Response to DougS,
Thank
you for your comments. I will attempt to respond to them as best I can.
Sometimes simple assertions can contain ambiguities and misconceptions
that are tedious to sort out. Careful analysis and adequate
explanations of technical issues can be time consuming, so I apologize
for the length of some of my responses.
"...you
often talk about a tilted VAWT with short blades compared to diameter
being able to intercept more area than if it were flat, as though it is
unique and as though it has no downsides."
I
don't know if it is unique, and I have never assumed or said that
tilting VAWT have no downsides. I tilted my VAWT as a form of overspeed
control way back in 1978. I only proposed tilting to increase the power
after the Delft wind tunnel test showed that an ordinary H-VAWT could
increase its power 35% by tipping 25 degrees into the wind. If you know
of someone who proposed tilting a VAWT to increase the power before
Delft, please tell me. As for the downsides of that technique, there
are downsides to most techniques. As you know, engineering usually
requires a great many compromises. I assume that my readers are
sophisticated enough to know that.
"Increasing
swept area by tilting it may be true, but this configuration would
still be judged and rated on its intercepted area when tilted."
At
first glance, your assertion seems like a simple and sensible solution
to the problem of measuring the swept area of tilted VAWT. But it isn’t
workable.
For
example, I use tipping (or swinging away) as an overspeed control
technique. The VAWT starts in a vertical position. As the wind speed
increases, the tilt angle increases. At first the power increases due
to tipping and then it decreases, which provides overspeed control. The
tilt angle varies with the wind speed. The tilt angle also varies with
the tip speed ratio because a lower TSR means a lower rotor drag, and
rotor drag is what determines the angle of tipping (or swinging away
from the wind). So what is the swept area?
Here is another complication: Placing a VAWT upright on top of the edge
of a building or at the top of hill can produce the same effect as
tilting, without tilting the VAWT at all, because the airflow is
tilted, not the VAWT. So what then is the swept area of the VAWT? Does
it change as the angle of the wind changes? If so, then there is no
standard way to measure the swept area.
If
you wish to insist that the intercepted area must be that which the
wind “sees”, then all wind turbines should be measured the same way in
order to maintain consistency. But since the direction of the wind is
always shifting from side to side and up and down, the swept area of
any wind turbine, as seen from the perspective of the wind, is
constantly changing. So your technique leads to the conclusion that all
wind turbines have a variable swept area. In fact, they all do, except
perhaps in a wind tunnel. But then the calculation of the Cp curve must
take that constantly changing swept area into account. But how, given
that the angle of the wind is variable and unpredictable? The measuring
of the swept area becomes almost impossibly complex.
From
a scientific perspective, it makes sense to simplify the definition of
the swept area -- to ignore the fluctuations in the angle of the wind
and to assume that the swept area is the same as usual, with the wind
flow at a right angle to the rotor. Similarly, it makes sense to ignore
the tilt angle of the rotor, which in some cases is constantly
changing, and to simply use the original swept area for the
calculations of the Cp curve. The purpose of the Cp curve and the power
curve is to allow different wind turbines to be compared.
From a scientific perspective, the matter is simple to resolve: Use the
original swept area as conventionally measured, and designate the
performance curve as the “equivalent coefficient of performance (Cpe)”
to make clear that the VAWT used tipping. It would also be informative
to mark the power curve by designating each 5 degrees of tipping.
If
you are still not convinced, then consider the effect of using your
technique when measuring the performance of a SuperTurbine®. Since your
rotors are pre-tilted, their swept area would be only what the wind
“sees” from its perspective. That would give the multiple rotors about
a 20% smaller swept area than when measured conventionally from a
position directly in front of the rotors, and it would inflate the
calculated Cp accordingly. That would make a SuperTurbine® seem much
more efficient than it actually is. That would make for a great sales
pitch. But do you still favor your method of measuring the swept area?
When a HAWT rotor is tilted to the wind, the swept area and power go down. When a VAWT with an initially rectangular swept area is tilted to the wind, the swept area and power go up at first and eventually go down as tipping angle increases further.
