Heat your home with a dehumidifier

Posted on October 25, 2009February 7, 2016 by Rob

A moisture problem

We (my wife and I that is) keep the temperature in our home relatively low in winter. As I’m writing this, it’s a balmy 16 degrees C in my living room. My lovely wife is wearing a toque and she’s about to put on another sweater because she’s feeling “a bit of a chill”, but she’s a trooper and wouldn’t have it any other way. That’s how she was raised. In Richmond, BC, where we live, winters are… well… wet. It’s pretty much a case of 100% relative humidity outside 24/7 and the water table is at ground level… well… truthfully sometimes it’s a few feet above ground level, but that’s why we have the pumps.

Combine 100% relative humidity outside with low temperatures inside and as you might expect, we occasionally have issues with condensation, especially on windows. “Experts” generally don’t recommend keeping interior temperatures below about 17 degrees C for exactly this reason. I don’t care much for expert opinions (experience has convinced me that I’m more expert than most of them), but I also don’t care much for condensation.

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A solution with a bonus: “free” energy

The solution (without simply raising the temperature of our home), is a dehumidifier. While I purchased it for its intended purpose (to reduce humidity levels) I now realize that it also makes a very effective heater. Ah… but doesn’t it cost money and energy to operate a dehumidifier? Well… actually… NO! At least not in the winter, when we’re heating our home with electricity anyway. In fact, a dehumidifier is MORE efficient than an ordinary electric heater, which is already 100% efficient. Yes, a dehumidifier is more than 100% efficient at heating your home. That is to say the amount of heat a dehumidifier will release into your home is greater than the amount of electrical energy it will consume. The reason is simple: a dehumidifier removes energy from water vapor in the air in order to condense it to a liquid. This energy is released into your home.

It’s all about enthalpy

There is a property of any substance known as the enthalpy of vaporization. “Enthalpy” really just means energy. The enthalpy of vaporization of a substance is a measure of how much energy it takes to convert a given mass of the substance from a liquid to a gas. It also indicates how much energy is released when a given mass of the substance is condensed from a gas to a liquid. The enthalpy of vaporization of water is 2257 kJ/kg.

What is the efficiency?

How efficient is a dehumidifier at heating your home? Let’s figure it out together. I mean that literally. As I write this, I haven’t actually figured it out yet myself. I’m flying by the seat of my pants here, people; I’m a scientist gone rogue. But luckily I’m also a scientist who recently acquired a portable dehumidifier. I plugged it into a Kill-A-Watt meter several hours ago to measure exactly how much electrical energy (indicated in kWh by the Kill-A-Watt meter) it consumed. It’s been running for about 8 hours and it has consumed 3.87 kWh of electricity. Thus, based on the first law of thermodynamcis I know it has put at least 3.87 kWh of heat into my home.

However I have also determined with a simple digital scale that it has condensed 3.23 kg of water in that same time. How much additional energy did it release into my home as a result of that? That’s where the enthalpy of vaporization comes in. 3.23 kg multiplied by the enthalpy of vaporization of water (2257 kJ/kg) gives 7290 kJ of energy. A kWh is equivalent to 3600 kJ so 7290 kJ is equivalent to 2.025 kWh.

Thus, the total amount of heat released into my home by the dehumidifier over the last 8 hours is equivalent to the 3.87 kWh of electricity consumed, plus the 2.025 kWh of energy released by the condensation of water. The “efficiency” is equal to the energy output divided by the energy input or in this case (3.87 + 2.025)/3.87 = 1.52 or 152% efficiency. An efficiency over 100% is more appropriately referred to as a “coefficient of performance” since technically, it is impossible to achieve greater than 100% efficiency (having more than 100% efficiency in energy conversion would defy the first law of thermodynamics). So if you ever measure more than 100% efficiency, as I just did, what it really means is that you have moved energy from one place to another rather than simply converted energy from one form to another. Such is the case with a dehumidifier which removes energy from water vapor and releases it into the home in the form of heat, condensing the water to liquid in the process. But whatever the terminology you want to use, the fact remains that I can release 1.52 kWh of heat into my home for every 1 kWh of electricity my dehumidifier consumes.

