Each vehicle has a sweet spot where it will shift in Drive without thumping or jerking. I find that 38 to 44mph works for the three automatic vehicles I have. I also wait for the torque converter to lock up before accelerating. It takes a couple extra seconds. It doesn't hurt to give it a 250 to 500 bump in RPM off idle before shifting to drive, BUT leaving it alone also gives good results.
"Rule of thumb", according to me, is to shift to drive about 5 to 8 mph above where the car normally shifts to overdrive. All of you should know where that is by memory if you practice hypermiling. That way you are shifting to Drive when the vehicle will be in overdrive and NOT the next gear down - probably where the thumping and shuddering comes in.
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