The bow traveling in a straight line, perpendicular to the string is an excellent point of departure. We practice for hours looking in the mirror trying to achieve this. As we become more advanced, we may realize that what appears to be perpendicular in the mirror, sometimes is not. Because the fingerboard is an arc, and the nut is narrower that the bridge, the strings are more like lines on the outside of a cone. One way that you might compare the perpendicular angles on the different strings is to take four letter or legal size pages (preferably from the recycle bin). Fold each leaf exactly in half. Wrap them around each successive string at the same distance from the bridge so that the fold is in full contact with each string. The difference in the angles may appear small, but imagine extending each perpendicular line another foot or so past the end of the paper, about where your frog would be if you were playing at the tip.
The perpendicular bow makes the best sound on single notes of one dynamic. The players whose bows travel the straightest on these notes are those with the most flexible grips. French bow players: Hold the bow with your thumb and one finger. Play several long tones up and down bow. German bow players: Hold the bow with your thumb over the stick and no fingers on the bow. Draw several long bows up and down. The point is that if you hold the bow in only two places, it will always find a perpendicular path.
As we shift up and down the string, and when we change dynamics and colors, we need to move the bow to and from the bridge. This is not accomplished by scraping a perpendicular bow to and from the bridge. This is accomplished by changing the bow angle so that the bow naturally moves in the desired direction. (Holding the bow in at least three points is required).
Try this: On any note, start at the frog, letting the tip drop from perpendicular. Maintain this angle while pulling a down bow. If the bow speed is not excessive and the angle not too great, the sound will not break and should result in a crescendo and change of color. Try an up bow with the same angle.(Diminuendo)
Starting at the frog near the bridge with the tip high, pull the down bow in such a way that the tip is near the fingerboard at the end of the bow. (Diminuendo) Try the up bow with this same angle. (Crescendo)
Some of our bow strokes use some arcing motion. (The tip starting low on the down bow, finishing with the tip high; the tip starting high on the up bow and finishing low, usually shorter notes played near the frog). The most important aspect of these strokes is that the hair only contacts one point on the string throughout the stroke.