"Hi, I was wondering if someone could explain to me how these P/D ratios
work. I don't understand what you measure, and what you can get from it."
"...well I use a commercial gauge from freedomflightmodels."
Shown here:
P/D is the ratio of pitch P to diameter D of a propeller. The pitch is the
nominal distance a propeller will move forward in one revolution. The idea
comes from screws. The pitch of a screw is the distance between adjacent
threads, which is the distance the screw would travel forward in a nut or wood in
one revolution. The same concept applies to springs. You are familiar with
the spiral bound notebook binding. The wire loops through a series of holes
in the edge of the paper. Every time the wire goes around once, it moves
one hole further on. The distance between holes is one pitch. This curve is
know as a helix.
With propellers we must distinguish between geometrical pitch and
aerodynamic pitch. Geometric pitch is based on the movement of a chord along a line
parallel with itself, as if it was a screw moving through a solid. The
propeller blade is like a twisted wing flying around in a tight circle. At each
point along the radius the cross section through the propeller blade is the
airfoil at that station. The chord of the airfoil is the straight line segment
joining the leading edge and the trailing edge, or some similarly defined
line. Often it is defined as the projection of the airfoil onto a straight line
that the airfoil would lie flat on. Whatever convention you accept to define
the chord line, it makes an angle with the plane of rotation of the
propeller, called the blade angle. The size of the blade angle will be different at
different distances out along the radius of the propeller. As the propeller
rotates and moves forward, the chord line moves along a helix on a cylinder.
If the chord follows a line with the same angle as the chord, it will move
forward one pitch distance in one revolution. If the chord traces a line on
the surface of the cylinder and you cut the cylinder and unroll it flat, you
will have a rectangle with height equal to the pitch and base equal to the
circumference of the cylinder, or pi times the diameter. The helical path will
flatten out to form a diagonal of the rectangle. The angle at the base is
equal to the blade angle. By relating the forward motion to the circular
motion we have found a triangle that relates the quantities. The ratio of the
height of the triangle to the base of the triangle is the tangent of the blade
angle. You can find the tangent function on most calculators, including one
on your PC. In other words, the pitch divided by pi times the diameter
equals the tangent of the blade angle. This can be turned around to say the pitch
is equal to pi times the diameter times the tangent of the blade angle. In
the general formula, the diameter is the diameter of the circle at the radius
of the airfoil in question. It also works at the tip, where the diameter is
the full diameter of the propeller. There is a close connection between
pitch and blade angle. Some authors use "pitch" to refer to the angle.
The picture shows the pitch gauge from _www.freedomflightmodels.com_
(
http://www.freedomflightmodels.com) . It uses a protractor to measure the blade
angle at a particular station along the blade radius. The pitch of the
propeller AT THAT STATION can be calculated from the radius and blade angle. To use
it, you must measure the distance from the propeller axis, the wire shaft, to
the protractor. Guestimating from the photo, it looks like the radius at
the protractor is about 2.5". The local diameter is thus 5" and the
circumference is pi times that or 15.71". The blade is resting flat on the edge of the
protractor. You can see that if the protractor read zero, the blade chord
would lie flat in the plane of rotation. The protractor shows that the blade
chord is at an angle of about 26 degrees to the plane of rotation. The
tangent of 26 degrees is 0.4877. Multiplying that by the circumference of 15.71"
gives a pitch of 7.66". This is at a 5" diameter, so the P/D is 1.532. We
can leave out the intermediate calculation of pitch and just say P/D equals
pi times the tangent of the blade angle.
A rough estimate of the P/D at the tip can be made by looking at the
triangle formed by the tip blade chord and the plane of rotation. The vertical rise
of the chord corresponds to pitch. The horizontal run corresponds to
circumference. About one third (one over pi, to be exact) of that corresponds to
diameter. So the ratio of the rise to about one third of the run is P/D. You
can usually estimate this well enough by eye to get two digits.
Depending on the twist of the propeller, the pitch could be constant along
the whole length, or it could vary. A prop with constant pitch all along the
radius is said to be helical. On a helical prop, the blade angle varies
along an arctangent curve. My measurements on an IKARA propeller showed the
blade angle varied linearly. It is a can formed blade. You can see it would fit
on a cylinder if you look at it along the right offset line. Mine is a
pretty good fit on a 4" diameter can. The pitch and P/D measured at one point
doesn't tell the whole story. It can be used as an indication of relative
pitch when twisting prop blades. When the whole blade is twisted at the root,
all blade angles change by the same amount. The pitch and P/D change by
different amounts along the radius.
When a propeller flies through the air, the chord must meet the air at a
slight attack angle. The blade does not make the same angle with the air as it
does in the helical movement described above. It follows a helix through the
air with a smaller base angle. Aerodynamic pitch is thus different from
geometric pitch.
For a given blade and motor torque, the lower pitch propeller may give
better efficiency transferring torque to thrust, but it will turn faster and run
down sooner. The higher pitch prop will run longer, but it will waste a lot
of energy. Somewhere between these two extremes is the propeller that
produces the bast combination of efficiency and running time. Finding the best
combination of motor and propeller for your airplane and ceiling height is a
matter of testing many combinations. This is why it is important to measure
things and write them down in a notebook. Keeping good notes is a foundation for
good scientific and engineering work.
Gary Hinze
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Received on Thu Feb 22 2007 - 23:07:47 CET