WIND ENERGY HARNESSING - THEORY AND THE ETHIOPIAN EXPERIENCE
Teferi Taye
Senior Mechanical Engineer
Energy Division, Equatorial Business Group (EBG) Plc., Addis Ababa, Ethiopia
Published in the Journal of the ESME, Vol. II, No. 2, October 1999
Reprinted with ESME permission by the African Technology Forum

ABSTRACT

The paper briefly discusses the underlying theory in wind harnessing by deriving some of the important equations, like the maximum attainable power factor, the various forces, moments, and their resulting stresses.  The experience of the author over the last two decades in research and development endeavor in wind energy harnessing is summarized.  Finally, the initiatives being taken by EBG to put this water lifting system to the benefit of the society, where the author is now in charge of this undertaking is introduced.

Energy From The Wind 
    Maximum Power Factor (C_p) 
    Rotor Blade Forces 
    Pump Load Forces 
    Stresses in the Rotor Spoke at the Hub 
    Calculation of the Combined Stresses 
Sizing of a Windpump 
    Assessment of Water Requirement 
    Calculating the Hydraulic Power Requirement 
    Determining the Available Wind Power Resource 
The Ethiopian Experience 
    Wind Resource
    Ethiopian Water Resources Authority (EWRA)
    American Presbyterian Mission at Omo
    Addis Ababa University (AAU)
    Lay Volunteers International Association (LVIA)
    The Experience of the Research and Development Services (RADS) of 
        the Ethiopian Water Works Construction Authority (EWWCA)
    Equatorial Business Group's (EGB) Initiatives
Conclusion

1.    ENERGY FROM THE WIND

Wind is simply air in motion.  It is the movement of the air mass, caused by uneven heating of the atmosphere by the sun.  That is the source of wind energy.  The wind contains energy by the virtue of .its motion, and this is called kinetic energy. [1]

1.1    Maximum Power Factor (C_p)

Fig. 1: Axial Momentum Theory Illustration

1.1.1    The Axial Momentum Theory

A windmill extracts power from the wind by slowing down the wind.  At stand still, the rotor obviously produces no power, and at very high rotational speeds the air is more or less blocked by the rotor, and again no power is produced.

From the air stream tube of Fig. 1, conservation of mass dictates that:

r * A₁ * V₁ = r * A * V_ax = r * A₂ * V₂            (1)
Where 
r    is the density of air [kg/m³]
A₁    is the area of the air stream far before the rotor [m²]
V₁    is the wind velocity of the air stream far before the rotor [m/s]
A    is the rotor swept area [m²]
V_ax    is the wind velocity at the plane of  the rotor [m/s]
A₂    is the area of the air stream far behind the rotor [m²]
V₂    is the wind velocity of the air stream far behind the rotor [m/s]

The thrust force (F) on the rotor is given by the change in momentum:

F = (r * A₁ * V₁ ) * V₁ - (r * A₂ * V₂ ) * V₂            (2)
Where 
F    is the thrust on the rotor [N]

With equation 1, the thrust force reduces to equation 3.

 F = r * A * V_ax *  (V₁ - V₂)            (3)

The difference in power before and after the rotor is the power extracted by the windmill which equals the product of the thrust force (F) and the velocity (V_ax) given by equation 4.

P_kin = 1/2 * (r * A₁ * V₁ ) * (V₁)² - 1/2 * (r * A₂ * V₂ ) * (V₂)²
= r * A * V_ax *  ( V₁ - V₂) * V_ax                                                                  (4)
Where
P_kin    is the kinetic power extracted by the rotor [W]

Solving for V_ax:

V_ax = 1/2 *  (V₁ + V₂)            (5)

Velocity of the wind in the rotor plane is, therefore, the average of the upstream and low stream wind speed.  Substituting the value of V_ax from equation 5 into equation 4, the power becomes:

P_kin = 1/2 * r * A * V_ax * (V₁² - V₂²)
= 1/4 * r * A * (V₁³ - V₂³ -  V₁* V₂² +  V₁² * V₂)           (6)

To find the maximum power extracted by the rotor, differentiate equation 6 with respect to V₂ and equate it to zero.

dP_kin / dV₂ = 1/4 * r * A * (-3 * V₂² - 2 * V₁* V₂ + V₁²) = 0         (7)

Since the area of the rotor (A) and the density of the air (r) cannot be zero, the expression in the bracket of equation 7 has to be zero.  Hence, using the formula for the solution of a quadratic equation, equation 7 yields:

V₂ = 1/3 * V₁            (8)

Substitution of equation 8 into equation 6 results in equation 9:

The theoretical maximum fraction of the power in the wind which could be extracted by an ideal windmill is, therefore 16 / 27 = 59.3%.  this fraction is called the Betz Coefficient.  Because of aerodynamic imperfections in any practical machine and of mechanical loses, the power extracted is less than that calculated above. 

