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 Propeller Dynamics Essential reading for model aircraft contest fliers. This is the only book on the market explaining propeller theory in non-mathematical terms. A rattling good read, I know, I wrote it. Read more...

## Fluid Dynamics Part 5: Propeller inflow field

By Joe Supercool

OK, here we are back in the Fluid Dynamics topic. But this time we will do something useful. Yup, we will apply it to a central problem in propeller design. And about time too! We will have a look at how the rubbish trailing along behind the propeller (like engine, wing, fuselage, pilot etc) affects the design of the propeller.

The key design parameters for propellers are diameter, RPM,engine power and airspeed into the prop disc. You might think this latter quantity, the velocity of flow into the prop disc,is just the airspeed. Well, it is and it isn’t. You see,the prop is really only interested in the axial component of airspeed, not the flow pushed out radially by the cowl and fuselage. It turns out that this axial component is slower than the airspeed, which means that we need less pitch than we might otherwise have thought. In fact, it can be quite a lot less if we have a big fat radial engine getting in the way.

So now we will find a way to calculate the axial flow as a function of the distance out along the prop.

Fluid Dynamics provides a method to follow. Here is the bit I like. The method is so good that we don’t need to do measurements to validate the calculations! Now that is a big claim! But unless you can think of some way to measure the flow field around an engine cowl, we might as well go with it. My attention was drawn to this method by E.R.Jones.Here is what he said. “The calculation is approximate, but is sufficiently accurate for its intended use..it has the added advantage of visualising the flow around the nose of the aircraft, and therefore permits a better understanding ofjust what is happening there.” Along with some illustrations and equations, he makes this aside. “For more information, the reader may consult any fluid dynamic textbook”

Well, let me tell you, that is not so easy as it sounds.I will skip the maths this time, and put it in a later document, which should please my usual readers!

Here is the method. Recall from the analysis we did of wind blowing over a hill, that we could model the shape of a ridge by finding the streamlines of airflow over the ridge. To do that, we introduced the idea of flow from a uniform stream and from a point source of airflow. This time, we will do that again, but this time we will try to get the shape of an aircraft fuselage.

We will need to have new equations, for this situation is 3 dimensional, not like the ridge, which is 2 dimensional. Also, we will only model aircraft with radial engines, like the Sea Fury, Wildcat, FW190 etc. These aircraft have fuselage shapes we call axisymmetric, which means they are near enough to round to make the maths easier.

Instead of using point sources of flow, we will use long, thin sources placed on the aircraft axis. We will use one line source each for the spinner, cowl, rear cowl and fuselage. We can adjust the strength and length of each of these line sources in the hope of getting a shape close to our chosen aircraft.

With that done, we find we have the streamlines around the fuselage and the axial velocities at the prop disc, which is just what we wanted to start with.

Here is what we get. With a little imagination, the spinner, radial cowl and rear fuselage are present. Near enough, anyway.

Notice the quantity Vratio. At 15 cm from the axis of rotation, the axial velocity is only 84% of the airspeed. That is a serious matter for the design of the prop in that region. Likewise as we move out toward the prop tip.

So there you have it. The radial distribution of pitch needs to be adjusted to suit the cowling design. Following this principle, I designed a prop for the 20cc AT6 class. This prop was so good, winning 6 Adelaide races in a row, that it has now been banned in favour of a poorer, weaker, imported prop. Good for the importers, I guess. C’est la vie.