What is the relationship between scale model size and playback rate that looks normal scale in video? 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!
 A: 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.
