Most frequently asked questions:
?? In various sources of the information upon windenergetic is spoken about theoretically
greatest possible factor of transformation of the wind power, equal 59,3 %.
In your article you specify number 68,6 %, whence it and where to this a
?? The theory and practice of wind power already it is a lot of years. Why you think,
your idea has not occurred to somebody earlier?
?? Whether you checked the idea practically, for example, on the reduced model?
?? As far as aerodynamic calculations on your website are exact,
and whether it is possible to use them for full calculation of a real rotor?
?? Why you have chosen concrete diameter of a rotorof 240 m and concrete capacity 120 MW?
?? Your rotor in diameter of 240 m has hub to which blades fasten, in diameter of 10 m.
imagine such design? And whether diameter of the blade in a place of connection
to hub Ц 3,5 m for such big diameter of a rotor is not too small?
?? The increase in rated speed of a wind for each turbine will increase unevenness of
received power and will reduce coefficient of loading of electric mains and power cables.
What do you think of it?
?? In the aerodynamic calculations suggested by you there is a parameter "A".
it mean and whence the formula of calculation of parameter "e" is taken?
?? I live in district with the big wind activity and I plan to mount own small wind turbine.
Whether I can take advantage of your calculations for definition of its efficiency?
?? Whether company Izosimov Windrotor of the sponsor has?
?? Whether the partner program with other websites interests the author of your website?
*** Question: *** In various sources of the information upon windenergetic
is spoken about theoretically
greatest possible factor of transformation
of the wind power, equal 59,3 %. In your article you specify number 68,6 %, whence it and where to this a
The answer: Value of 59,3 % is result of the theory of wind engines
which had offered A. Betz in the twentieth years of the last century.
Basic conclusions of this theory are used till now. However, the Soviet scientist Ц professor G.Sabinin (the pupil of professor N.Zhukovsky) in 1931 had
offered more exact theory in which had proved presence of so-called Ђthe attached massї. This theory increases the mentioned above value up to 68,6 %. I
to adapt the theory and formulas of G.Sabinin for modern opportunities.
I offer the calculations corresponding to his more exact theory.
who wants to find the primary source: G.Sabinin, УThe theory and aerodynamic calculation of wind enginesФ, collection BCHX the USSR УWorks
of scientific research institutes of the industryФ є 482, the Central Aero-Hydrodynamical Institute, Release 104. Theme Ц the Problem of use of a wind
power. The state scientific and technical publishing house, Moscow, Leningrad, 1931, 70 pages.
In the original in Russian (code: windows-1251):
* √. ’. —абинин, Ђ“еори€ и аэродинамический расчЄт ветр€ных двигателейї, сборник ¬—Ќ’ ———– Ђ“руды научно-исследовательских институтов промышленности ї
є 482, ÷ентральный јэро-√идродинамический »нститут (÷ј√»), ¬ыпуск 104. “ема Ц ѕроблема использовани€ энергии ветра. √осударственное научно-техническое
издательство, ћосква, Ћенинград, 1931, 70 страниц. *
*** Question: *** The theory and practice of wind power already it is a lot
of years. Why you think, what
your idea has not occurred to somebody earlier?
The answer: Attempts to investigate multibladed rotors were carried out in 30th years of the last century. However to realization of exact
comparative calculations was hindered by absence of computers, complexity of calculations and the reductions of formulas connected to it, simplifications
of calculations and additional errors because of insufficient optimization of the received parameters. Experimental data showed very small increase in
coefficient of use of a wind power of a multibladed designs because of their small sizes, so also of small size
of number of Reynolds. At transition
from 3-bladed designs to multibladed
the speed of rotation of a rotor decreased together with decrease of number
of Reynolds. It raised factor of
friction of an airfoil of the blade,
worsening aerodynamic quality and reducing the general prize.
