Efficiency
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Efficiency and Effectiveness:
General definitions.
Efficiency and Effectiveness of the end product are two key ways of judging how well the design process has been executed.
In general efficiency is defined as desired output divided by input given. It is expressed as a percentage.
In general effectiveness is measured by capital cost per unit of desired output. This assumes that the running costs are reasonable.
Where they are not effectiveness can be measured by weighted average of capital cum running costs per unit of desired output.
Some people use the Yearly Total Cost of Ownership per unit of desired output.
Where projects incur capital expenditure over a number of years or where there are large running expenses or moth balling expenses at the end of the project, time discounted Total Cost of Ownership per unit of desired output is used to measure effewctiveness. Lastly some people add the cost of recycling the project i.e. making it boo-neutral as part of Total Cost of Ownership.
Mo sat engineers concern themselves only with efficiency and design for maximum efficiency.
However good designs are possible with low efficiency and high effectiveness.
Solar Cooker Efficiency
NB':'The process described below assumes that we are trying to measure the fficiency of a focussing solar cooker.
It can easilky be adapted for a non focusing box solar cooker by replacing the area of reflector by the area of glass that lets the light into the box solar cooker.
If the box cooker has reflectors side panels, then their areas are also to be added to the area of glassn for calculating efficieny.
Input Energy
In case of a solar cooker input is measured by the amount of sunlight that falls on the reflecting surface.
If the reflector has portions that are not covered with reflecting surfaces or are hollow, they are ignored in calculating the input.
The Solar Constant is a Physical Constant that states how much energy each square centimetre of the earth receives in one minute time.
Its value can be expressed as 1.9 calories per square centimetres per minute.
Multiplying it by the reflecting area gives the input per minutes.
Further multiplying it by the time of the experiment gives the total input energy.
Desired Output
There are many ways to define the desired output and make the measurements to determine the efficiency.
The method outlined below is a simple method using readily available day to day tools.
It also allows inefficiencies due to tracking mechanism to be taken into account in calculating the efficiency.
The key measurement is the time taken to evaporate a measured weight/volume of water using the solar cooker.
Secondary measurements are the weight of the vessel that is used to boil the water and the ambient temperature while it is being evaporated.
Most vessels so used are made of aluminium whose specific heat is a physical constant that can be readily pulled off the net.
Its value can be expressed as 0.21 calories / gm.
Calculation Process
Calculate the Input
Multiply the Area of the reflector by Solar Constant and the time required to evaporate the water. This will yield input as Calories.
- Input = Area * Solar Constant * Time
- Typically this will be a large number and it is converted to a smaller number by dividing it by One thousand to give the answer in Kilo Calories.
Calculate the Output
The calculation of output obtained has three parts
- Calories required to heat the water to boiling point (100 degrees centigrade)
- Calories required to evaporate the water and
- Calories required to heat the vessel to the boiling point of water.
- The sum total of the three parts is the Output obtained.
Calories required to heat the water to Boiling point:
- Calories = Weight of water * ( Boiling Point – Ambient Temp)
- Calories = Weight of water * ( 100 – Ambient Temp)
Calories required to evaporate the water:
Converting water at boiling point into steam i.e. to evaporate it, requires a very large amount of heat known as latent heat of evaporation.
It is 540 calories per gram of water.
- Calories = Weight of water * Latent Heat of Evaporation
- Calories = Weight of water * 540
Calories Required to heat Aluminium Vessel:
Compared to Water, Metals need different amount of heat for a gram of them to rise in temperature by one centigrade. Aluminium, compared to water,for instance needs only one fifth the amount of heat.
This is expressed by stating that the Specific heat of Aluminium is 0.21
- Calories = Weight of vessel * Specific heat of aluminium*(100- Ambient Temp)
- Calories = Weight of vessel * 0.21*(100- Ambient Temp)
- The sum total of the three parts is the Output obtained.
Efficiency Calculation
Efficiency is simply obtained by dividing the Output Obtained by Input given and expressing it as a percentage.
Efficiency = Output/Input %
An Example Spread Sheet
On the next page I have placed an Example Spread Sheet where efficiency of two cookers with reflector areas of 2.5 Sq mts and 10 sq meters have been calculated.
The data used in the spread sheet is not actual data got from any physical model.
You are invited to calculate the efficiency of your own cooker and report the results here.
