Heat those Feet!

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.

38 thoughts on “Heat those Feet!

  1. You forgot my favorite method of warming up my feet (well, second favorite, I much prefer the shared warmth approach, but spouse doesn’t agree): the hot water bottle!

  2. You can use waste heat from a computer to warm your feet. I got a section of diameter flexible dryer vent duct and connected one end to the exhaust of my wife’s desktop computer and aimed the other end where her feet go. This has the direct benefit of keeping her feet warm while she’s on the computer, and also helping the computer to run a bit more efficiently since the hot air doesn’t pile up against the wall. When it’s not winter, I move the free end of the duct so that the heat is blown away from the computer user.

    Paul Wheaton, permaculture advocate, has some great tips for localized heating at this webpage: http://www.richsoil.com/electric-heat.jsp

  3. There is some Indian old story about how the sandals, foot ware was developed. It goes something like this: The ruler was not happy with all the rocks and thorns hurting his feet, so he ordered that the whole land would be smoothened and covered with leater so it would be pleasant to walk thereupon. But his smart advisor suggested that perhaps we could cut pieces of leather and fit to our feet……As a general approach in how one can adapt oneself to the environment rather than adapting the environment to us….

  4. For hot water down the drain, there are drainwater heat exchangers in which the cold water input to a hot-water heater is put through a copper pipe wrapped in a coil around the drain pipe, which during periods of continuous use (e.g. a shower) will pre-heat the water going to the heater.

    I’ve wondered how far one can get directing energy where it’s needed. Even though electric is a loser for overall efficiency, because you’ve thrown away 2/3 of the heat at a power plant already, it can be scaled down and directed to a much greater degree than gas or oil, as your heating pad example illustrated. Perhaps, in climates where an unheated house isn’t comfortable in the winter, one could use exclusively electric radiant heat, directed at the actual people in a room, instead of trying to heat an entire house. Sort of an array of (incandescent!) light bulbs that actually exploit the common criticism that they’re really just heaters: they’re heaters that can be readily turned on and off and pointed where heat is needed.

    • Drainwater heat exchange sounds nice, but the hot water heater usually kicks on near the end of my short shower (if at all), and most of its run-time is after the shower is over. I’ll be doing a separate post on showers in the coming weeks/months, so others out there may wish to save their comments on showering until then.

      • The water heater coming on at the end of shower or not at all does not mean the drain water heat exchanger doesn’t save energy. If you disagree, I’ll follow up after your shower post.

        • I really don’t understand what the timing of the thermostat in the water heater has to do with the percentage of recoverable heat from the exchanger in this example either. It only makes sense that the water heater would come on less often or for a shorter time periods to recover.

        • I was stuck in the mindset that cold water enters the water heater only when the heater turns on (after the used hot water is already drained away). But I wasn’t thinking straight: cold water enters at time of use, to be heated later. So yes, heat exchange with the effluent would result in higher temperature water re-stocking the reservoir, independent of when the burner comes back on. My bad.

  5. Rice Bag! I’d be interested in finding out how much energy is used to heat a rice bag in the microwave (I usually leave it in for 5 minutes). It comes out almost too hot to touch but keeps my feet warm in bed for several hours.

    • Approximately 1500 W for 300 seconds is 450 kJ. Basically the same as the space-heater under blanket number.

      • Thanks. Think I’ll shift to a heating pad. If it ever gets cold again in Texas.

  6. I recommend wool socks and slippers and wearing the socks in bed.
    Never any problems with cold feet no matter what floor or temperature.

  7. Have a pair of dry wool socks always available, insulate your feet with slippers or suchlike and insulate the body- thin bodytight wool underwear underneath an other layer and you will keep a couch potato warm in quite cold conditions,all the while wearing what appears to be normal indoors clothing. When it becomes even colder, a balaclava- given away almost everywhere now as promotional gifts- to insulate the head as brain wrappings lose quite a lot of heat. But keep them little piggies dry!

  8. Prof Murphy observes, “The main problem I have with cold feet is that they make it hard to go to sleep.”

    My wife has that problem. Her solution is to place her feet between my thighs, particularly if I am asleep. As time goes by, I am slowly convincing her of the advantage of wool socks, slightly oversize. When it is really cold, we both wear loose-fitting knit watch caps. (Wear sleep socks. Wear and don’t drink nightcaps.) And long underwear under the pajamas is far more effective than another blanket or quilt.

    My Dutch grandmother (from Groningen) told me that on cold wintry Sunday mornings, outside of church, men would rent out peat-heated stones (or bricks?) to the ladies, who would place them under their ample skirts and stay cozy. Apparently, option this was not available to men.

