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Washcloth drying time: the science of evaporation is key to defense in murder trial.

[ILLUSTRATION OMITTED]

I never thought I'd be asked to be an expert witness in a murder trial. To help establish the innocence of their client, the defense hired me to ascertain the drying time of washcloths found at the crime scene to help establish the time of the crime.

It began on Sunday morning. April 30. 1989. when the pastor for the Olive Branch United Brethren Church in Lakeville. Ind.. (a southern suburb of South Bend) did not show up for morning service. Some church members went to the nearby parsonage to check on him and found the pastor shot dead.

Police were called, and they discovered the bodies of his wife and two daughters in the parsonage basement. Video taken of the crime scene showed that at about 1:30 p.m. water was still on the bathmat of a bathtub/shower stall (Photo 1). and two washcloths on the rim of the tub were "fairly wet" (Photo 2).

The prime person-of-interest was the 17-year-old son, who had gone to the prom the previous evening. Although he may not have had permission to attend the prom on his own. His presence was accounted for from 5:20 p.m. Saturday until the discovery of the crime. Therefore. If the son had committed the crime, it would have occurred about 20 hours prior to the recording of the observation of the water on the mat and washcloths.

The son was interrogated but no charges were filed against him at that time. Thirteen years later a new county prosecutor did file charges. Because the time of death was not determined, the source and timing of the bathmat and washcloths' wetting became critical to the defense. Certainly, someone wetted these items. If someone else was proved to be in the parsonage during that 20-hour period, the guilt of the son would be at question. (A more detailed discussion of these events can be found in Reference 1.)

Natural Drying

For the purposes of this study, natural drying is the process of evaporation of water from a wet surface without the interference of artificial heating, cooling, wind or forced convection. This may also be called free convection. While there is an abundance of literature on forced heat and mass transfer of wetted surfaces, no helpful literature on the actual process of indoor clothes drying, or the like, could be found; additionally, time did not permit a vast review of relevant literature as a trial could possibly occur in a few weeks. An empirical approach was selected early in the program to determine the time required to dry a bathmat and washcloths in that particular parsonage bathroom, on that particular night.

Indoor Space Conditions

Of critical importance to determining the drying time of this process was estimating the space conditions for the bathroom. The residence exterior doors and windows were closed when the crime was discovered. Additionally, the bathroom was an interior space, and its door was open to the hall.

The space conditions (temperature and humidity) in the bathroom were not recorded by investigators. However, the space conditions of the bathroom can be estimated from knowledge of the structure and the weather data. The structure has a forced air heating system, as was seen from the police video of the floor diffuser in the bathroom. The air temperature and humidity in the bathroom should have been nearly identical to the air in the rest of the house, particularly as there was supposedly no activity in the house for 20 hours.

The low temperatures for April 28, 29 and 30 were in the 40s and the furnace likely was enabled and operated by a thermostat to keep the occupants warm in the evening. Additionally, there were no comments on the police video tape as to the space being uncomfortably hot or cold. The temperature limits for human comfort for low humidity conditions2 during the winter are between 69[degrees]F and 76[degrees]F (21[degrees]C and 24[degrees]C). The space temperature was estimated to be 72[degrees]F (22[degrees]C), but as will be seen, the exact temperature is not critical.

As the indoor dew point is overwhelmingly governed by the outdoor dew point, a certified copy of the weather data was obtained from NOAA for Michiana Regional Airport about 13 miles north of the crime scene for April 1989. For the period of interest, the outdoor dew point steadily dropped from a high of 52[degrees]F (11[degrees]C) (4 p.m. Saturday) to a low of 36[degrees]F (2[degrees]C) (1 p.m. Sunday). The time averaged dew point for that period was 42.1[degrees]F (6[degrees]C), the average wind speed was 8 mph (3.57 m/s), and the low temperature was 41[degrees]F (5[degrees]C) (Table 1).

