I was wondering if anyone could point me towards an example of how to fit a
function to G.V.R. Rao’s parabolic approximation of a bell nozzle given the
initial angle θn and corresponding start point as well as final angle θe and
point?
I’ve been following through the example on page 83 of Huzel and Huang
https://books.google.com/books?id=TKdIbLX51NQC&lpg=PA76&ots=slcXbGfst7&dq=modern%20design%20initial%20parabolic-contour%20wall%20angles&pg=PA83#v=onepage&q=modern%20design%20initial%20parabolic-contour%20wall%20angles&f=false
... which uses θn=27.4 (x,y) = 21.9,12.99 and θe=9.8 (x,y)= 102.4,46.7 but it
leaves out an example of how this is actually solved. Presumably because it is
so trivial but I’m getting a bit stuck on it. I believe an example of this can
be found in the Rao paper "Approximation of Optimum Thrust Nozzle Contour",
however, I cannot seem to find a copy online so I was attempting to work this
out on my own.
I understand a parabola can be calculated via several methods including via 3
points, which I could have if I use the top and bottom portions of the curve or
if I assume the vertex to be the middle of the throat. However, I’m thinking
that what is intended is that I’m supposed to use only the two points and
angles (eg. slopes) to calculate and it wasn’t clear to me how this should be
done.
Kind Regards,Graham
