Thanks for your post and question. I actually don’t know. My design for this wind tunnel just came from my experiences and best guess. I did not consult any text books or references for the exact best shapes. If you are actually building an expensive test facility it is very important to find optimal designs and so forth, but this is basement science and pretty good is good enough. I think research follows the 80/20 rule: the first 80% of ideal takes 20% of the time, while the final 20% of ideal takes 80% of the time. Therefore, here we are just shooting for that first 80%, at only 20% of the time required.

If you need references, I would go to your engineering library. My guess is that there were some papers published on this topic in the 40’s and 50’s and some references probably came out after that. It seems to me a lot of fluids and aerodynamic stuff was done then.

Best Regards,

Ben

Best regards,

Raquel Somavilla

]]>While hoping to avoid being trite, perhaps we can relate this to an Einstein quote. He said “The most incomprehensible thing about the world is that it is comprehensible.” We can add that it is completely incredible that we can have success in describing the world with incomplete understanding.

It would be great to continue thinking about this, but in the meantime we can reflect on how wonderful it is that this success is possible.

]]>Back to the main question: in some sense that I am still grappling with, physics is a part of mathematics which describes all possible and all impossible worlds. Physics without formalization is not physics. Having said that, I doubt very much that the Navier-Stokes equations are some kind of completely precise description of fluid flow. For instance, they ignore the conversion of mass into energy and quantum effects.

– retired mathematician

]]>1: 1

0: (1-1)

1: 1+(1-1)

succ(n) = n+1.

The fact that this property can be applied to any natural number allows us to infer that the cardinality of the set of natural numbers is infinity. Notice that we didn’t need to actually count till infinity to posit the conclusion.

Similarly, in our physical universe, we can do the same thing with time: if the universe is open (which is the current scientific consensus), every time instant has a successor.

succ(t) = t+1sec.

We can thus conclude that the cardinality of the set time expressed in second is infinite. ]]>

Another part of the problem is with modern math itself. Jacob Klein has written much about how math became unhinged from reality in the renaissance (with the rise of algebra), but he’s notoriously hard to understand. Prof. Joseph Cosgrove is a much more understandable expositor of his ideas.

LG

]]>Thanks for asking. Well, I have actually tried, but unfortunately failed! And then I have not tried again since my failure. When you are working for yourself you can let mess-ups linger. In your case looks like you need to find an answer. I would look in older literature since the rakes were probably developed quite some time ago…

Best Regards,

Ben