In result of the undercount reduction of number of Reynolds, developers came
to a conclusion, which the coefficient of use of a wind power of a rotor
does not depend on quantity of blades and presence 2 Ц 3 blades for any sizes of rotors
will be sufficient. Multibladed designs with simple cheap blades,
taking into account their much greater initial moment of rotation, have decided to use
only as windmills and pumps of pumping of water. This approach
has so taken roots and became indisputable and classical what to challenge it very rare developers were solved. Modern blades of the big rotors have
Reynolds's numbers on much exceeding critical number, therefore, small reduction of width
of blades and of speed of rotation of a rotor to deterioration
of aerodynamic quality because of reduction of number of Reynolds will not result. As the result, reduction of speed of rotation and other factors shown
in article, including influence of external and intermediate rings, will define an appreciable prize
in coefficient of use of a wind power and in
gathering of energy.
Other reason of relative passivity of inventors is complexity of the theory
of a rotor, complexity of aerodynamic calculations and nearness of the
coefficient of use of a wind power achieved in practice (40 Ц 46 %) to value of 59,3 % wrongly accepted for an ideal limit, instead of a real limit of
Also one of the reasons of underestimation of idea is more simple way of increase of capacity of the turbine existing till now Ц the increase in diameter
a rotor only due to lengthening blades. However it could not be infinite for a long time as the weight and the cost of blades has from their
length almost cubic dependence, and capacity of a rotor - only square-law. Therefore, my idea has advantages only for very big rotors. Even in 90th years
of the last century
the sizes of 3-bladed rotors yet have not reached limits of their opportunities,
and my idea was premature.
*** Question: *** Whether you checked the idea practically, for example,
on the reduced model?
The answer: No, did not check. The high factor of transformation of a wind power in my design will be only in case of the big sizes of a rotor,
when Reynolds's number is big. This number decreases with reduction of the sizes of a rotor.
For external edge of the blade it is equal 15 million at
diameter of a rotor of 240 m and 8 blades, at speed of a wind of 14 m/s at number of modules Z = 6,2.
If to leave other parameters without change and
to reduce diameter of a design up to 3 m (for a blow-down in a wind tunnel), Reynolds's number will decrease
up to 190 000, that much less than critical
number. For the comparative check
of the reduced model at preservation concerning low factor of friction it is necessary, that Reynolds's number remained
much above critical number (300 000 Ц 400 000). It means, that diameter of model should be more than 6 meters. Reynolds's number can be increased also,
increasing speed of a stream
(not changing the number of modules Z). However it will lead to sharp increase
in losses of friction and to sharp increase
in loading of a design because of cubic dependence of power from speed of a stream. Also the errors of comparison caused by approach of Circumferential
speed to speed of a sound will increase.
Certainly, I understand necessity of a aerodynamic checks and of a strength checks of model, however
I donТt have money for construction of a rotor
in diameter more than 6 meters and its a blow-down in a wind tunnel.
It is important also, that
aerodynamic calculation is necessary to perform
for airfoils family, intended for work with reduced Reynolds's numbers.
Parameters of such airfoils
still need to be found. Then it is necessary to express dependences of factors of each of airfoils of family from a corner "α" as formulas of
approximation and is necessary to carry out calculations. I am ready
to participate in it if there will be an organization interested in creation and
check of model.
*** Question: *** As far as aerodynamic calculations on your website are
exact, and whether it is possible to use them for full calculation of a real rotor?
The answer: Suggested on this website the technique of aerodynamic calculations, in my opinion, is one most exact of all existing.
However, the suggested calculations (not a technique) have essential lack
Ц in them are used aerodynamic characteristics of family of the airfoils,
not taking into account their big change with change of number of Reynolds.
In result Ц the error of calculations is too great for real application.
These calculations Ц only the example of use of a technique simplified for presentation, and their purpose Ц to show advantages of a new design.
For realization of exact calculations of a real rotor it is necessary to choose
first the family of airfoils most suitable to average of number of
for the considered rotor. The basic criterion of a choice Ц the maximum
of the best value of factor of aerodynamic quality at wide enough
of corners of attack (a minimum 1 Ц 2 degrees).