What’s the payback time?

I paid about $250 CAD for my dehumidifier. It consumes about 480W of electricity (3.87 kWh in 8 h) and outputs about 730W of heat (480W*1.52) into my home. I can buy a decent electric heater that will output 730W for about $50. So the difference in price is about $200. Let’s calculate the difference in the cost to operate. A 730W electric heater consumes exactly 730W of electricity. The dehumidifier only consumes 480W of electricity to produce the same 730W of heat. The difference (730-480) is 250W. Effectively I get a free kWh (1000 Wh)of heat for every 4 hours of operation. I currently pay about $0.07 per kWh for electricty, so I save about $0.42 per day when operating the dehumidifier in place of a heater. My heating season runs from October through March, or around 180 days of the year. Therefore, I can save about 180*$0.42 = $75 per year by operating the dehumidifier in place of a heater. That will take a little over 2.5 years to pay back the difference in price of $200.

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Will this work for anyone?

In a word, “No”. The human body is most comfortable at a relative humidity between 20% and 60%. I can run my dehumidifier continuously in winter and not expect to ever drop below 20% relative humidity inside my home. The same may not be true for homeowners in other locations maintaining their homes at higher temperatures than I do. Heating with a dehumidifier works for me because of the high relative humidity in Richmond, even in the winter, and because of the low temperature at which I keep the interior of my home. It could work well for anyone who lives in a similar environment and keeps their home at a low temperature. But if you live where temperatures are usually below 0 degrees C outside in winter then you likely have a much lower relatively humidity. In that case, a dehumidifier will not be able to condense nearly as much water for a given amount of input energy and its operation may bring the relative humidity below a comfortable level.

Clothes dryer vs a rack and a dehumidifier

If you’re considering hanging your wet clothing to dry inside your home, vs using your drier, then you should know that a dehumidifier will be far more efficient than a clothes dryer. In the case of a clothes dryer, electrical energy is used to vaporize the water in your clothing and the water vapor (and all the energy you’ve put into it) is expelled from your home through your drier vent. There is a net loss of energy from your home. If instead you use a dehumidifier, the heat already in your home is used to vaporize (evaporate) the water in your clothing. This energy is recaptured by the dehumidifier when the water vapor is condensed to liquid. Unlike the drier, the dehumidifier doesn’t expel any energy from your home.

Heat pump vs dehumidifier

A dehumidifier is effectively a heat pump. Rather than extracting heat from the ground or the outside air, a dehumidifier extracts heat from water vapor contained in a home’s inside air. In my home, for reasons given above, I can run my dehumidifier continuously without reducing the relative humidity in my home below a comfortable level and I’ve found the coefficient of performance (COP) is about 1.52. A typical air source heat pump has a COP of around 4 assuming an outside temperature of around 0 degrees C (a typical Richmond winter). A typical ground source heat pump has a COP of around 7 assuming a ground temperature of around 10 degrees C (a typical Richmond ground temperature). So clearly, a heat pump (either air or ground source) is much more efficient. If I had a heat pump, I would be consuming more energy than otherwise by operating my dehumidifier. That said, I feel secure in the knowledge that I can run my single dehumidifier continuously and consume less energy to heat my home than if I were running an electric heater. I’ll save the installation of a heat pump for another day… perhaps.

Can you heat your whole home this way?

No. If I were to install more portable dehumidifiers to provide all the heat my home requires (to maintain a balmy 16 degrees C all winter long) I would almost certainly bring the relative humidity below comfortable levels, and the COP would drop below the measured value of 1.52 simply because there isn’t enough water vapor in the air to be condensed. So the idea of using a dehumidifier to heat one’s home is clearly not scalable. At best a dehumidifier may provide suplemental heat. I think I might get away with using two portable dehumidifiers continuously which would each save me about $75 per year based on the calculations above. That’s about $150 per year in total. Currently, that’s about 10% of my home’s annual heating bill.

