Just for anyone that is interested in this topic in the future. Here is a summary of what I have learned, based on the reference provided below.
One thing I found interesting is that a bows potential energy, as represented by a draw weight line chart(greater volume to the right of the line = greater potential engery), doesnt always result in greater arrow velocity. Which, if I understand correctly, all else being equal is the only thing that really matters when measuring how well a bow transfers its energy into the projectile. Greater arrow velocity means the bow is putting more energy into the arrow. But, the study also looks at potential energy and efficiency. So there are many instances where a bow design has the most potential energy, but it isnt as efficient, so it doesnt translate into a faster arrow. Why? I'm not sure... Maybe there was a flaw in the study, maybe there is a way to build the bow where it can be more efficient. Maybe it doesnt really matter all that much in the grand schem of things, it flings an arrow, right?
Bridge/ string contact vs no contact:Bridge/ String contact: Stores more energy than non contact, however it was noted that this didnt translate to a greater arrow velocity, because it is less efficient.
No contact: Stores less energy, however gave a greater arrow velocity, because it is more efficient.
Siyah/ear angle (relative to contact with the limb): Three angles were tested, 0*, 30* and 60*. Where 0* and 30* did not produce string contact while strung and 60* did produce string contact while strung.
0*: Least potential energy, greatest efficiency, slowest arrow velocity(nearly identical to 60*).
30*: Middle of the road potential energy, middle of the road efficiency, fastest arrow velocity.
60*: Greatest potential energy, least efficient, slowest arrow velocity(nearly identical to 0*).
*Note: Something the study doesnt really talk about is stacking at the end of the draw. Shooting a 0* siyah on a short bow would have a lot of stacking toward the end of the draw.
Siyah/ear length: Two different lengths were looked at, 1/2 the overall limb length, and 1/3 the overall limb length. No change was made to the length of the working section of the limb. The original design length of the siyah, I believe, was 1/2 and the siyah was shortened to get the 1/3 length.
1/2: Greater energy potential, less efficient, slower arrow.
1/3: Less energy potential, greater efficiency, faster arrow
*Note: The numbers for this test are relatively close to each other, there wasnt a whole lot of difference. The reason for a longer siyah being less efficient is because it is heavier than the shorter one. Also, it should be noted that with a shorter siyah, even though you gain efficiency, you do loose mechanical advantage and potential energy. The overall length of the limbs in relation to angle of the siyahs come into play when approaching and when at full draw. So there is some give and take in the overall design of the bow and mechanical limitations of the materials being used.
Reference: Functioning of ears and set-back at grip of Asiatic bows, by Bob Kooi
http://www.bio.vu.nl/thb/users/kooi/kooi96.pdfAlso if anyone is interested, there is a great deal of other mathematical and engineering studies located here.
http://www.bio.vu.nl/thb/users/kooi/#soaa%20.