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CO Q NBS TECHNICAL NOTE 1107

U.S. DEPARTMENT OF COMMERCE/National Bureau of Standards
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards' was established by an act ot Congress on March 3. 1901. The Bureau's o\erall goal is to strengthen and ad\ance the Nation's science and technology

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AUS 17 \^7'f^

not; f)CC'- L^ucCy

The Use of Aerial Infrared

Thermography to Compare the ao (oy

Thermal Resistances of Roofs ^^^1

C.c5-

D.M. Burch

Center for Building Technology

National Engineering Laboratory

National Bureau of Standards

Washington, DC 20234

Sponsored by:

Department of Energy

Washington, DC 20585

I

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U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Luther H. Hodges, Jr., Under Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

^( NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued August 1979
National Bureau of Standards Technical Note 1107

Nat. Bur. Stand. (U.S.), Tech. Note 1107, 38 pages (Aug. 1979) CODEN: NBTNAE

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1979

For sale by the Superintendent of Documents. U.S. Government Printing Office, Washington, D.C. 20402

Stock No. 003-003-02102-4 Price $2. (Add 25 percent additional for other than U.S. mailing).
The Use of Aerial Infrared Thermography to Compare the

Thermal Resistances of Roofs

by

D. M. Burch

ABSTRACT

The paper investigates whether a comparative roof survey using aerial

infrared thermography can be used to rank the roofs of residential and

commercial buildings according to their thermal resistance. Mathematical models are presented for predicting the apparent radiance temperature of these roof systems. These models are used to investigate

the differences in apparent radiance temperature between roofs having

various thermal resistances. These predicted differences are then

compared with predicted differences in apparent radiance temperature

caused by typical variations in roof emittance, local outdoor temperature, and local wind speed throughout the macroclimate. The transmission characteristics of the atmosphere are reviewed, and the

required dew-point spread for preventing dew or frost formation on

a roof is examined.

Key words: Aerial flyovers; aerial infrared thermography; energy

conservation; roof heat-loss survey.

ACKNOWLEDGMENT

The author gratefully acknowledges the contribution of John Bean,

who carried out the computer analysis for this study.

ili
Nomenclature

A * surface area

C » specific heat of air

e * surface emittance

E * emittance factor

F " radiation heat-transfer coefficient

h = convection heat-transfer coefficient

I = rate of air infiltration

M = emitted thermal radiation (exitance)

R =• thermal resistance

T = temperature

V = vo lume

^ = air penetration rate per unit ceiling area W = wind speed

= field of view

p = density of air

a = Stef an-Boltzmann constant

Subscripts

a » apparent radiance property or attic property

c = ceiling property

e = attic end wall property

f = attic floor property

i = indoor property

o = outdoor environment

r = roof property

s =" soffit (eaves) property

sky = calorimetric sky property

sky' = spectral sky property

IV
CONVERSION FACTORS TO METRIC (SI) UNITS

Physical

Quantity Symbol

To Convert

From To Multiply By

Length I ft m 3.05 X

10"^

Area A ft2 m2 9.29 X

10"2

Volume V ft3 b3 2.83 X

10~2

Temperature T Fahrenheit Celsius T(, = (Tp-32)/1.8

Temp. Dlff. AT Fahrenheit Kelvin K = (ATp)/1.8

Density P Ib/ft^ kg/m^ 1.602 X lO"*"^

Thermal

Transmlttance

(or Conductance) U,h Btu/h*ft^*°F W/m^'K 5.68

Thermal Resistance R h*ft^*°F/Btu m^'K/W 0.176

Heat Flux

(Thermal Radiation)

q/A Btu/h'ft^ W/m^ 3.15

Heat Flow q Btu/h W 2.93 X 10"^

Volumetric Flow

Rate V ft-^/min m^/s 4.72 X 10"^

Wind Speed w ft/min m/s 5.08 X 10"3

Specific Heat Cn Btu/lb'°F J/kg'K 4.19 X 10^
Contents

Page

Abstract Ill

Acknowledgment ill

Nomenclature iv

Conversion Factors to SI Units v

Contents vi

1. Introduction 1

2. Concept of Aerial Infrared Thermography 2

3. Low-Slope Built-up Roofs 8

3.1 Mathematical Model 8

3.2 Description of Roof System 9

3.3 Heat-Transfer Parameters 9

3.4 Outdoor and Indoor Parameters 9 3.5 Results and Analysis 12

3.5.1 Effect of Thermal Resistance 12

3.5.2 Effect of Other Parameters 15

3.5.3 Dew-Point Spread 17

4. Pitched Ventilated Roofs 17

4.

1

Mathematical Model 17

4.2 Description of Roof System 21

4.3 Heat-Transfer Parameters 21

4.4 Outdoor and Indoor Parameters 23

4.5 Results and Analysis 24

5. Summary and Conclusions 29

References 29

VI
THE USE OF AERIAL INFRARED THERMOGRAPHY

TO COMPARE THE THERMAL RESISTANCES OF ROOFS

D. M. Burch

1 . INTRODUCTION

Aerial infrared thermography is an imagery process utilizing an infrared line scanner which produces an apparent radiance temperature

map of a portion of the terrain underneath an aircraft. Such a process

has been shown to be effective in locating regions on low-slope builtup roofs that have defective insulation [1,2], These regions will

show up as "hot spots" in the radiance temperature map. A common

problem with built-up roofs is that the exterior membrane becomes

ruptured, permitting water to penetrate the roof system and wet

the insulation. Regions having wet insulation will conduct more

heat and will appear warmer than regions having dry insulation.

