Keith Williams, what I am taking issue with is this:
because the road is stiff enough to resist the forces involved, it does not experience a rearward acceleration....Now getting back to our aircraft ...we will never get to 100% because the exhaust gas is not sufficiently stiff to resist being accelerated rearwards.
The stiffness of the road is irrelevant except insofar as it transfers force to something with more inertia. Stiffness is for springs and structures. In terms of propulsive efficiency it is nothing more than a distraction. The important metric is mass - it is one of the 3 basic quantities of mechanics. Stiffness isn't. A kilo of spuds accelerated by a metre/sec˛ will give you the same reaction as a kilo of air.
To test this argument let’s imagine that we have 2 identical cars standing back to back and tied together with a strong rope. The cars move forward until the rope becomes stretched and are then brought to a standstill....If I stand on the ground my feet exert a downward force equal to my weight. If the ground is stiff enough it exerts an equal and opposite upward force which prevents me from sinking into the ground. But this process does not cause the Earth to accelerate downwards.
Both examples of static equilibrium - no net external force on either car, body or ground and no motion. Propulsion is different, there is a net external force causing motion of one body and therefore by conservation law there has to be an equal and opposite change of momentum on another. Stiffness cannot replace the momentum change. Something with mass has to be accelerated.
As I have said above if we increase the friction on the wheel pivot, the resulting motion will become very different. So the motions of the bodies concerned ( in this case hamster and wheel) are not determined entirely by their masses alone.
Well just assume the normal fricition for a hamster wheel spindle. The wheel spins. The resistance is mainly due to friction in the spindle and to a lesser extent on the very small inertia of the wheel. None of the resistance is "because the material on which you are exerting your rearward force is stiff" like the ground under a car.
The point which I am arguing is that the thrust in our car or aircraft or whatever, is not generated by the rearward acceleration of whatever we may be pushing against.
According to Aerodynamics for Naval Aviators:
“the force of thrust results from the acceleration provided to the mass of working fluid”.