This section mixes up Imperial and SI units - be warned.

A primary purpose of the van is to be able to use it as a base when skiing. Most RVs are not well insulated, resulting in wet surfaces from condensation and high propane and electrical loads for heating. The goal for insulating the van was to be able to keep it a comfortable temperature in severe(ish) winter conditions while using no more than a 20 pound propane container per week. 20 pounds of propane contains approximately 436,200 BTU, so the heat loss had to be less than 2596 BTU/hr. However, a 'full' 20 pound container usually contains around 15 pounds of propane, and heater efficiency ranges from 75% to 90%, so the actual allowable heat loss should be less than 1460 BTU/hr, a significant difference!

Heat is lost by transport through the air inside the van (convection), through the walls, floor and ceiling (conduction) and finally through the air outside the van (convection). Radiation from the warm outside surface is also a major heat loss mechanism but I've got to re-jig my spreadsheet to include it so it isn't here yet. For a worst case scenario we assumed there would be a good wind blowing, stripping the warmth from the van with great efficiency.

The only real complication is that to calculate convective heat transfer you need to know the temperatures of the surfaces involved which requires knowing the heat loss rate. So you need to know the answer to find the answer. This conundrum is solved by guessing the unknown temperatures of the wall surfaces, using these guesses to calculate the convective heat transfer coefficients, and use these to solve for the the heat loss. Once you have the total heat loss you can calculate the inside and outside skin temperatures. These calculated values are then compared to your guesses. If they don't match, guess again, and repeat the process. This is repeated until the values match. Fortunately Excel (and LibreOffice Calc!) has a nice iterative function that does this automatically for you if you set the value of an input cell to the value of an output and enable iterative calculation.

There are many ways of approaching the problem. I chose to solve for the heat conductivity for each material type (insulated wall, wall with stud, and window) and further broke these up into walls, windows, and floor/ceiling for the the convective heat terms. The work was originally done assuming a stick-built box and I never got around to changing it. Thus, the studs, joists etc. are assumed to be 2" thick spruce. The actual van has 'studs' made up of foam filled steel support beams with an inch of spruce glued to them.

The details for calculating the heat loss can be founds here (Heat Loss Calculations). The test case consists of maintaining an inside temperature of 20 Celcius with outside temperature of -20 Celsius and a 30 km/hr wind (That's 68 F, -4F, and 18.6 mph for our southern neighbors). For the exterior convective term I got 8.08 W/m2K. For the interior floor and ceiling, interior walls, and interior windows I got convective terms of 0.91, 1.92 and 2.62 W/m2K respectively. The value for the windows was calculated separately since I figured the cold surface would set up a wicked convective current, increasing the heat transfer. With these values, plus the conduction through the paneling and studs or insulation, it is possible to estimate the total heat loss.

After plugging in all of the parameters I get a heat loss rate of 736 Watts, which is equal to 2510 Btu/hr. Uh-oh, this is way higher than allowable.

So where is all of the heat going?

A primary purpose of the van is to be able to use it as a base when skiing. Most RVs are not well insulated, resulting in wet surfaces from condensation and high propane and electrical loads for heating. The goal for insulating the van was to be able to keep it a comfortable temperature in severe(ish) winter conditions while using no more than a 20 pound propane container per week. 20 pounds of propane contains approximately 436,200 BTU, so the heat loss had to be less than 2596 BTU/hr. However, a 'full' 20 pound container usually contains around 15 pounds of propane, and heater efficiency ranges from 75% to 90%, so the actual allowable heat loss should be less than 1460 BTU/hr, a significant difference!

Heat is lost by transport through the air inside the van (convection), through the walls, floor and ceiling (conduction) and finally through the air outside the van (convection). Radiation from the warm outside surface is also a major heat loss mechanism but I've got to re-jig my spreadsheet to include it so it isn't here yet. For a worst case scenario we assumed there would be a good wind blowing, stripping the warmth from the van with great efficiency.

The only real complication is that to calculate convective heat transfer you need to know the temperatures of the surfaces involved which requires knowing the heat loss rate. So you need to know the answer to find the answer. This conundrum is solved by guessing the unknown temperatures of the wall surfaces, using these guesses to calculate the convective heat transfer coefficients, and use these to solve for the the heat loss. Once you have the total heat loss you can calculate the inside and outside skin temperatures. These calculated values are then compared to your guesses. If they don't match, guess again, and repeat the process. This is repeated until the values match. Fortunately Excel (and LibreOffice Calc!) has a nice iterative function that does this automatically for you if you set the value of an input cell to the value of an output and enable iterative calculation.

