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From a tuner on HPTuners Boards,

"You should use the scanner to change the gear ratio, if not you will get an incorrrect trans gear ratio and it will throw it into limp mode. I just did a 15 Jeep that had deeper gears and big tires and it would go limp till I changed the ratio and tire size."
 

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Has anyone installed the 3.70 gears with the 220mm axels? What was the impact on gas mileage? I’m leaning towards the 3.70 over the 3.09. I have the 2.62 open. I want to notice a difference without eating my gas mileage alive. Any input would be great
 

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The NAG1 with a 3.90 rear axle ratio gives you an overall first gear ratio of 14.00:1. That is less torque multiplication than the 8 speed with the Scat Pack/SRT standard 3.09, which has a 14.55:1 overall first gear ratio. So the 3.90 swap seems reasonable to me for the NAG1. Had I driven a Scat Pack or SRT with a 3.09 while I still owned my 2012 R/T, I would have done the 3.90 swap myself. But my 2012 was totaled and I wound up getting a Scat Pack!

Too bad Dodge doesn't offer the 3.09 with the 5.7L/8 speed that would have been a nice combination.

RamAirV1
The 2015 R/T Road and track comes factory with a 3.07 rear gear attached to the 8speed tranny. But a 3.90 does sound fun. :)
 
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