Main question: are longer pianos actually louder?
Context: When a musician plays on an acoustic instrument, I expect that the loudness produced corresponds to raw energy (as measured in Joules or Watts if taken per second) that the musician puts in. Thus, timpani are usually louder than a recorder (flute), because a mallet hit can have a lot of energy, while if you blow into a recorder too much, it sounds different.
But then, when playing loudest possible sounds, is a trumpet player putting in more energy/power (in terms of air flow) than harp player (plucking strings)?
I would guess a lot depends on the definition of loudness and psycho-acoustics, because timpani sound to me louder than a snare rimshot despite having less decibels. Dispersion of high frequencies is probably why flutes sound so loud up close, but not so strong from afar. On the other hand, the instrument in question certainly matters, e.g. soft vibraphone mallets will absorb more energy than hard wooden mallets.
Yet, even if we get two similar instruments – two acoustic grand pianos from the same manufacture but of different length – my personal impression is that the longer one is audibly louder. Maybe the bigger one has harder hammers, I don't know, but I doubt it. Usually, even among different brands, bigger pianos seem to me "on average" (in my small anecdotal sample) louder than smaller ones, despite me putting in similar amounts of energy/power. Is this only subjective, or perhaps there is a physical reason behind this?
So, are longer pianos actually louder (in terms of decibels, watts, loudness units, etc.)? Why is it so, or what makes them seem louder?