What method do you use for sizing fin-tube baseboard?

That method do you use for sizing fin-tube baseboard? If you’re like many practitioners your sizing procedure probably goes something like this:

Estimate the design heating load of each room. Assume there will be a 20 degree F drop around the baseboard circuit. Subtract half of this 20 degree F drop, (10 degrees F) from the boiler outlet temperature to get the average temperature of the water in the circuit. Look up the Btu/hour output per foot of baseboard element in the manufacturer’s literature. Divide this heat output per foot into the design heating load of each room to get the necessary length of baseboard.

This method, which has been standard practice for decades, is about as simple as it gets. But simplicity carried too far leads to inaccuracy. The building blocks of over-simplification are assumptions, and several are built into this procedure. Here’s a brief explanation of a few:

Assumption No. 1: The temperature drop of a hydronic circuit is always 20 degrees F.

It’s easy to draw a picture of a hydronic circuit, or even a solitary radiator, and label the supply temperature 180 degrees F and the return temperature 160 degrees F. Any of you ever done this? I have. But think about this for a minute. We don’t know what flow rate the circuit will operate at. Nor do we know how much heat the circuit will actually release. So how can we be so confident the temperature drop will be 20 degrees F? Are Btu’s smart enough to know they must comply with IBR guidelines? Will they make some kind of miraculous, and scientifically unexplainable adjustment near the end of every circuit to ensure the 20 degree drop occurs? If you think they will, you’re going to be disappointed.

The actual temperature drop that occurs depends on the actual (not estimated) flow rate in the circuit, as well as the actual (not estimated) heat output of the circuit. If we knew both we could calculate the temperature drop using the familiar formula:

## Formula 1

I’ve seen hydronic circuits operating with ³T’s anywhere from 2 degrees F all the way up to around 40 degrees F. A short floor heating circuit with a high flow rate would be an example of the former. A long series baseboard circuit with a low flow rate is an example of the latter. In both cases heat delivery can be just fine, assuming the designer knew how to predict the temperature drop that would occur and size the heat emitter(s) accordingly.

Assumption No. 2: It’s OK to size all baseboard based on the average water temperature in the distribution circuit.

The water temperature in a hydronic distribution circuit is constantly decreasing in the downstream direction. A baseboard near the beginning of the circuit operates at a higher water temperature than one near the end. If these two baseboards were otherwise identical it’s obvious the one near the beginning of the circuit will deliver more heat. End result: Over-heating at the beginning of the circuit, under-heating at the end.

With a proper design procedure you can accurately predict the water temperature at each baseboard and size them accordingly. Granted this requires a bit more number crunching, but the pay-off is properly heated rooms at all locations along the series circuit.

Assumption No. 3: The laboratory-tested heat output of baseboard is listed in the product’s literature.

Most baseboard sold in the United States is rated according to the IBR Testing and Rating Code for Baseboard Radiation standard. The results appear in product literature as heat output per foot of finned element length, (which is usually 3–6 inches less than the length of the enclosure). Heat output ratings are given for several water temperatures, and two flow rates (1 gpm and 4 gpm). However, a footnote to this table usually indicates that 15 percent has been added to the tested thermal performance values to account for something called “heating effect factor.”

The origins of the heating effect factor go back several decades when fin-tube baseboard began competing against standing cast-iron radiators. Originally it accounted for the fact that baseboard — unlike standing cast-iron radiators — was often installed in a “pool” of cool air at floor level, and thus transferred heat better than if installed higher on the wall.

So why do most baseboard manufacturers still apply the 15 percent heating effect factor to their output ratings? After discussing this with people who’ve been around this industry a long time, I’ve concluded it’s because: 1) the current IBR standard allows them to, (provided the previously mentioned footnote is included with the ratings table) and 2) because any manufacturer that chose not to include this “allowance” might be perceived as having a technically inferior product relative to their competition. Interestingly, if all baseboard manufacturers decided to drop the heating effect factor from their ratings, and advocate that baseboard be sized based on its actual tested heat output, they might sell 15 percent more baseboard! Sounds like another opportunity for hydronics solidarity.

Right Sizing: So much for over-simplified sizing methods based on assumptions. Here’s a more accurate sizing procedure for baseboards connected in a series piping circuit.

Step 1: Accurately estimate the design heating load of each room served by the circuit.

Step 2: From the baseboard manufacturer’s literature look up the heat output rating of the baseboard at 200 degrees F water temperature, 65 degrees F entering air temperature, and 1 gpm flow rate. The output rating will be in Btu/hour/foot of element length. While you’re at it, check out the footnote under the table regarding the 15 percent heating effect factor. Chances are it is included in the ratings. If such is the case divide the heat output rating by 1.15 to remove the heating effect factor. We’ll call the resulting number “b.”

