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I originally became interested in
PSS because it offered a way to fly models of jet fighters
without the expense, noise and complexity of ducted fans. My
normal flying site is Ivinghoe Beacon, the contours of which
are very good for the South of England but unfortunately it's
only about half the size of an equivalent Northern venue, so
PSS models need to be relatively light to fly well there
unless the wind is 15 mph+.
As a result, I've become
particularly interested in the aerodynamics of swept-wing
aircraft. Ideally, I'd like to be able to come up with an
achievable wing design and wing loading combination that will
enable a PSS jet to fly at least adequately in
"average" wind conditions; unfortunately, as with
most things aerodynamic, it's not that simple.
Arguing
with the Laws of Physics...
At the risk of stating the obvious,
many slope-soaring gliders have relatively high aspect-ratio
(AR) wings; as most people will be aware, long thin wings
produce less drag than short fat wings when generating lift,
because the tip vortices are smaller. Hauling the stick back
too hard with a Middle Phase will produce a tight loop, try
the same thing on a delta, and it will probably mush and lose
speed. Most of this effect is due to the much lower aspect
ratio of the delta, although it will be more sensitive to drag
changes because the wing loading will probably be lower (of
which more later).
As if this wasn't enough, another
fairly distressing effect starts to come into play at lower
aspect ratios - just the sort of aspect ratio that typical PSS
models use, in fact. As the aspect ratio falls to values that
any self-respecting jet fighter would regard as normal, the
maximum lift attainable by the wing is subject to an
increasing penalty. At an AR of around 5, only 70% of the
theoretical maximum lift is available, and at an AR of 3 the
value drops to 65%. What's happening as the aspect ratio
reduces is that the tip vortices are taking proportionally
more of the available wing span and interfering with more of
the normal flow over the airfoil, and the vortices are also
getting bigger as the wing chord increases.
What all of this means is that if
you have a low-aspect ratio airframe it will be a lot less
efficient than a typical sport model, and will not be able to
fly as close to the top of the slope lift band where the lift
is weak. A very low AR airframe might have its lift-generation
capacity reduced to such an extent that it might be difficult
to keep it above the slope lip, and in extreme cases it may be
incapable of sustaining flight and will proceed to the bottom
of the hill in an orderly manner.
Just to add insult to injury, a
swept wing is more prone to tip stalling than an otherwise
identical conventional wing, particularly if it is highly
tapered, although steps can be taken to reduce or sometimes
eliminate this effect. Washout is an obvious solution (of
which more later), and correctly placed wing fences can
transform a model from something you have to be quite careful
with to a complete pussycat - the Conway/Griffiths Hawk being
a case in point.
Finally, as aspect ratio reduces,
the average wing chord has to increase for the wing area to
stay the same. This can provide some benefits, but it
unfortunately means that the pitching moment increases by a
proportional amount, requiring a larger stabilizer or a larger
stabilizer trim angle to counteract it.
Surely
there must be some Good News?
Well, there is - that's the end of
most of the bad news! Seriously, it's not all doom and gloom
as there are some things working in our favour.
Size
Matters
A low aspect-ratio wing will be
operating at a higher Reynolds number (Re) as a result of the
bigger wing chord; if you halve the aspect ratio for a given
area, the wing chord and therefore the Re will increase by a
factor of about 1.4. At the sort of Reynolds numbers we’re
using, the efficiency gain from operating at a higher Re can
be well worth having. Figure 1 shows the relative drag of two
wings with the same wing area, carrying the same weight, one
with an AR of 3.1 and the other with an AR of 6.2. What this
shows is that low AR wings may operate in a more efficient Re
regime, and that with some wing sections a light model may not
fly as well as a heavier one.
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Figure 1  |
Wing
Design
It is possible to minimise the
efficiency loss inherent in a low aspect-ratio wing by
designing it to have as high a speed range as possible. By
using a more cambered tip section that has a slightly wider
useable lift range than the root section and applying
geometric washout to compensate for the fact that the higher
cambered section stalls slightly earlier, it is possible to
get the best of both worlds (to some extent). For instance,
E374 has 12.5 degrees alpha between zero and max lift, whilst
SD 7032 has about 13.7 degrees between the same points but
stalls about 1.3 degrees earlier. Using E374 at the root and
SD7032 at the tip with 1.3 degrees washout (and maybe a little
more to be on the safe side) will give a wing with reasonable
stalling behaviour, good efficiency at low speed when close to
maximum lift, and good performance at high speed (low lift)
because the whole wing reaches zero lift at just about the
same angle of attack. If the wing is swept, additional washout
or wing fences will be required to compensate for a tendency
to tip stall.
