Fixed costs and variable costs in your life

Good Evening FPO Readers,

This is a mini lesson in economics.  There are two types of costs, fixed and variable.  A fixed cost is one that remains the same independent of other variables.  A variable cost is a cost that changes based on a combination of variables.  Many bills and purchases in our life have a combination of fixed and variable costs.  A utility bill is a common example.  For any consumable, there is a fixed base account/delivery charge and a variable change based on the amount delivered.  This applies the same to a water, electricity, or natural gas bill.  The fixed cost must be overcome before any variable costs are encountered.

The important concept here is that it is easier to cut variable costs than it is to cut fixed costs.  However, the counter to this is that the price per unit consumed raises since the fixed cost becomes more of the dominant cost of the two.

A useful application of this principle would be a household that has both an electricity service and natural gas service.  The only device on the natural gas line is the hot water heater.  The fixed monthly cost is for delivery is $14 and the consumption by this house is low at approximately $8 per month average.  In this case, it is likely beneficial to switch to an electric water heater when the natural gas unit reaches the end of its life.  With a variable cost that would likely be $12 to $14 per month, the natural gas fixed cost is eliminated since hot water is now provided by the electric service, whose fixed costs are already covered.  Though an electric unit does not heat as fast, this should be an acceptable trade off since the hot water consumption was low enough to start.

An energy cost comparison

The below cost comparison is between the cost of heating with a propane furnace (standard 80% efficient) and an electric heat pump. An electric heat pump is a heat exchange device, where mechanical energy (in the form of an electric motor) is used to compress a fluid, and when decompressed, the fluid creates a difference of heat between two separate spaces. For heating, the hot side of the exchanger is inside the house, and the cold side is outside of the house. No net heat is created as a result except for the power consumed to facilitate this process. What happens is the inside becomes warmer by a given number of BTUs and the outside becomes colder by the same number of BTUs. 1000 Watts of electric power input to the motor can add 2500 watts of heat to the inside by removing 2500 watts of heat from the outside. The 1000 watts from the motor contributes to the heat of the outside because that is where the motor is located.

The ratio of the 2500 watts gained to the 1000 watts consumed is referred to the coefficient of performance (CoP). In this case the Cop is 2.5.  In reality this number is between 2 and 3.5. In our example we will use a CoP of 3.0.

Propane is currently $2.75 a gallon. A gallon has 92000 BTUs of energy. An December example usage of 9,000,000 BTUs consumed at the gas line (7,200,000 heated the house based on 80% efficiency) would cost $269.02. Propane and Gasoline are both expensive, but portable. A heat pump with a CoP of 3.0 would cost $70.32. Still more expensive than natural gas, but a good option. In freezing weather, the CoP of heat pumps goes down fast. In cold weather natural gas wins by a greater margin.

Fluorescent lighting and incandescents

There’s a lot of talk about Compact fluorescent Lights (CFLs) in news and politics. Lighting is a topic in engineering that I enjoy. The #1 reason people look to CFLs is the energy savings. Rightfully so, there are energy savings to be had, but not as much as advertised.

The common measurement of lighting efficiency is lumens per watt. Actually, that’s efficacy. Efficiency is unitless. Below is a table of various lighting technologies and their associated efficacies: (higher numbers are better)

Type of light source Color Luminous effectiveness in lumens per watt
Low Pressure Sodium   (LPS/SOX) yellow/amber 80 – 200
High Pressure Sodium   (HPS/SON) pink/amber-white 90 – 130
Metal Halide bluish-white/white 60 -120
Mercury-Vapour blue-greenish white 13 – 48
Incandescent yellow/white 8 – 25

source: http://en.wikipedia.org/wiki/Light_pollution

There is no question about the compact fluorescent’s luminous efficacy. The general range is 50-70 lumens/watt (http://www.energyfederation.org/consumer/default.php/cPath/25_44_784). The best household incandescents can do 20 lumens/watt.

