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My son just discovered the 240 FPS slo-mo setting on my iphone6. He used it along with his latest obsession - scale model pullback cars - to make some pretty cool video for a project. Apparently, most days at recess they go drive their cars across a crack in the sidewalk behind the school and watch them wreck.

He and I were both amazed at how cool this looks played back at 30 FPS. It definitely has the look of normal sized car crashing in slow motion. At 60 FPS it approximately looks about as if it were an actual non-scaled car.

My question is - What's the relationship between the scale of the model car (1:40) and the slowing down of video (4x slower) that makes this look like full scale? Is there a specific ratio that does it? Does it assume the weight of the model was scaled the same as the size?

Another similar effect would be keeping the mass the same, but changing the acceleration of gravity to produce action which looks sped up or slowed down from what we are used to.

Here is his crash video:

This was shot 240 FPS and played back at 1/8 speed, which makes it look slow motion even for a full size car. Not the precise match of my question, but fun to watch!

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  • $\begingroup$ You know, those videos ARE pretty awesome... $\endgroup$
    – Daniel Griscom
    Commented Sep 13, 2015 at 21:19
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    $\begingroup$ I'm voting to close this question as off-topic because it is about the human perception of full scale in a video, not physics. $\endgroup$
    – ACuriousMind ♦
    Commented Sep 14, 2015 at 11:39
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    $\begingroup$ @rmhleo - there is definitely a materials issue here, that would have to be considered for a real car crash. :) $\endgroup$
    – nfdavenport
    Commented Sep 14, 2015 at 22:20
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    $\begingroup$ @ACuriousMind - I don't think this is simply a perception issue. I'm pretty sure it's just a matter of algebra and framing the question correctly, which I didn't do a great job of. $\endgroup$
    – nfdavenport
    Commented Sep 14, 2015 at 22:24
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    $\begingroup$ I don't agree with @ACuriousMind. I think the human perception of how the small car should behave is strongly based on the observed phenomena, and an expectation on how the bodies should behave. This is to me the same reason why in some superhero movies some cgi scenes "look more real" than in others, when attention has been put to physical laws. $\endgroup$
    – rmhleo
    Commented Sep 14, 2015 at 22:30

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I'm going to take a crack at this using a simplified case of a dropping a ball. It's been a while so bear with me and my notation.

Having the time appear the same after scaling is what I think makes you not be able to tell the difference between the full drop and the scaled drop if you remove other contextual clues. You drop the ball from 2 different heights related by a scaling factor Sy. You want the times to be the same given a different scaling factor St.

Let's say I drop a ball from given height: Y1 = 1/2 * a * T12

And a second ball from a lower distance: Y2 = 1/2 * a * T22

Y1 is a scaled amount of Y2: Y1 = Sy * Y1

T1 is a scaled amount of T2: T1 = St * T1

I won't go through the algebra, but I believe this comes out such that

St = square root( 1 / Sy)

So if my model car was 1:40 scale, I would have to make the video ~6.325 times longer to make things appear full scale.

edit:

I ignored the Y0 because it cancels anyway. The ball would also need to be scaled to by St or else it would appear further away given the point of view context of a video.

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