| 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 |
