Just passed a helicopter on my way to work. We have read in some detail how an airplane gets forward thrust and lift by deflecting air. How does a helicopter with horizontal fans achieve that ?
In general, the forward thruswt is achieved by tilting the entire helicopter forward. This converts some of the lift produced by the main rotor into a forward component of force. The same is true for turns.
Yes, the swashplate may be used to create a thrust imbalance; but this imbalance does not provide any horizontal forces. It merely creates a force imbalance which tips the helo slightly, so that a component of the upward force of the main rotor gets converted into a lateral force.
Take a look at any helo moving with any kind of rapid forward velocity and you will see that the entire craft is tipped noticably forward. Same with sharp turns: the helo tilts noticably in the direction of the turn.