Step 3: Estimate the length of the baseboard piping circuit. This of course depends on how you intend to route the piping through the building. Remember to include the equivalent length of fittings and valves in the overall circuit length.

Step 4: Estimate the flow rate in the baseboard circuit. There are a couple of ways to do this. You could refer back to previous Hydronics Workshop columns that show how to establish a system curve for the piping circuit, combine it with a pump curve for the circulator and, thus, find the operating flow rate. Or you could use the graph shown in Figure 1 (refer to page 32), which shows the flow rate a typical 1/25–hp wet-rotor circulator will produce in piping circuits of either 1/2–inch and 3/4–inch copper tubing. If you plan to use a different circulator or add antifreeze to the system this graph should not be used.

Step 5: Select a boiler outlet temperature for design heating load conditions, 180 degrees F is typical. This will be the inlet temperature to the first baseboard in the series circuit.

Step 6: Calculate the average water temperature in the first baseboard as follows:

## Formula 2

where:

Tinlet = the inlet water temperature to the baseboard (in degrees F).

Q = the required heat output of the baseboard at design conditions (in Btu/hour).

f = the circuit flow rate (in gpm).

Step 7: Calculate the heat output of the baseboard at its average water using Formula 3. Note the values 0.04 and 1.417 in this formula are exponents, not multipliers.

## Formula 3

where:

q = the heat output of one foot of baseboard at a water temperature = Tave (in degree F).

b = the value determined in Step 2.

f = the flow rate of water through the baseboard element (in gpm) from Step 4.

Tave = the average water temperature in the baseboard from Step 6.

Tair = the air temperature entering the baseboard (65 degrees F is typical).

Step 8: Calculate the required length of baseboard element as follows:

## Formula 4

where:

Q = the required heat output of the baseboard at design conditions (Btu/hour) from Step 6.

q = the heat output of one foot of baseboard (Btu/hour/ feet) from Step 7.

Round off L to the next higher whole foot length, referred to as “Lrounded.”

Step 9: Calculate the outlet temperature of the baseboard using:

## Formula 5

where:

q = the heat output of one foot of baseboard (Btu/hour/foot.) from Step 7.

f = the flow rate of water through the baseboard element (gpm) from Step 4.

Step 10: Use the outlet temperature of this baseboard as the inlet temperature to the next baseboard, and repeat the procedure starting at Step 6. Repeat it until each baseboard in the series circuit is sized.

Here’s A Sample: Size the first baseboard in a series piping circuit for a room heating load of 8,000 Btu/hour. First, let’s take care of Steps 1–3.

Assume the overall piping circuit length, including the equivalent lengths of fittings and valves is 250 feet. The circuit is built with 3/4–inch tubing, and has a 1/25–hp circulator. Also assume the boiler outlet temperature is 180 degrees F, and the baseboard has a rated output of 600 Btu/hour/foot with 200 degrees F water, 65 degrees F entering air, and a flow rate of 1 gpm, after the heating effect factor has been removed. The air temperature entering the baseboard is 65 degrees F.

Step 4: From the graph in figure 1 the circuit flow rate is estimated to be 4.5 gpm

Step 5: Tinlet = 180 deg. F.

Step 6:

Step 7: Using Formula 3 with the stated data, the value of q is calculated:

Step 8: The required length of the first baseboard element is:

Step 9: The outlet temperature from this baseboard is:

If you were going on, this outlet temperature would be the inlet temperature for the next baseboard (Step 10).

Pencil & Paper: The best way to keep things organized on paper — if you must use paper — is to make a table like that shown in the following table. Work the calculations across the first row and then “feed” the outlet temperature from the first baseboard into the inlet temperature column for the second baseboard and so on. For our purposes, I’ve assigned a heating load of 8,000 btu/hour for each of five rooms. Use the methods presented to find the baseboard lengths for the last four rooms.

Now, all you ace number-crunchers ... why are the baseboard lengths different even though the heating loads are all the same? Answers are provided at end of the column.

This kind of design procedure cries out for a computer spreadsheet. You know, like the ones that come with almost every new computer, but for some strange reason still don’t include any hydronic design routines! Seriously, even the humblest of today’s spreadsheet programs can size up a large series string of baseboards using this procedure in the time it takes to press the return key. This approach also allows you to quickly answer all kinds of “what-if” questions. Next month I’ll get into this in more detail.