I'm interesting in testing some aerospace propulsion ideas at actual
hypersonic velocities, perhaps up to even orbital velocity. Of course
hypersonic wind tunnels are quite expensive and none even go up to
orbital
velocity.
What I wanted to do was have a rotor move at rim velocity at this
speed
range. For current materials this would be far beyond their tensile
strenth if
you are using a uniform rotor. However, I was wondering if tapering
might make
it possible using materials in common use.
Here's a post to sci.astro presenting the calculation for rotating
spheres made
of diamond:

Newsgroups: sci.physics From: snipped-for-privacy@cars3.uchicago.edu Date: Fri, 09 Jul 2004 19:56:04 GMT Local: Fri, Jul 9 2004 3:56 pm Subject: Re: What is the Fastest spinning man made Object? http://groups.google.com/group/sci.physics/msg/924fb8ea41244702

The example given there for a rotating sphere resulting in:

v_lim = sqrt(2*S/rho), where S is the yield strength and rho the density,

suggests that it might work, since this is larger than for a uniform rotating ring in which v_lim is:

v_lim = sqrt(S/rho).

So I'm thinking a sufficiently tapered rotor might be able be able to get orbital velocity rim speed using current materials (not diamond). I know that the highest speed flywheels are able to get a rim velocity in the range of 1,100 m/s using carbon fiber composites. But this is an anisomorphic material and might be difficult and expensive to produce in the right shape I need. So I'm thinking of using high strength aluminum, titanium, or steel alloys. I know that the theory for tethers proposed for the "space elevator" use exponential tethering. Then this tapering should also work if you were using a rotating rod-like structure. However, for my usage I need a disk-like or torus-like rotor. What's puzzling me is that with these kinds of shapes you need to worry about tangential stresses, not just radial ones. So my question is if you used the right tapering to take care of the radial stresses, would that be sufficient to take care of the tangential stresses as well?

Bob Clark

Newsgroups: sci.physics From: snipped-for-privacy@cars3.uchicago.edu Date: Fri, 09 Jul 2004 19:56:04 GMT Local: Fri, Jul 9 2004 3:56 pm Subject: Re: What is the Fastest spinning man made Object? http://groups.google.com/group/sci.physics/msg/924fb8ea41244702

The example given there for a rotating sphere resulting in:

v_lim = sqrt(2*S/rho), where S is the yield strength and rho the density,

suggests that it might work, since this is larger than for a uniform rotating ring in which v_lim is:

v_lim = sqrt(S/rho).

So I'm thinking a sufficiently tapered rotor might be able be able to get orbital velocity rim speed using current materials (not diamond). I know that the highest speed flywheels are able to get a rim velocity in the range of 1,100 m/s using carbon fiber composites. But this is an anisomorphic material and might be difficult and expensive to produce in the right shape I need. So I'm thinking of using high strength aluminum, titanium, or steel alloys. I know that the theory for tethers proposed for the "space elevator" use exponential tethering. Then this tapering should also work if you were using a rotating rod-like structure. However, for my usage I need a disk-like or torus-like rotor. What's puzzling me is that with these kinds of shapes you need to worry about tangential stresses, not just radial ones. So my question is if you used the right tapering to take care of the radial stresses, would that be sufficient to take care of the tangential stresses as well?

Bob Clark