Doing a real world comparison, the 13 watt CFL that is typically found in stores never seems to be as bright as a 60 watt bulb. Its using 21.67% of the power. There are always games that can be played with lumens and color temperatures. From observation, the 23 watt CFL (100 watt replacement bulb) is nearly identical in brightness to a 75 watt incandescent bulb. That’s still using only 30.67% of the power of the incandescent. For saving energy it’s a really good deal, considering how long they last and how much energy they save. The higher cost of the CFL bulb will be offset by these savings.

That said, there is a large list of uses for CFL’s that I would recommend against:

1. It wet locations. This includes bathrooms with showers. Not all CFLs are created equally, but I stopped putting them in the bathroom as moist air messes them up.

2. In rough service conditions. These bulbs present an environmental hazard (mercury) when broken. The mercury isn’t a problem if disposed of properly. I recommend a specific rough service light for these locations.

3. Vibration prone locations. Next to a furnace, evaporative cooler, washing machine; a CFL will lead a shortened life. This makes the higher cost of the bulb not worth it.  Incandescents last longer in these conditions. The electronics in the CFLs tend to be the issue when located in vibration prone locations. Integrated ballasted fixtures can help this problem, but that requires changing out the current fixture.

4. Dimmable fixtures. Incandescents, just plain dim better, (as they function as a “blackbody radiator”) and provide for better mood lighting when doing so. CFLs keep the same color temperature when dimmed. Only a “dimmable” CFL may be used in these fixtures. These lights are expensive, at least for the time being.

5. In the cold. CFL’s have improved greatly in this area, but 0 degrees F still serves as a limit on these lights. Incandescents work fine in the cold.

6. On-off-on conditions. CFLs take time to warm up and are not designed for locations where turning off and on the lights repeatedly is common. This is another reason why I refrain from using CFLs in bathrooms.

7. Hot locations. The heat can damage the electrical ballast components of a CFL, reducing its life.

Keep in mind CFLs save quite a bit during the summer in the form of reduced air conditioning loads. Then again, most of the summer is daylight, so I don’t use lights as much. In the winter, the extra heat from incandescents warms the house. The only loss there is the cost difference between electricity and your heating source; natural gas in my case. Electric heat in my area costs about twice as much as natural has heat for an 80% efficiency furnace. In that effect, using CFLs in the winter will save me only 33% on electricity costs when I get to consider the heat gained from incandescents less the difference of the cheaper natural gas fuel. Another problem of CFLs is that they decrease in efficacy over their life. What once was 60 lumens/watt can decrease down to 80% (48 lumens/watt) of that by the end of its life, with much of that decrease in the beginning of the lights life.

This doesn’t mean that I am anti-CFLs. I like the technology, and I use them in my house. The main floor lights; where I am at are either T-8 tube fluorescent of CFL’s. Those lights are my main use lights, not located next to any vibration sources, or moisture sources. The fixtures are simple with no dimmable features. Not too hot, not too cold in color temperature. The two fixtures, one a T-8 fluorescent, the other using CFL’s account for the majority of my light usage.

Fuel Economy Savings

The high price of gas is driving the increase in fuel economy for new cars.  Here’s the reason.  The higher the cost of gas, the higher the cost per mile of travel.  It is difficult to change the market price of gas, but it is possible to change to a more efficient car.  A four cylinder is the best choice in this case.  The chart below shows the cost per mile for $3.00/gal gas.

The x-axis is mpg, and the y-axis is cost per mile.  RVs are at the low end of this scale at around 5-10 Highway mpg depending on the setup.  Trucks are next at 10-20 MPG.  Large cars and performance cars are around 15-30 mpg.  Economy cars and hybrids top the chart at 30-55 mpg.  Each group of cars is significantly less expensive to operate than the last.  That’s where the change is.  People are trading in their RVs and trucks for less costly to operate vehicles.  The furthur to the right on the chart, the less percent increase there is in the money spent on gas.  11-13 mpg is a more significant change than 31-33 mpg.

Note that the change from 11-13 MPG is more significant than 31-33 MPG.  There is decreasing benefits once a certain Fuel Efficiency is reached.  The limit is eventually reached due to the laws of thermodynamics.

Note that the change from 11-13 MPG is more significant than 31-33 MPG. There is decreasing benefits once a certain Fuel Efficiency is reached. The limit is eventually reached due to the laws of thermodynamics.

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