Predicting Maximum Pavement Surface Temperature Using Maximum Air Temperature and Hourly Solar Radiation

Transcription

1 TRANSPORTATON RSARCH RCORD 1417 Prediting Maximum Pavement Surfae Temperature Using Maximum Air Temperature and Hourly Solar Radiation MANSOUR SOLAMANAN AND THOMAS W. KNNDY. A simple method is proposed to alulate the maximum pavement temperature profile on the basis of maximum air temperature and hourly solar radiation. The method was developed to be used mainly for Strategi Highway Researh Program binder and mixture speifiations and as a quik method of determining maximum pavement temperature for various regions in the United States and Canad The method is based on the energy balane at the pavement surfae and the resulting temperature equilibrium. Reasonable assumptions are made regarding thermal properties of the asphalt onrete. The auray of the method was tested by applying it to some field ases for whih measured pavement temperatures were available. n 83 perent of the ases, the proposed equation predited the pavement temperature within 3 C, whih is well within reasonable limits, onsidering the numerous unertainties that exist in material properties, auray of measurements, variability of environmental fators (wind, sunshine, et.), and inlination of the pavement surfae in reeiving radiation. The binde.r and mixture speifiations that are in development under the Strategi Highway Researh Program (SHRP) Asphalt Researh Program are tied to maximum and minimum pavement temperatures for various loations in the United States and Canad Therefore, it beame neessary to seek a quik and effiient way to determine the maximum pavement temperature profile with suffiient auray for various regions. Barber (J) was among the first researhers to propose a method of alulating maximum pavement temperature from weather reports. He applied a thermal diffusion theory to a semi-infinite mass (pavement) in ontat with air. n his theory, solar radiation was onsidered on the basis of its effet on the mean effetive air temperature. The resulting equation is simple. However, beause the method uses total daily radiation rather than hourly radiation, the alulated maximum pavement fomperature with this model is the same for different latitudes having the same air temperature onditions and the same total daily solar radiation. Another proedure was suggested by Rumney and Jimenez (2). They developed some empirial nomographs to predit pavement temperature at the surfae and at a 2-in. depth as a funtion of air temperature and hourly solar radiation. These graphs were developed on the basis of data olleted on pavement temperature in Tuson, Arizona, in June and July along with data olleted on measured hourly solar radiation. Dempsey (3) developed an analysis program, named limatimaterials-strutural (CMS) mo&l, that is based on heat trans- The University of Texas at Austin, Austin, Tex fer theory and energy balane at the surfae. A finite differene approah is used to deal with the resulting differential equation. The CMS model uses a regression equation to alulate the inident solar radiation from the extraterrestrial radiation. The program is useful for providing detailed information about pavement temperature variations during the day for a sequene of days. However, the program requires a onsiderable amount of input. The method proposed here an be used when one is interested in determining just the maximum pavement temperature with a minimum amount of input. One an also diretly use the harts that are developed for this purpose. The method is very simple and quik: a user who knows the latitude of the loation and the air temperature an use the harts to find a reasonable estimate of the maximum pavement temperature. The method is developed on the basis of the theory of heat transfer and takes into aount the effet of latitude on solar radiation. THORY The net rate of heat flow to and from a body, q eo an be alulated from the equation qs energy absorbed from diret solar radiation, qa energy absorbed from diffuse radiation (sattered from the atmosphere), qt = energy absorbed from terrestrial radiation, q energy transferred to or from the body as a result of onvetion, qk = energy transferred to or from the body as a result of ondution, and qr = energy emitted from the body through outgoing radiation. qs and qa are always positive for the surfae of a body suh as pavement exposed to radiation. The terrestrial radiation, qt, is positive for a body that is above the surfae of the earth or is tilted so that it an "see" the earth surfae. For the pavement surfae, qt an be onsidered to be. The onvetion energy is transferred from the pavement to the surrounding air if the former has a higher temperature than the latter. n this ase, q appears with a negative sign in the above

