My experience in aviation is essentially zero, but looking at Wikipedia it seems like the Tu-95 Bear offers high subsonic speed and extreme range.
I assume that turboprop engines are more fuel efficient than jet engines. If all the above are true then why we do not get to see more rotary engine planes in commercial airline flights?
Is it a noise concern? I see that the TU-95 is apparently the "noisiest military aircraft on Earth".
Well, first let's clear up a few terms: When you say "rotary" engine I'm assuming you're referring to radial engines, a type of piston engine that used to be pretty common on aircraft. (These days opposed piston engines are what you typically find on piston-powered aircraft, rotary engines are yet another design, but their usage died out around the end of World War I.)
The TU-95 is not actually a piston-powered aircraft. It's a turboprop – basically a turbine engine similar to what you'd find in a jet, only rigged up to turn a propeller rather than produce "jet thrust" directly.
From an efficiency standpoint, turbine engines are usually more fuel efficient than their piston counterparts, and jet fuel is denser and less refined than aviation gasoline and is consequently cheaper for operators to procure. Turbine engines also offer more reliability than piston engines, and the maintenance on a turboprop engine is also largely similar to a jet engine with a few extra components, which is an advantage for a company operating a fleet of jet and propeller driven aircraft.
The differences in operating efficiency and reliability are the major reason why gasoline-powered piston engines have basically disappeared from scheduled airline service.
So why don't we see more turboprops? Actually we see a lot of them, if you look in the right places.
Jets and Turboprops are good at different things: broadly simplifying, a turboprop is more efficient at lower altitudes and airspeeds while a jet engine is more efficient at higher altitudes and airspeeds.
As a result we see turboprop aircraft like ATR 72s in use for short-haul "commuter" service, but for trans-continental or trans-oceanic flights where they spend a long time cruising at high altitude jets dominate the sky.
Since most people are flying to go relatively long distances there are comparatively more jets in scheduled airline service than turboprops.
Noise is probably also a factor: fast turboprops like the Bear are LOUD not due to the engine, but due to the propeller. The tips of the spinning propeller on a TU-95 can approach supersonic speeds, which causes quite a bit of noise. The TU-95's contra-rotating propellers (which help produce thrust more efficiently) also contribute to a louder noise footprint. In the case of the TU-95 this doesn't matter – it's a military plane, and the Russian air force doesn't care if people complain as the aircraft has a mission to complete and that's more important than a few noise complaints. If United Airlines were to operate a TU-95 out of Kennedy departing over people's houses I suspect they would quickly reconsider their choice of equipment when the noise complaints started coming in....
Reading the answers here tells me to put a few facts into the discussion:
In all cases, thrust is created by accelerating a mass of air backwards. The general equation for propulsive efficiency $\eta$ is $$\eta = \frac{v_{\infty}}{v_{\infty}+\frac{\Delta v}{2}},$$ where $\Delta v$ is the speed increase of the mass of air due to that acceleration. This formula shows that it is better to accelerate a big mass of air only a little than a smaller mass by a lot. Propellers do this and for that reason offer the best efficiency. Turboprops use less efficient, but lighter gas turbines for creating power, but retain the efficient propeller. Civilian turbofans try to increase the mass of air by increasing their bypass ratio, and only the military is using the least efficient types with bypass ratios below 1, because they are the best choice at supersonic speed.
Below you see a plot of the thrust-specific fuel consumption in cruise condition of different engine types over their bypass ratio. The inverse relation is easily visible.
Plot of the thrust specific fuel consumption in lb of fuel per lb of thrust per hour of different engines over the logarithm of their bypass ratio (picture source).
To make a comparison between piston and turbofan engines possible, let's compare fuel consumption at take-off. The formula for static thrust of a propeller is $$T_0 = \sqrt[\Large{3}\;]{P^2\cdot\eta_{Prop}^2\cdot\pi\cdot d_P^2\cdot\rho},$$ where $P$ is the shaft power, $d_p$ the propeller diameter and $\rho$ the air density. For our example, we use a four-bladed prop of 3.4 m diameter and an engine with 1111 kW power. Its static thrust is 10.727 kN when we assume standard atmospheric conditions and a prop efficiency of 85%. The fuel flow will be 266.6 kg per hour, and relative to thrust this is 24.8 g/N-h or just 80% of that of a modern turbofan.
I wonder if even the enthusiasts could guess what airplane I used, because I obfuscated it by using those unfamiliar metric units. I guess nobody will argue that it is not optimized for fast flight, so this comparison should also hold for the Tu-95, for which I have less data available.
However, a propeller will force any aircraft to fly more slowly than jets. Their efficiency tanks once the propeller tips rotate at supersonic speed, so it is best to keep cruise Mach below 0.6. But commercial traffic wants to fly as fast as economically possible, and with turbofans this limit is only reached around Mach 0.85. The faster aircraft will fly more legs in the same time, carrying more people and earning more revenue. Also, by offering the faster connection, it will turn up in the booking systems on page 1 and be the favorite with business travelers, who account for almost all the profits of airlines. That is why we do not see many turboprops in civilian traffic anymore.
Noise should not be the problem. Modern turbo prop driven aircraft are even more quiet compared to similar aircraft driven by jet engines. It is - like always - all about economy.
Let's talk about the available engine types. (All you experienced aviators, I'll keep it very simple and so in some points even not 100% correct. If you don't like this, please skip this paragraph, if you like to have moe details on an engine type, please feel free to ask your questions) Piston engines are the earliest engines and still most common or light sport aircraft. You can compare them to the engine in your car, but instead of driving the gearbox which drives your wheels, they drive a propeller (sometimes also via a gearbox). Piston engines strong enough to power an airliner, as they did in the past, consume far too much fuel and oil to be efficient enough to compete with jet engines. There are different types of jet engines. The classic jet engine sucks in air with its fan, squeeze it in a compressor, makes it go bang in a combustion chamber and blows it out, while a turbine ahead of the nozzle uses a bit of this energy to drive the fan and the compressor - remember this four words and you will always know how it works ;) This simple kind of jet engine was used for early jet driven passenger planes, but nowadays you'll only find it in military jets. Modern passenger aircraft use the same principle, but their engines have a far bigger fan turbo fan engines. Most of the air is bypassed around the "core" of the engine. This air delivers more than half of the thrust.. There are also turbo prop engines: simply replace the fan with a propeller. And finally turbo shaft engines where all of the jet engines power is used to drive a propeller and the exhaust delivers no forward energy.
Where does all this noise come from? To keep it simple, we can say that differences in speed produce noise. Jet engines are noisy because of the high difference in speed of the air passed through the engine and the free air stream. The cold air stream of a turbo fan engine is slower so there is less speed difference at the exhaust and less noise. The noise of propeller engines is mostly dependent on the speed of the propeller. The tips of the propeller blades are obviously the fastes moving parts. Their design requires them to remain subsonic to deliver thrust but propeller speed as well as the speed of the fan in turbo fan engines is more and more reduced to reduce noise emissions.
An economic engine must not only be quite but also powerful as well as fuel efficient. You are right turbo prop engines are generally the most fuel efficient engines but would you as a passenger like to sit ten hours in an airplane to get from London to New York? I don't and most airliners won't like such a plane too, because flight time costs money. Turboprop aircraft are most efficient on short distances where the difference in speed doesn't makes such a huge difference in flight time.
Another problem with turbo prop engines are the passengers. There are many people who see an propeller and think that they are sitting in one of the oldest airplanes ever. They trust in jet engines, low wing design and everything you would find on an "modern" passenger airplane drawn by a seven years old child.
I hope you'll find your answer, considering all this really basic and simplified knowledge.
