INTRODUCTION
This text is an introduction to classical propeller theory for practicing engineers. It aims to give the reader an intuition on how a propeller works at its design point. The equations can also be used for off-design calculations, but those are mostly outside the scope of the present text.
Readers interested only in new material may choose to read only the chapters on viscous loss. This contains a simple, yet rigorous method of viscous optimization which I believe is in its details original to the current text.
The chapters on vortex theory contain material which is not new, but which is not often presented in this way. This section contains a complete, yet very simple lifting line code which reproduces Prandtl's tip function from first principles.
Classical propeller theory has a reputation for being "difficult". This may partly be due to the extensive use of the concept of circulation to express the blade element lift.
Circulation is closely linked to vortex theory and potential theory. These concepts are very convenient in describing the flow around a propeller but they tend to be less intuitive to practicing engineers, who are more familiar with wing section lift and drag coefficients. But ultimately, the justification of the flow pattern around the tip of a propeller ( and around a wing, for that matter ) can only be found from a vortex argument.
This book aims to give the reader the best of both worlds. The first part of the discussion of the tip loss avoids the use of vortex theory to an unusual degree.
The second part gives an introduction to vortex theory which is much more detailed than is usual in texts on classical propeller theory ( and, in fact, wings ), and is hopefully still quite straightforward.
The notation used mostly follows the literature, with the exception of the symbol for the tip speed ratio.
This text uses the small x for the local speed ratio
x = Ω r / V,
and the capital X for the tip speed ratio
Using the capital X instead is more intuitive, and avoids any such confusion.