Huh, I hope I can clarify the points so it is easy to follow (describing technical/physical things in a foreign language is not the easiest thing).
1- Draw weight calculated from one prod half:
You apply a force on one half of a flatspring and measure it with a scale.
But the angles between the limbs and so the directions the forces work play an important role.
Easiest way to determine the difference between adding (*2) the forces is by drawing a parallelogram of forces with the limb forces action in different directions and a resulting new force.
The resulting force alternates by draw length. The longer the draw the more changes the angle/draw weight.
2-J going to skip this since you stated it is not really needed
Sigma determines the stress that is in the material, the more stress, the higher is the stored energy.
So the better values in tensile strength are the higher stress can be put into a material the higher can be the stored energy.
In order to move the limb at an efficient speed (which you really want) you will have to put enough energy into the material.
Steel is, since it is quite heavy, not very grateful when it comes into moving.
The closer you get to the elastic limit the more force will be stored, the better will be the equation of mass to force -> resulting in a higher speed.
If you put little stress into a limb it will consume a lot of its energy by moving its own weight.
When you build steel prods considering very large savety values (which is not the worst, don´t get me wrong) you will lower the limb/projectile speed/energy.
I use the value to add it to calculated draw length when thinking of it as forged deflex without or little pressure.
Hope this helps.
Ok, you put up a really good argument with your first point.
What you say is absolutely right.
I probably advertised wrongly the scope of my sheet. The point of sheet is not to calculate the exact functionality of a prod, is more of a reference. The point was i cut a prod and the result was : damn probably i can draw it only with a goat lever! I don't want it that strong!
So i took up my book, did some research on the internet and ended up writing this simple sheet in order to reiterate the calculations, meaning: For my crossbow i already decided (most wrongly) the draw lenght, and i needed to reiterate the calculations to get a decent balance between draw weight, lenght, sigma etc, and i didnt want to take 10 times the time to do them by calculator (because you need to redo every single equation every time)
My scope was to give me a technical reference because i lacked empirical experience (if it does makes sense what i just wrote)
Then i thought, maybe somebody else that starts at square one may need something like this to get started.
Back to your first point: I took for implicit (damn thats why i need some feedback
) the fact that the sheet considers a simple straight beam, with a perpendicular force applied.
It is not completely right, but is enough to get started, and thats what i needed and thought people would need.
About sigma, you're right again but the scope of that (and all the sheet) is not towards efficiency/functionality of a particular crossbow, is will it break and get the prod on my nose or can i have some assurence that it will not?
Again i took my technical knowledge in general mechanics and tried to port it here, in order to get something that would work and in the meantime have a safety assurence.
About the forth point i may have an idea but i have to verify it.
Hope i cleared some doubts.