# Propeller Dynamics

Before making or selecting a propeller it is worth understanding propeller dynamics. A propeller is an assembly of radially disposed blades with an airfoil shape that when rotated in air produce thrust.

All propeller blade airfoils have a certain angle of attack range, in which the flow around the airfoil remains attached to airfoil′s surface. While this is the case, the efficiency of the axial fan is satisfactory, but, when the angle of attack of the incoming free stream exceeds this angle of attack range, efficiency goes down and noise goes up.

The thrust can be increased by increasing the rotational speed, increasing the angle of attack or increasing the diameter.

For all of these design parameters we need to understand the stall mechanisms of a propeller blade.

### Stall Mechanism

The stall mechanism can be viewed in four different ways:

1. Dynamic Behaviour – based on the encounter of the particles of fluid with the leading edge of the blade.
2. Bernoulli’s Law – based on the pressure variations of a particle when traveling along the airfoil’s contour.
3. Viscous Stall – based on the fact that the flow has viscosity, and its effect of the flow particles rubbing a surface, their intrinsic energy, be it static pressure or kinetic energy, is being dissipated in the form of heat due to viscosity.
4. Impedance Related Stall – depends on the static pressure presence or the impedance behind the propeller.

All these may occur simultaneously at the stall. The propeller dynamics are described in more detail below.

1. Dynamic Behaviour – Every time a solid object changes the trajectory of a particle of fluid, this particle is accelerated, no matter if there was or was not any change in its speed at the time. So, when a particle surrounds an object and its trajectory describes a circle (or any non-rectilinear trajectory), the particle is being accelerated in proportion to its speed squared and inversely to the radius of the circle. Every time there is this circular trajectory, there exists a fictitious “centrifugal force” that tries to pull the particle away from its curvilinear trajectory, If this pull is unsuccessful, the particle will continue traveling and “caressing” the surface. If the curvilinear trajectory is very sharp, and its radius very small, the centrifugal force will be high and it will be pulling the particle away from the surface and flow detachment or separation will occur. If the angle of attack is very high, there will be a chance for the centrifugal force to succeed in detaching the particle from the surface. Relate this phenomena to the increase of angle of attack of the flow with respect to the blade when going from the “free delivery” to “shut-off” condition and see how at a certain critical angle of attack the centrifugal force pulls the air particle from its trajectory causing the stall.
This pulling force that creates the detachment of the air flow from the surface is dependent on the velocity of the particle and the radius of curvature of the turn. The larger the velocity and the smaller the radius of curvature, the larger the pull on the particle and larger the chance to depart from its intended path, around the blade’s surface.
2. Bernoulli’s Law – A particle is traveling along the airfoil which at this point is thickening. While the thickness increases, the speed of the particle also increases, while at the same time the pressure decreases (due to Bernoulli’s law). This is happening at the first part of the airfoil, where the thickness of the airfoil goes from minimum to maximum. This region is called a region of favourable gradient where the air is “sucked” by the airfoil because it keeps finding lower and lower pressure. After the airfoil’s maximum thickness point, the inverse is true: the thickness decreases again, velocity decreases and most important, the pressure goes back up to the original atmospheric value, which means that the air particle sees in this other half of the trajectory an adverse pressure gradient. Higher and higher pressures are encountered by the particle as it approaches the trailing edge of the airfoil. This adverse pressure is resented by the particle and it’s reaction is a slow down and consequent separation from the surface and subsequent flow stall.
3. Viscous Stall – A group of particles with an initial static pressure and kinetic energy travel along the surface of the blade, while substantial friction between particles and blade surface is going on due to the presence of viscosity. This friction diminishes the intrinsic energy contained in the particles and forms a layer of low energy air called the boundary layer. As the particles travel downwind, more of the energy is being dissipated in the form of heat which means that the boundary layer thickness increases. This lack of energy of the air particles will cause them to stop and stagnate, creating more accumulation of particles behind them and this obstruction will create separation of the flow of particles from the blade’s surface.
4. Impedance Related Stall – This is related to the conditions around the propeller rather than the aerodynamics of the propeller itself. When the impedance behind the propeller is increased, a static pressure build up proportional to this impedance takes place at the exit of the propeller. Even though the propeller blades are working hard, the air going through the blades starts to sense the rapid increase in static pressure existing at the propeller’s exit and so the air velocity decreases resulting in the air particles separating and stall occurs. This stall mechanism is there, regardless of how good the propeller is designed.

Of the four stall mechanisms, the impedance related stall is the one that perhaps the most insurmountable of them all.

#### Propeller Size

The propeller size should be chosen to match the engine and airframe. However, it may take some trial and error before you get the right propeller for your particular installation.

Tables for two and four stroke engines give you a starting point for propeller size selection based on engine capacity.

#### Five Cylinder Rotary Engine

The propeller on my tiny five cylinder rotary engine was made by hand. The main reason for making this propeller was that the direction of rotation was clockwise. Most commercial model engines rotate counter-clockwise. A simple mistake I made, but meant I had to make the propeller.

It was a chance though for me to make a propeller that looked more appropriate for the engine. The laminations give it strength. The large diameter and small pitch give it an elegant look at slow speed. However, for all of this I carefully blended the blade pitch from root to tip. Also, the blade has a smooth aerofoil cross-section with a rounded leading edge.