The merit of such a survey technique is that defective regions can be located, permitting local repairs to be carried out instead

of replacing the whole roof system.

Aerial infrared thermography has also been used to compare the thermal

resistances of roofs included in an aerial infrared photograph [3-12].

Proponents of such comparative surveys assert that roofs which lose

more heat will be warmer and will therefore appear as having higher

apparent radiance temperatures. In an aerial infrared photograph,

such roofs are said to appear lighter in gray tone than roofs losing

less heat. It is normally recommended that aerial infrared surveys

not be carried out under an overcast-sky condition, in order to

avoid the problem of large variations in sky temperature affecting

the apparent radiance temperature. In addition, under a clear-sky

condition, radiation exchange with a cold night sky reduces roof

temperature below the ambient air temperature and thereby increases

roof heat loss. This process will cause the roofs to be displayed

in a greater range of gray tones, which increases the contrast in

the thermal image,

A controversial issue within the technical community is whether such

comparative roof surveys are actually successful in ranking roofs

according to their thermal resistance. An aerial infrared photograph

may include as much as a square mile of terrain, depending upon

the altitude of the flight. Considerable variation in local air

temperature and wind speed may exist throughout the macroclimate

of an aerial infrared photograph. In addition, roof emittance varies

from one roof to the next. Variations in local wind speed, local

outdoor temperature, and roof emittance may produce differences

in radiance temperatures of roofs which may mask out those differences

in radiance temperature due to roof resistance. This paper examines

this issue.
This paper also investigates the depression In surface temperature from

which the required dew-point spread for preventing the formation of dew

or frost on roofs can be determined. It is recommended that aerial

infrared surveys be conducted under outdoor conditions which preclude

dew or frost from occurring on roofs. The formation of dew or frost on

a roof may change its emittance, and the phase change which occurs releases latent heat to the roof which increases its surface temperature.

Both of these effects may substantially change the apparent radiance

temperature of a roof.

2. CONCEPT OF AERIAL INFRARED THERMOGRAPHY

The basic concept of aerial infrared thermography is that all objects

emit thermal radiation according to the Stef an-Boltzmann equation:

M = e*a»T^ (1)

where M = emitted thermal energy (exitance),

a = Stef an-Boltzmann constant,

T = absolute temperature, and

e = surface emittance.

As the heat-loss rate through an exterior surface of a building

increases, the exterior surface temperature of that part of the building also increases. The emitted thermal energy as given by eq. (1)

will increase if the surface emittance remains constant.

In conducting an aerial infrared survey, an infrared line scanning

system mounted in an aircraft scans the terrain, building up a thermal image as the aircraft progresses along a flight line, as shown in figure 1. The scanner is basically an optical telescope,

with its narrow field of view continuously redirected by a spinning

flat mirror. The mirror causes the system to scan in a plane

perpendicular to the direction of flight of the aircraft. Such

systems have one or more cryogenically cooled thermal radiation

detectors in the focal plane of the telescope which convert the

focused thermal energy received by the detector into an electrical

signal. This electrical signal can be processed into a visual

image on a cathode-ray tube (CRT) which can be photographically

recorded or digitized and recorded on a magnetic tape recorder

for future processing.

Much of this description was taken from ref. [3]
Eltctronict

Ratithg tcm mirror

Radiatnn from ground

Ttpo rteorder •r CRT serif

^n DftKlor

Akcnift skin

Horizon

Tmining sot

Ground

olomont

iwolution

Figure 1. Schematic illustration of the use of a line scanner to

perform aerial infrared thermography [3].
An aerial infrared photograph of a large number of residential roofs

is shown in figure 2. Variations in gray tone from light to dark

correspond directly to variations in apparent radiance temperature.

Parts of the thermal picture appearing in lighter gray tones have

a higher apparent radiance temperature than other parts of the thermal

picture.

Infrared line-scanning systems usually have a sweep angle (6) , as depicted in figure 1, which does not exceed 110 degrees, in order to

restrict distortion at the outer edges of the thermal picture [4]

Flights are most often conducted at altitudes between 1000 and 2000 ft.

The instantaneous field of view of the infrared line scanner varies

with the particular system but will generally range between 1 and 2.5

milliradians on a side.

Aerial infrared thermography is usually performed in the 8 to 14 jam

wavelength band because of the high atmospheric transmission over that

part of the infrared spectrum (see figure 3). Atmospheric transmittance data presented in figure 4 show that the average atmospheric

transmittance at a distance of 1640 ft above ground level is 0.93 and

0.97 at outdoor relative humidities of 95 and 20%, respectively. In

addition, the same data show that increases in path length due to

increases in the view angle have a very small effect on the atmospheric

transmittance over this particular wavelength band.

The thermal radiation sensed from surfaces such as roofs by an infrared

line scanner includes both self-emitted thermal radiation and reflected

radiation from the sky. The apparent radiance temperature (T ) is

defined as the temperature of a perfectly black surface which would

radiate the same amount of thermal radiation as a real surface at a temperature (T ) and having a surface emittance (e). An equation

relating the apparent radiance temperature of a surface to its actual

temperature has been derived by Goldstein [13] . For the convenience

of the reader, a derivation for the equation is given below.

For the 8-14 Mm wavelength band, the self-emitted energy from a perfectly black surface at the apparent radiance temperature (T ) is

equal to the self-emitted and reflected sky radiation from the actual

surface at a temperature (T ), or

n n.,..'.n .„.

2 Atmospheric transmittance is defined as the fraction of the flux of

infrared radiation which is not absorbed or scattered and is transmitted through a layer of the atmosphere.
RKW•• ,,,'.