There are many ways of approaching the problem. I chose to solve for the heat conductivity for each material type (insulated wall, wall with stud, and window) and further broke these up into walls, windows, and floor/ceiling for the the convective heat terms. The work was originally done assuming a stick-built box and I never got around to changing it. Thus, the studs, joists etc. are assumed to be 2" thick spruce. The actual van has 'studs' made up of foam filled steel support beams with an inch of spruce glued to them.

The details for calculating the heat loss can be founds here (Heat Loss Calculations). The test case consists of maintaining an inside temperature of 20 Celcius with outside temperature of -20 Celsius and a 30 km/hr wind (That's 68 F, -4F, and 18.6 mph for our southern neighbors). For the exterior convective term I got 8.08 W/m2K. For the interior floor and ceiling, interior walls, and interior windows I got convective terms of 0.91, 1.92 and 2.62 W/m2K respectively. The value for the windows was calculated separately since I figured the cold surface would set up a wicked convective current, increasing the heat transfer. With these values, plus the conduction through the paneling and studs or insulation, it is possible to estimate the total heat loss.

After plugging in all of the parameters I get a heat loss rate of 736 Watts, which is equal to 2510 Btu/hr. Uh-oh, this is way higher than allowable.

So where is all of the heat going?

Region |
Heat Loss (W) |

Walls (insulated) |
253 |

Walls (studs) |
47 |

Windows |
275 |

Floor/Ceiling (Insulated) |
144 |

Floor/Ceiling (studs) |
17 |

The results suggest that the windows are responsible for almost as much heat loss as the entire wall surface! This shouldn’t be too surprising - there is a reason nobody uses single pane windows in winter, or cover them up thoroughly.

So what if we add a 1" piece of foam over the windows when the weather gets extreme? Adjusting the coefficient of heat conduction on the windows to account for this reduces the overall heat loss to 576 Watts, or 1970 Btu/hr. Hmmm, closer to the desired 1460 Btu/hr.

We have one trick left - a human body at rest puts off approximately 250 Btu/hr. That means we get to subtract an extra 500 Btu/hr from the furnace load! That brings us to 970 Btu/hr that needs to be provided with propane. 2" of foam is adequate for our needs!

Anything else?

First off, the real van is far leakier than suggested in any of these equations. Areas around the doors and steel structural beams are suspect for additional heat conduction. As well, maintaining a reasonable inside moisture level requires bringing in outside air, another heat loss source. In our favour, we don't need the van to always be at 20 Celsius. At night we prefer a cooler temperature, and while we are away from the van it can cool off quite a bit before we have to worry about the water freezing. Ultimately, we just have to wait for winter to find out.

Choosing the Heater

RV heaters are often heavy electricity users as they have powerful (and inefficient?) fans. Searching for the most efficient heaters led us to two different propane powered units (we were looking at propane because we were already planning to cook with propane so would have it readily available already).The first is the Propex HS2000, a 6,480 BTU/hr (7165 input) heater than draws 1.8 amps. These are very popular with the Westfalia crowd, it seems. The second is the Atwood Everest Star II - 8012-II, which is rated for 9,120 BTU/hr (12,000 input), also drawing 1.8 amps.

I should mention the Eberspacher/Webasto heaters as well which are available to run off diesel or gasoline. Unfortunately, the cost is around 50% higher than the propane units.

If you want to run on diesel and prefer Russian to German engineering you can pick up a Planar 4DD heater for less than half the cost of the Eberspacher. They ship with small 7 liter diesel tanks as well, which would be ideal for our gas powered van. I would probably pick one of these if I did this again, particularly since we ended up cooking with gasoline so the propane tank is only needed for the heater. Upgrade to the 8D and you get 20,000+ Btu out of what looks like a small jet engine!

Results

We ended up with a Propex heater due to availability and its small footprint (no hole out the side of the van either).

We managed to run a simple test to check the heat loss from the van. In this case the windows, skylights and roof vent were bare, so this was a worst case scenario. We ran the heater until the temperature stopped changing. The outside temperature was 6 Celsius at the time of the test and the final temperature we reached was 29 Celsius with the heater running full out! This means that the heat loss with a 23 degree temperature difference was the full 6,480 Btu/hr that the Propex heater could put out! For comparison - from my calculations the heater should have been barely running to maintain this. Obviously we have way more heat loss than anticipated. We will have to be sure to add insulation to all of the high loss areas and see where we can improve the door seals. If that fails, we will have to upgrade the heater and live with higher electricity and propane consumption unfortunately. If not, that Planar jet engine might be part of our future!

As a further update - with the skylights and roof fan covered as well as extra seals around the doors we found that the van stayed 10 degrees C warmer than the outside air with just body heat (~500 Btu/hr). This is much more promising than the initial test with the heater. Once we have our winter window covers made we will try the full heater test again.

As a further update - after extensive driving on dirt roads we noticed a huge amount of dust collecting in the back of the van! Apparently the air leakage around the door is advanced - we will have to work on this...

