pabloman said:
You are having to overcome the downward pressure caused by the breakover angle AND the tension between the TOM and tailpiece. None of the formulas or mathematics that anyone has given account for these variables.
Ah - now I see where you guys are getting this from. That's an interesting argument, but sadly it's not correct.
Here's why: when a string is tuned to pitch, it's tension is governed by the pitch, per unit length mass of the string material, and the distance between the vibration endpoints. When the string is bent to a new pitch, effectively the tension on that string is increased to make it go to the higher pitch. Again the tension is governed by the pitch (higher), per unit length mass of the string material (unchanged), and the distance between the vibration endpoints (the same). As long as you don't change the scale length or the string gauge, the additional tension you need to apply with your finger to reach that bent pitch is same. It does not matter what the various break angles are, or how much string is on the other side of the vibration endpoints. It is tempting to think that if you have a pile of string on the other side of the bridge, it will be easier to bend the note because the additional string length will allow for the string to stretch easier. Well, maybe that string does move but the point is it does not matter - the increased tension to get to the new pitch is always only dependent on the scale length, the per unit mass of the string, and the pitch you're going for. Also, it does not matter how the tension is increased to get to that pitch - you could bend the note, use your wammy bar, or turn the tuning peg. The increased tension to get to the new pitch will always be the same.
As for where the additional string comes from, well, the string stretches or it moves over the bridge/nut. Still does not change the scale length or the per unit length mass of the string. In fact, in applications where there is zero friction at the bridge or nut, the tension would be the same on the other side of the bridge and nut.
As I mentioned earlier, this is backed up with my own experiences with my own guitars. Oh - and I also did this in undergrad physics lab with digital tension meters. Sadly threw out the lab notes 10 years ago, so you'll have to take my word on that.