What you are asking is engineering. Even if you can calculate the correct thickness for all "reasonable" impacts and forces thrown at a bicycle, you still need to take into account that the bicycle will be used, so the material will undergo hysteresis.
A frame can stand a single impact providing a force of X, but it may fail after one hundred impacts of smaller force X/1000 (yes, you are reading correct, standing a single impact of force X, but failing after a cumulative impact force of 1/10 of X).
If you then bring into the picture a material that evolves with time, like wood, you should expect ... a lot of trial and error.
An example: you draw your ideal wood bike, knowing the tensile strength and other parameters of wood you calculate that the top tube should be long 30cm, have a diameter 1.8 cm and a thickness of 2 mm. However, with the use you realize that such a tube will produce some resonance and some vibration, so for some unlucky reasons hysteresis will cause the connection of the seat stays (calculated to be long 22 cm, diameter 1.2 cm, thickness 1.9 mm) to fail on average after 500 km.
You try to reinforce the connection, but the solution maybe is just to have a top tube with a larger diameter, or shorter, to dampen the vibrations/resonance.
How to proceed? you have two choices:
- you take some frame building courses, where you get the experience of learning by doing, so you have a "feeling" for what is the right thickness/shape/angles etcetc.
It is not that the calculation of forces is complex or there are industrial secret preventing us from its understanding (well, there are industrial secrets on why a certain thing is built a certain way, but physics is not an industrial secret :D ).
The fact is that we have a very rough understanding of reality and forces at the microscopic scale, but we can obtain insight on the resulting macroscopic behavior of materials only via:
Kestrel co-owner Preston Sandusky credits the low weight to the bike's
"modular monocoque" frame, fabricated from three individually
bladder-molded parts: the triangular front frame, and two two-pronged,
U-shaped forks, which form the seat stay section (running from the top
of the seat tube to the rear wheel dropouts) and chain stay section
(from the bottom of the seat tube to the rear dropouts). Developed by
former aerospace engineers at Kestrel's headquarters in Santa Cruz,
Calif., U.S.A., using Pro-ENGINEER and RHINO 3-D Solid Modeling
software (PTC, Needham, Mass., U.S.A.), the frame structures are
- via empirical reasoning (Columbus steel tubes works great to build a bicycle with drops, why? because it does! )
I would NOT be surprised if, after doing some calculation based on very simple principle, you would find out that a steel frame with thickness 0.1mm and a weight of 500 grams would be able to stand all the forces related to a standard cycling scenarios.