  9. To Diana: My wife uses a large hot water bottle, and I measured the energy use once with a kill-o-watt (yes, I realize that in a blog called “Do the Math”, measuring is probably considered cheating). It came to 0.132 kWh for 1.7 liters, which google tells me is 475.2 kJ for slightly less than half a gallon. That puts us in space heater/blanket or rice bag territory.

    I think I’ll look into a heating pad. Thanks again, professor!

  10. I enlisted a local leatherworker to make some moccasins for me using some deer and elk. Four winters later (Great Lakes region), they show only minimal signs of wear, and they are very, very comfortable.

    As a side bonus, I supported a local craftsman and helped preserve a traditional skill.

    • Are you in a rural or urban area?
      I’ve always been afraid to wear traditional moccasins outside in the city for fear the salt they over-zealously spread on the roads here would degrade the leather too quickly.
      That said, there’s no better footwear in the forest.

      • Semi-rural. I don’t wear them outside though. We don’t allow outdoor footwear into our home, so these remain indoors. use them pretty much all the time I’m home though– wearing them right now!

  11. The issue is not as lame as it would seem. Everybody has seen those diagrams of a house showing the proportion of heat that that escapes thought he ceiling the walls, the windows and (always lowest figure of all) the floor. What the charts don’t mention is that the floor is the only surface in which we are in constant contact. So a cold floor challenges our senses directly, much more so that does a cold wall. This phenomenon results in people feeling generally cold because their feet are cold, which usually means heating up the whole body, or complaining that their house is too cold. So…. even though the floor may lose just 5% of a room’s heat, it’s probably wise to take that 5% a bit more seriously and insulate the floor.

    Now, there is one little problem with heating up feet: if you try to do it quickly you may get chilblains, and that’s worse than having cold feet. For those unfortunate people, insulation of your feet is much better solution than applying heat. Chilblains are largely caused by rapid differential temperature. Radiant heat is the worst culprit. Best is to not let your feet get too cold so you don’t then feel the need to heat them up. If you do warm them up, then do it slowly, and best via insulation.

    • Way too energy intensive.
      Very comfy though, I’ll be the first to admit.

  12. What do you think of floor insulation ? We live in a place where it gets quite cold in the winter (-19 C this winter). After insulating the loft and walls, and fitting energy efficient windows, I’m now considering insulating the floor.

    Normally I’d say this wasn’t particularly worth doing, because the majority of heat loss from a home is through the walls, ceiling and windows, and only about 10% through the floor. However, the better the rest of the house is insulated, the more loss will remain through the floor, and in any case looking at the whole house isn’t necessarily particularly interesting when you’re thinking about how cold it might feel in the downstairs living room in the evening. From the living room alone, I suspect that much more than 10% of our heat goes through the floor, because these days it can’t very easily be escaping upwards into bedrooms which are already warm due to the insulation, and I’ve noticed that after the work we’ve done, the upstairs now retains heat much better overnight when the heating is turned off than does the downstairs.

    There are several approaches to floor insulation. Some of them involve spraying liquid foam insulation underneath the floor. This doesn’t appeal due to the off-gassing effect. It’s difficult to assess whether the fumes would be dangerous, but I just don’t like bad smells. Here in the Netherlands we have an interesting alternative in the form of thermocushions made of reflective material like “space blankets”. This certainly could work, and would involve no smells, but I’ve yet to see a convincing third party test of its efficacy.

    The company who sells this type of insulation specifically mentions the problem of cold feet making people feel colder than they are on average, so that a lower thermostat setting feels more acceptable when you have floor insulation.

    I’ll still be wearing my slippers, unless it simply becomes too warm to do so. Oh, and in case you’re wondering we did of course keep on cycling here.

  13. Radiant heat from the floor is evil – massive losses to the ground; but many tout that by keeping your feet warmer you can lower your home temperature. Note: The homes I’ve seen with radiant heat are all hotter than our house! We took out carpet over a cold concrete slab (uninsulated and above ground) and added 1″ of foam insulation covered with plywood and bamboo flooring and we find it warmer than the carpet was. IR readings put the slab between 0C (at the building edge) to 15C while the carpet read 20C the bamboo reads around 18C.
    Crocks work well for keeping feet warmer inside.

    Another poster mentioned drain water heat recovery. It’s an excellent idea in multi-user dwellings but useless in a home like ours where the only use of hot water daily doesn’t overlap: I’ll shower in 7L of water and hand washing dishes is <10L daily. For people who take 80L+ blasting hot showers a "power pipe" is a godsend as it could let one get by with a smaller on-demand heater. In my house they'll run into the fact that the hot water heater will run out well before that. I'm not in the business of providing unlimited hot water. Other people have a lifestyle where they seem to require hot water for everything – rinsing hands for instance.