^

Low radiance , IlJBo * Hr*

y^' W :*m V .i-m^M'^

Figure 2. An aerial infrared photograph of a large number of

residential roofs (this aerial infrared photograph

was provided by Texas Instruments of Dallas, Texas).
4 S 6 7 8

Wavelength, microns

10 n 12 13 14

Figure 3. Transmittance of the whole atmosphere as a function of

wavelength [5].
5 0.7-

30

Angle, degrees

Figure 4. Average atmosphere transmittance as affected by incident

angle and outdoor relative humidity [6].
Here the radla^jit energy from the sky is based on the spectral sky

temperature (T , ) instead of the calorimetric sky temperature

(T 1 ), since raaiant energy is being considered only over the

8-14 vim portion of the infrared spectrum.

The spectral sky temperature is lower than the calorimetric sky

temperature because the atmosphere is relatively transparent over

the 8-14 pm wavelength band. The exponent n is 5 instead of 4

because radiation is only being considered between 8-14 pm instead

of the whole infrared spectrum .

Solving eq. (2) for T^ gives:

Ta = Tg. [e + (l-e)-3^]l/^ (3)

Here 3 is the ratio of the spectral sky temperature (T , ) to the

surface temperature (T ). The accuracy of equation (3) was investigated by numerically integrating the Planck distribution function

for the self-emitted and reflected components of the roof radiance.

Equation (3) was found to be accurate within a fraction of a degree

Fahrenheit over a representative range of surface temperatures and

sky temperatures. It should be pointed out that equation (3) does

not account for thermal reflections from nearby buildings.

3. LOW-SLOPE BUILT-UP ROOFS

3.1 MATHEMATICAL MODEL

For a low-slope built-up roof, the steady-state heat conduction through

the roof during the night is equal to the heat loss by convection to

the ambient outdoor air and the net radiation loss to the sky, or

(T.-Tg)/R = h. (Tg-T^) + F^. (Tg-T^i^y) , (4)

where

^i» '"s ' -^o' "^skv ~ temperatures of the indoor environment of the

building, the exterior surface of the roof,

the outdoor air, and the calorimetric sky,

respectively.

The spectral sky temperature (T 1^ ) is the equivalent black-body

temperature of the sky vault based on sky radiance between 8-14 um. The calorimetric sky temperature (T j^ ) is the equivalent black-body

temperature of the sky vault based on sky radiance covering the

entire infrared spectrum,

8
h = convection heat-transfer coefficient,

R = thermal resistance of the roof (does not

include resistance of the air film at

the exterior surface), and

F = radiation heat-transfer coefficient.

The radiation heat-transfer coefficient (Fq) is given by the relation;

^o

= ^s-c-(Ts^+ T^^y^-^T^ +T^^^) (5)

where c = emittance of the exterior roof surface and ^s

a = Stefan-Boltzmann constant

Solving eq. (4) for the roof surface temperature (T ) yields

Ts =

Tj^/R + h«TQ + Fq»T

h + Fq + 1/R

^^

(6)

3.2 DESCRIPTION OF ROOF SYSTEM

The built-up roof system used for the analysis was comprised of the

following components: 3/8-inch built-up roof membrane; perlite

aggregate board; 4-inch concrete deck; and 1/2-inch gypsum plaster.

Several thicknesses of perlite aggregate board were considerd in the

analysis.

3.3 HEAT-TRANSFER PARAMETERS

Thermal resistance values for the components of the built-up roof

system were taken from refs. [15,16] and are summarized in Table 1.

In a recent survey of built-up roof systems [17], perlite insulation

was found to be the most common type of insulation. This same survey

reported the percentage of roofing systems having various insulation

thicknesses (see Table 2). For the analysis in this paper, insulation

thicknesses of 0, 2, and 4 inches were considered.

The overall thermal resistances for built-up roofs having these insulation thicknesses were calculated using the series resistance method [16]

These values are summarized in Table 3.

3.4 OUTDOOR AND INDOOR PARAMETERS

The indoor temperature below the built-up roof system was taken to be

70°F. A search of the literature was made for emittance values of

exterior covering materials and materials which may deposit on builtup roofs. These values are summarized in Table 4. From this table.
it Table 1. Thermal Resistance Values for the Components of

the Built-up Roof

Component Thermal Resistance

h»ft2.°F/Btu

3/8-inch Built-up Roof Membrane 0.33

Perlite Aggregate Board (per inch thickness) 2.63

4-inch Concrete Deck 0.32

1/2-inch Gypsum Plaster 0.09

Interior Still Air Film 0.61

Obtained from refs. [15,16].

Table 2. Survey of Insulation Thicknesses of Built-up Roof

Systems

Percentage of

Roof Systems Surveyed

Insulation Thickness,

Inch

26

21

41

12

5/16 -1

1 1/16 -2 more than 2

Obtained from ref. [17].

Table 3. Total Thermal Resistance Values for Built-up Roof

Systems

Insulation Thickness,

Inches

Total Thermal Resistance

h*ft^»°F/Btu

1.4

6.6

11.9

Includes thermal resistances of the air films.

