In the P-38 Lightning could differential thrust be used to improve turn performance ? If so what was the procedure ?
According to WW2 pilots, no. Aside from the dangers in adjusting 1600hp on one side of the aircraft on the fly in the midst of a dogfight... With the P38, they didn't need to. The P38 had an inherent advantage over single engine prop fighters of its era. Its engines (and propellers) rotated in opposite directions, canceling out any torque effect. The counter rotating engines and props were considered a big secret on the P38 when it was first designed. (as if anyone couldn't look at the angle of the props on each side and tell that.)
The pronounced torque of the 1600hp-2000hp single seat fighters played a major role in aircraft handling: both in takeoff and power on maneuvers, something WW2 flight simulators never seem to reproduce. Single engine fighters would roll left far quicker than they could roll right, due to the immense torque of the engine/prop combination, aiding in the left roll but inhibiting a roll to the right. This was most evident at lower altitudes, where the air is thicker and the torque effect more pronounced.
Not so with the P38 - contra rotating engines and props canceled the torque, and the P38 could roll right far quicker than any single engine fighter. While the P38 did have several issues at high altitude, WW2/Vietnam ace Robin Olds held that nothing could beat a P38... down low. (revisit the Dogfights/Air Ambush episode for that)
So, no, they didn't use asymmetrical engine power for maneuvering with the P38 - they didn't need to. Just roll right and turn - no single engine fighter of that day could stay with you.
I know this question was asked years ago. But yes, differential thrust was used and was a trick up the sleeve of 38 drivers. Irv Ethel used differential thrust to escape a gaggle of 109s over Africa after his flight was jumped near Lake Bizerte in Tunisia. He taught the maneuver to other 38 pilots who then used it both offensively and defensively. The idea was to chop throttle on the side that you wanted to roll to. This could be used offensively to beat an enemy aircraft into a split-s, or could be used to rapidly reverse direction as if spinning the plane around a vertical pole. The P-38’s counter-rotating props combined with the prop’s airflow over the wings, which supplemented lift at lower speed made the Lightning capable of fantastic low airspeed and high angle-of-attack maneuvers that single-engine aircraft watched in disbelief.
It depends how you want to turn I reckon. If by rudder only and if both engines are not flat out, then yeah you could up the outer engine thrust and yaw faster.
But that is an uncomfortable and slow way and generally not how it is done, usually pilots bank the aircraft, tilting the lift vector. That is a big vector and can provide much more centripetal force than the yaw scenario: the wings provide lift, and increasing the AoA a bit creates much more force.
The vertical tail is dimensioned to fly with one engine out, the wing is dimensioned to support the weight of the aircraft. Difference between engine thrust and weight is easily a factor 5, often more.