  14. Our cat keeps my wife’s feet warm. Self regulating; cat moves when she gets too warm.

  15. My many years of backpacking in the wilderness taught me that the old saying is correct, if your feet are cold, put on a hat (preferably a knit one). It works remarkably well. You lose somewhere around 15% of your body heat through your head so your feet will not be nearly as cold since the body is not shedding heat as fast.

  16. Hi Tom, as always an interesting post. Can you tell me how you are taking the infrared photos? A hired camera, purchased? They aren’t the cheapest things to get hold of but rather handy for hunting down energy wormholes.

    • I have a FLIR 120×120 microbolometer array camera (B-CAM model) that I got for a variety of research reasons (thermal engineering; circuit troubleshooting), educational reasons (outreach, class demo, thermal lab), and to develop intuition about energy issues. A deep educational discount on a used demo model brought it down to $3k for me, but this is still a pretty pricy toy. I expect them to get cheaper over the coming years: the technological approach is pretty new, but may burn in.

      • One way to do this cheaply is to purchase a little $30 digital thermometer. You can aim it at any surface and record the temperature of that spot. By doing a cross grid on a ceiling (for example) you can then get the same result as per an infra-red photo (not quite as pretty but the information is all there). It’s a very handy tool for anyone who wishes to see heat losses visibly, from hot water cylinders, fridges, around windows and lights and so forth.

  17. I should have mentioned above that typically most heat loss through wooden floors is radiant heat, whereas heat loss through other surfaces is via a combination of conducted, convected and radiant heat. This renders reflective foil plus an air gap most effective for Winter floor insulation. BUT…. if you have air gaps around your flooring, thus allowing cold air to get into the room, then soft insulation can be an aid too.

  18. One method that I use in winter to keep my feet warm is to grease them up just before I put my socks and shoes on. I use vaseline (petroleum jelly) or some lanolin (wool grease). Really makes a difference in winter, plus the risk of tinea from sweaty feet is greatly reduced.

  19. Yep, I’m one for socks. When my wife’s feet are cold, we sometimes use the square bucket thingy that is barely big enough. We are lucky to have the tub “only 2 seconds away” from the hot water tank, but now realize… even that is still inefficient!
    Thanks for the mathematical approach (and for pointing out the simple relationship between joules and watts).

  20. Tom,
    Your point about delivering the heat where it is needed is a good one.
    I was in Japan some time ago where I saw both heated tatami cushions and kotatsu in use.

    I have always thought the Japanese keep some very sensible ideas about these types of things.

  21. I remember a guy who came up to me while I was giving a talk about energy effiiciency in the home and admitted, “I’m the classic energy waster. When I get cold I turn on the heater and then, when it gets too hot, I take off my jumper!”

    I wasn’t sure whether he was apologising or boasting but he said he picked up a few good ideas so I hope some of the information had an impact.

    On of the things I tell people is that, especially for me, it is much easier to feel comfortable when your feet are warm even when it is quite cold. If my feet are cold then I feel cold even if the room is quite warm.

  22. My son sent me a link to your site, since I live in a similar way. In the summer, I dress lightly and sit by a fan .At night we open the windows and doors, and in the daytime, we shut them. In the summer, I put a covering on the west window awnings. In the winter, I take them off. In the winter, I dress warmly and wear two pairs of socks and a pair of slippers.
    I live in Southern Illinois, so it’s cold in the winter and hot and humid in the summer. I prefer the cold, but I have to suffer through the heat.
    We have our energy phantom applicances on power strips, or wall switches, and shut them off when we’re not using them.
    As you mention, we evolved in such circumstances, and I also point that out often.
    My children suffered from peer ridicule, but may have come around, since my son is reading your blog. Thanks!

  23. Probably outside the charter for this blog, but there’s a long-running disagreement between people who claim that exercise “boosts their metabolism” and those who say that this is hogwash (and it seems to be actual experts saying that no such thing occurs). A microbiologist friend says that exercise does make your muscles more responsive to insulin, so may be that is the effect. But if this effect exists (and speaking anecdotally, it does seem to), that’s yet another way to stay warm.

    The heat from exercise is pretty substantial. We’re only about 25% efficient, so a 100W output corresponds to 300W of extra heat. An average-sized person in decent shape can put out 100W for a long time. Heavy work (bicycling hard, or shoveling snow) will have you sweating even in 20F weather.

  24. A hot water bottle is very efficient at heating cold feet. You can heat on a stove just enough water to fill it, then place it under your cold feet, with a towel or blanket wrapped around the water bottle and your feet. It stays hot quite a while and does a great job.
    There is even a water “bottle” you can wrap your feet in. By Fomentek, available in several sizes, these are bags made of two layers of strong plastic. Wonderful invention. (Easily punctured by cats kneading them, though.) We have purchased a long-time supply, for hard, cold times.

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