Please not this Kooi - Baker flat earth rubbish.
Alan Case wrote:If the string is perfectly inelastic (doesn't stretch when loaded) and had zero mass, and the bending area of the limbs acts across a small area so that it behaves almost hinge-like when drawn and shot, then the bow would be 100% efficient, regardless of how heavy the limbs are.
No it will not.
All it takes is Pythagoras and uniquity of zero to show this:
A "hickman bow" with infinite leverage must have measurable power stroke x
while the limb is static .
Thus the string at brace and string at x
will form a right angled triangle
where hypotenusa and one side are equal length while the other side is greater than zero.
I remember the Kooi paper (IIRC chapter 2.6.) having a stupid sophmore level error that it assumed continuous accelerating force function.
Now obviously the accelerating force behind arrow being vector sum of string tension will rapidly approach zero when string approaches straight position at brace height. - So if there is infinite string tension in the end , the final force behind arrow will not be infinite but infinite times zero. A discontinuity point. Wich is where Koois whole card house came down.
To Further illustrate the point why "100% efficient limb vibration" theory is garbage there is the trivial case of single hinged ideal bow braced to zero height:
Now obviously limb and string half will form a symmetrical triangle where the bow tip exactly in the middle between arrow and the hinge throughout the acceleration. The speed difference of arrow and limb tip is approaching maximum ratio of 2:1. So limb tip mass must have measurable kinetic energy at any point during acceleration.
Sorry if this comes a bit grumpy, but during last decade this Kooi nonsense has done horrible damage to the global bowyer community. Saddest thing was to see Tim Baker soil his good name.1) the proof above is freshman level university mathematics. If reader fails to comprehend it he/she is not qualified to take part in this conversation