Keith Williams
I have never argued that there is a direct relationship between the stiffness of a material and the acceleration produced.
This is what you argued in your own words:
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
If you have a problem with the idea that the acceleration of the gas does not actually produce the thrust let’s look at a slightly different scenario. You are driving down a motorway at 70 mph...your propulsive efficiency is 100%. But this is only possible because the material on which you are exerting your rearward force (the road) is stiff enough to prevent it form being accelerated
Now getting back to our aircraft sitting on the runway, if we release the brakes the aircraft will start to accelerate forward. So our propulsive efficiency is gradually increasing. This process will continue after lift-off. But we will never get to 100% because the exhaust gas is not sufficiently stiff to resist being accelerated rearwards.
Perhaps a more valid explanation of the conundrum...
There is no conundrum. F = m.a covers it succinctly. You have confused yourself with this stiffness idea. Stiffness is irrelevant, it is for structures and springs. Mass is the measure of inertia.
Life is not an equation, it is much messier than that.
As anticipated, you don't have an equation for your "road is stiff enough to prevent it from being accelerated" concept because it is not part of any scientific theory. 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.