A Peek Behind the Dimensional Change Coefficient Curtain for Solid Wood Floors

Dimensional change coefficients (DCCs) might seem like old friends, but have you ever wondered how DCCs were determined? How precise they are? How to determine a DCC for a “new” flooring wood? How to apply them correctly? How much measurement error or uncertainty in board width, grain angle, wood moisture content (MC), or the DCC itself could influence calculations of wood MC at the time of installation or manufacture?

If you haven’t wondered about some or all of these things don’t worry, because we did. We are professional nerds whose jobs are to sweat the tiny details, and the Forest Products Laboratory (FPL) published a research paper “Measurement and Practical Application of Tangential Dimensional Change Coefficients to Hardwood Flooring” (Glass et al. 2022) asking these questions (and others), as a part of a cooperation between FPL and the Flooring Inspectors Education Guild. Our purpose with this article today is to hit the high points of that report and give you the critical take-away messages we learned about DCCs.

A traditional experimental setup to measure dimensional change with changes in moisture content in wood.Markwardt and Wilson 1935The DCC origin story

Where does a DCC come from? Let’s be explicit about the fact that DCCs are laboratory-derived values, but they are used in the real world every day. For some woods they were determined by painstakingly measuring rectangular boards with changes in MC (see the photo above).

For most woods, however, DCCs were calculated from green to oven-dry shrinkage values without any additional measurements of dimension between green and oven-dry. We address this in some detail in the paper, but the DCC is most commonly calculated by assuming a fiber saturation point and indexing the dimensional change value at 10% MC, which is in the middle of the range for in-service wood, and represents the most reliable portion of the shrink-swell relationship (see the “Calculating a dimensional change coefficient” sidebar at the end of this article).

DCCs were first published in the 1974 edition of the Forest Products Laboratory’s “Wood Handbook – Wood as an Engineering Material,” and have been reprinted in all subsequent editions and in wood flooring industry publications (e.g., NWFA Moisture and Wood, 2017). Whether determined with many measurements or calculated from green-to-ovendry shrinkage values, these old-school methods of determining a DCC are not practical for already-dry flooring of a new wood for which a DCC is not available.

How to determine a DCC for a new wood?

As part of our experiment, we determined dimensional change coefficients for two species for which DCCs were previously unavailable: Acacia confusa (left) and Acacia mangium (right).Confusa photo: Forest and Kim Starr, Mangium photo: U.S. Geological SurveyWe compared a range of different ways to determine DCCs for new species by experimenting with two well-known flooring woods (red oak and hickory) and two woods for which DCCs were not available (Acacia confusa and Acacia mangium).

All the permutations we examined are too soul-crushing to enumerate (gluttons for punishment, please see the full paper referenced at the end of this article), but in synopsis we found that our experimental method to determine DCCs from already-dry flooring boards gives values consistent with the DCCs for oak and hickory in the Wood Handbook, and are also consistent with calculated values for the two acacia species. Our suggested method involves at least 20 purely tangential (or radial for a radial DCC) test specimens from different boards (and ideally different trees), conditioning the specimens to several known MCs, making careful measurements of specimen dimensions, and using a regression equation in our paper to determine the DCC. All this is to say, determining a DCC for a new wood is not a quick or trivial undertaking if you want to arrive at a scientifically defensible value, and it cannot be determined from a single board.

Do we really need so many decimal places?

In Table 13-5 of the 2021 Wood Handbook, DCCs are listed to five decimal places; for example, the familiar tangential DCC for commercial red oak is reported as 0.00369. We determined that, based on how DCCs are calculated, and in practical terms, reporting DCCs to four decimal places is scientifically and practically justified. Our example above would thus be a more wieldy 0.0037 instead of 0.00369, with no meaningful change in calculated values (that is, the 0.00001 difference in value doesn’t amount to much, practically). We didn’t complete our paper in time to make this change in the 2021 Wood Handbook, but we expect to update the DCC values the next time the Wood Handbook is updated.

Variability

Just as you can’t expect every rat terrier to act exactly the same way, you can’t accurately predict the shrinking and swelling for any single board.ShutterstockAll of these findings address underlying concerns we had about how best to use DCCs in the real world. As wood scientists, we know that any individual board of a given species is going to have its own properties, though those properties are likely to be within the normal range of variability for that type of wood. It is somewhat like meeting a dog on the street—if it is a rat terrier, you probably have certain expectations that it will be an energetic dog, but each rat terrier will have its own personality within that range of expected traits. So, to have a single number like a DCC and apply it equally to all boards of a given wood and expect it to correctly predict the shrinking or swelling of that exact board is unreasonable and not supported by experimental data—it doesn’t account for natural variability. Nonetheless, we would expect that, averaged over an ever-increasing number of boards, the DCC would accurately predict the shrinking or swelling of the whole set of boards—we overcome uncertainty about any one board or measurement by averaging measurements of many boards.