Because the house was not equipped with a humidifier or an air conditioner, the amount of water in the indoor air is governed by infiltration. While some amount of water is added to the air by showers, cooking and the like, these are very minor contributors, especially late at night in a house with no human activity. The residence was built in 1975. The construction techniques of 1975 are such that the house probably is of medium air tightness class. A medium class house surrounded by 7.5 mph (3.35 m/s) wind has approximately one complete air change every two hours.3 Note that the average wind speed was 8 mph (3.57 m/s) at the time of interest.

Since the weather data is reported at the middle of every three-hour period and the air is changed every two hours, the air in the house will have almost the same dew point as the reported outside air. The estimated indoor dew point was the outside air average of 42.1[degrees]F (6[degrees]C). However, as with temperature, the exact dew point is not critical. Although there is a hygroscopic flywheel in the house, the April dew point average was 34[degrees]F (1[degrees]C). Using a dew point of 42.1[degrees]F (6[degrees]C) was very conservative.

The space air condition of 72[degrees]F (22[degrees]C) and 42.1[degrees]F (6[degrees]C) dew point will be used as the space condition of the bathroom during the period of interest and will be referred to as SBSC (South Bend Standard Conditions).

Test Conditions and Data Correction

Originally, the use of an environmental chamber to replicate the space conditions of the crime scene during the period of interest was considered. Air conditioning manufacturers refer to these as psychrometric chambers. However, to prevent stratification, these chambers are deliberately windy. That windy condition would not accurately model the indoor conditions of a completely interior residential bathroom and would cause the bathmat droplets and washcloth to dry at an artificially high rate.

Testing was done in a residence and data corrected to anticipated space conditions of the bathroom (SBSC), as is done in fan testing to standard air. This residence is located in Phoenix, and testing was done in August 2003. The residence's air conditioning was operational. The original trial date did not permit the testing to be done during times when the indoor conditions were closer to SBSC and all testing was done in conditions less conducive to evaporation than SBSC.

A chart was developed to review the significance of the assumed space conditions Figures 2a and 2b. The chart is normalized and shows the relative time for a given drying process to occur at the different space conditions anticipated in the bathroom. The chart is generated from first principles. As can be seen from the chart. the evaporation rate varies by about [+ or -]25% from the reference condition to the extremes. This chart showed that the exact space conditions were not a critical issue in this case. A more detailed explanation follows.

Natural drying, as state previously, is the process of evaporation of water from a wet surface without the interference of artificial heating, cooling, wind or forced convection. In this situation, the rate of evaporation of water from a wet surface is only proportional to the difference in the water vapor pressure of the air immediately above the wet surface and the air reservoir surrounding the surface. This vapor pressure difference drives the water from the air layer immediately above the wet surface to the air reservoir around it. The vapor pressure of water vapor in air increases with the dew-point temperature of that air. Since the wet surface is evaporating water, the surface is being cooled to a temperature at or somewhat near the thermodynamic wet-bulb temperature of the surrounding air.

[FIGURE 1 OMITTED]

Deviations of wetted surface temperature from thermodynamic wet-bulb temperature are partially addressed in ASHRAE Standard 41.14 in a discussion of wet-bulb temperatures at various surrounding air velocities. Since the Lewis Number for water-wetted surfaces is actually 0.8945 and is less than 1. the energy loss due to water diffusion is greater than the energy gain from conduction. This effect tends to make the measured wet-bulb temperature lower than the thermodynamic wet-bulb temperature. Since the rate of heat and mass transfer to surrounding air at low air velocities is very small, adjacent radiant and conductive heat transfer can become significant, which tends to make the measured wet-bulb temperature greater than the thermodynamic temperature.

In Standard 41.1. this effect is quantified (see Figure 1). The measured wet-bulb temperature is increased by a percentage of the thermodynamic wet-bulb depression and the deviation is larger at low surrounding air velocities. While the figure only goes to 20 fpm (0.10 m/s), extrapolation to zero velocity implies that, at worst, an increase of 50% of the wet-bulb depression seems a conservative maximum deviation. As the air immediately above the wet surface is totally saturated with water, the temperature, dew-point temperature and wet-bulb temperature of that air layer are the same temperature. This principle permits the generation of relative drying time (Figures 2a, 2b and 3a, 3b). The relative drying times are fairly close, independent of the actual surface temperature. In this study, the test conditions were less conducive to evaporation than SBSC, and the use of the "a" charts produce smaller, more conservative corrections. The more conservative condition was used (Figure 2a) to correct test data results to SBSC. However, recent studies by the author with infrared sensor thermometers indicate the natural drying wetted surface temperatures to be closer to the 50% value used in the "b" charts.

