Hi flange.
Rolling resistance is greatly affected by pressure. If u notice, an under inflated tire runs extremely hot. A lot of heat us actually generated by the sidewall because it moves so much and creates excessive heat.
Yes, roiling resistance will increase with pressure but not too much because passenger car tires are all radial. The contact patch is controlled by the steel belt which is working very hard to keep the contact patch stable. This is different from bicycles bias constructed tires. Obviously with increased pressure comes less sidewall movement and hence lower rolling resistance. But it also affect overall grip and braking distance as the steel belt will still allow slight deformation.
That being said, for an equal everything else (pressure, tread pattern, carcass construction, etc), the LRR compound will produce a lower rolling resistance compared to a full carbon black tire.
If you want to squeeze max MPG, try 100% silica instead of silica blended tires
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View my fuel log 2013 Mirage (Malaysia) GS 1.2 automatic: 44.6 mpg (US) ... 19.0 km/L ... 5.3 L/100 km ... 53.6 mpg (Imp)