DESCRIPTION
INCREASING THE EFFICIENCY OF WIND TURBINE BY USE OF CENTRIFUGAL FORCE ON AIR INSIDE THE BLADES
1.0 Background
A wind turbine converts the wind's kinetic energy into electrical energy. Thousands of turbines, in an installation called a wind farms, produce giga watts of electricity. Wind turbines help in reduction of carbon footprint and the cost of electricity production. Small wind turbines are used for battery charging, to power traffic signs, individual houses, farms etc. Large turbines are used to supply power and unused power to an electrical grid.
Wind turbines are available in a range of sizes. They can have horizontal or vertical axes. The wind wheel of Hero of Alexandria (10 AD - 70 CE) was one of the first recorded wind machine in history [6]. The first practical wind power plants were built in Sistan, Persia, in 7th century. It had vertical axle, long vertical shafts with rectangular blades, made of six to twelve sails covered in reed matting or cloth. These windmills were used for grinding grain, draw water, grit milling and sugarcane crushing [5]. The England started using wind mills in the 11th century. The Germans used windmills in Syria around 1190 AD [7].
The first electricity-generating wind turbine was a battery-charging machine installed in 1887 by James Blyth to light his holiday home in Marykirk, Scotland [12]. Charles F. Brush built a wind turbine with the help of local University and his colleagues Jacob S. Gibbs and Brinsley Coleberd to make the blueprints for electricity production [12]. This turbine was uneconomical. By 1900, in Denmark, there were about 2500 windmills used for mechanical work, producing nearly 30 megawatts. By 1908, there were 72 wind turbines operating in the United States producing 5-25 kW electricity. Around the time of World War I, Americans produced 100,000 windmills a year, mostly used for water pumping [10]. By the 1930s, wind mills for electricity were common on farms, in the United States.
A modern horizontal-axis wind generator was installed at Yalta, USSR in 1931. This was a 100 kW machine on a 30-meter tower, connected to a local 6.3 kV distribution system. In 7?Sl94!l?#iriegawatt4lSsstwind tuiibineiwas built that worked for 1,100 hours and had failure. It was not repaired, due to war related complexities.

The first utility grid-connected wind turbine in the UK was built by John Brown & Company in 1951 [12]. In the early 1970s, anti-nuclear protests in Denmark spurred artisan mechanics to develop super micro turbines of 22 kW.
2.0 The working of a wind turbine
According to the principle of conservation of mass the amount of air entering and exiting the turbine must be same. The Betz's law gives the maximal achievable extraction of wind power by a wind turbine as 1627 (59.3%) of the rate at which the wind strikes the turbine [10]. If the effective area of the turbine is A, and the wind velocity v, the maximum power output P is:
_ 16 1 * . 8 J .
27 2 27'
where p is the air density.
Wind-to-rotor efficiency, blade friction and drag affect the power generation. The gearbox losses, generator and converter losses, reduce the power production. Efficiency may slightly decrease with time, due to dust and insect carcasses stick on the blades. Stable and winds produce about 15% more electicity than that in unstable weather. Wind turbine wakes recover faster in unstable atmosphere than in a stable weather [8].
3.0 Types of Wind Turbines
Wind turbines are designed to rotate about a horizontal or a vertical axis, the former being more common. They can have blades or can be bladeless. Large 3-blade horizontal-axis wind turbines (HAWT) with the blades upwind are more in use. Small turbines are moved to face wind by a vane. Large turbines use wind sensor coupled with a yaw to turn it to face the winds. Most of the turbines have a gearbox that turns slow rotation of the blades into a faster rotation to run a generator. Some turbines do not need gearbox and are called direct-drive. They couple the rotor directly to the generator. These gearless turbines are sometimes preferred over gearbox generators [4]. There is also the pseudo direct drive mechanism that has advantages over the permanent magnet direct drive mechanism.
Turbines used in wind farms for commercial power production usually are of 3-blades. These have low torque ripple, high reliability. The size and height of turbines has increased over a period of time. Offshore wind turbines have capacity up to 8 MW and have a blade length up iH6580ftelers.;Ai5 isl^+lvSh thlel" riSJr&ters blades is likely to be available shortly.

