# Performance Theory

2.1 INTRODUCTION

Unlike a conventional fixed wing aircraft, which has separate means of generating forces for lift and forward propulsion, the helicopter uses only the thrust from a rotor to meet these two essential requirements for sustained flight. This limitation does, however, afford the helicopter a unique advantage over most fixed wing aircraft: the ability to generate a lift force even when the vehicle is stationary. Understanding the basic manner in which a rotor system develops thrust is fundamental to any study of the measurement of rotorcraft performance. It is also required in any introduction to the stability and control attributes of a typical helicopter. There are two basic theoretical approaches to understanding the generation of thrust from a rotor system: momentum theory; and blade element theory. Other more complex theories tend to build on the fundamentals introduced by these two approaches. Since many standard texts on helicopter performance cover momentum theory and blade element theory [2.1 to 2.7] it is only necessary for us to review the key points here. Forward flight produces asymmetric flow across a rotor disk and thus it is desirable for us to start by restricting our discussion to purely axial flight.

2.2 AXIAL FLIGHT: MOMENTUM THEORY

Momentum theory was initially developed by Rankine and Froude from their study of ship propellers or water screws. It later found application in the design of airscrews

[2.3] and is used here to represent a climbing rotor. The theory makes certain assumptions:

• Air is an inviscid and incompressible fluid.

• The rotor acts as a uniformly loaded or ‘actuator’ disk with a infinite number of blades so that there is no periodicity in the wake.

• The flow both upstream and downstream of the disk is uniform, occurs at constant energy and is contained within a streamtube.

• No rotation is imparted on the fluid by the action of the rotor.

These assumptions necessarily limit the accuracy of the Froude theory. The momentum approach has, however, been extended to cover the more realistic case of a compressible fluid [2.7]. Other real effects such as swirl and unsteady flow can be accommodated by appropriate empirical factors [2.4, 2.6 and 2.8].