The words which you have quoted do not argue that there is a direct relationship between stiffness and acceleration.
Our aircraft propulsion systems exert rearward forces on the air in their immediate vicinity, but not in the wider atmosphere. If we were to gradually increase the stiffness of the air, this would cause a gradual increase in the volume and mass of the air affected. This in turn would reduce the rearward acceleration, but would not reduce the propulsive force. If we continued to increase the stiffness we would eventually reach a point at which the entire atmosphere would be affected. The rearward acceleration of the air would be vanishing small, but again the propulsive force would not have changed. If we now make the air even stiffer, the entire atmosphere and Earth would be affected. Once again the acceleration would be smaller but the propulsive force would be unchanged. If we now increase the stiffness even more, there would be no change in acceleration or propulsive force. So although we can influence the acceleration by changing the stiffness of the air, there is not a direct quantifiable ratio between stiffness and acceleration.
In an earlier post you said:
There is no such thing as a propulsive force that does not involve a change of momentum.
But my examples of the two cars and the two hamsters illustrate the fact that it is entirely possible to create a propulsive force without any change in momentum.
The job of scientists and engineers is not to marvel at the messiness of life but to unravel its mysteries and reduce them to their component parts.
You are correct, but it also not the job of scientists and engineers to carry out experiments then simply dismiss unwanted results with comments such as
“If there doesn't just happen to be a second car”
, which you used earlier.
The job of scientists is to compose hypotheses, carry out experiments to prove or disprove them, analyse the results of these experiments then amend their hypotheses accordingly. Your approach in this thread has been to ignore results which you do not like and then simply restate the laws of motion.
The job of engineers is to look at how the world really works then use these observations to devise solutions to problems. An example of this is contra-rotating propellers as used in the Fairey Gannet aircraft. The Gannet was powered by a Twin Mamba turbine engine, which produced a great deal of power. If this power were to be fed into a single propeller the torque reaction would cause the fuselage to rotate very rapidly in the opposite direction to the propeller. This would make the aircraft uncontrollable and would probably tear it apart.
To prevent this the designers used two propellers spinning in opposite directions, but on the same axis of rotation. The front propeller was driven by a drive shaft which passed through the centre of rear propeller drive shaft. In this way the torque reactions of the two propeller were set against each other within the gearbox, causing them to be cancel each other out, so no torque was applied to the fuselage.
For all of this to be possible it was necessary for the gearbox structure to be sufficiently stiff to resist the two opposing torque reactions without being destroyed. Had the designers simply looked at the equations of motion and not beyond them, they would simply have said “we’re stuffed”, and gone home.