I'm afraid nuclear powered aircrafts are far away in the future.
There are two reasons for this: the energy density is pretty good in kerosene and fossilized fuels (compared to current batteries for example). This fact rules out battery based systems, unless somebody figures out dramatic improvements on the energy density.
The second reason is that no matter what, there is a need of dense materia around the reactor, otherwise radiation will make a short work of pilots (and the passengers too). This increases the weight of the aircraft quite radically. And, unfortunately the materials (aluminum, ceramics, titanium) used elsewhere in the airframe aren't getting stronger at the same time, unless somebody adds more of them (which increases weight -> which increases power demands of the reactor -> which increases the weight of the reactor and thus the weight of the plane...)
Before someone says to install it in the tail of the aircraft, the answer is most likely not possible with current technology (says my common sense). The reason being that airliners are according to my understanding, designed to be stabile, so their COGs should be located in the fore parts of the aircrafts. Adding a reactor behind will shift the weight heavily towards aft part, making aircraft unstable by nature, meaning that it doesn't want to fly straight and it doesn't want to recover - though this can be overcome with electronics, but I haven't heard about this being done in airliners (modern fighter aircraft are another case).
Besides, who of the passengers would then like to sit in the aft part? Discussions like these make me always think that in engineering point of view, oil has been pretty good compromise in the energy density, storage, safety and weight sides in the end. The only bad things are CO2 outputs and that it is running out. Let's say it is well understandable why it has been chosen as the main energy source in many applications.
Mika
