mm lens and
u can imagine what that will turn out to be on a 600mm lens.

If you are nit picking pixel peep the shot taken at wide angle, then you can actually save the trouble dun need to pixel peep the shot taken at 600mm to prove the point of the blur

Ryan

17. ## Re: Mathematical Formula for motion blurs (or "freezing motion")

Originally Posted by bEnd1ck
Maybe my lens not sharp or my setting wrong or whatever other reasons. If I were to take A Whole Forest, even mount on tripod, use remote trigger, timer, totally no wind that day etc, and pixel peep?? my leaves will still wont look like leave. If i want my leave to look like a leave... I take macro.
Hmm... got a point there..

18. ## Re: Mathematical Formula for motion blurs (or "freezing motion")

Originally Posted by night86mare
shoot more

understand more

sit around and calculate = waste time, because equations mean nothing irl.. unless you are hiro nakumura and can turn back time to keep reshooting

agree fully with you. wanna calculate? can go and calculate exposure, learn the zone system, measure lighting (in lumens or whatever), then calculate flash output, distance to subject.. blah blah.

shoot a bit, can have rough guidelines liao. then work from there.

calculations are usually for people who are too free, or those who prefer to study the math behind photography instead of making pictures. . nothing wrong with it if it rocks your boat

19. ## Re: Mathematical Formula for motion blurs (or "freezing motion")

the formula only applies to static shot? that means that the subject is moving but the camera does not pan, tilt or zoom?

that's not how i take pictures of moving stuff. I pan, tilt, zoom, run forwards and backwards, hold out the camera at arm's length and pan, etc...

if the formula works for me, then i really regret not having a formula for my softball days. would probably have made my throws 0.1% more accurate

anyway, i do salute TS for his effort, though they are largely misplaced, IMHO. Ok, then again, they may be of some use in future, but definitely cannot be compared to getting out and shooting a lot more.

i did notice the TS distilling some ballpark shutterspeed figures for blur (at a given moving speed of the subject). that is more useful imho. but a bit of practice and "agaration" would lead one to a similar conclusion

20. ## Re: Mathematical Formula for motion blurs (or "freezing motion")

Originally Posted by boyboy
the formula only applies to static shot? that means that the subject is moving but the camera does not pan, tilt or zoom?

that's not how i take pictures of moving stuff. I pan, tilt, zoom, run forwards and backwards, hold out the camera at arm's length and pan, etc...

if the formula works for me, then i really regret not having a formula for my softball days. would probably have made my throws 0.1% more accurate

anyway, i do salute TS for his effort, though they are largely misplaced, IMHO. Ok, then again, they may be of some use in future, but definitely cannot be compared to getting out and shooting a lot more.

i did notice the TS distilling some ballpark shutterspeed figures for blur (at a given moving speed of the subject). that is more useful imho. but a bit of practice and "agaration" would lead one to a similar conclusion
Haha thanks for participating anyway.

Back in my JC days, my PE teacher taught us the physics of javelin throwing... we had to recognize that our arms acted as 2nd class levers (or was it 1st? serious can't remember), and we had to understand the physics behind the whole throwing process. Even though he didn't make us plug in actual figures, it was almost there...

In any case, if you're panning a subject, the formula calculates the length of your panned background blur. Not necessary, but at least it does something. =) Becomes like another kind of DOF calculator. hah.

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