2 2 formula for a pavement. The ondution energy appears with a positive sign if the surfae temperature is lower than the temperature at a depth below the surfae (as might be the ase during old winter days). Condution energy will have a negative sign when the surfae temperature is higher than the pavement temperature at other depths. This is espeially true during the hot days of summer. Finally, the energy emitted from the pavement surfae, qn is always negative. Therefore, during summer, when the greatest interest in prediting the maximum pavement temperature exists, the net rate of heat flow to the surfae of the pavement an be written as ah of the quantities in this heat flow equation is disussed later. Diret Solar Radiation The energy absorbed from diret solar radiation, qs, an be alulated as a is the surfae absorptivity to the solar radiation and R; is the inident solar radiation. The part of the inident solar radiation that is not absorbed by the surfae [(1 - CX 51 a,) RJ will be refleted bak to the atmosphere. The surfae absorptivity a depends on the wavelength of the inoming radiation. For some materials a varies within a very wide range depending on the wavelength. For example, polished brass has an absorptivity of about.8 for long-wave radiation (9.3 µm) at 1 F and.49 for solar radiation that is onsidered shortwave radiation (less than 2 µm). White paper has an absorptivity of about. 95 to long-wave radiation and.28 to shortwave radiation. For asphalti materials it seems that a 51 ar does not vary substantially over a wide range. Typially a 51 ar for asphalt mixtures varies from.85 to.93. The inident solar radiation R; depends on the angle between the diretion of the normal to the surfae reeiving radiation and the diretion of the solar radiation and an be alulated as R; = Rn os i (3) Rn = the radiant energy inident on a surfae plaed normal to the diretion of the rays of the sun and i = the angle between the normal to the surfae and the diretion of radiation. Rn an be alulated from the solar onstant R, whih is the impinging rate of the solar energy on a surfae of unit area plaed normal to the diretion of the sun rays at the outer fringes of the earth's atmosphere. The solar onstant is about 1394 W/m 2 (442 Btu/hr ft 2 ). The rate of solar energy reeived at the surfae is substantially less than the solar onstant beause a large portion of the radiation is absorbed by the atmosphere and its ontents before reahing the earth. Gases, louds, and suspended partiles in the atmosphere satter and (1) (2) TRANSPORTATON RSARCH RCORD 1417 reflet about 26 perent of insolation (inoming solar radiation) into spae. The atmosphere and the earth's surfae together absorb about 7 perent of insolation. The solar energy reeived at the surfae depends on the loation, time of the day, and time of the year. The value of Rn an be alulated as R = solar onstant; m = relative air mass, defined as the ratio of the atual path length to the shortest possible path; and Ta = transmission oeffiient for unit air mass. The value of Ta is less in the summer than in the winter beause the atmosphere ontains more water vapor during the summer. The value also varies with the ondition of the sky, ranging from.81 on a lear day to.62 on a loudy one. The relative air mass mis approximately equal to 1/(os z), z is the zenith angle (the angle between the zenith and diretion of the sun's rays). The zenith angle depends on the latitude <f, the time of day, and the solar delination. The time is expressed in terms of the hour angle h (the angle through whih the earth must turn to bring the meridian of a partiular loation diretly under the sun). At loal noon h is, but in general it depends on the latitude and the solar delination, S. The zenith angle an be found from os z = sin <t sin Ss + os Ss os h os <t (5) For horizontal surfaes os i = os z, but for a surfae that is tilted at an angle "' degrees to the horizontal, i an be obtained from R; = os i = oslz - \jll - sin z sin \jj Rn + sin z \jj sin A \jj = tilt angle, A = the azimuth of the sun, and = the angle between the south meridian and the normal to the surfae measured westward along the horizon. Development of the preeding formulas was explained else (4). The solar and surfae angles for a tilted surfae are shown in Figure 1. Brown and Maro (5) have developed graphi relationships from whih the values of the required angles an be obtained for northern latitudes. One of these graphs giving solar angles for.the period from May to August for latitudes between 25 N and 5 N is shown in Figure 2. Atmospheri Radiation Atmospheri radiation absorbed by the pavement surfae may be alulated through the following empirial formula developed by Geiger ( 6) and reported by Dempsey (3): (4) (6) (7)

3 Solaimanian and Kennedy 3 Normal to tilted surfae South Vertial to Horizontal Plane (Zenith) North Horizontal Plane FGUR 1 Definition of solar and surfae angles for quation 6 (4). -ast a G - J (lo-pp), er Stefan-Boltzman onstant = 5.68 x 1-s W (m 2 OK4), the air temperature ( K), and p the vapor pressure varying between 1 and 1 mm of merury. G, J, and P an be represented by onstant values of.77,.28, and.74, respetively, aording to Geiger (6). Condution nergy The ondution rate of heat flow frorp the pavement surfae down an be approximately alulated as Td T -qk = -k--d s k = thermal ondutivity, Ts = surfae temperature, d = depth, and Td = temperature at depth d. Radiation nergy mitted from the Surfae The rate at whih the surfae emits radiation is given by is emissivity. missivity as well as absorptivity is involved in any heat transfer by radiation. For a body at the same temperature, they have the same numerial value. However, as mentioned before, absorptivity may be signifiantly different from emissivity if the radiation absorptivity is not from a blak body (8) (9) "' Q ::l en... bo : <(.: ;;i $ '<t: P.M.A.M N.L t. / 3 v 35 4 ' 45 /5 --: '..., '"!for N.lat r',,. '-... ' ' \- """ f'--..._ "' " ' A.M..- 6 P.M..-6 A for 45 N. lat :;;:,., "" '.,,,,_:. ' '-, Mean Sun Time ',, ' & -..o "- "....- \... ',.., \''" 4.J FGUR 2 Solar angles for the period from May to August in northern latitudes (5). or if it is from a body at a very high temperature (suh as the. sun). For asphalti materials, the emissivity and absorptivity to shortwave radiation (suh as solar absorptivity) have been reported to be idential (about.93). Convetion nergy The rate of heat flow by onvetion to the surrounding air is given by 1 (1) he is the surfae oeffiient of heat transfer (average onvetive heat transfer oeffiient). n general, he depends on the geometry of the surfae, the wind veloity, and the physial properties of the fluid (in this ase air). n many ases, it also depends on the temperature differene. quilibrium Temperature at the Pavement Surfae The equilibrium temperature at the pavement surfae an be obtained by setting the net rate of heat flow, qnw equal to. (11) Then, by writing eah of the above flow rates in terms of temperatures, an equation involving surfae temperature, air

