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Now available, a Monograph on "Critical Mach number", airfoil design with application to propellers.. only $AUD50 post paid anywhere

4th May 2014
Meredith Effect: Making Sense Of It

4th May 2014
Meredith Effect: Fact or Fiction

9th August 2013
A propeller for compressed air motors

25th May 2012
Analytic analysis of team race performance

 

Propeller Dynamics

Chapter 9: Model pylon race propellers

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The design process for pylon race propellers may be used to illustrate the material presented in the previous 8 chapters of this book. Pylon race propellers are particularly interesting because they operate at advance ratio's which are getting beyond the range at which the Betz-Prandtl-Goldstein  vortex theory is known to be reliable. Of most interest are the Madera class giant-scale racers and the international pylon racing class, F3D. It is with the latter class that the author has most experience, so we will start there.

The model characteristics in F3D are quite the reverse of those expected in a classical racer, which has the smallest possible wing consistent with landing. The FAI rules for F3D require a wingspan of 1150mm, with a section thickness at the root of 22mm. Total projected area of the flying surfaces is a minimum of 34 dm^2, with a minimum weight less fuel of 2200 g. Maximum engine capacity is 6.6cm^3, tuned pipes being permitted, but no nitro methane: they are true alky burners.

F3D model aircraft are powered gliders, pure and simple. The sink rate is so low that landing is their most hazardous manoeuvre. With a bit more section camber they would do well in F3B glider.

Their flat-plate drag is something less than 2 square inches, so that by the time you put 3 HP in the nose, these are going to be VFPG's (very fast powered gliders). Despite this low frontal area, we will see that all is not well, especially in regard to the propeller.

The problem is that the 3 HP mentioned above is produced by very low torque Schneurle-ported engines operating at 29000 RPM. With the VFPG's racing at about 200 MPH, this translates to ridiculously small propellers. Indeed, anything much over 7.5" diameter is in trouble with high Mach numbers (>.8). Also, the propeller only protrudes past the full depth of the engine cowling by about half an inch, which is not very much. More of this anon.

Also curious about the configuration of the propeller is that the pitch required is up around 8". That is, the pitch is greater than the diameter. One could say that the propeller is "over-square". This is fairly unusual for model aircraft, if one recalls for example the ubiquitous 10X6 which was the maid-of-all-work in the 1960's.

However, in modern times (1995),  F2C team race and F3A aerobatics are looking at 6x6.5's and 14x14's. Recalling the Supermarine S6B Schneider Trophy racing seaplane of Chapter 2, the pitch was nearly 20' for a diameter circa 9'. Now that's what you call over-square! The Rolls-Royce "R" engine, which was later developed into the 2300 HP "Griffon", really had something to chew on! While things are still irrelevant, note that the Supermarine Aviation company originated in WW1, originally started by Noel Pemberton-Billing. The name was adopted circa 1916, when PB sold out to his co-directors.

Clearly over-square propellers are acceptable, the question being as to what price is paid in terms of efficiency. Since airspeed is determined by pitch, and diameter by critical Mach number at the tip, the designer does not have much room to move. Nature had better be smiling.        

************************************************************

 Thus 2 possible problem areas are present in pylon race. These are:

    1. the presence of a bluff body immediately    behind the propeller, and

    2. the over-square condition of pitch-to-diameter ratio.

 ************************************************************

Be reassured reader, these are real problem areas, so tuck them away in your memory banks. But before we tackle them head on, let us examine a conundrum (a sort of riddle turning on some odd resemblance between things quite unlike: Cambridge English dictionary, 1990).

In the early days of F3D, wood 9x6 propellers cut down to 8x6 were the way to go. Times were around 1:40 and would have been better if the motors didn't keep breaking. Then composite propellers were allowed, provided they only had 2 blades (!!?). Motors improved, times went down to 1:25, and anybody under 1:20 was a God. At this point, an extra-ordinary non-event took place.

The Australian Nationals, held at Hawkesbury race-course, was favoured with some 35 hopefuls in F3D. They had the most motley collection of propellers ever to escape from Pandora's model box; from cut down woods to the latest carbon fibre specials. And here's the rub: they all went at about the same speed. Only the flying skills made the difference, and in those days going 50m past #1 pylon was all too common.

Now surely this was wrong. Surely one of those propellers could have been a standout. The conundrum is this: either all of those propellers were duds or they were all good. Believe what you like, but by a law of physics laid down Murphy-Newton, they were all duds.

Now we are getting somewhere: what was needed then was a propeller designer to step forward and save the world. At last, a place in the sun for yours truly. But the black cloud of insufficient knowledge darkened the sky, and evolution by file and Carborundum continued.

