Awkwardness of planar graphs

Some planar graphs are more awkward to draw on a plane using only straight edges than other planar graphs.

We might speak of the awkwardness of a particular two-dimensional embedding of a graph, or the awkwardness of the graph itself, implicitly minimized among all possible embeddings.

What is a good measure of awkwardness? Most acute angle? Ratio of longest to shortest edge? But I don't feel a wheel graph is that awkward.

Generalize to sphere.