No video exists of this, but a hungarian group called Mathias Rex did a quite extensive test. They used a reflex-bow, not a longbow actually (which is better for purpose I really bon't know. I belive that makes not much difference. Reflex-bows are said to be generally better, but they are not easily manufactured and shot). That had 45 pounds, meaning it would be around half as strong than a military example in the medievals. They shot this armour:
http://www.sword.sg18.net/gallery/G01/images/AUT_0408.jpg (you can actually see some points in this picture where the arrows hit). There was absolutelly no penetration, not even from 15 meters.
- They used no armour piercing head.
- The armour is probably a bit thicker than the average medieval.
- This armour is not very accurate.
I believe there is a point in this ongoing converesation that is not well stressed: mail was called armour as well! I need not to say that mail has absolutelly no chance to resist an arrow! Most stories of archers shooting down knights come actually from a time, where mail was more common than plate. Think of Visby, Crecy for example: in best case they had transitional armour. Even the Black Army of Hungary had only breastplates above the mail with a kettlehat and sometimes a bevor, and that was in the 15th C.
The big talk about huns and osmans shooting down entire regiments of knights also come from the 10th to the 12th C.!
As a final note, I belive History makes his own proofs. Like, personal steel armour was around for almost a 1000 years.
And what about today? All bulletproof modern armour can be beaten by armour-piercings. Still the cops and corps are using them. Not everyone is equipped with enough resources for such rounds or can use them correctly.
Szab