10
Table 4. Emittances for Various Exterior Covering Materials

and Materials which May Deposit on Built-up Roofs

Material Emittance

Aluminum Roofing 0.22

Bituminized Roofing Felt 0.91

Concrete, rough 0.94

Frost, rime 0.99

Ice, smooth 0.91

Soot 0.95

Water 0.97

Asphalt 0.93-0.96

Dolomite Gravel, 0.;5-cm rocks 0.96

Snow 0.82

Reference

18

14

19

14

14

20

14

5

27

21

Table 5. Calorimetric and Spectral Sky

Temperatures Used for the Analysis

Calorimetric Spectral

Outdoor Sky Sky

Temperature Temperature Temperature

°F °F °F

-54 -121

10 -40 -102

20 -27 - 83

30 -13 - 65

40 - 47

11
it is seen that the emittances of most exterior covering materials

vary over a range of 0.91 to 0.96, except for metallic roof surfaces

such as aluminum roofing. It is noted that the accumulation of ice,

soot, water, or frost can change the roof emittance. Roof emittance

will usually have a weak dependence on the view angle, except for view

angles exceeding 60° from the normal [5]. For the thermal analysis,

the roof emittance was assumed to be 0.90, unless otherwised specified.

Calorimetric and spectral sky temperatures for a clear winter sky

which were used for the analysis are given in Table 5. The calorimetric sky temperatures are based on measured data of Swinbank [22],

and the spectral sky temperatures were obtained from Goldstein [25].

The convection heat-transfer coefficient (h) was calculated using the

following relation:

h = 0.5 + 0.38*W. (7)

Here W is the wind speed in miles per hour. This equation is based on data for a concrete surface [24] with the radiation portion of the

overall heat-transfer coefficient subtracted. Equation (7) applies

to a roof that has no obstructions to the flow of air.

3.5 RESULTS MP ANALYSIS

3.5.1 Effect of Thermal Resistance

The mathematical model described in the previous sections was used to

predict the difference in apparent radiance temperature between builtup roofs having and 2 inches of perlite insulation under a wide

range of outdoor conditions. The results of this analysis are given

in figure 5. Under low wind conditions (wind speeds less than 5 mph)

,

the radiance temperature differences between built-up roofs having

and 2 inches of insulation are substantially greater than at higher

wind speeds. Mean winter wind speeds for the United States are well

above 5 mph [23]. It is likely that most aerial infrared surveys

would be performed under conditions for which the surface wind speeds

would be greater than 5 mph. Under such conditions, the maximum

radiance temperature difference between built-up roofs having and 2 inches of insulation would be 12°F. For an outdoor ambient temperature

of 20°F and a 10-mph wind speed, the radiance temperature difference

between these roofs would be 5°F, which perhaps could be considered

a representative value.

Predicted differences in apparent radiance temperature between the

exterior surfaces of built-up roofs having 2 and 4 inches of insulation are given in figure 6. These temperature differences are seen

to be considerably less than those between roofs having and 2 inches

of insulation. For wind speeds in excess of 5 mph, the difference in

apparent radiance temperature is seen to be less than 2°F.

12
30

CLEAR-SKY CONDITION

10 15

Wind speed, mph

Figure 5. Predicted differences in apparent radiance temperature

between, the exterior surfaces of built-up roofing systems

having and 2 inches of insulation as a function of wind

speed for various outdoor temperatures.

13
30

CLEAR-SKY CONDITION

25

^ 20

f

15

Wind speed, mph

Figure 6. Predicted differences in apparent radiance temperature between

the exterior surfaces of built-up roofing systems having 2 and

4 inches of insulation as a function of wind speed for various

outdoor temperatures.

14
3.5.2 Effect of Other Parameters

In this section, the mathematical model is used to compare differences

in radiance temperature between roofs having different thermal resistances to differences in radiance temperatures resulting from variations

in roof emittance, local outdoor temperature, and local wind speed.

For this analysis, the outdoor temperature of the macroclimate is taken

to be 20°F.

The difference in radiance temperature between two roofs, one having no insulation and the other having 2 inches of insulation, is given in curve a of figure 7. The emittance of these two roofs was taken to be

0.9. Similarly, the radiance temperature difference between two roofs, one having 2 and the other having 4 inches of insulation, is given in curve b of figure 7.

Differences in radiance temperature due to variations in roof emittance, local outdoor temperature, and local wind speed for a roof with

2 inches of insulation are also plotted in figure 7. Curve c gives

the difference in radiance temperature between two roofs, one having

an emittance of 0.9 and the other having an emittance of 1.0. Such an emittance range is consistent with the range in emittances of common roofing materials given in Table 4. Curve d gives the difference in

radiance temperature between two roofs, one exposed to a local outdoor

temperature of 20°F and the other exposed to a local outdoor temperature of 25°F. It was believed that a 5°F variation in the local outdoor temperature throughout a macroclimate would be representative of

actual conditions. And finally, curve e gives the difference in

radiance temperature between two roofs, one exposed to a particular

wind speed and the other exposed to a fifty percent reduced wind speed.

Variations in terrain elevation (such as hills and high-rise buildings)

will shelter certain roofs from the wind. It was assumed for this

analysis that such sheltered roofs would be exposed to winds having

one half the wind speed of unsheltered roofs. Similar results were obtained for roofs having different insulation thicknesses.

From this analysis, it can be seen that variations in roof emittance,

local wind speed, and local outdoor temperature produce differences

in radiance temperature which mask out those differences in radiance

temperature between roofs having 2 and 4 inches of insulation.

Therefore, it will often be difficult to distinguish a roof with

2 inches of insulation from one having 4 inches of insulation. On the

other hand, the differences in radiance temperature between roofs

having and 2 inches of insulation are larger than those differences

in radiance temperature due to variations in other parameters when the

wind speed is less than 7.5 mph. Therefore, there is a good chance of

distinguishing a roof having inches of insulation from one having

2 inches of insulation, particularly if the wind speed is less than

7.5 mph

.

15
^— ,

SUiLT-UP ROOF WITH 2 INCHES OF INSULATION

To =20''F

I

1

I

.s

5.0 15 10.0

Wind speed, mph

1S.0

Figure 7. A comparison of the effect of emittance, thermal resistance,

local wind speed and local outdoor temperature on the

apparent radiance temperature of a built-up roof having

2 inches of insulation.