Measure the drag coefficient of your car

Posted on October 10, 2007December 24, 2015 by Rob

Purpose

The purpose of this experiment is to determine your vehicle’s drag coefficient Cd and coefficient of rolling resistance Crr. This is done by measuring your vehicle’s speed as a function of time while coasting in neutral (also known as a coast down test).

Why would you want to know Cd and Crr for your vehicle? Well, suppose you’re interested in modifying your vehicle for improved fuel efficiency. You might consider modifications such as air dams, wheel skirts, removing mirrors, switching to low rolling resistance tires, etc. Cd and Crr offer a quantitative method of comparing vehicle performance before and after these types of modifications to see if you made any improvement.

Equipment

You will need the following equipment:

a vehicle (and someone with a driver’s license)
a clock or stopwatch
a pen and paper (and someone other than the driver to record data)
a flashlight (driving at night avoids traffic)
a long stretch of flat road with little traffic or wind
Excel or another spreadsheet application. I prefer OpenOffice Calc which you can download and use for free, but its Solver function does not handle non-linear systems (yet) so you’ll have adjust input variables manually by an iterative process to minimize the error between the model curve and your data (it’s not too hard, I promise).
The spreadsheet I created to analyze the results. You can download it here: Drag_Coefficient.xls

Background Information

First, let’s define some quantities:

Fd is the force on the vehicle due to air resistance (drag) in Newtons
Frr is the force on the vehicle due to rolling resistance in Newtons
F is the total force on the vehicle in Newtons
V is the vehicle’s velocity in m/s
a is the vehicle’s acceleration in m/s²
A is vehicle frontal area in m²
M is vehicle mass including occupants in kg
rho is the density of air which is 1.22 kg/m³ at sea level
g is the gravitational acceleration constant which is 9.81 m/s²
Cd is the vehicle’s drag coefficient we want to determine
Crr is the vehicle’s coefficient of rolling resistance we want to determine

Now for some formulas:

Fd = -Cd*A*0.5*rho*V² (formula for force due to air resistance or drag)
Frr = -Crr*M*g (formula for force due to rolling resistance)
F = Fd + Frr (total force is the sum of Fd and Frr)
F = M*a (Newton’s second law)

Note that both Fd and Frr are negative indicating that these forces act opposite to the direction of the velocity. Note also that Fd is increases as the square of velocity. This is why driving at high speeds is much less efficient than driving at low speeds. Combining these formulas with a bit of algebra gives us the acceleration due to air and wind resistance as a function of velocity:

a = -(Cd*A*0.5*rho*V²)/M – Crr*g

Note that the acceleration is negative indicating that air and wind resistance will cause the velocity to decrease.

I created my spreadsheet (see Equipment section above for download) based on these formulas to generate a model of velocity vs time that can be compared to actual data. The model values for Cd and Crr can thus be adjusted until the model matches the data. This adjustment can be done manually, by overwriting the values of Cd and Crr with new values till the model matches the data, or it can be done using a “Solver” function.

Procedure

You can determine Cd and Crr from the same set of test data by measuring velocity with respect to time as your vehicle coasts in neutral. Note that Crr will not be pure rolling resistance but will include some drive-train resistance as well.

1. Drive to a flat road with little traffic or wind.

2. Have the passenger ready with stopwatch and paper to record data.

3. Have the driver accelerate up to above 70 km/h or so, and shift into neutral.

4. Record data as follows. The driver should indicate when the speed drops to exactly 70 km/h. At this time (t=0) the passenger should start the clock. The passenger should indicate every 10 seconds after that and the driver should call out the current speed to the nearest whole km. The passenger should record this value next to each time.