It was slowly realised that propellers with extra pitch at the tips were performing very well. Considering that some of these propellers were reworked by fliers who didn't even own pitch gauges, this was a minor miracle. However, tests using airborne telemetry confirmed the observations, the results being very positive indeed.

A typical expert's opinion on this result went something like this : "We used to put extra pitch on the woods to allow for them flattening out, so we kept on doing it with the carbon fibre props".  Or from a well known engine designer "Ah don't know about that. Ah just get more power. Someone will come up with a propeller to use it". 

Also from the dreaming, it was found that reduced pitch and chord at the root helped get the engine on the pipe. At last, 2 hypotheses that could be tested, maybe even proved. Better still, now we can hunt around for a theory to match the evidence. But now the times are down to 1:06, and the theorists are sadly in arrears. If only the theorists can get a propeller under 1:00, before the empiricists, then their honour may yet be saved.

 Return now to the present, and the bluff-body problem. The effect of the fuselage and cowling on the propeller must be determined and allowance made in the propeller design.

The effect of the bluff body is to reduce the axial free-stream velocity of the air entering the propeller disc. The reduction in axial velocity is not small: on full size aircraft the reduction at 70% radius may be by 35%, whilst even at the tip the inflow velocity may be only 90% of the free stream velocity. This is drastic. The propeller sees slowly moving air, and this is equivalent to an increase in pitch, and hence load. Furthermore, this load change varies everywhere across the propeller disc.

 To compensate for this effect, the pitch near the roots must be reduced in some average way to control both profile and induced losses. Because the cowl may be present at only one sector of the propeller disc, this average can never compensate fully for the effect of the cowl on the free-stream.

For completeness, the effect of the bluff body on the tangential and radial inflow velocities must also be analysed. The curves of the spinner and cowling induce radial and tangential components of the inflow velocity. The radial component of flow runs down the along the blade, not across it, and so does not contribute to the forces on the aerofoil.

The cowling splits the stream into left and right tangential components, which the propeller sees in turn as axial flows. However, since these flows are oppositely sensed, the effect on the airfoil is balanced and may be considered to have no nett effect.

In a previous chapter, it was noted that rising pitch was necessary to compensate for the change in zero-lift angle of propellers with radially-graded airfoil sections. The effect above is additive to this, and may be as great if not greater, depending on just how bulky is the cowling.

One may speculate that some compensation for this bluff body effect may arise if the number of propeller blades is varied. For example, a single-bladed propeller will experience a considerable arc where its performance is totally degraded. A 2-bladed propeller will experience 2 occasions during one rotation when each blade is in the cowling shadow, but in both situations at least one blade remains fully efficient. Perhaps this is better. If so, then 3-blades would be better still.

 We leave the bluff body problem here, and return to concerns about the over-square propeller. Now is a good time to re-read chapter 5, its only a page and a half, and we are going to revisit its concepts now.

The thrust produced by a propeller is equal to the increase in momentum of the air crossing the propeller disc. These are the words used by physicists: they just mean the air has been speeded up, and that this produces thrust. Any idiot knows that. The question of interest is, just how does the propeller produce this change in momentum?

If one looks at a blade, it is pretty apparent that this blade is in close interaction with the air passing over it. Indeed, the air is pushed away from the blade as a down-washed column of air; or more elegantly, as a rotating helicoidal vortex sheet.

That is OK for the air at the blade. But what about the air passing in between the blades? Well the helicoidal vortex sheet is sure as hell going to collide with it, so that this air becomes entrained and is pushed rearward along with the rest of the slipstream. In this process, the entrained air gains in velocity and so contributes its share to the total change in momentum, and hence to thrust.

Now a propeller is most efficient when all the air in the slipstream has much the same axial velocity. If the entrained air has a lower velocity than that downwashed at the blade surface, then efficiency is lost. This is indeed the case, and for some crazy long-forgotten reason the loss in efficiency is called "tip-loss". This has nothing whatsoever to do with tip vortices, so do not be mislead.

The ability of the downwashed air to entrain the free-stream air between the blades is an important consideration in propeller design. Prandtl, and later Goldstein, developed an expression to account for this entrainment. It was found to be a function of the advance per revolution, the radial distance along the blade and the number of blades. The higher the advance ratio, the closer to the tip and the fewer the blades, the weaker the entrainment.

One can picture these processes by means of the Archimedian screw (like a deeply cut wood-screw). The more closely set the screw teeth, the more closely they interact with the fluid between the teeth. At low advance ratios, the helicoidal vortex sheets are close together and the entrained air strongly impressed into movement.