The following stage of exact calculations Ц the deriving of aerodynamic characteristics
for each of airfoils of family for every speed of the wind
at Reynolds's real numbers with the subsequent approximation of these characteristics
by formulas. Further calculations proceed by the specified technique. Complexity increases that Reynolds's real numbers are beforehand unknown,
therefore, sometimes it is necessary to recalculate characteristics anew.
The information for those who plans to use an external ring in a rotor.
I have made a mistake in the calculations applied to the second part of article,
at calculation of losses of braking of a rotor because of an
(texts of both parts of article will stay without changes). I have considerably overestimated these losses. I did not consider,
that value Cx (or CD) of a ring will multiple decrease that, first, its relative thickness will decrease for a wind
in a radical from
(Z2 + 1) time (a slanting flow of a ring),
second, on the same size will increase Reynolds's number of an external ring.
In May 2009 I have finished aerodynamic calculation of the reduced
(diameter 4 м) model of a rotor of my design for its
and a testing in a wind tunnel.
Its basic calculated parameters: - number of Reynolds 250 000 Ц 420 000;
- family of airfoils Ц
modifications of airfoil FX 63-137 with relative thickness
from 8 % up to 29 %; - width of each of 8 blades varies from 10,63 up to 25 sm;
number of modules on the end of the blade Z = 3,8 (3,24 - 5); - number
of cycle of a rotor in a second nc = 4,38; - width of an
external symmetric ring
of 10 sm, thickness Ц 2 sm. Calculation is made for speeds of a wind 11 Ц 17 m/s.
The choice of a airfoil, its modifications
and deriving of characteristics of family were made with the help of program XFLR5, and the files of coordinates
for a choice have been taken from websites of
University in Illinois, the American
National Renewed Energy Laboratory and others (Many thanks to developers
of the program
and to authors of the publication of coordinates of airfoils).
The result received theoretically and expected at testing:
of a wind power Cp = 62,3 % at speed of a wind of 14,5 m/s
even at Reynolds's such low numbers. The purposes of a testing of model
the practical evidence of efficiency of a new design, of accuracy
of a technique of calculations and of inaccuracies of law of A. Betz.
Taking into account, that not everywhere there is an opportunity of testing
of model in diameter of 4 m, I have calculated the second variant of
in diameter of 2 m. As difference from the first variant: - width of each
of 8 blades varies from 5,22 up to 12,5 sm; - number of cycle of
in a second nc = 17,52; - width of an external symmetric ring of 5 sm,
thickness Ц 1 sm. Calculation is made for speeds of
a wind 20 - 35 m/s
for preservation of number of Reynolds in the same limits.
Calculated Cp = 62,3 % at speed of a wind of 29 m/s.
If there will be the organizations, wishing to make model and to test it in a wind tunnel Ц I is ready to present all necessary initial data,
materials of calculations and their results. At the publication of results of testing the reference
to my authorship of calculations and onto
my website are obligatory.
*** Question: *** Why you have chosen concrete diameter of a rotor
of 240 m and concrete capacity 120 MW?
The answer: Diameter of a rotor of 240 m is chosen as maximal at preservation
of a technical acceptability and concerning small expenses
at manufacturing and transportation of components of a rotor in variant when a rotor has only one intermediate ring. Capacity 120 MW is optimized for the
chosen sizes of a rotor. At realization of idea each company can choose the own variants of the sizes
and capacities of a rotor.
*** Question: *** Your rotor in diameter of 240 m has hub to which blades fasten, in diameter of 10 m. Do you
imagine such design?
And whether diameter of the blade in a place of connection to hub Ц 3,5 m
for such big diameter of a rotor is not too small?
The answer: Diameter of 3,5 m should be enough if blade in junction with hub
to strengthen, having increased thickness of its envelopment.