3.1 Vertical axis wind turbines
Vertical-axis wind turbines (VAWT) have the vertical shaft. An advantage of this type is that the turbine does not need to be pointed towards the wind. These are more suitable for sites of highly variable wind direction. It has also an advantage if the turbine is integrated into a building. The generator and gearbox are placed near the base, increase accessibility of the components for maintenance. However, these turbines produce much less energy [11][3].
3.2 The Blades
The efficiency increases with blade length. The blades need to work for about 20 years. Therefore the blades must be stiff, strong, durable, light and resistant to fatigue [1]. Materials include composites like polyester and epoxy, glass fibre and carbon fibber.
3.3 Non-blade materials
The parts other than the blades are largely made of steel. Smaller turbines and the megawatt
turbines began using aluminium alloys for these components. Pre-stressed concrete has been
increasingly used to build the tower. It still requires much reinforcing steel for strength. The
step-up gearboxes are increasingly used with variable speed generators that need magnetic
materials [1]. The turbines use copper for the generators, cables etc.
References
[1] Ancona, Dan, Jim, McVeigh, 2001, Wind Turbine - Materials and Manufacturing Fact
Sheet, CiteSeerX 10.1.1.464.5842.
[2] Aravitnh R, Sharath M, Karthikeyan A., Redesigning and Analysis of Aerospike Nozzle
by Spike Length Optimization, 2015, International, Journal of Engineering Research &
Technology (IJERT), ISSN: 2278-0181, http://www.ijert.org, NCRAIME-2015
[3] BarrfardnM,P2e4^edlhgiical Axis Wind Turbines: Great in 1890, Also-rans in 2014.
Clean Technica. [4] Bywaters G, P. Mattila D. Costin, J. Stowell; V. John; S. Hoskins, J. Lynch, T. Cole, A.
Cate; C. Badger; B. Freeman, 2007, Northern Power NW 1500 Direct-Drive Generator,
[5] Dona ,ra3tfoeu^1*,eMctt?craTCEli gineering in the Medieval Near East, Scientific
American, 1991, pp. 64—69. (cf. Donald Routledge Hill, Mechanical Engineering) [6] Drachmann, A.G. 1961, Heron's Windmill, Centaurus, 7: 145-151.
[7] Grogg K., 2005, The Physics of Wind Turbines, Carleton College, p. 8
J/81 Han Xingxing,.t4^,pe.you,f X41 Chang, Shen Wen Zhong, 2018, Atmospheric stability
and topography effects on wind turbine performance and wake properties in complex
[9] iilaoro5 fer?R!fe^rn^5)fraartiriez .etsiae.upm.es, accessed on Oct 24, 2022

[10] Morthorst, Poul Erik, Redlinger, Robert Y, Andersen, Per, 2002, Wind energy in the 21st century: economics, policy, technology and the changing electricity industry.
[ii] IfeTMklW^
[12] Price, Trevor J., 2004, Blyth, James (1839-1906), Oxford Dictionary of National Biography (online ed.). Oxford University Press. doi:10.1093/ref:odnb/100957.
4.0 OBJECTS OF THE INVENTION
(i) To improve the efficiency of wind turbines,
(ii) To build wind turbines that can work efficiently, in low wind speed.
4.1 BRIEF DESCRIPTION OF THE INVENTION
The blades in a horizontal axis wind turbine (HAWT) of large wind turbines are generally hollow pipes, with aerodynamic design to have maximum efficiency of the turbine. The air inside the blades rotates with the blades and experiences centrifugal force. It, in turn builds higher pressure on the tip side. If the air having high pressure is released into the atmosphere, vertical to the blade, in the plane of the blade's motion, it will put a thrust on the blade. Being released from the tip side the length of the blade that works as arm of the torque and thus it increases the force available to run the wind turbine. The figures
Fig 1: Analysis of force on blade of a turbine
Fig 2: A usual 3 blade horizontal axis wind turbine.
Fig 3 : A wind turbine with nozzles near the tip to enhance efficiency of the wind turbine
give a short description of the innovation developed.
4.2 DETAILED DESCRIPTION
4.2.1 EXTRA FORCE AVAILABLE
In this analysis we shall consider a HAWT with three blades of length R. The calculations are done for one blade. VAWT turbines can be dealt with similarly considering the arm plus blade width and designing them suitably. Let us consider a small element of width dr at distance r from the axis of the wind turbine (Fig 1).
The blades have aerodynamic design. These are hollow pipes. The cross-section of the blade may vary in shape. The cross section area from the centre to the tip may also be varying. For the simplicity of calculation we may define equivalent cross sectional area B for the turbine.

