Your time would be better spent calculating energy storage, and how to successfully transfer said energy to the shaft..... Food for thought... Kirk
Calculating energy storage is relatively easy, calculating how it is transferred during a shot is very hard.
Why do you chose to trap the belly side on longbows? From a structural standpoint it makes more sense to trap the back as it has a bigger margin to failure. Until a belly failure occurs I don't think it will make any difference to how the bow shoots, though.
Since the limb width did not change I would assume the stresses on each side of the limb did not change... If this is so would it not be more correct in saying the back is weaker by 6.6 percent compared to it's limb thickness and of the previous rectangular section?? Or percentage wise the back has to handle the same amount of stress but at a decreased strength of 6.6 percent??
The stresses do change because the neutral axis shifted towards the belly. This increases the maximum stress on the back and decreases the maximum stress on the belly. I wouldn't say the back is 'weaker', in engineering terms strength generally refers to the strength of the material involved. You could say it is less stiff because there is less material on the back to carry the loads. The way bowyers use the terms strong and weak make sense for bows, but they are not the same as how engineers use the terms in relation to materials.
Another question... Since the back is more stronger in tension vs the belly in compression wouldn't the numbers be different?? Wouldn't there be some kind of curve?? Lets say the back is 6% weaker and the belly is 2% stronger compared to thickness of limb.. Or could be the back is 2% weaker and the belly 6% stronger... I am not sure about numbers but you get the idea... At least, I hope...
You are confusing strength and stiffness. Stiffness (the modulus of elasticity) is what matters here. The FG lam is the same stiffness in both directions (that it, it deflects the same amount in tension or compression for any given load until a failure occurs), but will fail sooner in compression due to buckling, which is a stability failure and happens at stress levels below the actual maximum strength level of the material.
Another question... Unidirectional glass, since tension trumps compression in this case wouldn't the neutral zone be located slightly towards the back in a rectangular section and moved more towards the center when the limb is trapped and material removed from the back??
Because the FG is the same stiffness in both directions (and it dominates the load carrying compared to the core material) the neutral axis is located on the mid-thickness plane of the limb. You are correct that it shifts away from the side that is trapped and that it would be closer to the back than the belly if the back material was stiffer in a rectangular cross section.
Just as a note, the equal stiffness in both directions thing may not apply to all woods. I have seen this discussed before and there doesn't seem to be any good data on the hardwoods we typically use for bows. I would really like to know more about this as it does change my design work if there is a significant difference between MOE in tension and compression.
But I personally think toying with that neutral zone and moving it around could possibly aid in better energy transfer...
The only ways you can move the neutral axis around are by changing the limb cross section (which is what trapping is doing) or by using different lam materials or different thicknesses of FG lams on back and belly.
Mark
Topic: Trapping? (Read 2568 times)
