Many turboprops are certified to fly well above those altitudes, actually, but most become very performance-limited. I used to fly a turboprop airplane at FL410 with regularity; it performed quite nicely there.
Unlike a turbojet aircraft, turbopropeller powerplants achieve only about 10% of their thrust from the turbine; the rest comes from the propeller. The propeller loses efficiency as altitude increases, and due to design of the powerplant, the ability to operate at higher RPM values to assure efficiency is limited. Turbopropeller powerplants also typically offer lower thrust values than turbojet engines found on large airliners; this is a tradeoff for weight and efficiency, appropriate to the size and design of the airplane.
Turbopropeller aircraft are limited somewhat in their forward speed that can be achieved, by design of the propeller. When the propeller tips exceed critical mach (the point on the propeller blade at which airflow first exceeds the speed of sound for a given air density/temperature), their efficiency drops markedly, and harmonic vibrations can be set up. The airflow over the propeller, unlike the wing, is a function not only of forward airspeed, but of RPM. Propeller driven aircraft become speed limited because they're propeller driven aircraft.
Because this is the case, turboprop aircraft aren't designed for high-speed operations, or operations involving high mach values. Most aircraft which fly high tend to do so because it is a place where they can operate most efficiently, and where they can go fast. Whereas the turboprop aircraft can't necessarily go that fast (the fastest production turboprop is the Piaggio Avanti, and it does 395 KTAS at altitude), such aircraft don't utilize swept wings, or other features of high altitude, high speed equipment.
Turboprops tend to operate on shorter legs than many turbojet aircraft, and often have no need to climb as high.
Unlike a turbojet aircraft, turbopropeller powerplants achieve only about 10% of their thrust from the turbine; the rest comes from the propeller. The propeller loses efficiency as altitude increases, and due to design of the powerplant, the ability to operate at higher RPM values to assure efficiency is limited. Turbopropeller powerplants also typically offer lower thrust values than turbojet engines found on large airliners; this is a tradeoff for weight and efficiency, appropriate to the size and design of the airplane.
Turbopropeller aircraft are limited somewhat in their forward speed that can be achieved, by design of the propeller. When the propeller tips exceed critical mach (the point on the propeller blade at which airflow first exceeds the speed of sound for a given air density/temperature), their efficiency drops markedly, and harmonic vibrations can be set up. The airflow over the propeller, unlike the wing, is a function not only of forward airspeed, but of RPM. Propeller driven aircraft become speed limited because they're propeller driven aircraft.
Because this is the case, turboprop aircraft aren't designed for high-speed operations, or operations involving high mach values. Most aircraft which fly high tend to do so because it is a place where they can operate most efficiently, and where they can go fast. Whereas the turboprop aircraft can't necessarily go that fast (the fastest production turboprop is the Piaggio Avanti, and it does 395 KTAS at altitude), such aircraft don't utilize swept wings, or other features of high altitude, high speed equipment.
Turboprops tend to operate on shorter legs than many turbojet aircraft, and often have no need to climb as high.