Given an existing 2 column 52x28 ft canopy with existing column height of 12ft: is it possible to increase the height column height by 4ft on existing footing? By what percent the turning moment would increase as a rule of thumb?
Assuming the canopy is supported by fixed base plates, the increase in overturning moment is just (h+4)/h no? Original moment was likely calculated as M=P*l (plus any additional moments due to gravity loads but this shouldn't change overturning unless you are deflecting so much that P-delta affects are large), and now you are calculating M=P*(l+4). Of course your P may increase as the wind constants increase due to height (Ce in Canada) but thats probably pretty negligeable.
A quick and dirty estimate would be related to the percent increase in height. So, the overturning would increase by something like 33%.
(12+4) / 12 = 1.33.
That's a reasonably significant increase. There's no way to know if the existing footing can handle it without doing a more complete investigation / calculation.
Also, if this is a seismic area and this thing is old you may have other modern code issues relating to cantilever style lateral resisting systems that cause you problems.