Question: I would like to avoid having to dig my hole any deeper than necessary. Instead of digging my base hole about 3.5 ft. wide by 7.6 ft. deep (example), can I just dig a 5' x 5' hole, since it's about the same volume of concrete?
Answer: No, sorry, not really. Yes, it may be about the same volume of concrete, but volume or weight in the base is not the key factor. The key factor in the stability of the base is the amount of bearing resistance the base structure has in the ground in which it is planted. Giving depth to a base is like adding a extension lever to a fulcrum: it gives it mechanical advantage/potential momentum in resisting the forces trying to move or tip the base and tower over.
As one insightful engineer put it, 'If you had a superstrong, lightweight substance, like styrofoam, that would not corrode or break, you could use this as a substitute for concrete and the tower base would be almost the same size as a concrete one.' The deadweight of concrete only contributes about 5 -10% of the resisting moment in many typical tower bases; the rest is from the resisting force in the bearing surface of the hole.' This also explains why soil types are important in determining the size of the concrete pad.
Most people own property with sandy or clayey soils. Clayey soils are a little softer than sandy soils, e.g. a soil classified as some variation of 'clayey' would be considered to have a soil pressure of 100 lbs/cubic or sq. ft., while sandy soil combinations would usually have about 150 lbs. /cu.ft. rating. Our bases are typically designed for 'sandy' soild types or sub-types--to be installed in clayey soil types would require us to usually increase the depth requirment by about 10-15%.
If you or your building department are concerned about the exact soil type you have, you should get a professional soil bore sample. (Sorry, we can not offer references in your area). If you are fortunate enough to live on bedrock or shale or very hard soil (every cloud has a silver lining!), then a tower base at your site may only need to be 3 or 4 ft. deep and narrow enough to fit your base legs and rebar inside of.