## Heat Loss Tests

As a test of the actual heat loss from the van I ran a series of tests. Initially the hope was to reach a steady state temperature in the van with a known heat source. For example, the Propex puts out 1.8 kW, our Mr. Heater tank-top radiant heater puts out 11,000 BTU on high, our 'lighbulb board' from a ski building cure oven puts out 240 W. If I can find the heat difference that a know energy source can maintain in the van I can calulate an 'R' value (m2*K/W) by multiplying the temperature difference between the van and outside by the van surface area and dividing by the heat output of the heat source.

It turns out that I lack the patience to wait for the system to reach steady state (the theory suggests it will take infinity anyway). Instead I plotted the natural log of the rate of temperature change against the elapsed time of the test. This was based on a very loose model of what was happening during the heating process. This produced a roughly linear relationship that could be used to extrapolate the final temperature the van would reach.

The R-value that I calculated from theory was 3.1. The quasi-steady-state tests that I carried out had different answers. They were: 240W test R-value = 1.4, Radiant propane heater test R-value = 1.1, Propex heater test R-value = 1.4. Although the results varied, the final conclusion is that the heat loss is about twice what I predicted. Darn.

It turns out that I lack the patience to wait for the system to reach steady state (the theory suggests it will take infinity anyway). Instead I plotted the natural log of the rate of temperature change against the elapsed time of the test. This was based on a very loose model of what was happening during the heating process. This produced a roughly linear relationship that could be used to extrapolate the final temperature the van would reach.

The R-value that I calculated from theory was 3.1. The quasi-steady-state tests that I carried out had different answers. They were: 240W test R-value = 1.4, Radiant propane heater test R-value = 1.1, Propex heater test R-value = 1.4. Although the results varied, the final conclusion is that the heat loss is about twice what I predicted. Darn.

## Winter Trip Results - Success! (with some help)

Out first real winter trip was an 18 night trip that let us finally test the heating system in anger. As luck (?) would have it the temperatures were very low. The first night hit -32C/-25F. This sort of thing continued for the whole trip, with overnight temperatures hitting the -20's on the Celcius scale and negative teens on the Fahrenheit scale.

During the heat loss tests I realized that while the Propex would maintain a reasonable temperature in the van it was woefully inadequate for fast heating. Because the forecast was for low temperatures and I didn't want to spend the trip shivering while the van slowly warmed up we bought a Mr. Heater radiant heater as a means of kicking the temperature up quickly when we got back to the van after a day of skiing. The model is the F232060, a 4000-9000 BTU output heater that runs on 1 lb propane containers.

It turned out that the combination of heaters was perfect for us. When we were away we kept the van just above freezing, and overnight we kept it around 10C/50F. - our comfortable sleeping temperature. This left just the mornings and evenings as times when the van would be much warmer. When we wanted a bit of boost we would turn on the Mr. Heater for 15 minutes. As an additional factor, cooking added a lot of heat during both the morning and evening - reducing the load on the heater even more. Because of this we used a lot less heating than expected, even with the worse than expected performance of the van insulation system.

On midnight of the last night the 20 lb propane container ran out. We let the van temperature fall as we slept and then warmed it up in the morning with the last of 3 one lb'ers in the Mr. Heater. Ultimately, with temperatures below my theoretical worse case scenario, the one 20 lb. container and 3 one pound 'boosters' made it more than twice as long as predicted from the rosy heat loss calculations I started with!

During the heat loss tests I realized that while the Propex would maintain a reasonable temperature in the van it was woefully inadequate for fast heating. Because the forecast was for low temperatures and I didn't want to spend the trip shivering while the van slowly warmed up we bought a Mr. Heater radiant heater as a means of kicking the temperature up quickly when we got back to the van after a day of skiing. The model is the F232060, a 4000-9000 BTU output heater that runs on 1 lb propane containers.

It turned out that the combination of heaters was perfect for us. When we were away we kept the van just above freezing, and overnight we kept it around 10C/50F. - our comfortable sleeping temperature. This left just the mornings and evenings as times when the van would be much warmer. When we wanted a bit of boost we would turn on the Mr. Heater for 15 minutes. As an additional factor, cooking added a lot of heat during both the morning and evening - reducing the load on the heater even more. Because of this we used a lot less heating than expected, even with the worse than expected performance of the van insulation system.

On midnight of the last night the 20 lb propane container ran out. We let the van temperature fall as we slept and then warmed it up in the morning with the last of 3 one lb'ers in the Mr. Heater. Ultimately, with temperatures below my theoretical worse case scenario, the one 20 lb. container and 3 one pound 'boosters' made it more than twice as long as predicted from the rosy heat loss calculations I started with!