The shaft power of a wind rotor is given by equation 10:

P = C_p * 1/2  * r * A V³           (10)
Where
P    is the shaft power [W]
C_p  is the rotor coefficient (ratio of shaft power of the windmill to the power in the wind in the cross-sectional area of the rotor)
V    is the velocity of the wind [m/s]

Equation 10 clearly shows that:

• The power is proportional to the density (r) of the air which varies slightly with altitude and temperature

• The power is proportional to the area (A) swept by the blades and thus to the square of the radius (R) of the rotor; and 

• the power varies with the cube of the wind speed (V³).  This means that the power increases eightfold if the wind speed is doubled.  Hence, one has to pay particular attention in site selection.

1.1.2 Axial Wind Thrust

The maximum axial force acting in the plane of rotation occurs when the rotor extracts the maximum power from the wind, i.e. when the low stream wind speed is 1/3 of the upstream wind speed.  By substituting this value into equation 3, the maximum axial wind thrust is obtained as shown by equation 11.

1.2    Rotor Blade Forces

Loads on a rotor blade arise from torque, thrust, weight and forces imposed by the load.

1.2.1 Torque

The torque on the rotor is the resulting moment of the rotor axis of the aerodynamic forces on the blades.

Fig. 2: Acceleration Forces on a Blade Element

The equation of motion for a blade element (dm) is described by the Second Law of Newton (equation 12)

dF = a_t* dm = r * d²q /dt² * dm            (12)
Where
dF    is the differential force on the differential mass [N]
dm    is the differential mass at radius r [kg]
a_t    is the tangential acceleration, which is equal to the radius (r) times the second derivative of the position angle q  [m/s²]
q    is the position of the blade, positive when measured from the negative z-axis [rad]
r    is the radius of the mass element dm [m]
t    is time [s]

The torque (Q) [N-m] is, therefore, given by equation 13.

Q =  r * dF = r² * d²q /dt² * dm             (13)

The moment of inertia (I) [kg-m²] is given by equation 14.

I = r² * dm             (14)

The torque, therefore, reduces to equation 15.

Q = I * d²q /dt²                                     (15)

The shearing force (F_b) on a blade (near the hub) being the resultant force of all acceleration forces (dF) is given by equation 16.

F_b = dF = r * d²q /dt² * dm
= d²q /dt²  r * dm = d²q /dt²  * J_b                                     (16)

Where the first moment of inertia of a blade (J_b) [kg-m] is given by equation 17.

J_b = r * dm                (17)

Substituting  d²q /dt² from equation 16 into equation 15, the torque becomes

Q = I * F_b / J_b                                            (18)

Hence,

F_b =Q *  J_b / I  = Q *  J_b / (i * I) , acting at   I_b / J_b           (19)
where
i     is the number of spokes [-]
I_b   is the moment of inertia of a blade [kg-m²]

The bending moment per blade (M_blade) [N-m] is given by equation 20.

M_blade = Q / i            (20)

1.2.2 Thrust

The thrust force (F), assumed to b linear with the radius (r), imposes a shearing force as well as a bending moment on the rotor blade at the hub.  The shearing force per blade (F_i) can be calculated from equation 21.

F_i = 4/9 * r * A* V₁² / i  , acting at 2/3 R          (21)
where
R    is the radius of the rotor [m]

The bending moment (M_b) due to the shearing force is calculated from equation 22.

M_b = F_i * 2/3 * R            (22)

1.2.3 Gravity

The weight of a blade imposes a bending moment (M_bg), a tangential force (F_gt) and a radial force (F_gr) upon the rotor blade at the hub.

Fig 3: Weight of a Blade

M_bg = - m * g * L * sin (q)        (23)

F_gt = - m * g * sin (q)                (24)

F_g = - m * g * cos (q)                (25)

1.2.4 Inertia (Gyroscopic Effect)

Simultaneous yawing of the head around the z-axis and turning of the rotor around the x-axis imposes inertia forces and moments on the rotor blades and the shaft.