The same goes for the number of blades. The more blades, the more helicoidal vortex sheets and the closer they are together. This is the reason that induced losses fall as the number of blades is increased.

Return now to F3D pylon propellers. These operate at high advance ratios (high is anything greater than .5) and the vortex sheets are a long way apart. Since the entrainment effect reduces radially toward the tip, the ability of the blade to transfer momentum is lessened: the loss in thrust is then called "tip loss", although a more inappropriate term would be harder to find.

Indeed, some authors totally ignore the entrainment effect, and correct for it later in their theories as an effective reduction in diameter. N.A.V. Piercy gives an interesting expression which is worth noting here:

 

 De/D = 1 - 1.386*J/(B*sqr(PI^2+J^2))

         where De = effective diameter

 D  = actual diameter

 J  = advance ratio

 B  = number of blades

 PI = 3.14159

  For an F3D model, J is not too different from unity. The change in effective diameter going from 2 to 3 blades is then about 8%, which is a pretty handy number to have up your sleeve when you've already got sonic tip problems.

The point to be made here is that over-square propellers reflect high advance ratios, with the concomitant drop in efficiency associated with the so-called "tip losses". Piercy makes the telling point that the profile loss arising from the narrow chords of a 3-bladed propeller may be less than half the gain in induced efficiency resulting from the effective increase in diameter.

One wonders if the Supermarine S6B would have done better with 3 blades, considering its ridiculously high advance ratio. Indeed, its contemporary, the Macchi M-67 had 3, but was in 1929 defeated by engine trouble. The even more impressive Macchi-Castoldi MC-72 had 4 blades, but these were in contra-rotating pairs. I guess any air sneaking past the front 2 blades had it coming from the rear 2: that 1932 world airspeed record of 440 MPH didn't just come from the 3100 HP Fiat engine. Also, 8-blade propeller units on the TU-95 Bear, with their vast pitch, make a lot of sense when you analyse them this way.  

 

Collecting the foregoing facts for F3D, it would appear that a case exists for the use of 3-bladed propellers. Such a propeller would require a unique pitch and chord distribution, especially near the roots. To provide the same power absorption as a 2-blade propeller, the mean chord must be reduced by 30%. This is a long skinny blade, which could run into structural and Reynolds number problems. The former is a technicality, but Reynolds number must always be taken seriously in any analysis.

F3D props typically run a Reynolds number around 200000 at the 70% station; this will fall to 130000 for a 3-blader, a value at which airfoil performance is somewhat degraded. Inboard of this, the numbers become worse until at the hub they are bad. The result is a fall in profile efficiency; however, taking into account the hoped-for increase in induced efficiency, this is by no means disastrous. The bluff body effect on the root section will be far worse, with the blade angle lucky to be optimum for 70% of the rotation arc.

The situation at the tip is rather different. Even though the Reynolds number is low, it may be irrelevant. The section lift and drag characteristics at transonic speeds are dominated by compressibility effects; they become functions of the thickness-to-chord ratio, rather than just the chord alone. In the absence of low Reynolds number, high Mach number, data, one must speculate.

An analogy may be drawn between flow at transonic speeds and the flow in a pressurised wind tunnel. In the latter, Reynolds numbers are increased as a result of the high pressure in the tunnel. In model testing, this is a useful expedient if one wishes to keep the Mach number constant. Unfortunately, the effect of compressibility is the same as low Reynolds numbers, delaying flow separation and yielding high drag on separation (NASA Oshkosh 1995).

Whatever, the amount of lift from a given section at a given angle of attack increases, this being a favourable compressibility phenomenon. More power may be pumped into the propeller without increasing the diameter, thus avoiding a premature entry into the compressibility stall.

At the tip, Reynolds number effects may reasonably be neglected, with due care being taken in airfoil selection. The concept of a 3-bladed F3D propeller consequently survives as a worthwhile concept. So what does this 3-bladed propeller look like now?

Well, its a pretty ratty old piece of hardware. Geometrically, the pitch and chord are low at the root, both rising toward the tip. Along a blade length of about 3", the inboard 1" is more or less useless, serving mainly to join the tip to the crankshaft. The next 1" has bad Reynolds numbers and moderate bluff-body effects; however, the induced efficiency is not too bad, giving strong entrainment and perhaps even a modicum of thrust.

The final 1" seems to be where it all happens. Entrainment is weaker, but not as bad as a 2-blader. Thrust is good as a result of compressibility, and the bluff-body losses are the least of any station along the blade.

