Convergence?
I think the discussion so far is getting close. Any incorrectness in the discussion so far appears to be based on terminology and modulated to account for intuition.
The gas entering the engine must leave the engine faster: unless there is acceleration there isn't any forward thrust. The exhaust jet must move backwards compared with the swallowed air. All viewers agree: people on the ground, any people floating in the air, people on the plane.
That does means that the exhaust jet has to travel in the opposite direction to the aircraft as far as the undisturbed local air is concerned, although not necessarily at any particular speed. (Thanks to the following post for prompting the edit). Viewed from the undisturbed air, the exhaust gas must move backwards to produce a forward thrust. That's not so for a rocket.
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The extreme case of exhaust speed (efficiency) is probably the space shuttle main engine: mass flow rate at liftoff is 1000 lb/s (from a ~500s burn and ~500,000lb of fuel/oxidiser per engine); quoted thrust is 480,000 lbs/2.1 Meganewtons. 500 Kg/s mass ejected and 2.1 Meganewtons thrust implies an exhaust speed of 2,100,000/500 = 4200 m/s, which isn't going to change much with height. However, orbital speed is about 7500 m/s. So, above some point in the climb, the exhaust still moves in the same direction as the shuttle compared with the earth, by about 3 km/s when the fuel is cutoff.
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For low-speed thought experiments, you need to be careful when quoting numbers, because the speed that air hits the fan is faster than the pitot airspeed from the nose: the airflow has already been sucked faster when it enters the nacelle.
Last edited by awblain; 29th Jun 2009 at 19:02.