Aside: If you have a digital camera capable of recording several minutes of low resolution video (as most people seem to have these days), the process is much easier and more accurate. You don’t need any equipment except the digital camera. Simply have your passenger record a video of your speedometer during the coast down tests, or find some way of mounting the camera so you can do the recording without an assistant. Using a free program such as Avidemux (http://fixounet.free.fr/avidemux/) you can play the video back on your computer frame by frame and view the speeds at desired times.

5. Repeat the test in the opposite direction.

6. Repeat the test in both directions twice more (6 trials in all, 3 in each direction). All these values will be averaged for a more accurate analysis.

7. Download the spreadsheet I created (see Equipment section above) and enter all your data following the instructions included. The spreadsheet averages data from all 6 trials to create a single data set representing velocity (V actual) as a function of time. It then generates it’s own model for velocity (V model) based on entered constants and initial guesses for Cd and Crr. Excel’s “Solver” function can be used to adjust Cd and Crr in order to minimize the error between the model and actual data. If you are using OpenOffice Calc (which I highly recommend and which you can download for free from http://www.openoffice.org ), unfortunately, the solver function currently only handles linear systems, so you will have to adjust the input values manually to minimize the error between the model and the data. Once the error is minimized and the model data matches the actual data as best it can, then Cd and Crr are correct.

Results

Here are the quantities I measured for my car (a 1992 Geo Metro):

M = 1000 kg (about 850kg curb weight plus 150 kg of occupants)
A = 2.3 m² (a reasonable approximation based on measurements of my car)

A plot of velocity vs time is shown below. It is based on the averages from my 6 trials. You can see that the model curve closely matches the data points.

The values of Cd and Crr for the model are:

Cd = 0.370
Crr = 0.0106

Therefore, these are the drag coefficient and coefficient of rolling resistance calculated for my car.

These values are nice to know. However, in practice, if you want to compare performance before and after making modifications to your car, you can get faster results just by measuring the time to decelerate from speed A to speed B. Pick high to medium speeds if your modifications are likely to affect drag. Pick medium to low speeds if your modifications are likely to affect rolling resistance. Don’t forget to take multiple measurements in each direction and average the results.

For more experiments you can do on your car see my website IWillTry.org .

Update 2009-01-02

I’ve learned a lot since originally posting this 16 months ago. I’ve played with measuring Cd and Crr under different conditions on a number of vehicles and other experimenters have picked apart and tweaked my spreadsheet for their own uses.

My experience is that there IS a mistake in one of the underlying assumptions of the model: namely that the force of rolling resistance is constant independent of V. Vehicles are designed with negative lift (so they get pushed into the road more at higher speeds, improving handling) so the force of rolling resistance also has a component that varies with V like the drag force. The force of rolling resistance also includes a small component of viscous force (drivetrain) which varies with V.

The model assumes that the drag force is related only to V² and that the force of rolling and drivetrain resistance is constant. In reality the force of rolling and drivetrain resistance is also related to V2 and V. So a better model of the force on a moving vehicle is:

F = iV² + jV + k where i, j, and k are constants.

A curve based on that model more closely matches actual coast down data indicating it is a more accurate model. But after solving for i, j and k, there is no way to extract meaningful values of Cd and Crr since by definition, they assume i is related only to drag, and j is 0, neither of which is entirely true. To think of it another way, Cd and Crr values define a model which is only an approximation of the real world. A physical object doesn’t really have a drag coefficient. Only the model of the physical object does.

As mentioned above, if you want to compare performance of a vehicle before and after making mods, the difference in coast down time itself is more meaningful than the change in Cd or Crr extracted from coast down data.

Update 2012-03-06

One reader, Frank Bernett, has used the above techniques to determine drag and rolling resistance as a function of velocity for his MG Midget electric vehicle. He has gone a step further and also used GPS data from his drive to work to build a simulation of sorts to test how vehicle modifications (reduced mass, rolling resistance, and drag) will affect energy consumption for his particular commute. Very clever. Check it out.