On Tue, 2 Jul 2002, Ian Woollard wrote:
> OTOH I found a water rocket web page that implies that the Cd for a nose
> cone varies between 0.6 and 0.8 or so; and Randall was using 0.7 for his
> simulations (as was I).
Those are awfully high numbers. Several references show plots more like
0-15-0.2 at subsonic speed, rising sharply to a peak of 0.5-1.0 just after
Mach 1, declining smoothly to around the original at about Mach 6. (One
source adds a comment that an overall average Cd is *not* a good
substitute for a Mach-dependent one -- even a vague approximation to the
shape of the curve is much better than trying to pretend it's flat.)
One caution: there are a lot of variables here. Those plots probably
assume a traditional rocket shape, long and pointy. Even going from a
narrow cone to a wide cone on the nose of a cone-cylinder shape raises Cd
a *lot*. Anderson's "Fundamentals of Aerodynamics" shows experimental
data on a cone-cylinder shape with a 30deg half-angle in the cone:
subsonic Cd about 0.5, peak about 1.0, hypersonic limit about 0.6.
Whereas "Handbook of Astronautical Engineering" shows a 12.5deg half-angle
cone-cylinder at 0.2, 0.4, 0.1, and Anderson shows a 15deg one having a
hypersonic limit of about 0.15.
> There's an equation for a flat plate that gives Cd of about 0.15 or so
> for a 1 in 4 angle to the flow...
What do you mean by "1 in 4"? If that's an angle of arcsin(1/4), that's
about 15deg.
Newtonian Cd for a flat plate is (as seen in both that web page and
Anderson's "Fundamentals of Aerodynamics") is 2*sin^3(alpha). But note,
that Cd is based on the plate area, as is usual for wings, not on its
cross-section perpendicular to the flow, as is usual for body drag
coefficients! Cross-section is area*sin(alpha), so the "real" Cd ends
up being 2*sin^2(alpha). For alpha = arcsin(0.25), that's 0.125.
That's at Mach infinity, mind you. Much of the drag loss a rocket
experiences (for orthodox trajectories, climbing out of the atmosphere
quickly) is at relatively low speeds where that won't be a good
approximation. And even at hypersonic speeds, various empirical modified
forms of Newtonian theory tend to be preferred over the original.
> I think a cone should be the same Cd.
Not a safe assumption! Two-dimensional and three-dimensional flow are
different animals. In this particular case, Newtonian theory actually is
pretty close to the real hypersonic limit of the cone -- much closer than
it is to the real flat plate!
> Conclusions? Nope. I must admit I'm a bit confused right now. I haven't
> managed to explain why some sources give a Cd of 0.7...
Check those references, and the shapes they use, carefully...
Henry Spencer
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