In archery we often use the term hysteris when checking for losses of energy due to internal friction in wood. One of the tests we use is to simply hold a length of thinly cut wood stationary and then bend it down a specified amount and release it. We measure the distance past center that it flicks back up past it’s resting position and anything short of the amount we pulled it down is attributed to hysterisis. I see this test as having some meaningful benefits but find it hard to believe that if the wood only returns 90% of what it was pulled down then 10% hysteris becomes the amount of wasted energy identified when tracking energy losses in a finished bow and arrow set up. Would anyone else have a test more accurate of meaningful when tracking energy losses.
It seems to me that energy loss and hysteresis are two separate things. Hysteresis normally means that the behaviour of the system depends on previous inputs. Some energy losses may be stored in the system due to hysteresis but I think most would just be lost as heat.
The standard test you describe seems like a pretty good way to measure the energy loss though.
In terms of the final bow system - the approach I can see working is to measure the pull (using a Newton meter) force for a specified draw, then using that draw to fire arrows of a known weight and measure the distance the arrow travels.
Since you know the stored force (based on the pull) and the applied force (based on the weight of the arrow, the distance travelled and the firing angle), you can calculate the energy losses. Then compare the result with your hysteresis results to determine the validity of that approach.
You will need several data points for a statistical analysis, and for more accurate results, carry out the experiment in a vacuum with spherical cows 
Some of the loss will be in arrows also. They deform under the force of the release causing the same type of hysterisis plus increasing drag in flight perhaps. This method could be used in relative comparisons between woods, and against other materials with more well established properties such as carbon fiber or steel.
Fair comment. I was thinking (for measurement purposes in the experiment) of aluminum shaft arrows - regular weight and more rigid than wooden/fiberglass arrows, to reduce that sort of energy loss.
We have pretty well established most of the losses, in this particular question I am only concerned with losses within the wood itself and how to possibly indentify superior specimens of wood before actually building the bow. My hobby is flight shooting where performance is everything. I have been able to identify a significant loss of energy in the wood caused by damage due to the normal bending involved in building and shooting a bow.
An example would be that a bow never drawn past 24" may show and efficiency of 84% but once the bow had been finished and shot in at 28" draw efficiency had dropped to 72% when retested at the same 24" draw and force draw curve retaken and calcualted in.
The energy loss percentage won’t be the same as the loss in distance it bounces. Assuming that the wood follows a nice simple Hook elasticity relation, the energy ratio would be the square of the distance ratio (thus, for instance, if the wood springs to 90% of the distance, you’d have 81% of the energy). In reality, the relation is probably more complicated than simple Hook elasticity, but I would expect that in any event the energy loss would be larger than the distance loss.
That is more closely related to what I was looking for.