Let the variables be $x_1 , x_2 , x_3 ... x_n$. The distance between two variables is defined as $d(x_a , x_b) = |a-b|$. The distance between two literals is the distance between the corresponding two variables.
Suppose I have a 3-SAT instance such that for every clause $(x_a , x_b, x_c)$ we have $d(x_a , x_b) \leq N \wedge d(x_a , x_c) \leq N \wedge d(x_b , x_c) \leq N$ for some fixed value $N$.
Conceptually you can picture this as all the literals being physically on a line and all the clauses are incapable of reaching beyond a certain length for physical reasons.
Given this constraint are there any hard instances of 3-SAT? How small can I make the neighborhood and still find hard instances? What if I allow a few clauses to violate the constraint?
By hard I mean a heuristic solver would fall back on the worst case.