16
3.5.3 Dew-Polnt Spread

The mathematical model was also used to investigate the depression in

surface temperature for a built-up roof due to radiation exchange with

a clear night sky (see figure 8). For the analysis, the built-up roof

having 4 inches of insulation was used, since the depression in surface

temperature would be greater for this roof than for roofs having lesser

insulation. Dew or frost would form on this roof before it would form

on roofs having less thermal insulation. A criterion for precluding

the formation of dew or frost would be that the dew-point spread

(difference between the dry- bulb and dew-point temperatures) of the

outdoor air should be larger than the depression in surface temperature.

To illustrate the use of figure 8, consider the following example: An

aerial infrared survey is carried out at an outdoor temperature of 20°F

and a relative humidity of 75%. The dew-point temperature corresponding to this psychrometric condition is 14°F, giving a dew-point spread

of 6°F. From figure 8, the depression in surface temperature for wind

speeds less than 7 mph is greater than 6°F. Therefore, if this aerial

infrared survey is to be performed without dew or frost formation on

a built-up roof, then the local outdoor wind speed should be greater

than 7 mph.

Under still-air conditions, the radiation exchange between a roof and

a cold night sky can reduce the surface temperature as much as 19°

F

below the ambient air (see figure 8). This figure agrees with measured

data of Cullen [28] which show as much as a 20°F depression in the

surface temperature of a roof due to radiation exchange with a cold

night sky. As the wind speed across a roof increases, the roof temperature approaches the outdoor air temperature and the likelihood of

dew or frost formation is reduced substantially.

4. PITCHED VENTILATED ROOFS

4.1 MATHEMATICAL MODEL

A mathematical model for predicting the exterior surface temperature

of a pitched ventilated roof is presented herein. Using the attic

space as a control volume for a steady-state heat balance, the rates

of heat gain into the attic space by way of convection from the attic

floor and air penetration through the attic floor are equal to the

rates of heat loss by convection to the roof, heat conduction through

the soffit region and attic end walls, and the rate of heat loss due

to the exchange of attic air with outdoor air, or:

A^-hf-(Tf-T^) + V-A^-C -p-d.-T^) = VV^V^r) +

17
5.0 IS 10.0

Wind speed, mph

15.0

Figure 8. Depression in surface temperature on a built-up roof having

4 inches of insulation as a function of wind speed.

18
where T. , T , T^:, T = temperatures of the indoor air, attic space

air, surface of attic floor, and underside

of the roof, respectively,

A , A^, A , and A = surface areas of the ceiling, roof, soffit

(eaves) region, and attic end walls,

respectively,

I = attic ventilation rate,

p = density of air,

C = specific heat of air,

V = volume of the attic space,

V = rate of air penetration per unit ceiling

area, and

h^,h = convection heat-transer coefficients for

the attic floor and underside of the roof.

Performing a heat balance on a unit area of attic floor, the rate of

heat conduction through the attic floor is equal to the convective

heat loss and the net radiation exchange between the attic floor and

the underside of the roof, or:

(T.-T^)/R^ = hf-(Tf-T^) + F^-(Tf-T^), (9)

where R = thermal resistance of the attic floor (ceilng) and

F„ = radiation heat-transfer coefficient between the attic d

floor and the underside of the roof.

The other symbols are as previously defined. The thermal resistance

of the attic floor (ceiling) (R„) does not include the air film

resistance at the attic floor. The radiation heat-transfer coefficient

(F„) is defined by the relation:

a. 2 2 F^ = E'a«(Tf + T^)*(Tf + T^) , (10)

where E = emittance factor (see eq. 18) and

a = Stef an-Boltzmann constant.

Performing a similar heat balance on a unit area of the underside of

the roof, the rate of heat conduction through the roof is equal to

the convective heat gain from the attic air and the net radiation

exchange from the attic floor to the underside of the roof, or

19
where T = temperature of the exterior surface of the roof and

R = thermal resistance of the roof.

The thermal resistance (R^) does not include the air-film resistances

at the exterior and interior surfaces of the roof. The radiation

heat-transfer coefficient is defined by equation (10).

At the exterior surface of the roof, the rate of heat conduction

through the roof is equal to the rate of convection heat loss

to the ambient air and the radiation heat-loss rate to the sky,

or:

(Tr - Ts)/R^ = h^.CTg - T^) + F^-CT^ - T^j^y), (12)

where h = convection heat-transfer coefficient at the exterior

surface,

F = radiation heat-transfer coefficient between the roof and

sky,

T ,T , = temperatures of the outdoor air and the sky, respectively.

Equations (8), (9), (11), and (12) can be rearranged respectively

as follows:

A , A V

-^ . 1 + _§.

^^CSCR A

(h

^ + VC-p +^ -h +-^ .1 +-^ -R +1 .p.c • -^).T P AirARA e a'^pA^a

-^f-'f -/'^ •^r=V.S.,.T,^(^i-H-l,.,.Cp4i^^4^).T, ^,3)

-F^.T^ + (1/R^ + hf + F^).Tf - hf .T^ = T./R^

(1/R, + h^ + F^).T^ - F^.Tf - h^.T^ - l^/R^ =

• ^.Tr + Ts.(l_ + h^ + FJ = h^.T^ + F^ .Ts^y •

20

(14)

(15)

(16)
These four linear algebraic equations for T^ , T , T , and T can be

solved simultaneously. An iterative procedure is required, however,

in order to converge to values for F and F .