The derivation of these forces and moments due to inertia is done by writing equations for the position of a mass element dm (Fig. 4) in terms of r, f, q , q_y, W_x, W_z, and differentiating twice the resulting equations, so as to get the respective acceleration in the x, y, and z directions.  The products of these acceleration sand the differential mass (dm) result in forces.  only the final results are listed hereunder for the sake of brevity.

The axial, tangential and radial forces and moments about the axial and tangential axis are given by equations 26 to 30 respectively.

Fig 4: Gyroscopic Effect

F_ia = 2 * cos (q) * W_x* W_z *  J_b - f * W_z² * M_blade       (26)

F_it = sin (q) cos (q) * W_z² * J_b                                          (27)

F_ir =  W_x² * J_b + sin² (q) * W_z² * J_b                                 (28)

M_bia = sin (q) cos (q) * W_z² * I_b                                       (29)

M_bit = 2 * cos (q) * W_x* W_z *  I_b - f * W_z² * J_b            (30)

Where
W_x    is the angular speed of the rotor [rad/s]
W_z    is the angular speed of the head (yawing) [rad/s]
f        is the eccentricity of the rotor plane with respect to eh vertical axis of the rotor head [m]
M_blade    is the mass of the blade [kg]
Subscripts a, r and t are for axial, tangential, and radial.

1.3    Pump Load Forces

The pump rod force (F_p) arises from static, acceleration, friction and shock loads of water and pump rods.  F_p can be calculated, realizing that work dome by the wind during one cycle is equal to the work done by the pump load force:

Fig. 5: Pump Load Force

F_p = 2 * p * Q / S                 (31)
where
S    is the stroke [m]

The bending moment (M_bp) on a rotor blade at the hub due to the pump rod force (F_p) is given by equation 32.

M_bp = - (F_p / i) * sin (q + q_b)        (32)
where 
q_b    is the angle between the crank and the blade in question.  b is positive when measured from the blade to crank in clockwise direction.  [rad/s]

The shearing force on the blade at the hub due to the pump rod force is given by equation 33.

F_bp = M_bp * (J_b / I_b)                        (33)

1.4    Stresses in the Rotor Spoke at the Hub

1.4.1 Shearing Stress

Since axial and tangential forces are perpendicular, the resulting shearing stress (t) [N/m²] can be calculated using equation 34.

t = ( (S F_a)² + (S F_r)² )^1/2 / A_s       (34)
where
As    is the area of the spoke [m²] 

1.4.2 Tensile Stress

Radial forces on a rotor blade cause a tensile stress stress (s_t) [N/m²] given by equation 35.

s_t = S F_r / A_s                                   (35)

1.4.3 Bending Stress

The combined moment (M_tot) of the axial moment (M_a) and tangential moment (M_t) is given by equation 36.

M_tot = ( (S M_a)² + (S M_t)² )^1/2             (36)

The resulting bending moment (M_tot) causes a bending stress (s_b) [N/m²]which is given by equation 37.

s_t = M_tot * C / I_s                            (37)
where
C    is the distance from the neutral axis of the rotor spoke to the outer fibre in the direction of M_tot [m]

1.5    Calculation of the Combined Stresses

The combined stress (s_comb) [N/m²] of shearing stress (t), tensile stress (s_t) and bending stress (s_b) is given by equation 38.

s_comb = ( (s_b + s_t)² + 3t² )^1/2             (38)

Substituting the respective values of the stresses from the preceding equations, s_comb reduces to equation 39.

s_comb = [ [ [ (S M_a)² + (S M_t)² ]^1/2 * (C / I_s) +  (S F_r / A_s ) ]²  + 3 * [ (S F_a)² + (S F_r)² ] / A_s²]^1/2           (39)

This combined stress should be equal to or less than the admissible tensile stress of the material.

2.    SIZING OF A WINDPUMP

The steps to be followed in selecting the optimum size of a windpump for a site are:

• Assessment of the water requirement;

• Determination of the hydraulic power requirement;

• Determination of the available wind power resource;

• Identification of the design month; and

• Sizing of the windpump

2.1    Assessment of Water Requirement

The amount of water needed to irrigate a given area depends on a number of factors.  The most important of these are:

• Nature of crop, crop growth cycle;

• Climatic conditions;

• Type and condition of soil;

• Topography of the terrain;

• Conveyance efficiency;

• Field application efficiency; and

• Water quality

The pumped volume required per day for irrigation is calculated using equation 40.

