Why does the bank angle in the primary turn change with aircraft?

One of those things was that every aircraft has a bank angle that ensures an acceptable safety factor from the possibility of an accelerated stall, while still giving a reasonable option to return to the runway. Why are they not the same value for every aircraft?

The two goals stated above are competing with each other. On one hand, we would like our glide speed and stall speed (in the bank) to be as far apart as possible for safety. On the other hand, we would like to make the primary turn as tight as possible to minimize the time and altitude loss during the turn. But there are just two variables, glide speed and stall speed that we can manage. Stall speed is defined by the fundamental design characteristics of our aircraft, and increases with increased bank angle. Glide speed is chosen by us, but due to the complex way this choice affects the aircraft flight path, only the Calculator can be used to understand how it works. In any case, we can only push up stall speed, and reduce glide speed to achieve our goals.

Contrast the above with the knowledge that we know that V best glide gets our aircraft to where we want to go with the least loss of altitude. But V best glide relative to Vx, Vy, and Vs1 is all over the place with different aircraft. With that in mind, I assembled the table below to compare the aircraft in the Calculator's menu.

In the first four rows are fundamental characteristics of each aircraft. Note that the blue columns are aircraft with Vbg in between Vx and Vy, and the green columns are aircraft with Vbg greater than Vy.

The fifth row is the Glide back speed. Following the rules of the "Bolon Method", Vbg is chosen as the glide back speed for aircraft with Vbg between Vx and Vy, Vy is chosen for aircraft with Vbg higher than Vy. Row six then is the ratio of the glide back speed to the stall speed.

Row seven is the arbitrary ratio between the glide speed and the stall speed that we deem is safe. In this case, this is 1.25, or a 25% safety factor.

Row eight is a calculation of the maximum stall speed that will satisfy the minimum safe glide back speed to stall speed ratio.

The last row is the calculated maximum bank angle for each aircraft. These values are not surprising as we have gotten to those values in the Calculator for a long time.

Digging a bit deeper, we notice that in general aircraft with higher glide ratios, have generally higher allowable bank angles. Except for the J-3 C85 Cub, which has the highest glide ratio, and the lowest safe bank angle.

All of these aircraft have similar drag profiles for their fuselages and tail feathers. So the answer to the conundrum lies with the NACA wing profile for each aircraft. This has a major impact on the fundamental drag constant for the aircraft as a whole. Bottom line is that different wing profiles just give different aircraft a higher ability to glide, and at the same time keep the stall speed at a lower value. Kudos to the designers of those aircraft. For your information, below is a table of values I found published on the internet;