Trim
Drag
A conventional airframe will
generally require some load to be generated by the tail in
order to balance the lift generated by the wing and the weight
of the airframe. Ideally this load should be as small as
possible because any upward or downward lift produced by the
tail - which is a lot smaller than the wing and operating at a
lower Re - will generate tip vortices and therefore induced
drag. A tailless aircraft can achieve balance by sweeping the
wings back and applying washout at the tips to balance the
airframe weight.
As previously discussed, a swept
wing will normally require washout to control the tip stall
and, fortuitously, this will reduce the amount of lift (and
therefore drag) generated by the stabilizer, possibly to a
very low value. It will usually require some experimentation
to arrive at a suitable centre of gravity position, but very
good results are possible with this set-up; experience
suggests that 30% of the mean aerodynamic chord is a good
starting point.
Recommendations
Wing
Section
A lifty section will counteract the
loss in lift caused by very low aspect ratio to some extent,
but many jets have quite thin wings (circa 6%) so a
"normal" wing section might not look right.
Here are some candidates:
Gottingen
795 has been used successfully thinned to 8% with 2.5%
camber (with no washout) on Steve Griffiths' Saunders-Roe
SR.53 at about 10 oz/sq ft. High speed performance was very
good and the low speed performance was described as
"perfectly acceptable".
Eppler
374 is a very common PSS section as it has a good speed
range, and has been used on a wide variety of models (F-86,
MiG 15, Hawk, Tornado, etc.). Its maximum lift capability is
not quite as high as more cambered sections such as S3021, and
it seems to perform best at wing loadings of at least 12 oz/sq
ft. E374 also seems to work well when thinned to 6% whilst
retaining the original 2.24% camber. Andy Conway uses a 6.5%
E374 on his Su-27 and 5% E374 on his Skyhawk. It's not as good
as some of the more modern sections (e.g. S3021) at low Re,
but it does have a low pitching moment so the tailplane has
less work to do.
Selig
3021 has been used on straight-wing jets and is a good
choice if a wide speed range is appropriate, it seems to be a
very good compromise between high and low speed performance,
has enough camber to deal with quite high wing loadings, and
is better than average at low Re. I understand it requires
accurate building to give of its best, particularly in area of
the leading edge profile. S3021 thinned and de-cambered to 8 /
2.5% might be a profitable area for experimentation…
Twist
It is perfectly possible to fly a
swept-wing PSS model with no washout, particularly on BIG
slopes where the model is naturally flown fast. At more
genteel venues, it is highly likely that a sharp tendency to
drop a wing will be uncovered - particularly in gusty
conditions - as it will be flown closer to the stall. A
working rudder can be used but given my limited piloting
skills I've never been able to catch the wing-drop before it
reaches 90 degrees of bank. One and a half to two degrees of
washout on a wing with 35 degrees of sweep will probably do
little harm to the overall performance, but will make piloting
a much more relaxing experience.
Wing
Loading
If you’re lucky enough to fly from
a big slope, this section will probably be of no more than
academic interest. Those of us not blessed with such
facilities are obliged to build light and hope for good
weather.
As aspect ratio decreases, the
available lift will decrease so a lighter wing loading will be
required to fly in the same conditions. It's rare to find a
slope that won't support a PSS model in wind speeds of 15
mph+, but many slopes are more challenging in the lighter
conditions (8 to 12 mph) that seem to prevail whenever I turn
up.
As a general guide for less
well-endowed slopes and average conditions, I suspect that
10-11 oz/sq ft is probably about right for an AR of around 3,
and an AR of 5 will probably be O.K. up to 14-15 oz/sq ft if
the wing section is reasonably lifty. Wing loadings of more
than about 15 oz/sq ft on low aspect-ratio subjects are, I
suggest, to be avoided unless the height of your slope is
measured in thousands rather than hundreds of feet. Or unless
you're prepared to consider ducted fans....
Visit Andy's own website for
details of his models and more on design...
www.voyager.zen.co.uk
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