Vol = Plot * Canopy * Demand / Eff
where
Vol         is the pumped volume [m³/day]
Plot        is the plot size [ha]
Canopy is the canopy fraction ( the fraction of the plot covered with plant branches and leaves) [-]
Demand is the crop water demand.  As a rule of thumb, take 5-6  l/day/m² of crop canopy in cooler 
                or more humid climates, and 7-8  l/day/m² in hot, dry climates. This figure can be converted
                to its equivalent in m³/day/ha of crop canopy by simply multiplying is by a factor of 10. [m³/day/ha]
Eff           is the field application efficiency [-].

2.1.2    Water Requirement for Rural Water Supply

A water consumption of about 20 litres per capita per day is considered reasonable for the rural population of Ethiopia.  Thus, for a typical village population of 500, water supplies will have to be sized to provide about 10 m³ per day, and typical daily water requirements for a range of livestock is shown in Table 1.

Table 1: Water Requirements for Livestock; Source Ref. 3.

2.2    Calculating the Hydraulic Power Requirement

Once the water requirement is known, the hydraulic power requirement (the potential power needed to raise a certain quantity of water through a certain head) can be determined, using equation 41.

P_h =r_w * g * q * H = 9.81 * 1000 * q * H            (41)
where
P_h    is the hydraulic power [W]
q    is the pumping rate [m³/s]
r_w     is the density of water = 1000 kg/m³
g     is the acceleration due to gravity = 9.81 m/s²
H    is the total head [m]

The head (H) that is "felt" at the pump is the sum of:

• The depth of the static water level below the surface;

• The maximum expected draw-down, i.e. the lowering of the water level due to pumping;

• The height of the tank (if any) above the surface; and 

• Additional dynamic head due to frictional losses.

So,

P_h = 9.81 q * H if q is expressed in l/s
P_h = 0.113 q * H if q is expressed in m³/day

2.3    Determining the Available Wind Power Resource

2.3.1    Wind Speed Profile at One Location

The wind is stronger higher up, and weaker near the ground.  This is due to the friction between the wind and the ground.  The type of surface affects the way the wind is slowed down.  If the wind speed V(Z_r) is known at some reference height Z_r, the wind speed V(Z) at any other height Z up to 60 m at he same location can be estimated by equation 42.

V(Z) / V(Z_r) =[ ln (Z/Z_o) ] / [ ln (Z_r/Z_o) ]            (42)
where
Z     is the height where the wind speed is required. In our case, it is the height from the ground level to the rotor axis. [m]
Z_r    is the reference height, where the wind speed is known [m]
Z_o   is the roughness height related to the type of the terrain according to Table 2 [m]
ln    is the natural logarithm

Table 2: Roughness Height (Z_o) in Meters; Source; Ref. 2.

After the average wind speed at the hub height is calculated, the air density (r) is determined from Table 3.

Table 3: Dry Air Density in kg/m³ at Different Heights (h) Above Sea Level; Source: Ref. 3.

Having determined the air density and the wind speed, the specific wind power is then calculated using equation 43.

P_wind  = 1/2 * r * V_av³ 
where
P_wind     is the specific wind power [W/m²]
V_av        is the average wind speed [m/s]

2.3.2    Determination of the Wind Month

The sizing methodology is based on the concept of the critical month or design month.  This is the month in which water demand is highest in relation to he wind power resource, i.e. the month when the system will be most heavily loaded.  The design month is found by calculating he ratio of the hydraulic power requirement to the wind power resource for each month.  the month is which this ratio is a maximum is the design month. [3]

2.3.2    Rotor Diameter

The rotor diameter is the most important characteristic of a windpump, determining both its output and cost.  The exact determination of a rotor size depends on the power factor (C_p) of the wind rotor, the combined efficiency of the transmission and pump (h) and the density of air (r).  However a fairly accurate size of a windpump can be found by taking representative values of 0.3, 0.7 and 0.945 for C_p, h, and r respectively, and equating the mechanical power of the windpump system with the required hydraulic power as shown in equation 44.

h * C_p * 1/2 * r * A * V_av³ = 0.133 * q * H            (44)
where
h    is the combined efficiency of the transmission and the pump ~ 0.7 [-]
C_p    is the power factor ~ 0.3 [-]
r    is the air density. At 2000 m altitude and 20 °C,  = 0.945 [kg/m³]
A    is the swept area of the rotor [m²]

Substituting these known parameters into equation 44, the area of the rotor (A) [m²] is, therefore, given by equation 45.

A = [ 0.113 * q * H ] / [0.7 * 0.3 * 0.5 * 0.945 * V_av³] = 1.14 * q * H / V_av³             (45)

Since a windpump is usually specified in terms of its rotor diameter (D) its size is given by equation 46.