That’s just basic solid-geometry and basic physics. It is an inherent
advantage of VAWT over HAWT. It is not some phony partisan attempt to
inflate the value of VAWT. It’s just a fact.
“The factors you do not mention:
Twice
the tip-losses because each "short" blade has two ends (two sources of
tip-losses), and that becomes more important because of the short
blades, and”
First, some preliminary comments:
As
you know, the inner end of HAWT blades produce very little lift and
thrust because they typically have a solidity ratio that is far too low
for their very low TSR. So the inner end of HAWT blades are close to
useless. However, despite that disadvantage, the outer blade tips can
move fast enough, and sweep a much larger area, so that compensates --
because lift is proportional to the square of the air speed.
VAWT blades are analogous to airplane wings (especially glider wings),
which have two blade tips. Both large airplanes and small airplanes can
use wings with a high aspect ratio. Tip losses are minimized by using a
high aspect ratio wing (blade), plus tip vanes or tapered tips. The
whole wing (blade) moves at the same speed. Airplanes move upwind,
downwind, and cross-wind, as do VAWT blades.
The
average air speed of the blades of H-rotor VAWT and 3-bladed HAWT are
about the same (3 to 3.5). But HAWT blades are more efficient due to
the higher TSR of the blade tips. But some VAWT blades (that pitch) are
potentially more powerful because they sweep the swept area twice each
revolution, and because the rotor can be tipped, plus additional
advantages.
Now
to your comment: You seem to be saying that the way you would design a
very wide VAWT is to use the same three blades of a tall VAWT, but
greatly reduce only their span, and not their chord. The result would
be blades with an aspect ratio of something like 2 or less. So the
blades would suffer enormously from tip losses. If that is what you are
saying, then you would be correct. But what is not clear is why you are
saying that. No aerodynamicist would design a VAWT like that.
Consequently, your supposedly omitted “factor” is a non-problem. So why
would you expect me to mention a non-problem as if it were a real
problem?
If
a VAWT is made very wide, instead of tall, it will require many small
blades in order to maintain a reasonable blade-aspect-ratio and an
adequate solidity ratio. Those blades will have both a shorter span and
a shorter chord. But the blade-aspect-ratio could still be 10 or more
to minimize tip losses. Tip vanes (or shaping the tips) could also be
used to further reduce tip losses, as is often done for airplanes and
VAWT. So tip losses need not be an issue for a very wide VAWT.
Please
note carefully: The biggest problem for a very wide VAWT is not tip
losses. It is that the many-more smaller-blades would have a
substantially lower Reynolds number. They would not be as efficient as
much larger blades of a tall VAWT.
However,
because the VAWT is very wide, a relatively small amount of tipping can
expose a large percentage of the downwind blade pass to clean air,
while also reducing the back pressure on the upwind blade pass. So the
gains could be much larger than the losses. The gains should still
equal, or exceed, the 35% increase in power achieved by a Delft wind
tunnel model with a more squared swept area.
Since
you apparently assume that it is not possible to design a practical,
wide VAWT, here is a brief description of one of many ways to design
one that tilts to increase its swept area:
Use
a very large-diameter, narrow, horizontal ring. Place a vertical shaft
at the center of the ring. Use 3 spokes (cords or wires) from the ring
to the top of the shaft, and 3 spokes to the bottom of the shaft. That
creates the rough equivalent of a bicycle wheel shape with a wide hub
section. Suspend the top of the shaft from an overhead cable using a
long enough cord and a swivel bearing. Many such VAWT could be
suspended from the same overhead cable strung between two guyed towers.
Mount
many Sharp Cycloturbine blade-units around the circumference of the
ring to achieve a solidity ratio of 0.2. Use a blade aspect ratio
between 6 and 10, and add tip plates. Mount 3 RATs on the ring and
space them 120 degrees apart.
Add
a weight to the bottom of the shaft to control the rate at which the
suspended VAWT swings away from the wind. Add an electrical cord and
slip rings at the bottom of the shaft, and extend the electrical cords
to the ground. Leave a lot of slack to allow the VAWT to swing in any
direction. If the wind becomes too strong, the VAWT swings farther away
from the wind and disrupts the pitch control to limit the power and the
rpm. Additional refinements can be added if necessary. This VAWT has
some downsides, but it would be cheap and efficient.
