Before we get on to what, in my view, is the most important exercise of all for vocal development - the messa di voce, I think we need to understand what exactly is meant by forte and piano, as the interpretation of their meaning will effect how we vocalise them.
 

Forte doesn't mean loud, it means strong. And although piano means quiet, it also means soft and gentle. Therefore, in contrast to strong, it is the last two epithets that apply. So forte and piano are colours, not dynamics.

If you sing a medium note in the upper middle register at around mezzo piano and you think louder, the tendency will be to force the air through and distort the vocal tract in an attempt to get as explosive a sound as possible. This may sound loud in the head, but because the soundwaves are disturbed out of their natural flow and the apparatus is under stress, it will undermine the impact of that sound in the auditorium. If, however, you sing the same note and think stronger, then the air pressure will increase, the soundwaves will flow more energetically and the pliable walls of the resonators will gently expand to produce more resonance. Yes, the effect will be of more sound, but the approach of stronger is much healthier and safer than louder. This process also encourages the development of overtones which create more sound for no extra cost. Such an approach has its parallels in the playing of instruments. A violinist wouldn't whack his bow onto the strings. This would create a harsh sound that would have little reverberation in it. Instead, with a firm, but gentle pressure, he would tease out the resonance. To make a bell 'sound' and continue to sound, you wouldn't hammer it with all your strength, but would strike it cleanly and firmly. And a timpanist would do the same thing with a drum. It's all about the setting up of vibrations to create resonance. Not about force or violence.

Equally, if you sing a medium note and think the opposite of loud - i.e. quiet, the danger is that that sound can just shrink, be unsupported, fall off the resonance and become somewhat swallowed, making it simply inaudible. However, if you think soft and gentle and keep the volume (and volume means space, not loudness!), the quantity of sound waves is kept, but they take on a soft, velvety quality enabling the voice to project to all corners of even the largest auditorium. And those of us who have heard Fischer-Dieskau and Vickers sing in an absolute whisper in large halls can testify to this.