Meanwhile, in the Ukraine, in September, the world’s only production-ready unducted-fan aircraft resumed its test program. The on-again off-again political history of the Russo-Ukranian transporter, and the similarly parabolic story of unducted-fan engines is far more complicated than any of the concepts behind the technology. Unducted-fan engines can be properly thought of as special-case turboprops; the only real distinction is the unducted-fan propellers are optimized around slightly supersonic tip speeds. Regardless of the label, all but a small percentage of thrust comes from the propellers.
A Word On Contra-Rotating Propellers
The first contra-rotating propellers appeared in the early 1930s, notably on the 441mph 1933 Macchi M.C.72 that still holds the speed record for piston-powered seaplanes. As engine outputs continued to increase, propellers needed larger and larger diameters and more and more blades to remain effective. But this quickly led to problems with packaging, fatigue in long blades, and aerodynamic interference between closely spaced blades. Simply using two propellers doubles the effective area, and having them rotate in opposite directions eliminates the torque effects of 5,000-15,000hp. 
As far as driving the propeller, some turboprops are directly connected with the same shaft as the final turbine stages, and some are driven through reduction gearboxes. Contra-rotating propellers tend to use a planetary gearbox. However, the first Napier Nomad used a diesel engine for one direction and a turbine for the other, and the GE UDF used extremely sexy interlaced turbine stages which themselves rotated in opposite directions, with one set connected through a rotating outer case.
Traditional propellers run into problems when the tip speed around the prop circle approaches the speed of sound when combined with airspeed. At transonic tip speeds, the air in the path of the propeller begins to compress instead of flowing around, and the higher the speed, the thicker the layer of compressed air becomes. The propellers need more power to compress a path in the air as well as move through it, and therefore have less power to propel the aircraft. Additionally, the pressure spike around the propellers is heard as a sonic boom. A few sturdily built propeller aircraft overcome the barrier with sheer brute force, such as the Tupelov Tu-95 Bear and its airliner derivatives. With tip speeds of up to Mach 1.15, they are noted as the loudest aircraft in the world, while and the Republic XF-84H Thunderscreech used tip speeds up to Mach 1.18 and famously caused nausea in ground crews.
The New Hope Is Old Technology, But Updated!
In the wake of the second energy crisis, the theoretical efficiency of a big propeller was the subject of intense study. By optimizing tip speeds around Mach 1.1, while sacrificing only a small amount of speed, initial calculations and tests suggested a 30% efficiency gain over contemporary turbofans. The big three jet engine manufacturers all began work on their own unducted designs, augmenting a longrunning NASA project. All worried that the public and airline executives would think of propeller aircraft as old-fashioned, noisy, slow, and inefficient, while jets were merely noisy and inefficient. Carefully constructed surveys led the public to approve of the ‘new’ propfans. Different models flew on a Gulfstream II, a 727, and an MD-80; the sound signature of a swath of supersonic blades necessitated rear mounted engines. Engineers, magazines, and Boeing executives championed unducted-fans as the engines of the future. In the meantime, oil prices plummeted during the 1980s, noise regulations got stricter, and turbofan development continued.
Bridging The Spectrum
Like a turboprop, a turbofan generates most of its thrust from air that bypasses the turbine entirely. The shroud, though a significant source of drag, can increases efficiency by slowing the intake air before it reaches the fan and power turbine. It also allows fan tip speeds in excess of 1000mph while still being the quietest solution for heavy aircraft. And any debris is contained in the incredibly unlikely event of a blade loss. In addition to mitigating the noise problem of early jets, modern multispool designs have have better throttle response and part-throttle behavior, as well as being more efficient. 
Today, the general wisdom and theory about aircraft propulsion is unchanged. Turboprops are the slowest and most efficient, unducted-fan designs are slightly faster and less efficient, and turbofans are the fastest and least efficient of the three. But while the speed differences between the three have not changed, and are unlikely to ever change, the efficiency gap has closed noticeably. Early high-bypass turbofans had a 3:1 fan to turbine mass flow ratio. Today, a common figure is 10:1, which sucks up most of an unducted design’s benefits in terms of doing a smaller amount of unit work on a larger mass of air. Fan stages have gotten so large and so slow that Pratt & Whitney is developing a family of engines with a geared reduction, further increasing the overlap between turbofans and turboprops.
The theoretical 30% advantage in fuel economy is 30 years out of date. To outstrip today’s enormous turbofans, unducted-fans would have to grow larger and heavier. Packaging problems and the legendary noise of high-speed propellers are barriers that unducted-fans are unlikely to break through. In the case of the An-70, where noise is not an issue, a high wing mount has the additional benefit of sending extra airflow overtop the wings for shorter takeoffs, and variable geometry blades further improve responsiveness. But its maximum and cruising speed are both lower than the Tu-95. The unducted-fan has not risen to challenge the jet engine. At best, the design is a more efficient alternative to a high-speed turboprop.
The unducted-fan is a great success story in terms of going from an image problem to a pipe dream with just a little bit of marketing.  If energy prices had remained high, they might have been a decade long stopgap in airline business models, though the raw extravagance of any air travel makes me skeptical they could have ever won the war with turbofans. Meanwhile, in Russia, they never quite got around to installing unducted fans on their jet powered fire-fighting surface-skimming flying boat.
 Powerful single-engine planes are also considerably easier to handle with contra-rotating props, thanks to the elimination of torque effects and the P-factor. This occurs during climb, where due to airspeed differences on the upward and downward side of the angled propeller, thrust is asymmetric, like a helicopter and causes the plane to yaw.
 In turbofans, unducted fans, and some turboprops, a multispool design is a torque converter: The high pressure compressor and turbine can spin up quickly, loading up the slower, low pressure turbine, compressor, and fan. A spool is a rotor is a turbine. While turbine can refer to an entire powerplant, technically it is only the set of blades that convert fluid flow into mechanical work. What I’m not 100% on is why creating jet thrust to turn a shaft to create fan thrust is more efficient than just creating jet thrust. I imagine it has something to do with generating blade pressure in the direction of travel as opposed to fluid jet pressure spreading in all directions, and maybe centrifugal swirl.
 The NASA account of the project and its sensitivity to image is particularly hilarious.
Sources, Images, and Further Reading
Let’s be honest: This is an almost all-Wikipedia article. As of 12/6/2012, the Wikipedia entries on these topics rock more comprehensively and readably than almost any other source I found. Highly recommended.
Stamp Of The Ukraine – Public Domain, via Wikimedia
An-70 Engines – Marianivka and Threecharlie, via Wikimedia
Advanced Turboprop Project – Public Domain, via NASA
Beriev A-40 – Yevgeny Pashnin, via Wikimedia
An-70 Aircraft Conducts Test Flight After 2-year Delay, by RIA Novosti
Contra-rotating Propellers – Wikipedia, the free encyclopedia
P-Factor – Wikipedia, the free encyclopedia
Propfan – Wikipedia, the free encyclopedia
Turbofan – Wikipedia, the free encyclopedia
Bypass Ratio – Wikipedia, the free encyclopedia
Beriev A-40 – Wikipedia, the free encyclopedia
Bearing Down: A Return to the Cold War?, by engineerd
Against the Flow, by Owen Zupp
Don Talks About Contra-rotating Props, by Don Stackhouse
The Short, Happy Life Of The Prop-fan, by Bill Sweetman
Toward Future Flight, SPINOFF Magazine
GTF Versus Open Rotor – Which Is Best?, by Max Kingsley-Jones
Rolls-Royce Pursues Open Rotor, by Geoffrey Thomas