Contents:
Abstract
Introduction
Moisture Control Strategies Presently Employed
Proposed Moisture Control Strategy
Developing the Algorithms
Using the Algorithms
An Example
Comparison with Existing Methods
Conclusions/Future Work
References
Calculator

Using the Algorithms
The following procedures can be used to the predict moisture tolerance of a roofing system using
these algorithms for the four quantifiable requirements for moisture control in lowslope roofing
[1].
Determine the parameters listed below for the roofing system to be evaluated.
Type of insulation (fiberboard, foam or a composite of the two);
H = Heating degree days for the location;
h_{r} = Relative humidity of the indoor environment (40% = 0.4);
r = Membrane absorptance (0.7 for white and 0.1 for black);
P = Deck permeance (in English perms [See chart below]); and
T = insulation thickness (in inches).
Requirement 1: The average yearly moisture content of the roof must
not increase with time.
Results showed that all roofing systems in all climates evaluated satisfied this requirement. The
"algorithm" for this requirement is therefore simple: If the roofing system is located in the
continental US (H<8992), it passes requirement 1.
Requirement 2: No condensation can occur under the roof
membrane.
The flow rate of water into a roof occurs during the winter uptake period when the indoor vapor
pressure is greater than the vapor pressure at the outer membrane of the roof. This creates a
vapor pressure drive which forces moisture into the roofing system.
Calculate p_{vm}, (the average vapor pressure at the roof membrane during the winter uptake period,
in psi) and t, (the length of time of winter uptake, in months):
p_{vm} = 
0.93414+ 0.284h_{r} + 4.850x10^{4}H 
7.995x10^{8}H^{2} + 4.215x10^{12}H^{3} 
2.053x10^{5}Hh_{r} + 161.0/H + 0.002305P 
8.013x10^{5}P^{2}  1.343x10^{7}HP  0.008889r; 
(Eqn. 1) 
t = 
66.1  1.514h_{r} + 0.03390H  5.655x10^{6}H^{2 } +
3.067x10^{10}H^{3} + 0.004424Hh_{r} 
4.327x10^{7}h_{r}H^{2} + 11430/H. 
(Eqn. 2) 
Compute p_{vi}, (the vapor pressure of the indoor air):
p_{vi} = 
h_{r} p_{vsat }, 
(Eqn. 3) 
where p_{vsat} is the saturation vapor pressure, found in any standard saturated
steam table at the indoor temperature. p_{vsat} at 68°F is 0.342 psi; at
70°F, it's 0.363 psi [8].
Now calculate m (the moisture accumulation in the roofing system, lb/ft^{2}):
m = 
0.215 x t (p_{vi } p_{vm})/(R_{bl }+
R_{d }+ R_{i}) 
(Eqn. 4) [7] 
where R_{bl} is the air boundary layer vapor resistance (0.211 reps) and R_{d }and R_{i }are the deck and
insulation vapor resistances (in reps), respectively. Table 2 lists the vapor resistances for typical
roofing materials.
Table 2
Vapor Resistances for Decks and Insulation Materials

Vapor Resistance (Reps) 
Tight metal deck 
1.56 
Loose metal deck 
1.00 
Perforated metal deck 
0.20 
Metal deck with holes 
0.10 