D = (4 * A / p)^1/2                (46)
where
D    is the diameter of the rotor [m]
p    is equal to 3.14

3.    THE ETHIOPIAN EXPERIENCE

3.1    Wind Resource

The total wind resource of Ethiopia is estimated at 20.064 million TJ/year [4].  Wind energy is one of the resources which is virtually unexploited in Ethiopia.  Only sporadic attempts were made by a few organizations to harness this free and inexhaustible source of energy.

According to Adams [5], "the Rift Valley and the Eastern lowlands have a moderate wind regime well suited for medium machines... the Western province 9all around the Sudanese border) are generally poor in wind energy.  The rest of the country (mainly the Central highlands) are suitable for low or medium running machines, especially if careful site selection is used."

Wolde-Ghiorgis [6] has mad a wind energy survey using wind data collected by the National Meteorological Services Agency (NAMSA) and showed that mean winds speeds grater than 2.8 m/s are found extensively in Ethiopia.

Munoz [7] studied 18 drought stricken sites and concluded that wind energy was the most economical and expeditious natural resource to be used for pumping applications in those areas.

3.2    Ethiopian Water Resources Authority (EWRA)

A few commercial windmills - multi-bladed Australian Southern-Cross windpumps - were imported and installed by the then EWRA, notably in the Rift Valley basin. Most of these machines were either blown down by severe storms or were damaged for lack of proper maintenance [Author's observation].

3.3    American Presbyterian Mission at Omo

In 1973, the "Food from Wind Project" had used a series of locally manufactured Cretan Sail windmills for irrigating small plots of land on the banks of the Omo River [8].

3.4    Addis Ababa University (AAU)

During the "Development Through Cooperation Campaign", three types of' vertical-axis and two types  of  horizontal-axis rotors were manufactured and tested by the Mechanical Engineering Department, Faculty of Technology of the AAU. Experimentation on the above wind turbines was discontinued when the Campaign ended in 1976.

3.5    Lay Volunteers International Association (LVIA)

The other main organization that is engaged in wind pumping technology is LVIA.  It is based in Meki and engaged in partially manufacturing multi-bladed windpumps with rotor diameters of 5 and 6 metres locally. Some components of these units are produced in Addis Ababa, others are fabricated in Meki and a few components are imported from Italy. The density of installation of these water abstraction devices is highest in the Rift Valley basin.

3.6    The Experience of the Research and Development Services (RADS) of the Ethiopian Water Works Construction Authority (EWWCA)

An extensive research work was undertaken by RADS on windpumps  using  different construction materials, over-speed control mechanisms and various types of pumps.

RADS had designed, manufactured and tested 7 types of windpump prototypes ranging in diameter from 3 to 10 metres. Only one of these prototypes was a vertical-axis windpump, known as the Filippini Rotor. From the scanty information available to the author, the 10 metre diameter windpump (Fig.6) is believed to be the largest ever built in Africa. It is also reckoned as the first of its type to employ all feathering blades (turning of the blades edgewise by means of fly weights against a return spring to reduce thrust force and power) for high speed protection on windpumps. This feature however, is very common on wind electric generating rotors having blades of not more than 3 in number. The earlier units were high speed runners with aerofoiled Zigba wooden blades, while the later ones were slow runners with steel sheet blades (Fig. 7). Both types of windpumps have their own pros and cons.

Fig. 6: 10 m Diameter Wind Pump and Fig. 7: 7 m Diameter Multi-Bladed Wind Pump

The rotors with high tip-speed ratios (ratio of the blade tip speed to the wind speed) require minimal material for their construction. Nevertheless, their inherent low starting torque feature makes them appropriate only for very high wind speed regimes or require additional torque minimizing devices, a clutch for example, as used by RADS, if they are to be operated in the low wind speed areas.

On the other hand, rotors with more blades (high material consumption) run slower but they are able to pump with more forces. This type of windpumps are suited for low wind speed regimes.

The lessons learnt from this endeavour were:

• Local fabrication of windpumps in Ethiopia is feasible;

• Wind powered pumping for small scale irrigation schemes and potable water supply is appropriate, at least for most of the Rift Valley basin in Ethiopia, where the average wind speed is greater than 3 m/s;

• Field installation of windpumps is simple and can be done with hoists and frames made for this purpose;

• High speed piston pumping must be avoided because:
   - Cavitation and shock loads can cause damage to the water supply system;
   - Buckling of the pump rod can occur; and
   - Reversing of the loads cause slack components to hammer with each other; 
       thereby reducing their life expectancy.