4.2 DESCRIPTION OF ROOF SYSTEM

A schematic drawing of the attic model is given in figure 9. Using

this attic model, the surface areas of the ceiling (A ), the soffit

(eaves) region (A ), the attic end walls (A ), and the roof (A^) were determined and the following dimensionless ratios of physical parameters were defined:

A^/A = 1.16; \/\ " 0.187; and

Ag/A^ = 0.0667; V^/A^ = 3.73.

The mathematical model developed in the previous section was expressed

in terms of dimensionless ratios with the idea that such ratios would

vary much less than the physical parameters themselves from one attic

to the next. The construction details of various components comprising

the attic model were selected as follows: the roof consisted of shingles

and roofing paper laid on top of 1/2-inch plywood sheathing which

was nailed to nominal 2 x 6-inch rafters placed 16 inches on center;

the soffit region consisted of 1/2-inch plywood sheathing; the attic

end walls were comprised of wood-bevel siding attached to 1/2-inch

insulating sheathing, which was nailed to nominal 2 x 4-inch studs

placed 16 inches on center; and the ceiling consisted of 1/2-inch

gypsum board attached to nominal 2 x 6-inch joists placed 16 inches

on center. Various amounts of ceiling insulation were considered

(see Table 6)

Table 6. Thermal Resistances of the Components

of the Attic

Component Thermal Resistance

h»ft^«°F/Btu

Roof 1.50

Soffit (eaves) region 1.83

Attic End Wall 3.57

Ceiling

° No Insulation 1.19

° R-11 Insulation 11.3

° R-30 Insulation 28.7

4.3 HEAT-TRANSFER PARAMETERS

The thermal resistances of the various components of the attic space were calculated using the series resistance method as outlined in

ref. [16]. For these calculations, wood structural members were

21
2il RAfTERS «-mCH O.C.

WOOD BtVEL SIOING,K-INCH INSULATING SHEATHING, 2x4 STUDS PLACED It-INCH O.C.

H-fNCH GYPSUM

BOARD CEILING

K-INCH PLYWOOD SHEATMIttS

ROOFING PAPER

SHINGLES

BLANKET mSULATIOR UID BETWEEN THE JOISTS

Figure 9. Schematic drawing of roof system.

22
treated as parallel heat-flow paths. Thermal resistance values for the

various components were taken from ref. [16]. Thermal resistance values

for the various components of the attic are summarized in Table 6.

The thermal resistance values for the soffit (eaves) region and attic

end walls include the thermal resistances of the air films at the

exterior and interior surfaces. The value for the roof does not include

the air film, while the attic floor (ceiling) values include the

air film at the interior surface (living-space side). The convection

heat-transfer coefficient (h) at the underside of the roof and floor were assumed to be governed by the relation:

h = 0.2*(AT)^-^^. (17)

Here AT is the surface-to-air temperature difference. This relation

is applicable to natural convection heat-transfer with heat flow in

an upward direction. The emittance factor (E) was calculated using

the relation:

E =

^f ^r

(18)

where e^ and e are the emittances of the attic floor and the underside of the roof. Taking the emittance values to be 0.9, the emittance

factor (E) is found to be 0.82.

The attic was assumed to have a natural ventilation rate of 2 volume

changes per hour, unless specified otherwise. The rate of convective

air penetration through the ceiling was taken to be 0.025 ft /min per

square foot of ceiling. This figure is based on a house overall air

infiltration rate of 0.75 volume changes per hour. It was assumed

that 25% of the house exfiltration occurred through cracks in the

ceiling construction.

The most common exterior surface covering for the roofs of residences

is asphalt shingles. Emittance values for asphalt shingles could not

be found in the literature. It was estimated that the surface emittance of asphalt shingles would probably be between 0.85 and 0.95 [26].

Variations would be due to differences in such factors as surface

roughness, density and type of top covering material, dust and soot

deposits, moisture absorption, etc. For this analysis, the emittance

of the shingles of the roof was taken to be 0.90, unless specified

otherwise.

4.4 OUTDOOR AND INDOOR PARAMETERS

The outdoor and indoor parameters used for the analysis were the same

as those used for the built-up roof analysis given in section 3.4.

23
4.5 RESULTS AND ANALYSIS

As in the case of the previous section, the mathematical model was used

to predict differences in radiance temperature between ventilated

pitched roofs having R-0 and R-11 ceiling insulation (see figure 10)

and ventilated pitched roofs having R-11 and R-30 ceiling insulation

(see figure 11). These differences in radiance temperature are seen

to be approximately a factor of 3 smaller than corresponding differences

in radiance temperature between built-up roofs having various insulation

thickness (see figures 5 and 6). This is due to the decoupling of the

roof from the attic floor by the ventilated attic space.

As in the case of the previous section on built-up roofs, the mathematical model was used to compare the differences in radiance temperature caused by variations in roof emittance, local wind speed, and

local outdoor temperature to those differences due to variations in

ceiling thermal resistance. For this analysis, the range in emittance

was taken to be 0.85 to 0.95, sheltered roofs were assumed to be

exposed to fifty percent lower wind speeds, and some regions within

the macroclimate were assumed to have a local outdoor ambient temperature of 5°F higher than other regions. In addition, the effect of

changing the attic ventilation rate from 2 to 4 volume changes per

hour was investigated. The outdoor temperature was taken to be 20°F.

The results of this analysis are presented graphically in figure 12.