This is cross section of a uniform cylinder, which can produce same centrifugal forces on rotation as the actual blade. The equivalent diameter D is the diameter of such a cylinder.
Volume of the element =Bdr
Mass of the air in the element = B dr p p is the air density
2 2
Centrifugal force on the element = B dr p co r /r co is blade's angular velocity
2 = B p co r dr
Thus the total force adds up. R is radius of the area covered by the blades and Ro is the radius
of the rotor hub. The last element on the tip side will experience force:
2 2 2 2
= B p co R 12 - B p co Ro 12
2 ~ B p co co R 12
as R is very large compared to Ro
2 2 Pressure exerted on the tip side = p co R 12
2
= p V 12 V is the tip speed (V= co R)
(1)
2 Thus the pressure inside the blade on the tip = Po + p V 12, Po is ambient pressure. If the air
inside is released into the atmosphere, it can gain speed say V\. Applying Bernoulli's equation:
Po + pV,2/2 = Po + pV2/2
This proves V]=V. Thus if the tip speed is V, it can generate air flow equal to the tip speed. This is the situation when the tip is open and has aperture equal to cross-sectional area.
If we allow the air to exit from holes near the tip, perpendicular to the blade in the opposite
direction of the blade motion, the air released will.push the blade in the direction of its motion.
The torque = p V .V R (2)
4.2.2 ESTIMATION OF TORQUE DUE TO BLADE MOVEMENT
The blade's element interacting with the air is moving at a speed cor. This movement is almost
perpendicular to the wind flow. Striking angle is optimised through the aerodynamic design.
2 2 2 Jkus w^£an take the^ffective spped as^:|qrt(v + co r ).
2 2 2 Mass flow rate of the air striking the infinitesimal element = p sqrt(v + co r ). L dr
L is the length of element, approximately the diameter of the blade.

2 2 2 2 2 2
The momentum associated with mass flow= p sqrt(v + co r ) L dr sqrt(v + co r )
2 2 2 = p L(v + co r ) dr
2 2 2 Torque =pL(v + co r )rdr
2 2 3
= p L (v r dr + co r dr)
Total torque is obtained by integrating the above quantity from Ro to R. Thus
22 24 22 24
The total torque = pL((v R 12+ co R /4) -( v Ro 12+ co Ro /4))
2 2 2 4
~ p L (v R 12+ co R /4)
as R is very large compared to Ro
= p L( v V 12 + V2R2/4) (3)
as V= R co Let us examine if the two quantities given in equations (2) and (3) are comparable.
4.2.3 COMPUTATIONS
Let us assume a typical wind turbine and situation as:
R = 80 meter,
v = 3 mps to 20 meter per second,
V is tip speed in the range of 20-80 meter per second
L= D =1 meter the effective diameter of the blade. For making comparison of the two torques: (i) thrust generated at the tip by diverting air flow perpendicular to the blade and (ii) due to the blade movement, we calculate the torque for the two forces and percentage increase in the torque. Table 1 gives details of these computations.

wind speed
V
(mps) Blade
size R
(m) Blade's
Effective
Diameter
D(m) Tip Speed
V (mps) Tip speed ratio Pressure
increase
at tip
(hPa)
....(1) Pressure
Ratio
at 1013
hPa (Sea
Level) Pressure
Ratio
at 950
hPa Torque due to
centrifugal force
(kg m2ps) Normal
Torque
on blades
(kg
m2ps) %
increase
in the
torque
3 80 20 7 244.0 0.806 0.796 39200 819280 4.78
4 80 24 6 351.4 0.742 0.730 56448 1191680 4.74
5 80 28 6 478.2 0.679 0.665 76832 1634640 4.70
6 80 32 5 624.6 0.619 0.603 100352 2148160 4.67
7 80 36 5 790.6 0.562 0.546 127008 2732240 4.65
8 80 40 5 976.0 0.509 0.493 156800 3386880 4.63
9 80 44 5 1181.0 0.462 0.446 189728 4112080 4.61
10 80 48 5 1405.4 0.419 0.403 225792 4907840 4.60
11 80 52 5 1649.4 0.380 0.365 264992 5774160 4.59
12 80 56 5 1913.0 0.346 0.332 307328 6711040 4.58
13 80 60 5 2196.0 0.316 0.302 352800 7718480 4.57
14 80 64 5 2498.6 0.288 0.275 401408 8796480 4.56
15 80 68 5 2820.6 0.264 0.252 453152 9945040 4.56
16 80 72 5 3162.2 0.243 0.231 508032 11164160 4.55
17 80 76 4 3523.4 0.223 0.212 566048 12453840 4.55
18 80 80 4 3904.0 0.206 0.196 627200 13814080 4.54
19 80 80 4 3904.0 0.206 0.196 627200 13959120 4.49
20 80 80 4 3904.0 0,206 0.196 627200 14112000 4.44
Table 1: Comparison of torques due to (i) blade motion and (ii) centrifugal force
We observe from the above table, the efficiency gain is in the range of 4.5 to 4.8 % for the wind speed (v) in the range of 3-18 meter per second.