Diameter of a hub
if it is necessary, it is possible to reduce, having applied to each blade the steel extension pieces as conical pipes with flanged
interconnection on the ends. Such extension pieces fasten at installation of a rotor. For example, if to choose small diameter of a cone of 2 m, the big
diameter of a cone of 4 m and length of a cone of 2,6 m the diameter of hub will decrease up to 5,2 m, diameter of the blade
in a place of fastening
will increase up to 4 m, and its length will be reduced.
In such extension piece it is possible to place the device of turn of the blade
corresponding bearing. In this case the big diameter of the extension piece can turn around of an axis of a cone concerning small diameter.
*** Question: *** The increase in rated speed of a wind for each turbine
will increase unevenness of
received power and will reduce coefficient of loading of electric mains and power cables. What do you think of it?
The answer: Yes, the coefficient of loading of electric mains will decrease, however the length of the same power cables will be reduced due
of quantity of turbines and reduction of the areas of power stations at equal capacities. The unevenness of received power will increase
taking into account grouping of turbines in power stations and smoothing
due to this of short-term peaks of power. Speaking about
long-term unevenness, it is known, that already now there is a necessity in stations of accumulation
of the energy, which is connected not so much with
unevenness of manufactures of the electric power, how many with unevenness its daily expenditure.
Such stations will eliminate the unevenness, in
addition promoting increase
in an allowable share of wind energy in its total amount. The task before wind power stations will consist in maximal
"harvesting" of wind capacity.
With this task the proposed turbines in the best way will manage.
*** Question: *** In the aerodynamic calculations suggested by you there
is a parameter "A". What does
it mean and whence the formula of calculation
of parameter "e" is taken?
The answer: The parameter "A" is auxiliary. It groups all combinations of use
of parameter "e" in the formula b = f (Cy, Cx, Zu, e, i, r),
b Ц width of an element of the blade; Cy, Cx, Zu, e Ц aerodynamic parameters;
i Ц quantity of blades; r - distance of an element of the
blade from the center.
In calculations it is more convenient to find A = f (Cy, Cx, Zu, i, b, r),
and then to find е = f (ј). The equation
ј = е/(1+е)/(1-е)2 will be transformed
in е3 Ц е2 Ц (1 + 1/ј)е + 1 = 0 and is solved with use of the formula
(it is specified in mathematical directories). Result of the decision is the formula
in cells "e" in calculations applied to article.
*** Question: *** I live in district with the big wind activity and I plan
to mount own small wind turbine.
Whether I can take advantage of your calculations for definition of its efficiency?
The answer: Yes. For this purpose it is necessary for you to learn (for example, on the nearest meteorological station) the wind characteristic
of your district (mid-annual wind speed and parameter Weibull K), and also parameters
of concrete wind turbine to substitute them in the calculation
table and to count up annual gathering of the received energy. Accuracy of calculation depends
on conformity entrance data to real values. Knowing
cost of wind turbine and term of its service it is possible to count up cost of each received watt. After these calculations it is possible to argue about
efficiency of your wind turbine.
At experiments with Excel table remember, at some your actions, option of cyclic references of Excel table can be
changed. For reconstruction of this option
it is necessary to open the table, to press "service" in a line of the menu,
then to find and press
"parameters", to find and press "calculations".
In this window switch on "iterations", fill values "limiting number of iterations" 100 and accuracy Ц
*** Question: *** Whether company Izosimov Windrotor of the sponsor has?
The answer: Izosimov Windrotor (windrotor.info) company is independent
of external programs, has no external financing and carries out
researches, calculations, patenting, licensing and other activity for own money.
We can interest potential sponsors or their advertising on this website,
or preferential licensing of idea offered on a website (after reception
of the internationals patents). Other variants are possible also.
*** Question: *** Whether the partner program with other websites interests
the author of your
The answer: Yes. I would like that on other websites which represented windenergetic there were references to this website. It can be
on pages of "links" and/or in messages (it is desirable with the resume) on pages of news. In exchange I could add references about these
websites on the own page "links", and probably to place banners. The page of news on this website
is not planned.
At occurrence of questions and offers please address through contact page of a website.