‘Loudness’ can be a subjective term, particularly when you consider that, for any given instrument, ‘loudness’ will vary across the frequency spectrum that they produce (ie, will not produce a flat frequency response for the same energy level inputed across the spectrum). If you’re looking to compete with a grand piano, are you chasing more bass frequencies, or better upper & mid-bass projection so that the harmonies are more obvious? (I personally think that our perception of bass-loudness is driven more from the latter than the former, as our ears are tuned mostly to vocal frequencies than top or bottom end).
In general, though, think in terms of energy; the more efficiently your instrument can convert mechanical energy into sound (at whatever frequency), the louder it will be. By ‘efficiency’, we’re talking about how little energy is lost or damped, so the more energy you can put in with fewer energy-sinks (or vibration-damping factors/mechanisms) present, the better. As has been mentioned previously, there are many factors that contribute to this, but start by categorizing them into groups that are either not easily changed (ie, fundamental instrument construction eg, top thickness, physical body volume, bass bar thickness etc) and those that are (strings gauge/weight/tension, tailpiece weight, string-height); obviously, start with the easier, latter group.
There are some generalizations that seem to work fairly universally (such as string height; more room to vibrate = bigger vibrations = more energy. Maybe this is because that’s an energy input factor, not a sink), but others will vary according to your instrument. For example, heavier strings will impart more energy into the top than lighter ones, but if the extra tension chokes or damps the top too much (at certain critical/a significant range of/all frequencies), then the opposite effect is achieved; the top vibrates less and the bass is quieter overall.
I’ll re-float my theory here that the older the wood, the better suited to heavy strings a bass is; I reckon that due to a loss of natural ‘springiness’ within the wood (and a resulting drop in resonant frequency for a given top-thickness as the fibres change with time & moisture loss), more energy is required to get the wood to ‘speak’. Newer wood has more springiness (and a higher resonant frequency) and too heavy a string will actually damp that, so lighter strings are better (at least, in allowing the mid/upper range to speak more & therefore allow the bass the sound louder). (Caveat: That’s just my own $0.02 theory based on general observations from what’s worked on my bass and for those of other players around me; no flames, please!)