1inch fiberboard 
0.024 
3inch fiberboard 
0.071 
1 inch polyisocyanurate foam 
0.46 
3inch polyisocyanurate foam 
1.39 
Composite (2 in. of foam between two layers
of 1/2 inch fiberboard) 
0.95 
Now compare m, the calculated moisture accumulation, with the appropriate failure threshold
shown below. See Reference [9] for information regarding the derivation of these thresholds.
Insulation 
Failure Threshold 
lb/ft 
kg/m^{2} 
Fiberboard 
0.20 lb/ft^{2} 
1.0 kg/m^{2} 
Foam 
0.012 lb/ft^{2} 
0.06 kg/m^{2} 
Composite 
0.14 lb/ft^{2} 
0.69 kg/m^{2} 
Systems with moisture accumulation, m, greater than or equal to the failure threshold do not pass
the requirement. This method is conservative, in that it tends to slightly overpredict failures. For
the given database, the accuracy in predicting failures is 98%. For passes, it is 95% [9].
Requirement 3: If a leak occurs in the roofing system, no condensation
can occur on the deck.
Condensation at the deck is most likely to occur during the summer, when the vapor pressure at
the outer membrane of the deck is greater than the indoor vapor pressure. This is also the time
when drying occurs, as water vapor is pushed into the indoor environment.
The analysis is separated by insulation type. Read the conditions listed in order for each
insulation type. If a roofing system meets one of the conditions, pass or fail is decided. If not, the
analysis must be continued.
Composite
All the composite roofing systems passed this requirement for all conditions tested. Therefore,
any composite system, as described above, passes this requirement.
Fiberboard
 If H is greater than or equal to 6151, T is less than or equal to 1 inch, and the
indoor relative humidity, h_{r}, is less than or equal to 50%, the system
fails.
 All other fiberboard systems pass.
Foam
 If the vapor resistance ratio, R_{i}/R_{d} is less than or equal
to 1.5, the system fails.
 If the above condition is not met, continue with the vapor pressure drive
calculations shown below.
Vapor Pressure Drive Calculations
Calculate the deck vapor pressure, p_{vd} :
p_{vd} = 
48.41 + 0.3261 h_{r}  0.02054P  0.01661r 
0.0004427H  0.01734R_{i} + 0.0005972P^{2} 
0.02675 h_{r} ^{2} + 0.002402R_{i}^{2} +17322/H +
0.01288P h_{r} + 0.002315Pa + 4.769x10^{7}PH + 0.01776/P 
2534135/H^{2} + 5.5574768*LN(H) + 5.626x10^{8}H/R_{i} 
(Eqn. 5) 
Calculate the vapor pressure drive, D_{vp} (the determination of p_{vi}
is discussed in the previous section on requirement 2).
D_{vp} = 
p_{vd}  p_{vi} 
(Eqn. 6) 
If the vapor pressure drive, D_{vp}, is greater than or equal to the failure
threshold of 0.038 psi (0.19 kg/m^{2}), then the system does not pass this
requirement.
This method is also conservative, because it over predicts failure. The accuracy in
predicting failures for the given database is over 99%, and for passes, it's 93%.
Requirement 4: If a leak occurs in the roofing system, drying time
will be as short as possible.
Simulations were performed for each roofing system to determine the drying time after a
leak of 10% by volume occurs. Separate correlations were developed for each insulation
type: wood fiberboard, polyisocyanurate, and the composite of the two.
Calculate the relative time to dry. For a fiberboard system:
t = 
5.848+0.05641P + 5.6449r + 0.001264H +
7.463 h_{r} + 0.4522r^{2} + 0.0002384rH +
7.7516x10^{4} h_{r} H + 3.75 h_{r}r 
6.2 h_{r} ^{2}  7.83853x10^{8} H^{2}  0.05417T +
678.4/H  0.5576/P  0.00462rP  1.627665x10^{12}H^{3} 
12.2547r^{3} 
(Eqn. 7) 
For a foam system:
t = 
601.6 + 0.1774P + 4068r + 0.1309H  67.88 h_{r} 
5112r^{2} + 0.001416rH + 2.9644x10^{3}Hh_{r} +
50.2083h_{r}r +53.12h_{r} ^{2} 
2.172x10^{5}H^{2} + 0.7542T + 44324/H + 2.037/P  0.3933rP +
1.1374x10^{9}H^{3} 
(Eqn. 8) 
For a composite system:
t = 
18.74 + 0.02002P  35.10r + 0.01328H + 0.6807 h_{r}
 28.98r^{2} + 0.000255rH + 5.86x10^{4}Hh_{r} +
2.083h_{r}r + 1.25 h_{r}^{2} 
2.0185x10^{6}H^{2}  14.28T + 4702/H  0.3850/P  0.006140r +
9.866815x10^{11} H^{3} + 102.4r^{3} 
(Eqn. 9) 
It is recommended that the drying time should be less than one year. The "drying season"
typically happens during the spring and summer months when the vapor drive pushes water
vapor out of the roofing system and into the indoor environment. If the moisture is not removed
during this time, it will remain in the roofing system until the next drying season. This method is
also conservative and tends to slightly over predict drying time. For the given database, it
predicts whether drying time is greater than 12 months with 100% accuracy. It predicts whether
the drying time is 12 months or less with 97% accuracy.
Previous Section  Developing the Algorithms
Next Section  An Example
