I took a look at the tool box you have so far and I have a couple comments.
- In the tube comparison you have J=2I which is correct for polar moment of inertia but it is incorrect for calculating torsional stress or deflection in a thin walled section. J for a thin walled closed section is given by: J=4A^2t/S where A is the cross sectional area at the mid line of the wall, t is the wall thickness, and S is the perimeter measured at the mid line of the wall. For the example of an internal dimension of 13mm and outside dimension of 16mm as in the example:
This gives a stiffness improvement of 2744/2155.3=1.273 or 27.3%, not 38.2%
It should also be noted that this applies to stiffness only. For strength calculation the sharp corners on a square section will change the failure mode and in composite may well be lower than the circular section.
- In the battery calculator it shows a linear relationship. The useful capacity of a Lipo battery drops as the current increases. You can increase the useful energy in a battery by discharging it slower. This is traditionally calculated with the Peukert formula. Here is a paper on the Peukert formula applied to Lipo batteries:
The Peukert formula is C=T*I^k where C=capacity, T=discharge time, I= discharge current and k is the Peukert coefficient. From this paper it can vary from 1 to 1.3 for a Lipo. At 1.3 it is a huge effect.
Unfortunately suppliers don’t provide k (unless they are very good batteries). If you know the capacity of a battery pack at 2 different discharge rates you can calculate k. This is why you see a different size and weight for the same capacity battery pack rated at 10C versus 65C.