The effect of variations in roof emittance (curve c), local wind speed

(curve e), and local outdoor temperature (curve d) on the radiance

temperature are seen to be approximately the same magnitude as for the case of the built-up roof (see figure 7). However, the differences in

radiance temperature between ventilated pitched roofs having R-0 and

R-11 ceiling insulation (curve a) and those having R-11 and R-30

ceiling insulation (curve b) are seen to be usually smaller than

those differences in radiance temperature caused by variations in

roof emittance (curve c). This means that the effect of an emittance

range from 0.85 to 0.95 makes it difficult, if not impossible, to distinguish insulation levels in pitched ventilated roofs. For wind

speeds in excess of 4 mph, variations in local wind speed (curve e)

and local outdoor temperature (curve d) throughout the macroclimate

produce differences in radiance temperature which mask out those differences in radiance temperature due to ceiling thermal resistance.

It is interesting to note that varying the attic ventilation rate from

2 to 4 volume changes per hour (curve f) has an insignificant effect on the radiance temperature of the roof. This is because the radiation

exchange between the attic floor and the underside of the roof is

large in comparison with that from convective heat-transfer processes.

The mathematical model was also used to predict the depression in surface temperature for a ventilated pitched roof having R-30 ceiling

insulation (see figure 13). Comparing figure 8 to figure 13, it is seen that the depression in surface temperature is slightly greater for

the ventilated pitched roof than for the built-up roof.

24
1 1 r

CLEAR-SKY CONDITION

2.5 5.0 7.5 10.0

Wind speed, mph

12.5 15.0

Figure 10. Predicted differences in apparent radiance temperatures

between the exterior surfaces of ventilated pitchea roofs

having R-0 and R-11 ceiling insulation as a function of

wind speed for various outdoor temperatures,

25
10

9

-

7

-

!•

.s

CLEAR-SKY CONDITION

_L 2.5 5.0 7.5 10.0 Wind speed, mph

12.5 15.0

Figure 11. Predicted differences in apparent radiance temperatures

between the exterior surfaces of ventilated pitched roofs

having R-11 and R-30 ceiling insulation as a function

of wind speed for various outdoor temperatures.

26
— 1 1

CLEAR-SKY CONDITION

Ta=20»F Effect of emittance

(0.8S vs 0.96)

5.0 7.5 10.0

Wind speed, mph

Figure 12. A comparison of the effect of emittance, thermal

resistance, local wind speed, and local outdoor

temperature on the apparent radiance temperature

of a pitched ventilated roof.

27
5.0 7.5 10.0

Wind speed, mph

15.0

Figure 13. The depression in surface temperature for a pitched ventilated roof having R-30 ceiling insulation as a function of

wind speed.

28
5. SmiMARY AND CONCLUSIONS

When aerial Infrared surveys of pitched ventilated roofs are carried

out under optimum and preferred clear-sky conditions, variations in

roof emittance and variations in local wind speed and local outdoor

temperature throughout the macroclimate were shown to cause differences

in apparent radiance temperature which mask out those differences in

radiance temperature due to variations in ceiling thermal resistance.

In other words, gray tone differences between pitched ventilated roofs

observed in an aerial infrared photograph were found more likely to be

due to variations in roof emittance and variation in local wind speed

and local outdoor temperature thoughout the macroclimate than due to

variations in ceiling thermal resistance.

In the case of low-slope built-up roofs, variations in roof resistance

cause differences in apparent radiance temperature among the roofs

displayed in an aerial infrared photograph which are approximately a factor of three greater than those for pitched ventilated roofs.

Variations in roof emittance and variations in local wind speed and

local outdoor temperature throughout the macroclimate produced differences in radiance temperature which were larger than those between

built-up roofs having 2 and 4 inches of insulation, but smaller than

those between built-up roofs having and 2 inches of insulation.

Therefore, there is a good chance that built-up roofs which have little

or no roof insulation will be displayed in a lighter gray tone than

more insulated built-up roofs included in an aerial infrared photograph.

However, if all the built-up roofs displayed in an aerial infrared photograph are well insulated, then variations in other parameters such as roof emittance, local wind speed, and local outdoor temperature may also cause particular roofs to appear warmer than other roofs, which may be

incorrectly interpreted as the absence of roof insulation.

The optimum condition for carrying out an aerial infrared survey is a low-wind condition. As the wind speed decreases, differences in radiance temperature due to variations in roof resistance become larger.

Under such a condition, differences in radiance temperature caused by

variation in roof emittance, local wind speed, and local outdoor temperature are less likely to mask out those differences due to roof

resistance. However, the depression in surface temperature and cor- responding required dew-point spread under such a condition becomes

large. For instance, the required dew-point spread was shown to

vary between 20 and 8°F for wind speeds ranging from and 5 mph.

References

1. W. Tobiasson and C. Korhonen, "Detecting Moisture in Roof Insulation with a Hand-Held Infrared Camera," Second International

Symposium in Cold Regions Engineering, University of Alaska,

August 1976.

29
2. R. -E. Link, Jr., "Air Borne Thermal Infrared and Nuclear Meter

Systems for Detecting Roof Moisture," Paper No. 30, Proceedings

of the Symposium on Roofing Technology, National Bureau of

Standards, September 1977.

3. F. J. Tanis , R. E. Sampson, and T. W. Wagner, "Thermal Imagery

for Evaluation of Construction and Insulation Conditions of Small

Buildings," report prepared for the Federal Energy Administration,

Contract No. CO-04-50233-00 , July 1976.

4. "Aerial Infrared Thermograms and Residential Heat Loss," Ecological Services of Texas Instruments Incorporated, February 1978.

5. W. R. Hazard and S. A. Underwood, "Modeling Heat Loss with Aerial

Thermography," report prepared for the Department of Energy,

Contract No. EM-78-C-01~4148, June 1973.

