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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.

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Doppler Wind Correction.

28th Jan 2005

This is a topic I have been avoiding for some time, but it's the Western Australian Summer now and wind is unavoidable. Never been to WA? Well its home to the biggest Kangaroo ticks I have ever seen, and supposedly Perth is the third windiest city in the world (after Auckland and Chicago).

These ticks are no joke. Unlike the lethal and lethargic blue-bottle ticks of New South Wales, these ones won't kill you or your pets. But in the months of October and November they are very active and aggressive, and can run quite fast. Up your leg in a flash, they can latch on anywhere: I do mean 'latch'. Their mouthparts include a pair of massive hooks that remain in the flesh even after the body is torn away. This leaves an itchy spot; which is annoying for months afterward.

I tried killing them insitu with kerosene. They died alright, but didn't release their grip. Now I cut them out with a modelling knife. I poke the knife in about 4mm below the head and slice up toward the head. Usually this cut releases the hooks, but if not a second incision will get them free. The wound heals quickly, there being no itchy spot afterward. No pain either, as the tick injects its own anaesthetic so you won't notice its presence.

Unfortunately, wind is not so easily dealt with; Perth has 3 periods of strong winds. There are the August/September gales in Winter/ Spring, usually occurring on F/F days at Meckering. The Summer wind pattern comprises strong, hot, morning Easterly's, followed by a lull of about one hour at noon, then a strong South-Easterly rips in. This latter is affectionately known as the 'Fremantle Doctor'; affectionately, as it is a cool wind which drops the noon temperature from 38 down to about 29 in a few minutes. If the Doctor doesn't come in, then we here in Perth are in for a hot, sweltering night. The 3rd period of wind is everything else.

As it happens, most of our F3D flying is coincidental with the Fremantle Doctor. At our local field (KAMS), the sport fliers and glider guys pack it in at noon, leaving the field free for some noise and speed. By the time Mark has his Phelan F3D gear ready to roll, the wind is in at 20 to 30 kph (at ground level).

There are 2 phases for testing F3D props. The first is to see if the prop lets the motor get up on pipe; the second is to see if the prop allows the engine to develop full power in the air. This latter implies that one must know the in-flight RPM, and, hopefully, also the airspeed. The Doppler method permits RPM and airspeed to be known, but one must be careful to apply the correct correction for height and wind. I have covered this method previously, so you may like to divert to www.supercoolprops.com at this point for a refresher course on Doppler measurement.

Briefly, one places a tape recorder outside the course, well up past number one pylon. In this position, there is a point between pylons 3 and 1 when the model is flying directly at the tape recorder, a second point lying between 1 and 2 when the model is flying directly away from the tape recorder. Using a computer program called 'Spectrogram', one can readily determine the frequencies of the sound emitted by the model at these 2 points; the frequencies are designated 'Fcoming' and 'Fgoing'. They are readily noted, as the frequency 'Fcoming' is the highest value of frequency visible on the Spectrogram, while 'Fgoing' is the lowest (for a given harmonic).


Click to enlarge

The magic part of all this is that these 2 frequencies tell us the RPM and airspeed in the straights! No in-flight telemetry, no extra weight: indeed, something for nothing! How often does that happen!

Unfortunately, sound is carried by the wind. This affects the perceived values of 'Fcoming' and 'Fgoing'. In the case of F3D, we locate pylon number 1 upwind, so that we may launch the model into the wind.

When flying into the wind, from pylon 3 to 1, 'Fcoming' is reduced below the value for no wind. Similarly, flying from 1 to 3, 'Fgoing' is also reduced. Remember, this is for the tape recorder placed upwind past #1 pylon .

First consider the Doppler equations for still air (no wind). With F the number of revs per second, V the speed of sound in m/s and Vs the speed of the model, also in m/s, the still air equations are:

Fcoming = V * F /(V-Vs)
Fgoing = V * F /(V+Vs)

Before we can use these Doppler equations to yield RPM and airspeed, the wind-distorted values of 'Fcoming' and 'Fgoing' which we observe must be fitted in to these equations.


Click to enlarge

If the speed of the airplane is Vs in still air, then downwind its speed is Vs + w, and upwind its speed is Vs w, where w is the wind-speed in m/s. This is an approximation, since the model may not be flying exactly upwind or downwind, but its good enough.

Further, the speed of sound is reduced to the value V-w, since it has to travel upwind to the tape recorder.

Substituting these values in the Doppler equations and solving for Vs, the still air speed of the model, we get:

Vs = V * (Fcoming Fgoing) / (Fcoming + Fgoing)

This is a surprising result, as the wind-speed 'w' is not there! So the result holds, irrespective of the wind speed! I guess we don't need the anemometer after all!

But we still want the RPM. Substituting Vs w for Vs and W w for the speed of sound in our equation for Fcoming yields:

F = Fcoming * (V Vs) / (V w)

Oops, 'w' is back in our equation; we still need the anemometer! So the RPM determination depends on wind speed. That is not real nice. The problem is that the anemometer reading at ground level can be quite a lot less than the wind-speed at 30m height, but I guess we are stuck with that.

Now to do a worked example. Let us take the following values measured in windy conditions:

Fcoming = 685 Hz
Fgoing = 410 Hz
W = 340 m/s velocity of sound
'w' = 9 m/s wind speed

then Vs = 340 * (685 410) / ( 685 + 410) = 85.4 m/s = 307.5 kph

and F = 685 * (340 85.4) / (340 9) = 526.9 m/s = 31600 RPM

The still air airspeed of the model is 307.5 kph, while the engine RPM is 31600.

How does this compare with World Class F3D models? After the last World Champs at Melnik (2003) in the Czech Republic, the duel between Chris Callow and Robert Bosch continued the following week at Tours, or more correctly, St Martin Le Beau, a village some 20 minutes train journey out of Tours. It's a beautiful spot for camping, right on the river Ther. La Grappe D'Or is a caravan park only a few hundred meters from the flying field, right on the river, and an easy walk via the Gypsy camp. In the morning, we were surprised to find mounds of dirt outside our tent, like little volcanoes, had appeared during the night. The culprits are Moles!!

Come the final, conditions were perfect for Doppler. I could position myself 200m past #1 pylon, there being no wind. These guys fly low, so there was no height correction either. Robert was doing 325 kph at 33000, while Chris ran an identical 325 kph at 31600. Robert sprays around a bit, while Chris might as well be running on steel tracks, so it was easy to identify the pilots on the Spectrogram trace.

Those speeds are good for sub-60 times, so that is the target. Mark's speed above is not height corrected. He was up around 30m, so a correction of 5% would see him at 323 kph, not a bad start!

Lets hope I have my algebra right on this one. A.E.E McKenzie's book, 'Sound', is a little hard to follow on this topic.

Download WINF3D.BAS and WINF3D.EXE

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