take too long to change speed, the flight control system will
have a very difficult time, and you could end up with a poorly
controlled and sluggish quad. I think that for many hobby-sized multi-rotors, this is not a huge concern, but could
certainly become an issue at the larger end.
The pitch of the propeller is a more complex concept.
Pitch is the second number in the propeller specification; 4. 5”
in our example. The larger the pitch, the more “aggressive”
the propeller is and the more steeply the blades will be
inclined to the plane of the propeller.
Imagine that we had a way to slowly rotate the propeller
into a block of soft foam. The propeller would screw into the
foam much like a screw would into a piece of wood. If we
traced out the path of the propeller in 3D, we would see a
helical path that looks very similar to a screw thread. Suppose
we made a mark at the tip of a blade when the propeller was
vertical, then rotated it one complete turn and marked the
position of that same blade tip. We would have two marks at
the same angular position, but offset in the direction of
motion by some amount. That amount is the pitch of the
propeller — how far it would move in a solid media in one
complete revolution (Figure 3). For model airplanes, people
often use the mental model of how far the airplane is
screwed through the air for each turn of the propeller,
though this breaks down somewhat as the air is not a solid
media but a compressible gas.
You might wonder why we don’t specify the pitch of a
propeller in terms of degrees. Take a propeller and literally or
mentally attach a pen to the tip of one blade and to the
middle of the same blade. Rotate the propeller though a full
turn. You’ll see that the outside pen travelled a much greater
distance than the inner pen. For a rotating solid body, we
know that every point on the
propeller will have the same angular
speed (the center and tip both go
through 360° in the same amount
of time). The tangential speed of
the propeller must vary with
distance from the center of the
propeller because the tip at radius r2
has much farther to travel than the
middle of the propeller at r1 (Figure
4). If we do the math, we can plot
the tangential velocity of the
propeller along its length (Figure 5).
A consequence of this is that the
angle of the propeller blades must
change along the length of the
propeller to have a roughly constant
thrust along its length. Look at your
propellers closely and you’ll see the
angle becomes much more shallow
towards the tip (Figure 6).
There are further complications as well that are beyond
the scope of what we want to do here. Some of the other
features you’ll observe on the propellers are designed to
direct their thrust towards the center so that the thrust is
concentrated just behind the propeller instead of in a flat
sheet. This is effectively like ducting the propeller!
Let’s consider two propellers: a 6x3 and 6x4.5. The
propellers are both 6” in diameter, but have a pitch difference
of 1.5”. The propeller with the smaller pitch will be easier to
spin through the air and will require less current flowing to
the motor to maintain a given speed. It will also produce less
turbulence and utilize the torque peak operating range of
your motor. For multi-rotors that are
designed to be aerial video platforms, we
generally use lower pitch propellers. For
multi-rotors that need high speed capability
— like racing quads — higher pitch
propellers are often used.
The bore of the propeller describes the
diameter of the hole used to mount it to
the motor (Figure 7). Many multi-rotor
propellers are cast with a pretty large bore
and come with a set of hard rubber
bushings to reduce that bore to the
common motor shaft diameters (Figure 8).
Never use a propeller with an incorrectly
sized bore. The chances of being able to
mount it so that it is centered on the axis
of rotation are virtually non-existent. That
SERVO 12.2016 47
Figure 4: At two different radii, the
same solid propeller has to travel much
different distances. The circumference
of the circles traced is linearly
proportional to the radius of the
propeller at that point.
Figure 3: Following the tips of a propeller through three
complete revolutions, we can see the spacing between each
spiral is equal to the pitch of the propeller.