A sword guy running at archers should never get near them if cover was not used.
They also invented this thing called armour.
Not sure how good your history is but, arrows could penetrate most kind of armors, not plate of course but that is why we came up with the crossbow.
Crossbows were invented because anyone could use them. You don't have to hold tension in the bow to shoot it, aiming is easier, you could even put iron sights on them. They were remarkably weaker, though, except in China, where the cho-ko-nu, or foot archer, was invented. That is a notable exception though, and arrows remained the superior to the inferior bolt in almost all of Europe throughout history. As far as the penetrating power of arrows, only English longbowmen, with their heavy self longbows, could hope to penetrate plate armor, and even then, only at a moderately close range (around 100 yards). Mail was all that was needed to stop most bowmen's arrows, like Geparden said. Padding was just there to stop the superficial scratches that arrows would leave when hitting mail. This was due to the difficulty in drawing and firing a bow. The best archers throughout history often had malformed skeletons, bone spurs, and other deformities, from the strenuous use of bows. Even their skeletons still show this to this day. So no, bows did not have much penetrating power, and crossbows were not more powerful than bows. Take it from a renaissance European history major.