• Low speed piston pumping could be used (with large diameter) for irrigation, and for bore-hole pumping with smaller diameter;

• Rotary pumps can be used with medium or fast runners; and

• Because of their high material consumption and the difficulty encountered to accommodate -high speed protection on vertical-axis rotors, future efforts should concentrate only on horizontal-axis rotors.

3.7    Equatorial Business Group's (EGB) Initiatives

Fabrication of windpumps, among others has the following advantages and benefits:

• Develops indigenous skills;

• Increases employment;

• Makes available spare parts;

• Reduces importation of fossil fuels;

• Where there is no grid power and the average wind speed is greater than 3 m/s;

• Unlike engine pumps, windpumps have no fuel requirement;

• There is no harmful pollution as the result of their use;

• Windpumps have long life, typically 20 years; and

• Local manufacture offers the potential for self reliance of the Country and, therefore, carries with it benefits that reach beyond financial gains alone.

The Energy Division of EBG has embarked on the manufacture of a 6 metre diameter, multi-bladed windpump.  This windpump is mainly based on Tozzi and Bardi's design, an Italian windpump manufacturer employing both casting and welding technologies.  Orientation of the rotor into the wind is realized by a spring loaded tail vane, while the over-speed control is achieved by eccentrically positioning the rotor axis from the tower centre. The manufacturing of these mills is done partly in EBG's own workshop and by sub-contracting other workshops for components that require special purpose machines.

Once again, this venture has vividly demonstrated that windpumps can be manufactured in small engineering workshops in Ethiopia. The attempt has also shown that manufacturing of a product need not necessarily be carried out under one shade. By combining the skilled manpower and machinery of different organizations, high quality products can be manufactured locally.

4.    CONCLUSION

The prevailing customs regulation, which stipulates payment of above 30% taxes on raw materials and only 10% on finished products does not encourage local manufacture at all.  It goes without saying that such a skewed regulation will have to be reversed in favour of lo cal production, if a meaningful industrial growth is to be achieved. Hence, all sorts of incentives are anticipated from the government to change the low manufacturing base of the country to a vibrant manufacturing industry.

REFERENCES

1.  Frankel, P.L. and et al, 1993, Windpumps: A Guide for Development Workers., Intermediate Technology Publications Ltd., UK, London ISBN 1-85339-126-3.

2.  Lysen, E.H., 1982, Introduction to Wind Energy, Steering Committee on Wind Energy in Developing Countries (SWD, later renamed CWD), SWD 82-1, Eindhoven University of Technology.

3.  Meel, J.V. and Smulders, P., 1989, Wind Pumping: A Handbook, World Bank Technical Paper Number 101. Industry Energy Series, The World Bank, Washington DC, USA, 1989. ISSN 0253-7494.

4.  CESEN & ENEC, 1986, Executive Summary. Cooperation Agreement in Energy Sector between the Ministry of Mines and Energy of the Provisional Military Government of Socialist Ethiopia, Ethiopian National Energy Committee (ENEC) and CESEN - ANSALDO/FINMECCANICA Group.

5.  Adams, R.J., 1985, Meteorological Wind and Solar Energy Applications in Ethiopia, (A Report for the World Meteorological Organization).

6.  Wolde-Ghiorgis, W., 1974, Wind Survey in Ethiopia, Department of Electrical Engineering,  Faculty of Technology, AAU, Addis Ababa.

7.  Munoz, C.A.,1974, Analysis of Wind Data In the Drought Affected Areas in Ethiopia., United Nations Development Programme.

8.  Frankel, P.L. ,1975, Food From Windmills. Intermediate Technology Publication Ltd. UK, London.

ABBREVIATIONS

^°C            Degree Centigrade
ha            Hectare
kg            Kilogram
l               Litre
m            Metre
m²           Square metre
m³          Cubic metre
rad          radian
S              Second
TJ            Terra Joule (10¹² J)
W            Watt
N             Newton
AAU      Addis Ababa University
CWD      Consultancy Services in Wind Energy for Developing Countries
EBG      Equatorial Business Group
ENEC      Ethiopian National Energy Committee
EWRA      Ethiopian Water Resources Authority
EWWCA      Ethiopian Water Works Construction Authority
LVIA      Lay Volunteers International Association
NMSA      National Meteorological Services Agency
Plc.      Private Limited Company
RADS      Research and Development Services
SWD      Steering Committee on Wind Energy in Developing Countries

Go back to the updated ATF site or to the main ATF home page at MIT.