4.2.4 USE OF NOZZLES
The convergent and the convergent-divergent (CD) nozzles can improve the efficiency through air released from high pressure inside the blades into the atmosphere. The airflow released in the direction perpendicular to the blades' motion, in the plain of rotation and opposite to the direction of blade's motion (Fig 3) will generate maximum torque. As the pressure inside the blade that increases with wind speed, at the tip, there is variable pressure inside and constant pressure outside. Controllable nozzles to release the air with maximum flow rate and maximum flow speed will increase the speed of the blades optimally and consequently increase the efficiency of the wind turbine.
If a convergent nozzle of, say, 50 centimetres entry diameter and 5 centimetres as exit, is used the air speed from the nozzle, will increase about 100 times. It is seen from Table 1 that critical pressure ratio for air 0.528 is achieved at wind speed 7.3 meters per second (with 4.63% correction due to centrifugal gain) for the typical turbine. At this speed and beyond the convergent nozzles can generate sonic speeds of the air flow exiting the nozzles. The Table 2 shows results for enhanced torque, for a convergent nozzle of area ratio 100.
On increase of the exit speed through nozzle, the value 7.3 meter per second, described above, will reduce due to increased torque and so increase in the rotational speed of the turbine.

wind speed
V
(mps) Blade
size
R(m) Blade's Effective Diameter
D(m) Tip
Speed
V(mps) Speed
for
Con
Nozzles Pressure
increase
at tip
(hPa) Torque of centrifugal
force (kg m2ps) Torque due
to blade's
Motion
(kg m2ps) % increase
in torque
3 80 20 200 244.0 3920000 819280 478
4 80 24 240 351.4 5644800 1191680 474
5 80 28 280 478.2 7683200 1634640 470
6 80 32 320 624.6 10035200 2148160 467
7 80 36 331 790.6 10736978 2732240 393
8 80 40 331 976.0 10736978 3386880 317
9 80 44 331 1181.0 10736978 4112080 261
10 80 48 331 1405.4 10736978 4907840 219
11 80 52 331 1649.4 10736978 5774160 186
12 80 56 331 1913.0 10736978 6711040 160
13 80 60 331 2196.0 10736978 7718480 139
14 80 64 331 2498.6 10736978 8796480 122
15 80 68 331 2820.6 10736978 9945040 108
16 80 72 331 3162.2 10736978 11164160 96
17 80 76 331 3523.4 10736978 12453840 86
18 80 80 331 3904.0 10736978 13814080 78
19 80 80 331 3904.0 10736978 13959120 77
20 80 80 331 3904.0 10736978 14112000 76
Table 2: Enhanced torque for a convergent nozzle

4.3 CONCLUSION
From table 2 we observe that at wind speed 6.5 meter per second the sonic speed is achieved in the throat of the nozzle. At higher speeds the flow is sonic, so the mass flow rate becomes constant. It will require increasing the nozzle exit area to have maximum air mass flow, similar to Aerospike nozzle [2] used in airplanes to gain maximum thrust at low and high altitudes both. With this technology the wind turbines can take higher load and produce considerably large amount of energy as compared to ordinarily used wind turbine (Fig 2).
We can get supersonic speeds of air flow by use of CD nozzles or other geometries of the nozzles [9], if issue of increased level of noise is resolved. Also the Betz's law need be reviewed in view of the theory developed herein.
If the air flow from the nozzles is released in the opposite direction of the motion of the blade, perpendicular to the blade in the plain of the blade's movement, there will be extra force applied on the blades that will increase the speed of the blades and thereby produce more energy. In this work we found that at low wind speeds the turbine is expected to perform at very high increased efficiency (last column of the Table 2). This will help in producing wind energy efficiently in the places of low wind speeds.

5. CLAIM

We claim:
1. Efficiency of wind turbines can be improved by releasing compressed air due to pressure built up inside the blades because of centrifugal force, by using nozzles near the tip of the blades, in the direction perpendicular to the blade, opposite to the direction of motion of the blade and in the plane of the motion of the blade.
2. The efficiency gain is high at low wind speeds. Thus wind farms can be installed in regions of low prevailing wind speeds.