An explanation is needed. For Figure 3b, if a particular drying process takes one hour at SBSC, it will take 1.2 hours at 65[degrees]F (18[degrees]C) dry bulb, 35[degrees]F (2[degrees]C) dew point; but only 0.8 hours at 80[degrees]F (27[degrees]C) dry bulb. 50[degrees]F (10[degrees]C) dew point. The condition of 66[degrees]F (19[degrees]C) dry bulb, 26[degrees]F (-3[degrees]C) dew point. should permit identical drying times as SBSC.

Test Procedure

Two pieces of evidence to consider were:

* Water droplets were present on the bathmat in the shower of the bathroom; and

* Two washcloths at the crime scene bathroom were reported to be "fairly wet" at 1:30 p.m. on April 30. 1989.

The presence of water on the bathmat was the evidence with the most variables but was also the most valuable for the defense. Many tests were done on sample shower mats at the test residence. All of these tests had drying times less than 10 hours and were done during drying conditions less conducive to drying than SBSC. One such test had a time averaged space condition of 72.6[degrees]F (23[degrees]C) drying bulb. 53.3[degrees]F (12[degrees]C) dew point and a drying time of six hours. Examining Figure 3a. a one-hour drying process at SBSC would take 1.3 hours at these conditions. translating into less than a five-hour drying time.

Many other tests were made that also had bathmat drying times of less than 10 hours. I urge the readers to try this test themselves. Unfortunately, evidence rules would not permit me to suggest the jurors do this test on their own, as they had to make a determination based on the facts and opinions presented in court only.

[FIGURE 2 OMITTED]

The more interesting focus of the study was to determine what the maximum length of time is between the initial wetting of the washcloths and the time when their condition was still considered to be "fairly wet" in a space at SBSC.

The authorities sent the two washcloths to us that were found at the crime scene resting on a bathtub rim. One of the washcloths had a plaid pattern, which enabled the determination of the width of the rim. An acrylic rim was made to mimic the original rim.

After many preliminary tests. a test procedure was refined in which the washcloth was set on the rim and fully wetted (an unrealistic start condition because the usual procedure would be to wring it out before setting it on the rim). The weight of the rim and the washcloth were measured about every two hours for about 24 hours, until which time there was a negligible loss of water. Additionally, the space dry bulb and relative humidity were simultaneously recorded.

The plaid washcloth was measured to be about 11 in. by 11.5 in. (279 mm by 292 mm) and weighed 29 grams (dry). While the placement of a washcloth on a bathtub rim seems a fairly arbitrary task. the plaid cloth and the police video showed its placement on the bathtub rim provided a means to closely replicate the placement of the washcloth on the fabricated bathtub rim. Four tests were done that agreed closely. considering all the variables (see Figures 4a through 4d).

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

The cloth maintained its dry weight of 29 grams during testing. The cloth was repeatedly tested from a dripping wet (or nearly dripping wet) condition until almost completely dry. The tests have the same basic characteristics. Initially. water drips from the cloth and the cloth rapidly loses water for a couple of hours. Then the cloth loses weight at a constant rate until nearly dry. When the cloth is nearly dry. the available wet surface area decreases, the drying process slows down, and the drying process is no longer linear. The critical number from the test is the grams per hour evaporated during the constant weight loss portion of the test. The fact that the loss of water is nearly linear for the main portion of the drying process is significant, since this means that the capillary action driving the water to the surface can move the water substantially faster than it is evaporated and that evaporation of water at the surface is the sole significant driving force for water loss.

