PROPS... without the math.
Originally printed in Flying Models, Aug. 96

The fact that the propeller pushes on the air was known by
inventors dating back as far as Leonardo da Vinci's toy helicopter.
However, these early propellers were crude and reflected no
understanding of the angle at which a prop pushes on the air or
the aerodynamics of the propeller.

The purpose of a propeller is to change rotational motion to
forward motion. A rotating propeller pushes backwards on the
air to move it forward.

When the air is pushed backwards behind the flat plates a force
is generated that tries to thrust the plates forward and gives the
propeller forward motion. The force generated by pushing air
backwards is called propeller thrust.

Twist
A machine screw moves through a hole and pushes on threads
at the outer diameter. In the case of the propeller, there is no
hole in the air. Therefore, each section along the span of the blade
must have a twist. Ideally, the twist at each section moves the prop
forward an equal amount. (Fig A)


The circular path of the propeller increases in length towards the tip.
Therefore, the angle of twist must be larger near the center than at
the tips. If the angle of twist is the same along the span of the blade,
the tips will try to move forward more than the rest of the blade.

As the prop moves forward, the path of each section is a combination
of both circular and forward motion. For the same distance forward in
one revolution, the path at A is shorter than the path at B as seen
in Fig B.
The paths at A and B are called helical paths.



Pitch & angle of pitch
The theoretical forward distance that a prop section moves in one
revolution is called pitch. The angle of twist at each blade section is
called the angle of pitch. (Fig. C)

For each section we can calculate the pitch (distance moved forward)
for a helical path.

Pitch = 6.28 - (Radius to the section) - (Tangent of the Angle of Pitch)

Theoretically, the pitch should be the same across the span of the blade,
a constant pitch. In other words, the angles of twist at each section
along the span should be designed to follow a helical path that will move
each section forward the same distance.

Airfoil and blade shapes.
The propeller is a rotating wing. However, the velocity of the air
approaching the prop is different from that approaching the wing. In
the case of a wing, the speed and direction of the velocity is the same
across the span. In the case of a propeller both speed and direction
of the approaching velocity change across the span of the blade. (Fig. D)

The amount of air that the prop pushes at each blade section is
determined by the speed and direction of the air and the blade width.
The total amount of air that the propeller pushes is determined by the
props diameter.

The resistance to the rotation of the propeller is due mostly to drag of
the prop blades. The drag of a propeller is determined by surface
smoothness, air foil shape, and blade shape.

It should be noted that it took a decade after the Wright brothers'
flight to develop the theory and design of a wing. It took another decade
to develop the theory and design of a propeller.