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Heat those Feet!

Infrared image of a cold left foot (25°C with 19°C toes), compared to a warm (33°C) right foot.Infrared image of a cold left foot (25°C with 19°C toes), compared to a warm (33°C) right foot.One of the more bothersome aspects of living in an unheated house (with tile floors in much of the house, in my case) is having cold feet. Spring has arrived, so perhaps this post is not as timely as it might otherwise have been. But let’s consider the energy costs of various approaches to warming up cold feet.

The main problem I have with cold feet is that they make it hard to go to sleep. Otherwise cold feet don’t seem to distract me from normal activities. But let’s say that your feet are cold and that you cannot stand it any longer, and therefore must warm them up. I’ll look at a number of options, assessing how much energy is consumed for each. We’ll try hot water in the sink, a space heater (or blow dryer) under a blanket, a heating pad wrapped around the feet, or good-old metabolic energy.

Defining Cold Feet

First, let’s establish an energy scale for cold feet. Normal body temperature is 37°C (98,6°F). Feet can feel pretty cold at 25°C (which is what my left-foot measured in the infrared picture above). Let’s say that this is their temperature through-and-through. Let’s further say that your feet occupy a liter of volume together (at the density of water, this corresponds to a mass of 1 kg, weighing 2.2 lbs). At the specific heat capacity of water (4184 J/kg/K), the 12°C decrement amounts to a 50 kJ energy deficit. Remember this number.

Hot Water Treatment

Let’s say you fill a sink or small basin with hot water in which to stick your feet. Better that than a whole bathtub—requiring vastly more water to creep up over the feet. About a gallon and a half (6 ) should do it.

Because cold feet are associated with the cold season, the water probably enters the hot water heater at a cold temperature. I’ll be conservative and say it’s 10°C. We’ll pretend the water is heated to 40°C. The hot-water heater surely heats water to a warmer temperature, but it will get mixed with cold water to keep the water from stinging the cold feet (some of this is probably inevitable, but the water should be at least as hot as normal body temperature). In the end, it’s just the added thermal energy that counts—even in the mixing case—so heating 6 of water 30°C takes 750 kJ of energy. This is 15× more than is needed in the feet, for an efficiency of 7%.

But we’re not done. Unless the hot water heater is right next to the tap, a fair bit of hot water is lost in the pipe on its way to the sink. For distant sinks, this might require at least 4 of water before a single hot drop emerges. And this “lost” water is at full-temperature: perhaps 50°C, adding another 670 kJ of energy—roughly doubling the energy outlay. We’ll assume you use a less distant sink, and consume a total energy (sink plus pipes) of something like 1 MJ, for a net efficiency of 5% into your feet.

Why such low efficiency? Think about the fact that when your feet are warmed up, the water temperature in the sink is still pretty high, and this thermal energy either dissipates into the room or is simply dumped down the drain—where it does not even contribute to house heating. Also, the hot pipes between the heater and sink will sit there oozing heat into their environment after the tap is shut off. Very little is available to your feet.

Fire-Prone Power-Heating

Alternatively, you could put your feet in front of a toasty space heater. Or you could direct a blow dryer onto your feet. Again, you should expect low efficiency, since the air bouncing off your feet is still pretty warm: very little gets transferred into the feet.

So you can help matters by putting a towel or blanket over the heater and your feet in a little tent, limiting the air volume and thus retaining more of the heat. I don’t actually advise this as a strategy for warming feet. Besides being a fire hazard, it’s got other problems like overheating the space. I’m using it purely as a thought experiment for its value in illustrating a quantitative approach. Let’s say that the heater runs at 1500 W, and you leave it on for five minutes. Since a Watt is a Joule per second, multiplying 1500 W by 300 s yields 450 kJ. I can’t vouch for this being the right amount of time, but it should take at least this long for your actual feet to warm up, given the timescale for thermal diffusion (though aided by circulation).

In any case, we have a crude approximation for the energy associated with this method. It requires something on the order of 500 kJ: less than for the hot water approach, but still only getting 10% of the energy into your feet. You’ll be much better off (and safer) if the heater is thermostat-limited, but will still lose significant heat through the surface area of your “tent.”

Heating Pad

A heating pad a little larger than a sheet of paper can get plenty toasty with just 40 W of power input. It may take five minutes before it feels warm, and then perhaps another 10–15 minutes wrapped around your feet to bring them up as well. But even running the pad for half an hour, we’re looking at only 72 kJ of energy consumed. This is suddenly vastly more efficient than the previous methods.

The efficiency stems from applying heat exactly where it’s needed. Picture the pad wrapped around your feet (folded over the toes, for instance), and a blanket swaddling feet and pad in a thick, immobilizing bundle. The geometry strongly favors transmission of power straight to the feet. And the modest power demand of the heating pad means confinement in this manner does not lead to excessive build-up of heat, as would more easily happen with the space heater under a blanket.

Our electric mattress pad (30 W per side over a much larger area) is a variant on this theme, and is what I typically rely upon to prepare cold feet for sleep-mode.

Burrito Power

No, not that kind of power. I covered natural gas a few weeks back. I’m referring to metabolic power to get the feet back in line. If you eat 2000 kcal/day, this is equivalent to about 100 W of continuous power. If you could magically channel all of this straight to your feet, it would take 500 seconds (a bit over 8 minutes) to get 50 kJ into your feet. Of course, a much smaller fraction of your metabolic power will be routed to your most extreme appendages, so it will naturally take much longer to warm up. If only 5% of your metabolic energy is channeled to your feet, it may take 2–3 hours. But heat flow is always proportional to temperature differences, so as long as circulation to your feet is decent, a disproportionate amount of energy may be exchanged there. In my experience, less than an hour is required for feet to warm up on their own, once insulated well.

The idea is to put your cold feet into super-insulated socks and shoes or slippers, and let your body do the rest. I have down booties (from REI) that work very well for this. Of course, the primary role of the slippers is to use my metabolic energy to prevent my feet from getting cold in the first place. But I sometimes get distracted and end up with poorly-clad cold feet. My response to this is always to put on my down slippers and wait for the magic (while continuing to be distracted).

If you want to up the ante, exercise. Then you ratchet up your power plant considerably, and probably more importantly stimulate increased circulation to your active feet. Jump rope, jog in place, or some other activity to get your feet moving, and I’ll bet five or ten minutes will do the job.

As an amusing variant, a friend suggested the spousal belly power approach. Cold feet? No problem: just place them on hubby’s warm tummy for a few minutes and all is right with one person’s world.

Who Cares?

A post on warming up cold feet may seem pretty lame. After all, are not our problems much bigger than cold feet? Indeed. But the post serves to illustrate a few valuable lessons:

  • We can approach questions about which responses make the most sense energetically based on estimation techniques. It may not be precise even to a factor of two, but this is often plenty good enough to sort out the energy-frugal from the energy wasteful.
  • It is best to put heat where it’s needed, with laser focus. As an alternative to quantitative estimation, think about where the heat goes. Does it heat up things you don’t care as much about, like pipes, the sink, the sewers, the air in the room, etc.? If it’s the feet you want to heat, concentrate on putting the heat only there.
  • Energy reduction is a personal choice, with personal impacts. Cold feet is one of those personal issues that may give people, well, cold feet about reducing heating in their home. Illustrating ways to cope with these annoyances (or barriers) is an important part of moving forward.

For what it’s worth, I wrote this post with one cold foot, in preparation for the banner image. So discussing cold feet was more than an idle abstraction during the process. Yet I had so much fun, I hardly noticed.

What do you think? Leave a comment below.

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