6. R. B. Headley, R. J. Larsen, G. G. Goldberg, and R. J. Boyd,

"Infrared Thermography Requirements Study for Energy Conservation,"

report prepared for the Energy Research and Development Administration, Contract No. EX-76-C-O1-2109 , April 1977.

7. R. E. Sampson and T. W. Wagner, "University of Michigan Infrared

Study," Plant Department, The University of Michigan, Ann Arbor,

Michigan, March 1976.

8. "Infrared Energy Loss Survey," Report of Brookhaven National Laboratory Associated Universities, Inc., Daedalus Enterprises, Inc., Ann

Arbor, Michigan, March 197 7.

9. F. A. Schmer and J. M. Dick, "Aerial Infrared Users' Manual,"

Department of Energy Report No. HCP/M4161/D, August 1978.

10. "Detection of Heat Loss from Buildings by Remote Sensing: Summary

of the Methodology," Ontario Center for Remote Sensing, Ministry

of National Resources, Ontario, Canada, August 1976.

11. P. A. Lapp, "The Assessment of Heat Loss from Buildings by Means

of Aerial Thermography," Canada Center for Remote Sensing, Ministry

of Natural Resources, Ontario, Canada, August 1977.

12. "Detection of Heat Loss from Buildings by Remote Sensing Techniques,

Part II: Applied Heat Loss Detection," Ontario Center for Remote

Sensing, Ministry of Natural Resources, Ontario, Canada, July 1976.

13. R. J. Goldstein, "Application of Aerial Infrared Thermography,"

ASHRAE Transactions, Vol. 84, Part 1, 1978.

14. J. S. Cammerer, "The Thermal Properties of Wood and Materials

Containing Wood," Holz als Roh-und Werkstoff, Vol. 1, No. 6,

p. 206-213, 1938.

30
15. W. J. Rossiter and R. G. Mathey, "Effect of Insulation on the

Surface Temperature of Roof Membranes," NBSIR 76-987, National

Bureau of Standards, February, 1976.

16. ASHRAE Handbook of Fundamentals , American Society of Heating,

Refrigerating and Air-Conditioning Engineers, Inc., 1977.

17. "Project Pinpoint," The Roofing Spec, National Roofing Contractors

Association, 1977.

18. R. H. Heilman, "Surface Heat Transmission," Mechanical Engineering , Vol. 51, p. 287-304, 1929.

19. "Heat Emission and Radiation," Heating and Ventilating , Vol. 43,

p. 72a-72b, 1946.

20. M. Wenzl and F. Morawe, Temperaturmessungen von flussigem GupElsen Thomasroheisen und Stahl, Stahl und Eisen, Vol. 47,

p. 867-871, 1927.

21. R. V. Dunkle, J. T. Gier, and J. T. Bevans, "Emissivity of

Ice, Snow, and Frozen Ground," Preliminary Communication, 1958.

22. W. C. Swinbank, "Long-Wave Radiation from Clear Skies," Quarterly

Journal of the Royal Meteorological Society, Vol. 89, No. 381,

July 1963.

23. Climatic Atlas of the United States , U.S. Department of Commerce,

June 1968.

24. F. B. Rowley, A. B. Algren, and J. L. Blackshaw, "Surface Conductances as Affected by Air Velocity, Temperature and Characteristics

of Surface," ASHRAE Transactions 36, 429 (1930).

25. Personal communication from R. J. Goldstein, Chairman, Mechanical

Engineering Department, University of Minnesota, November 1978.

26. Personal communication from Joseph C. Richmond, Senior Research

Engineer at National Bureau of Standards, November 1978.

27. Konrad J. K. Buettner and Clifford D. Kern, "The Determination of

Infrared Emissivities of Terrestrial Surfaces," Journal of

Geophysical Research, Vol. 70, No. 6, March 1965.

28. W. C. Cullen, "Solar Heating, Radiative Cooling, and Thermal

Movement - Their Effects on Built-Up Roofing," Technical Note 231,

National Bureau of Standards, December 1964.

31
NBS-114A (REV. 8-78)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBS TN 1107

3, Recipient's A<i:(;^s5l<jrt Ii<o»

4. TITLE AND SUBTITLE

The Use of Aerial Infrared Thermography to Compare the

Thermal Resistances of Roofs

5. Publication Date August 1979

S. Performing Organization Code

7. AUTHOR(S) 8. Performing Organ. Report No. D. Mo Burch

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, DC 20234

1% Project/Task/Work Unit No.

11. Contract/Grant No.

12. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS rs(ree(, city, st^te, ziP)

Department of Energy

Washington, DC 20585

13. Type of Report & Period Covered Firal

Ml'^jonsofifig Agency Code

15. SUPPLEMENTARY NOTES

Q Document describes a computer program; SF-185, FIPS Software Summary, Is attached.

16. ABSTRACT (A 200-word or less factual summary of most significant infoimation. It document includes a signi ficant bibliography or

literature survey, mention it here.)

The paper investigates whether a comparative roof survey using aerial infrared

thermography can be used to rank the roofs of residential and commercial buildings

according to their thermal resistance. Mathematical models are presented for predicting the apparent radiance temperatures of these roof systems. These models are used to investigate the differences in apparent radiance temperature between roofs

having various thermal resistances. These predicted differences are then compared

with predicted differences in apparent radiance temperature caused by typical variations in roof emittance, local outdoor temperature, and local wind speed throughout

the macroclimate. The transmission characteristics of the atmosphere are reviewed,

and the required dew-point spread for preventing dew or frost formation on a roof

is examined.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name;

separated by semicolons)

Aerial flyovers; aerial infrared thermography; energy conservation; roof heat-loss

survey.

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