This prop looks more and more like a bumble-bee's wings. This cheerful aviator gains lift by sweeping its wings fore and aft, thus shedding vortex rings on which it suspends itself in space. On a frame of reference fixed to the airframe, it is hard to avoid the mental picture of a donut shaped vortex ring sitting on the arc of that last inch of the F3D propeller.

As with the bumble bee, it never pays in propeller analysis to accept the intuitively obvious. If one did, then the poor bumble bee would be walking. Assume now that everything discussed so far is at least half true.

The evidence relating to pitch at the tip is "the more the better". Fast props have high pitch at the tips. Could it be that the tip loss effect is in someway mitigated by the compressibility found at the tips? That is, that the momentum transfer to the entrained air between the blades is better than that predicted by Prandtl. If so, then the requirement for constant slip may also be met by wider tip sections, rather than just more pitch. Now what did that prop of Maxim's look like again?

 

 

This leaves the analysis of the Madera class pylon racers open for discussion. Clearly, all that said earlier for F3D applies to this class, as the laws are quite general.

However, the option of 3 blades may not be available, especially for the Formula 1 class. The power loadings are just not high enough to yield a practical 3-blader. Thus induced efficiency gains may not be available, other than by the conventional process of optimising radial chord distribution and blade angle.

This leads back to the bluff-body problem, which in the case of scale model racers is sure to be severe. It must be bad enough on the full size Formula 1's.   

E.R. Jones has provided a quantitated approach to the bluff-body situation in PDAP, his propeller design and analysis suite. As mentioned previously, this provides an averaged correction to the axial inflow velocity, which is substantial and cannot be neglected. Jones' data for a Cessna 140 spinner and cowling appear at first glance quite radical.

The axial fraction of free-stream velocity at the 20% station is 23%. At 50% it is 59% and at the tip still only 90%. No wonder Hamilton Standard don't lose too much sleep over their round-shanked variable pitch propeller blades. These figures may even flatter the inflow to the Madera and F3D classes, at least at some points in the propeller arc. The corresponding required reductions in pitch are large indeed.

Due to the roughly axially-symmetric disposition of the spinner and cowling on most Madera F1's, plus their sheer bulk, the method of Jones for inflow correction looks to be promising. If no allowance is made in the propeller design for the presence of the cowl bluff-body, then propeller efficiencies fall to around 65% or less. With the Jones correction applied, this improves quite markedly to be in the 75-80% class. The improved propeller has reduced pitch at the root, and a slightly increased chord.

Consider F3D in more detail. With a single cylinder cowl, there is considerable asymmetry, which in consequence will limit the accuracy of Jones' method ( which works best for an axially symmetric body). Neglecting this, a reasonable figure for the equivalent F3D cowl/spinner is a circular body of cross-section 3.5 sq.in., with a 1.75" spinner. Then the axial fraction of the free-stream velocity at the 20% station is 73%, at 50 % it is 94% and at the tip 99%. These figures apply at an airspeed of 190 MPH.

The corresponding pitch reduction adjacent to the spinner is about .5", reducing very rapidly to negligible proportions at the 50 % station. It must be doubted as to whether this is meaningful. In respect of small racing aircraft, Larrabee has even suggested that the pitch at the root be increased by 5%, the increase blending out after 1.5 spinner diameters. The reason appears to be to compensate for the increase in velocity along the streamlines tangential to the spinner.

Diagrams in this chapter show the flow streamlines and velocity profile for a "typical" F3D propeller. The low speed diagrams illustrate the loss of thrust due to radial flow arising the near static freestream inflow. The stream tube is narrowed, so that a small volume of air is accelerated to high speed, resulting in wasted power. At 190 MPH, by contrast, the radial flows are negligible, while the axial inflow variations arise from the presence of the spinner and cowling bluff-bodies. Correctly modelled propeller pitch distributions can largely eliminate losses due to this effect.

 

Further reading:

Jones E.R.,1994. "Propeller Design and Analysis Program (PDAP)". Published by E.R.Jones Engineering, 98 South Halifax Drive, Ormond Beach, Fl 32176-6539, USA.

Duval,G.R.,1977. "World float planes". Published by D. Bradford Barton Ltd., Trethellen House, Truro, Cornwall, England.

Rubbra,A.A.,1990. "Rolls-Royce Piston Aero Engines". Rolls-Royce Heritage Trust, PO Box 31, Derby, England.

Gunston,W.T.,1976. "Night Fighters". Patrick-Stephens Ltd., Bar Hill, Cambridge, CB3 8EL, England.          

 Larrabee,E.E.,1977. "Analytic design of propellers having minimum induced loss". National Free-Flight Symposium, 1977.

Errata for the book