I'm writing a little game with a top-down view of some sliding objects, like curling or shuffleboard. (I happen to be using PyMunk for the physics, but since this question is about physics simulations in general, don't worry about language specifics.) Before I start tweaking all the values in my little sim to get behaviour that 'feels' right, I thought I'd better check to make sure that I'm at least modelling the right kind of velocity curve in the first place. However, finding a clear answer about this has turned out to be substantially harder than expected.
Model A
To simulate the way an object slides to a halt, pymunk allows the programmer to set space.damping, which works like this (quoting from the API reference): "A value of 0.9 means that each body will lose 10% of its velocity per second."
That makes sense, but it seems that that would produce a velocity-over-time curve with this basic shape (never mind the exact numbers):
|*
v |
e |
l | *
o |
c | *
i | *
t | *****
y | ****************
---------------------------*----
time
In other words, acceleration decreases over time. (Some might prefer to say "deceleration" or "negetive acceleration" decreases, but in the purest physics sense any change in velocity is 'acceleration', and in the chart above the change in velocity becomes smaller over time.) Because such a curve will approach but never cross 0, a cutoff is employed under which a body's velocity is forced to 0. Pymunk provides a setting for the cutoff, too: space.idle_speed_threshold.
This seems straightforward enough but gave rather unsatisfying results when I tried it in my little simulation. So, I began to consider Model B, below.
Model B
Thinking about it intuitively, it seems like the acceleration would increase over time, making a curve like this:
|********
v | ******
e | ****
l | ***
o | ***
c | **
i | **
t | *
y | *
--------------------------------
time
If I imagine pushing a book across a level table it seems like it maintains most of its speed at first but then comes to a halt very quickly (possibly because the friction causes the rate of slowdown to increase? Although the 'why' of it isn't so important here). This is a little harder to implement in pymunk, if only because there isn't a built-in method for it, but it can be done. It's not that I don't trust the chipmunk/pymunk developers, but I'm not sure if they meant for damping to simulate what I'm trying to simulate.
So, my question is not how to implement either of those curves in code, but rather - which type of curve accurately models an object sliding to a halt on a level surface?
You might think "Why is this person asking a physics question on a programming website?", but after looking at physics websites for the past four hours and getting nowhere, my hope is that, since physics modelling is common enough in programming these days, someone in the SO community might have prior knowledge about this that they can readily share.
I'm aware of this discussion on SO: how to calculate a negative acceleration? in which both types of curves are suggested, but while the asker got his question answered (someone helped him implement a Model-B type curve), the community did not come to a consensus about which is more 'physically accurate'. (I also borrowed that asker's ASCII art for one of the charts - thanks.)
I'm also aware of this example of a carrom board simulation from the pymunk showcase: https://github.com/samiranrl/Carrom_rl This also uses the built-in damping (model A, above). It seems to work fine for their purposes. But it might be that we human observers wouldn't notice if model A wasn't right since the carrom pieces are not in motion for very long. Model A looked wrong when I tried it in my sim, but then, but I am trying for much longer, slower shots, so maybe it's more noticeable there.
Or, maybe what 'seems' right to me (Model B) isn't right after all. Any thoughts are appreciated. Thanks!