My last example with the trucks was a bad one. And my statement that 3rd would pull harder than 5th given the same speed and power with just a different rpm along the super flat power curve was wrong. The acceleration would be the same. The starting speed was the same in each example and so was the power being applied. And so was the rear wheel torque in either gear. More on this coming right up.
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Even though I was wrong in that statement, it helped me get back to the premise I am trying to prove.
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First gear accelerates at a much higher value than 6th. And not because of air resistance at speed in 6th.
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Because we are comparing changes in energy.
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Lets use horsepower hours for energy to keep the terms we have already been using. Or, horse power seconds to put into the appropriate scale. If I have to come up with exact equations for mass and speeds to support my point, I will. But I think we can get the idea from the concepts, without resorting to using exact numbers which will waste a lot of time to throw together.
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We have a CBR250R and the area under the power band we are using as we shift from the high side of the power peak to the low side with each gear is the same from 9,500 rpm to 7,500 and averages 20 hp. Let's say we start with 20 horse power seconds to begin with and 226kg at 6.7 meters/ second in 1st. So we pin the throttle while cruising at 7,500 rpm in 1st, 1 second later we have added 20hp seconds of energy to what ever we had before. Now we are up to 9.47 m/s and are carrying 40 hps. At the end of 2 seconds we will be carrying 60 hps and 11.6 m/s. We have doubled our energy vs the starting point in the first second and added another 33% to that in the second second. These are big changes of energy vs time. And big changes of speed vs time. So, a high acceleration. .276 G over the first second and .217 G over the second second. Now we continue to accelerate and shift up through the gears each time we reach 9.500 rpm until we hit 5th at the ten second mark. We now have 220 hp seconds of energy and 22.22 m/s. One more second later we have 240 hps and 23.21 m/s. We only gained 1 meter per second which is .1 G of acceleration. Less than half the acceleration we had between the first and second seconds of the run when the speed was low.
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This has nothing to do with wind yet which will indeed have a big effect on such a small amount of horsepower and acceleration. It is because the energy we are putting in is just increasing linearly with time but the speed is squared on it's side of the equation.
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And this brings me to the real revelation I had from the truck's dynos and 3rd accelerating the same as 5th. Power is the metric of how fast you can gain speed as I have been saying. And in the end, the torque multiplication of the different gears doesn't really do anything to make something pull harder other than to match the engine power band to the needed wheel speed.
sendler screwed with this post 01292013 at 03:07 AM
