Originally Posted by enigma
Someone feel free to check the following math.
Assuming a flywheel of ~10kg, 0.15m radius
I = 0.5 * 10 * (0.15) ^ 2 = .1125
E = 0.5 * I * w^2 = 0.05625 * w^2
At 8400 RPM: E = 0.05625 * (8400/60*2*3.14)^2 = 43.48 KJ
At 6000 RPM: E = 0.05625 * (6000/60*2*3.14)^2 = 22.18 KJ
So after shifting we have ~21KJ of energy stored by the cars flywheel (not counting the other moving engine bits) that has to go somewhere.
If the car (1650kg) is going ~44mph in 1st (20m/s) the car currently has:
1650kg * 20^2 = 660KJ of energy.
If the DCT simply disengages the previous gear and engages the next and dumps that stored energy to the rear wheels you now have 660 + 21 = 681Kj
sqrt(681Kj / 1650) = 20.32 or a sudden velocity increase of 0.32m/s or almost 1 mph. Thats the jerk, its not simulated or made up, they just don't try to hide it under the cover of "smooth" like Audi.
You could apply the energy over time, burn it in the clutches, or reduce the engine output to cover it up. None of those help you go faster.
I suspect by the time you add in the other engine components the stored energy is considerably larger. Enough to put it into the 1-2mph range.
BTW: one "G" is 9.8m/s So if they accelerate the car 0.32m/s in 0.1s. that generates a spike of ~0.3g for that brief instant over the normal acceleration.
Nice analysis. Even if the numbers nor method are perfect the point is. A couple questions/corrections:
1. How close are your flywheel mass and radius? I know we don't have actual numbers and I know you are using estimates, but what is your guess?
2. The clutch friction will cause energy to not be conserved. However, even with a lossy joining of spinning disks angular momentum will be conserved. This is the begining of the correct calculation but since you have linear and angular momentum/energy it is a bit more complicated. I don't think you can even calculate the velocity change without a reasonable estimate of the total clutch back moment of intertia.
3. Even if energy were conserved, E = .5
* m * v^2 as you stated, but didn't you leave off the 2? So you are off by sqrt(2) = 1.4 in the 20.32 number. It is 1.4 x larger.
4. Footie either does not own a calculator or does not even understand the concept of a percentage (see the recent top speed threads), don't even bother with the forumlae and physics.
: Come on I expect better from a fellow physics person