Calculation of the speed of wind

Calculation of the speed of wind required to sufficiently power 500 houses
through wind driven turbines
Table of contents
Contents
Executive summary...................................................................................................1
Introduction...............................................................................................................1
Scenario of the question............................................................................................2
Solution I (Power consumption for 500 houses)....................................................3
Solution II (Required speed of wind).....................................................................3
Solution III (safe speed of blade tips)....................................................................3
Speed of blade tips..............................................................................................4
Conclusion.................................................................................................................5
References.................................................................................................................6
Executive summary
This report presents a detailed analysis and answers to questions in a scenario of
power consumption in households and wind turbines being the source of energy.
Given some turbine parameters such as the number of blades and their length,
other important factors such as speed of wind required is determined by calculation
in order to meet the energy consumption demand for 500 households.
Introduction

Power given out (output power) from wind turbines is dependent on factors such as
speed of wind, density of air, size of the wind turbines, the length and radiusof the
turbine rotor blades and efficiency factor.
Regarding speed of wind, reference is made to the speed at one point in time and
not the avearge speed. The density of air depends on humidity, temperature and air
pressure. Efficiency factor is a measure of the amount or part of the wind blowing
through the turbine blades is converted to electricity. The formula therefore used to
work out power output from wind driven turbines is given as; (Casini, 2015)
P= π
2 × r2 × v3 × ρ ×η
Where r denotes the radius of turbine blade, given in meters.
V denotes speed of wind, measured as meters per second (m/s).
Air density ρ in kg /m3
η denotes the efficiency factor.
And P is the output power calculated in Kilowatts.
1 watt= 1kg m2
s3
In order to achieve a high output power, it entirely depends on the speed of wind as
the most important factor.This is evident from the fact that the speed of the wind
taken into consideration goes into the formula as a power of three. The length of
the rotor blade is taken into the calculation squared since it caters for the area
through which the wind blows.

Scenario of the question.
In accordance to statistics from British gas company, consumption of electricity in
households on average was established to be 720 kWh on average, over a three-
month period. By making an assumption that the rate of consumption is annually
consistent, the task is to make an estimation of the output power from a wind
turbine that can sufficiently power 500 houses.
Solution I (Power consumption for 500 houses)
1 household consumes at the rate of 720 kWh, therefore for 500 houses, the power
consumption will be;
720 ×500=360,000 kWh
Expected output power from turbine ¿ 360,000 kilowatts .
Solution II (Required speed of wind).
The required speed of wind sufficient to supply power for 500 houses;
P= π
2 × r2 × v3 × ρ ×η
Parameters of the wind driven turbine are:
Efficiency of the turbine (C) is 0.4.
Air density is 1.2 kg/m3
Length of blade is determined by the last digit of student ID + 30 m. (34 m)
Substituting parameters in the power equation we get;
Taking r =34 m