Each
RAT would move at 3 to 4 times the wind speed. So it would produce the
equivalent of roughly 27 to 64 stationary rotors of the same size. The
RAT generators would spin 3 to 4 times as fast as stationary
generators, so they could be much smaller and cheaper. A more
sophisticated version of this VAWT, if necessary, would use two
concentric rings rotating in opposite directions to cancel any
gyroscopic effects. Other refinements are possible.
The
main problems with this very wide VAWT are RAT rotor noise and bearing
wear. Both can be solved reasonably well. Rotor noise can be reduced
using higher solidity RAT rotors with a ring around the blade tips.
Bearing wear can be reduced by using magnetic bearings or concentric
bearings (one inside of the other to reduce the rpm of each).
“2)
You could remove the blades of any such vertical-axis turbine and throw
them in the dumpster, then apply airfoils to the arms that held the
blades, turn the whole thing 90 degrees, and make more power than the
original vertical-axis machine. V-A machines have quite a
history: They seldom, if ever, work out, for many very good reasons,
most of which I'm pretty sure you are aware of, but maybe tend to
overlook when promoting V-A machines..”
You
might be surprised to know that I consider most VAWT to be inherently
flawed or handicapped when compared to the Sharp Cycloturbine. Please
note carefully: The main problems with most VAWT are that they allow
blade stall and they produce a narrow and sharply peaked Cp curve. So
they are not nearly as good as they could be at capturing the large
amount of energy in wind gusts. When a gust hits, they lose a lot of
that energy. But according to my informal observations and the hundreds
of research papers I have read, the Sharp Cycloturbine should be able
to capture most of the additional energy in wind gusts because the
blades don’t stall, they react quickly to changes in the velocity of
their apparent wind, and the torque curve is very wide. So when I refer
to VAWT, I usually have the Sharp Cycloturbine in mind unless I
indicate otherwise.
Way back in the 1970’s, as you may recall, Terry Meekram sold
medium-scale HAWT that had blades with no twist and no taper. They
worked fine. They could not have been as efficient as HAWT with more
refined blades, but his blades were relatively cheap to build, as I
recall. And currently, the excellent Bergey small-scale HAWT uses
blades with no twist or taper. So you are correct that just the blade
support arms of an H-VAWT could be converted into useful HAWT blades.
And that nicely illustrates that VAWT usually require more material,
and weigh more, than HAWT. That is a disadvantage for most VAWT.
(Although, the Bird Windmill has no support arms or shaft, and the Lux
eggbeater Darrieus rotor has no support arms, no shaft, and no tower.)
But it is not a decisive disadvantage because some VAWT may be cheaper
to make than conventional HAWT. When comparing VAWT and HAWT, there are
dozens of different designs and variables to consider. And there is
still a lot of testing to be done of existing designs. One of my
focuses is bringing new VAWT advantages to people’s attention. The
bottom line is the average cost of the energy over the lifetime of the
wind turbine.
You claim that a HAWT made with just the support arms of a VAWT could
produce more power than the original VAWT. That would depend on the
aspect ratio of the VAWT because a tall VAWT would have relatively
short support arms that would make for only two small HAWT rotors
relative to the much larger swept area of the VAWT. So your assertion,
as you stated it, is both right and wrong, depending upon the aspect
ratio of the VAWT. Plus, some VAWT (as above) do not require support
arms at all, so that comparison would obviously favor VAWT.
It’s
true that most VAWT have not worked out. The same is true for most
HAWT, especially small-scale HAWT. There are now a lot of new VAWT and
HAWT being sold, and it is not yet clear which ones, if any, will
endure. You know far better than I how difficult it is to develop a
reliable wind turbine, and nothing is more important than reliability.
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As for your SuperTurbine®, as you know, I’m a fan. I love it. It
inspires me. I kick myself for not having invented it. I use it as a
standard for comparison when inventing wind turbines.
PeterS