Is there a common method for measuring "curviness" of a line?

Question

I have a bunch of GPS tracks in a Postgres+PostGIS database and want to extract a single metric as a measure of turns shown in the data. Some of the GPS targets travel in almost straight lines while others do some curves. The curves are sometimes all right/left hand turns but most of the time it's just squiggles. I've tried to use the length of the line vs the distance between start/end, or area covered by the convex hull but these aren't perfect.

Can you think of a function that would be able to determine the "curviness" of a linestring and could, possibly, differentiate between straight lines, regular turns, or random paths?

This paper makes mention of taking the sums of the delta in bearing for each vertex but I was wondering whether PostGIS has something built in that would make it easier.

There's no guarantee that any GPS track would be complete, cover a set time period, have the same length etcetc

Here are some examples of the GPS tracks:

Answer 1

One measure is Sinuosity which is the line length divided by the shortest distance from the line start and end points:

select id, 
       st_length(geom)/st_distance(st_startpoint(geom), st_endpoint(geom)) as sinuosity, 
       geom
from test.testlines

The values will range from 1 to infinity, 1 for straight lines:

Answer 2

I'm not sure if this will be of great use to you, it might be too specific, but I have a function that tests for what I call cutbacks in lines. This is where a line bends more than a certain amount of degrees.

First create a new type:

create type cutback_flag as (hascutbacks bool, cutbackgeom geometry);

Then create the cutback function - you will need to adjust the degree ranges to use the threshold you want. Currently it flags bends greater than 90 degrees (more than a right angle bend, an acute angle rather than obtuse). The function returns true if there is a cutback in the source geometry and also returns a point at the cutback:

create or replace function flag_cutbacks(g geometry)
returns cutback_flag language plpgsql as $$
declare
    numpoints int;
    cutbackgeom geometry;
    hascutbacks bool;
    r cutback_flag;
begin
    select st_numpoints(g) into numpoints;
    for i in 1..numpoints loop
        if  degrees(st_angle(st_pointn(g,i+1),st_pointn(g,i),st_pointn(g,i-1),st_pointn(g,i))) between 0 and 90
            or degrees(st_angle(st_pointn(g,i+1),st_pointn(g,i),st_pointn(g,i-1),st_pointn(g,i))) between 270 and 360 then
            hascutbacks := true;
            cutbackgeom := st_collect(cutbackgeom, st_pointn(g,i));
        end if;
    end loop;
    select hascutbacks, st_union(cutbackgeom) into r;
    return r;
end; $$;

Use the function:

select (flag_cutbacks(geom)).*, id, geom from super_awesome_geometry_table;