In summary, the conversation discusses the mechanics of riding a wall of death and the factors that limit the speed and radius of the wall. The main limiting factor is the G force acting on the rider and bike, which increases with smaller radius and higher speed. The conversation also touches on the cost and practical limitations of building a larger wall of death. Additionally, the concept of lean angle and torque is mentioned as a factor in maintaining balance while riding. Ultimately, the question remains: is there a maximum radius for a wall of death or is it simply a matter of going faster as the radius increases?
Just as a side note, ##a = v^2/r## is just the centripetal acceleration. If you want to find the total acceleration experienced by the rider, use Pythagoras' theorem to find that
$$
a_{\rm tot}^2 = g^2 + \frac{v^4}{r^2}.
$$
For a total acceleration of ##Ng## this would give a velocity
$$
v = \sqrt[4]{N^2 - 1}\, \sqrt{gr},
$$
indicating that for a fixed target acceleration, ##v## needs to grow as ##\sqrt{r}## (this was true already for the centripetal acceleration and follows directly from basic dimensional analysis). The angle is always the same for a given acceleration, ##\cos(\theta) = 1/N##, where ##\theta## is the angle of the rider from the vertical position.
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Jimbo54321
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I am the first to admit that I am not good at mathematics and have struggled all my life, but I do try, and I will persevere in improving my understanding.
I can see from other threads that this forum is used by Ladies and Gentleman that are so far above me in the league tables, that when it comes to understanding mathematics, physics and science, you guys leave me feeling like a Bum at a banquet. LOL.
Anyway, the only reason I questioned my math was to answer a nagging thought of how many G's Patch would be pulling at 48mph (as stated in the program), but when I worked out that there is no way he could do 48mph, I had to question (1) my math, or (2) the programs statement.
I'd like to thank you guys for helping me, mfb, Doc Al and Orodruin you three have given me a lot of self homework, (trying to decipher the formulas you used) PMSL.
But I will strive to understand this math. Oh the late nights.
Thanks again.