A start and end condition of the history of the cloth must be established. It was assumed that the washcloths were not placed on the bathtub rim in a dripping wet condition (such a condition is not what the expected initial condition of such an event would be) but was moderately wrung out. A test of the cloth was done and the average weight of the moderately wrung out cloth was 89 grams. Since the dry weight of the cloth was 29 grams, the water in such a cloth weighs 60 grams. That is the assumed start of drying condition.

The investigator reported on the police video that the cloth was "fairly wet" on or after 1:30 p.m. April 30, 1989. While such a description is fairly subjective (knowing the actual weight of the wet cloth would have been very useful), it is safe to say that the cloth held less than 10 grams (about 2 teaspoons of water evenly distributed on the cloths) at that moment.

The maximum time between when the investigator felt the cloth was "fairly wet" and when the cloth was placed on the bathtub rim was estimated to be the time required to evaporate 50 grams of water from the cloth. Such times were found to be about 12 to 14 hours. Table 2 shows the test result summary.

Instrumentation consisted of a simple digital postage scale and two digital space temperature and relative humidity meters. The postage scale was remarkably accurate over the range of interest. At study's end, an independent lab calibration tested the scale for accuracy. Two digital temperature and relative humidity meters were used as a check to each other. These devices were in close agreement, giving confidence in their accuracy. Additionally. replicating exact space conditions was not required.

The conclusion of the study was that human activity must have occurred in the bathroom long after the son had supposedly committed the crime.

Trial Testimony

As air-conditioning engineers. we have five moist air properties to specify the amount of water vapor in humid air: dew point, wet bulb, relative humidity. absolute humidity and enthalpy. Yet. only two gas components exist: dry air and water vapor. While as engineers. each of these moist air properties have enormous value, the concepts can be very confusing to the general public. It can lead to statements like "90 degrees and 90 percent relative humidity" (a condition not even on the standard sea level ASHRAE Psychrometric Chart). During testimony. every effort was made to focus only on temperature and dew point and to make the defense report as simple as possible. At the end of the testimony. jurors were allowed to ask their own questions. The nature of those questions made it clear that I had not made my point with all of them. I would like to provide guidance for others in this matter but I can only say that explaining the nature of moist air to the general public is a challenging task.

Despite the evidence, the jury convicted the son. On appeal, it was deemed that the speedy trial rules of the state were not followed. However. the prosecution persisted, and the Indiana Supreme Court overruled the Court of Appeals. The son remains in prison.

References

[1.] Smith. C. 2009. The Prom Night Murders. New York: St. Martin's Press.

[2.] 2001 ASHRAE Handbook--Fundamentals. Ch. 8. Fig. 5.

[3.] 2001 ASHRAE Handbook--Fundamentals. Ch. 28. Table 8.

[4.] ANSI/ASHRAE Standard 41.1-1986 (RA 2006). Standard Method for Measuring Temperature, Figure 6.

[5.] 2001 ASHRAE Handbook--Fundamentals. p. 5.9.

Roy Otterbein, P.E., Member ASHRAE

About the Author

Roy Otterbein, P.E., is president of Otterbein Engineering in Phoenix. He is a past Handbook chairman, a member of two standards committees and has served on TC 5.1, Evaporative Cooling.
Table 1: Weather data for Michiana Regional Airport.

Test Start        Temperature             Dew Point     Wind Speed
Dates             ([degrees]F)         ([degrees]F)        (Knots)

                               Saturday, April 29,1989

4:00 p.m.                64                      52              4

7:00 p.m.                61                      50              6

10:00 p.m.               55                      45             10

                               Sunday, April 30, 1989

1:00 a.m.                49                      41              8

4:00 a.m.                41                      37              5

7:00 a.m.                42                      38              6

10:00 a.m.               49                      38              8

1:00 p.m.                53                      36              9

Table 2: Results from washcloth testing.

Test Start Dates             Time to Loss            SBSC Corrected
                                  50 grams     Time to Loss 50 grams

August 11                             12.2                      11.3

August 16                             15.3                      13.3

August 21                             17.6                      14.4

August 23                             17.4                      14.6
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Author:Otterbein, Roy
Publication:ASHRAE Journal
Article Type:Case study
Geographic Code:1USA
Date:Apr 1, 2010
Words:3283
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