An arrow or other projectile that strikes armor plate at an angle other than perpendicular is less likely to penetrate. Alan Williams’ The Knight and the Blast Furnace gives the following values as a first approximation, and found them to agree reasonably well with tests on 1, 1.5, and 2 mm mild steel.
If the energy required to penetrate the plate equals 1, then the energy required at the following deviations from the perpendicular are:
20 degrees: 1.1
30 degrees: 1.2
40 degrees: 1.3
45 degrees: 1.4
50 degrees: 1.6
60 degrees: 2
This, however, assumes the arrow remains intact. At a sufficiently oblique angle either the point or shaft of the arrow may snap if the arrow does not ricochet. The angle at which this occurs will depend on the thickness of the arrow, the thickness and shape of the head, the strength of the bow and the thickness of the armor plate struck. If the thicker plate is penetrated at all it will not be penetrated as deeply as a thinner plate, and deceleration will be more violent.
Hardy includes a report by Peter Jones on tests with a long bodkin headed arrow against 1.5mm mild steel. At 60 degrees the point penetrated perhaps 2 mm beyond the inner surface of the plate and then broke while the rest of the arrow ricocheted. At 70 degrees the arrow ricocheted.
Mark Stretton in Soar et al found that heavy lozenge shaped bodkin was defeated by a 2mm plate at 40 degrees. Stretton didn’t specify the bow weight for that particular test, but he habitually shoots with heavy bows of 140 lbs in draw weight or more.
For a curved plate like a cuisse, roughly circular in cross section, striking halfway between the centerline and side of the plate would be similar to striking a flat plate at 45 degrees. In the simplest case, with the limbs vertical, about half the frontal area of the limbs would be stuck at effective angles of 45 degrees or more. In practice as a man at arms moved forward with a weapon at the ready his limbs would generally be at various angles to the vertical at any given moment, and so the oblique angle of impact would be increased.
Hardy, Robert Longbow: A Social and Military History New York 1992 ISBN: 0-685-62481-1
Soar, D. H. Hugh, with Joseph Gibbs, Christopher Jury, Mark Stretton Secrets of the English War Bow Yardley, PA 2006 ISBN 1-56416-025-2
Williams, Alan The Knight and the Blast Furnace: A History of the Metallurgy of Armour in the Middle Ages and Early Modern period History of Warfare, 12. Leiden: Brill, 2003 ISBN 90-04-12498-5.