The Efficiency Game
Pick The Most Efficient Energy Source
Question: In terms of fuel-in to power-out, which of the below is the most efficient device? Pictured top-left to bottom right are:
(A) a steam locomotive circa 1900, (B) an efficient diesel generator, (C) a thick-film solar cell array, and (D) a modern wind turbine.
See the answer below.
Question: In terms of fuel-in to power-out, which of the below is the most efficient device? Pictured top-left to bottom right are:
(A) a steam locomotive circa 1900, (B) an efficient diesel generator, (C) a thick-film solar cell array, and (D) a modern wind turbine.
See the answer below.
While you're deliberating the above, check out this problem on production efficiency:
An Efficiency Problem
Which widget-making system would be the most efficient to use?
System 1: 100 widgets made, 90% good, 10% rejects. Cost to make: $2.00 each.
System 2: 100 widgets made, 98% good, 2% rejects. Cost to make: $2.75 each.
We waste 10 bad widgets x $2.00 each = $20 in the first system, and 2 bad widgets x $2.75 each = $5.50 in the second system. If the demand for widgets is inelastic (price does not matter), then the second system is obviously preferable. Less physical product and less investment is wasted within its manufacture. Another way to view this is to see the cost of a widget, net of rejects. For the first system, the cost per finished widget is actually $2.22, and for the second, $2.81, because we would average the total manufacturing costs ($200 and $275 respectively) over the number of widgets that can be sold (90 and 98).
If demand is elastic, however, it may be best to accept the 10% loss rate of the first system. We could simply manufacture 10 more widgets, costing an extra $20, for a total cost of $200 + $20 = $220, which is $55 less than system 2, yet it would provide us with 99 sellable widgets. In case you're wondering why 99 widgets, that's because of the 10 extra widgets made, statistically, 1 of those too will fail, with the first system's 10% failure rate. Therefore, 10 - 1 = 9 good widgets can be expected of the 10 made. Add 9 good widgets of the second batch to the 90 good widgets of the first, and we get 90 + 9 = 99 widgets, made for a total cost of $220.
There are many factors that could change the outcomes of this simple example, but it helps to illustrate that the answer really depends on what you are trying to accomplish, what the customer wants, and what is affordable.
System 1: 100 widgets made, 90% good, 10% rejects. Cost to make: $2.00 each.
System 2: 100 widgets made, 98% good, 2% rejects. Cost to make: $2.75 each.
We waste 10 bad widgets x $2.00 each = $20 in the first system, and 2 bad widgets x $2.75 each = $5.50 in the second system. If the demand for widgets is inelastic (price does not matter), then the second system is obviously preferable. Less physical product and less investment is wasted within its manufacture. Another way to view this is to see the cost of a widget, net of rejects. For the first system, the cost per finished widget is actually $2.22, and for the second, $2.81, because we would average the total manufacturing costs ($200 and $275 respectively) over the number of widgets that can be sold (90 and 98).
If demand is elastic, however, it may be best to accept the 10% loss rate of the first system. We could simply manufacture 10 more widgets, costing an extra $20, for a total cost of $200 + $20 = $220, which is $55 less than system 2, yet it would provide us with 99 sellable widgets. In case you're wondering why 99 widgets, that's because of the 10 extra widgets made, statistically, 1 of those too will fail, with the first system's 10% failure rate. Therefore, 10 - 1 = 9 good widgets can be expected of the 10 made. Add 9 good widgets of the second batch to the 90 good widgets of the first, and we get 90 + 9 = 99 widgets, made for a total cost of $220.
There are many factors that could change the outcomes of this simple example, but it helps to illustrate that the answer really depends on what you are trying to accomplish, what the customer wants, and what is affordable.
Answer for the above:
Pick the Most Efficient Energy Source
Pick the Most Efficient Energy Source
Although the typical efficiency of a mid-19th century steam locomotive (A) averaged a dreadful 1-10%, depending upon the speed and temperature it was operating at, modern day steam engine technology today is much more efficient. Using cogeneration and other economizing techniques, they can now provide a remarkable 50-85% efficiency. We didn't show a modern steam engine in the picture, but such an engine would have taken a solid second place.
The very best solar cells (C), made from multi-junction or dual-layer GaAs, have surpassed 40% efficiency but they are expensive. Although the curve of solar cell efficiency has recently flattened, photovoltaic development seems to go through periodic leaps and bounds, with improvements of 5% or better happening almost overnight. In sunny regions, the cost per installed-watt has continued to drop to about that of many power grids, requiring a 7-10 year payback period. Considering the expected life of modern solar cells is 30 years or better, they are very much a viable and attractive alternative in many regions. Once paid for, the 40% efficiency is arguably less important, providing the owner with essentially free, off-grid electricity.
Wind turbine efficiency (D) is a tough question, because it depends upon the design and height of a given turbine, which must be optimized for local wind velocity to realize its best potential. Betz's Law predicts a theoretical maximum of 59.3% efficiency for any wind turbine, although a more recent GGS model calculation predicts a real-world 30.1% in any practical application. This is further reduced as most wind turbines do not operate at their optimized speed all of the time, with perhaps an average efficiency of around 20-25%.
Of course, some of you will wonder just what "efficiency" really means in these contexts. It could also be measured as a % of cost to manufacture a device like a wind turbine, versus what it earns over its expected or actual lifetime. Alternatively, we could compare the energy needed to make and run the device -- its carbon footprint -- versus what it generates. Or, one device may be much more efficient over another because of an existing source of energy (e.g. steam already being released in an industrial process).
As you can see, every device has some role where it might be the most efficient choice. The answer really depends on what someone is trying to do, and what they have available to work with.