Uncertainty

The fact that no two flatsawn boards have the exact same grain angle contributes to the inherent uncertainty in calculating their dimensional change.Courtesy of Joe DawsonWe all know what this word means in a casual context, but in science, “uncertainty” is the idea that a value we measure will have some portion of the measurement that is error— some portion that could be specific to that single measurement—and thus a degree to which that particular measurement may not be reflective of the larger thing we are trying to estimate. For solid wood flooring and DCC calculations, we have several sources of uncertainty: uncertainty in board or gap measurements, uncertainty in wood MC, uncertainty in board grain angle, and uncertainty in the DCC value itself. When we do a traditional calculation using DCC, we implicitly assume that we are using the true values for each of the inputs, even though it is widely known and accepted, for example, that a moisture meter—even when properly calibrated—could easily give a MC value ±1%. By mathematically including uncertainty, we can calculate more scientifically defensible numbers.

Okay, fine, you might say, in theory uncertainty matters, but how much of a role does it play in my calculations for a specific job? By incorporating uncertainty, we get a range of values that represent realistic variation and error (uncertainty) inherent to our measurements. For example, in an installed floor, it isn’t realistic to measure the actual grain angle of the boards. Instead, for flatsawn flooring we assume the full tangential DCC is the applicable value, even though that is rarely the case. In our paper, we found that a grain angle steeper than 20 degrees from true tangential was common in our boards. Because you cannot measure the grain angle in an installed floor, it makes sense to include uncertainty. We don’t use grain angle directly in our calculations, so instead we can include uncertainty in the tangential DCC value itself, though please note that the DCC itself, irrespective of board grain angle, has its own variability and uncertainty.

A practical example on a wood flooring job

To explain what we mean, let’s look at a practical example from a wood flooring job site.

Say an installer notices a slight difference in board width between material from two bundles of nominally identical hickory flooring from the same manufacturer. The installer measures the MC and width of 20 boards from the suspect bundle. The average MC is 8.0% and the average board width is 2.938 inches. The manufacturer’s specification is 3 inches. with a tolerance of 0.008 inch. The installer suspects the boards had a high MC at the time of manufacture.

Putting these numbers into the calculator, we get an average MC of 13.0% at the time of manufacture:

But that’s not the whole story. Taking into account measurement uncertainty in MC and board width, manufacturing tolerance, and uncertainty in the DCC, we get an uncertainty of 1.4% in the MC at the time of manufacture, which translates to a range from 11.6% to 14.5% MC (the difference between 14.4 and 14.5 is a result of roundoff of 13.0 and 1.4):

To arrive at the result in the example above, we used the DCC calculator incorporating uncertainty. This is downloadable as an Excel file from FPL.

Using this calculator, you can take advantage of uncertainty in your calculations of dimension change in flooring without having to worry about getting the mathematics correct.

Not surprisingly, floors shrink and swell

Time-lapse videos of wood flooring assemblies shrinking and swelling are available at https://bit.ly/fpldccvideos.A final component of our paper was time-lapse movies of wood flooring installed in test assemblies shrinking and swelling with changes in MC.

Even through “everyone” knows that wood floors move, we were asked to document this process in test floor assemblies, so we constructed an entire humidity chamber within a room and collected time-lapse images of the assemblies (one oak, one hickory, one Acacia cf. mangium, and one Acacia cf. confusa). We assembled those images into movies you can download.

Conclusions

DCCs are familiar but their origins vary, and experimentally determining DCCs for new woods is not trivial. Wood, as a natural material, is variable, and this variability influences the uncertainty in the parameters one measures or assumes at a job site. By using the DCC calculator we provide, you can incorporate realistic degrees of uncertainty into your calculations and make use of the best available science in your work.

Now take a quick quiz on what you've read:

Simultaneous publication: We are publishing this article verbatim and simultaneously in WFB and Hardwood Floors in an effort to ensure that everyone in the industry has access to this information, and especially to our DCC calculator. We have coordinated with the editors of both publications to ensure that timing and access are equivalent.