Nice post. I really appreciate having others who are not afraid to come out and play. It makes me think. This whole thing is an ongoing thought experiment for me which I have never worked through before and I will undoubtedly make mistakes along the way.
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Originally Posted by niky
Raw wheel torque or force numbers plotted against road speed look like this:
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True. My point exactly. In all gears those lines will all show the same power at the wheel as the engine is sending out even though the torque is much higher in the lower gears, the wheel speed is much lower. It's a wash. The power at the wheel is the same in any gear.
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Originally Posted by niky
Or translated into acceleration potential, thus:
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Yes. the acceleration inlower gears is always much greater than the higher gears because the speed is much lower. Hence, the energy of the vehicle is much lower. So any new energy that is added from the engine power is a big change. At faster speeds the energy of the vehicle can be 20 times, ect, what it was at the slower speed. But you are still only adding more energy from the same engine output 1 unit at a time. Now each time you look at it, you have increased the energy of the vehicle only 5%.
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Originally Posted by niky
So, yes... third gear should pull harder than fifth at any speed where the two gears intersect (unless you have a really weird powerband).
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Look at the dyno of the trucks again. They are modern turbo diesels and they do have a very weird, ultra flat power band. At any identical wheel speed where the gears have an rpm that is on the power band, say 3rd is 3,500, 4th is 3,000 and 5th is 2,500, The acceleration would be exactly the same. The gearing can't transform the power it is given. It only transforms the wheel speed to the engine speed.
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Originally Posted by niky
If gearing had no multiplication effect, you would NOT be able to do a wheelie in first gear, no matter how hard you tried.
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The torque is much higher in first so the so the action of rotating the front of the bike up and over is much stronger true. But the torque in and of itself does not accelerate the bike. Power accelerates the bike. which is again, much easier to change when you add more energy to a very small amount. A wheelie is also caused by the vicious change in the rate of acceleration. Jerk. Because the power is being applied to the road. Which is way below the cg of the vehicle. The bottom of the rear wheel is trying to drive right under the front of the vehicle and leave it behind.
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Originally Posted by niky
"horsepower per second"
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I'm not using horsepower per second. I am using horsepower times seconds. Which is energy. The same as a Watt hour or a Joule. Momentum is just one of many forms of energy.
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Originally Posted by niky
speed-of-light related relativistic effects
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Obviously my statements about energy increasing have nothing to do with the mass changing at these speeds. Only V squared is changing with more and more energy added.