The limiting factor for having an infinite number of "to and fro" goes is probably the diagonal length of the car, assuming the three cars involved are the same width. So, using pythagoras.
gap = square root of (length squared plus width squared).
In practical terms you aught to add a very small ammount to the figure produced, so you don't jam with no room for manouvre.


Surely theoretically you can get into any space as long as there is even a fraction of an inch clearance? What really matters is how many backwards and forwards goes you are prepared to use to make the exercise worthwhile.
I once extricated my Volvo 240 from a space that had only about 4" of clearance. I was boxed in with no chance of contacting the culprit, so it was worth about 50 movements for the sake of being able to get home that evening.
Also I wasn't too careful about avoiding bashing his car with the tow bar.

If the track is equal to the width of the parking car, and the width of the parked cars is also equal to the track
E = wheelbase
t = track
alpha = maximum steering angle
b=sqrt( (E/sin(alpha))^2  ((E/tan(alpha))t)^2)
If I put more thought into it, the expression for b could probably be simplified a bit  but it is the weekend!!
The distance between the two parked cars has to be
Front overhang + b + rear overhang + some skill dependent clearance!!
This is actually a slight overestimate because the front overhang is at an angle as it swings past the corner of the parked car  but it is probably a small error.
Number_Cruncher

mmm can't get head round that tonight.
Supposing you're parking a handcart with only two wheels located centrally  doesn't that make E = zero ?
Also can you write equations using MS Office or do you need a separate package?

Supposing you're parking a handcart with only two wheels located centrally  doesn't that make E = zero ?
The equation isn't any use for handcarts! It assumes that your steering is done conventionally, rather than by pivoting the entire axle.
It's much easier to understand the equation with a drawing of the geometry, which, alas, I can't include in a post!
You can play about with this type of equation in Excel easily enough, although for choice, I would either use MATLAB, or code it up in Fortran. It depends what you want to do with the equation really  Excel is good for seeing what each term is doing, but is poor if you want to use complex numbers, or useful things like Fourier Transforms. MATLAB is very powerful, has great plotting and graphics, but is not cheap (although the Student version is good value), and Fortran can be had cheaply, and can produce very fast programs, but it takes more programming skill to use.
If you prefer to work with symbols rather than numbers, the MAPLE or Mathematica may be more suitable. Sometimes I do cheat, and I paste Mathematica output into my MATLAB code!
Number_Cruncher

N
FORTRAN! Ooh I've come over all nostalgic. If it begins with I,J,K,L,M or N it must be an integer!
JH

>>I've come over all nostalgic
I don't use Fortran anywhere near as much as I used to. The newest releases of MATLAB now can run very fast code  and of course you can just cut snippets of code and run them at the command prompt instead of compiling and linking, which makes debugging much simpler. You need to be doing something a bit special now to make the extra effort of Fortran coding worthwhile.
Number_Cruncher


>>Fortran can be had cheaply
Indeed. This compiler is free
www.silverfrost.com/32/ftn95/ftn95_personal_editio...p




Think you need to include a term for the camber of the road and differential vehicle heights. Outside my house is a sleeping policeman and using rhe slope of this to lift the front end by 6 inches means that my bumper will pass over the next cars bumper thus reducing the required space. Need to brake sharply as the car runs down the slope of the sleeping policeman though or face embarassing chats with the neighbours.




