General Mutley,
After the initial horizontal acceleration, which will require additional TRT to maintain height - and accelerate, the horizontal component of the induced flow will cause the total reaction to tilt forwards, thereby reducing rotor drag and increasing TRT as a result. The reduction in rotor drag means that to continue in balanced flight (ie no more acceleration either vertical or horizontal) the corresponding power required to maintain rotor RPM is reduced - OR if the collective is left alone, TRT can be said to increase. This situation remains relative up until the total drag (IE rotor, profile and parasite drag) increases (as a square of the airspeed) cancelling out the benefits of the horizontal airflow component, and eventually the power required to accelerate further increases. Hence the unique shape of the helicopters power-required for level flight graph). The lowest point of which we exploit as a "Safety Speed" for performance purposes.
You need to look at the TRT and TR diagrams in a POF book and revise what happens when the horizontal component of the induced flow increases (normally by flying forwards).
Up until a couple of months ago this was gobbldee-gook to me. but I had to revise for an interview and found WJ Wagtendonks POF book a godsend. Its on the net if you google.
Having vomitted all that up bear in mind I am not an FI(H)!!!!
DB