4 4 TRANSPORTATON RSARCH RCORD 1417 temperature, and temperature at a depth an be obtained. The air temperature should be available through measurement. Reasonable assumptions ould be made about the temperature differene between the surfae and a prtiular depth. The final equation obtained in this way will be the following fourth-degree equation, whih an be solved to yield the surfae temperature. Maximum Pavement Temperature and Required Thermal Parameters Maximum air temperature and maximum hourly diret solar radiation an be used to alulate the maximum pavement temperature. The maximum hourly solar radiation is obtained by using the minimum z angle from the Brown and Maro hart. This angle has the lowest value at noon sun time for different latitudes. For the months between May and August, at the noon sun time, z an be approximately alulated as z = latitude - 2 degrees (for latitude 22 degrees) The value of Ta for alulation purposes is assumed to be.81, whih represents a lear sunny day. An investigation of several different sets of data onerning maximum temperature differene between the surfae and a 2-in. depth during hot summer days indiates that this differene varies between 1 F and 2 F with an average value of 15 F. Calulated maximum pavement temperatures reported in this paper are based on the 15 F differene assumption. The oeffiient a for atmospheri radiation, as defined in empirial quation 7, depends on vapor pressure. A hange in vapor pressure from 1 to 1 mm of merury inreases a from.53 to.72. The alulated atmospheri radiation varies between 246 and 331 W/m 2 (78 and 15 Btu/hr/ft2) in extremes for an air temperature of 27 C (8 F). The variation is between 284 and 378 W/m 2 (9 and 12 Btu/hr/ft2) for an air temperature of 38 C (1 F). Therefore, the effet of vapor pressure on hanging the atmospheri radiation is not signifiant, onsidering the magnitude of other forms of radiation that are involved in the surfae energy balane. A value of. 7 was adopted for a, onsidering the above disussion and the fat that during the summertime the vapor pressure is higher than at other times of the year. The most reas9nable values for thermal parameters O'. (solar absorptivity), (emissivity), k (thermal ondutivity), and he (surfae heat transfer oeffiient) need to be input to obtain the best estimate of the maximum pavement temperature. The emissivity of a surfae varies with temperature, its degree of roughness, and oxidation. Therefore, the emissivity in a single material may vary within a wide range. Absorptivity depends on the same parameters as emissivity as well as the nature of the inoming radiation and its wavelength. For asphalt materials, it seems that these two parameters vary within a narrow range ( ). The range of variation in the thermal ondutivity of asphalt onrete appears to b signifiantly larger than that of absorptivity and emissivity. Highter and Wall (7) report that values of thermal ondutivity for asphalt onrete range from.74 to 2.89 W/m 2 C (.43 to 1.67 Btu/hr/ft2 F/ft) after reviewing a onsiderable number of referenes regarding this property. Beause aggregate is the major portion of the asphalt onrete, it seems reasonable to assume that signifiant variations in thermal properties of the aggregates ause large differenes in the thermal ondutivity of the asphalt onrete. The surfae oeffiient of heat transfer seems to be more diffiult to determine than the other parameters. The oeffiient he is not really a thermal property of the material in the same sense that k is. t is not a onstant and depends on a lot of variables. t is mainly used to yield a simple relationship for onvetion heat transfer. The empirial formula developed by Vehrenamp (8) and reported by Dempsey (3) appears to be the most suitable for determining he for a pavement surfae. he = (.144 T?;, 3 U (Ts - Tair) 3] he = surfae oeffiient of heal transfer, Tm = average of the surfae and air temperature in K, U = average daily wind veloity in m/se, Ts = surfae temperature, and Tair = air temperature. (13) The expression in brakets yields the onvetion oeffiient he in terms of gram alories per seond square entimeter degree Celsius. The fator is used to give the result in terms of Watts per square meter degree Celsius. For an average wind veloity of about 4.5 m/se (1 mph) and for typial ranges of maximum air and pavement temperatures, the formula yields a value varying between 17 and W/m 2 C [3 and 4 Btu/(hr/ft 2 F)]. Sensitivity Analysis A sensitivity analysis was performed to investigate the effet of various thermal parameters on the predited maximum pavement temperature. Some of the results of the sensitivity analysis are shown in Figures 3 and 4. ssentially a linear relationship is observed between alulated maximum pavement temperature and solar absorptivity. The relationship between thermal ondutivity and maximum pavement temperature is also approximately linear. As expeted, surfae temperature drops as thermal ondutivity or absorptivity inreases. The results reported in this paper are for the following typial thermal parameters: for asphalt onrete, O'. =.9; =.9; k = 1.38 W/m 2 C; he = 3.5 W/m 2 C. Comparison of Measured and Predited Temperatures Disrepanies between the measured and alulated pavement temperatures are unavoidable beause of the influene

5 Solaimanian and Kennedy 5 7 (.) e 65 e Cl., 6. :::J ' 55 k- t.38 W/m C (.8 Btu/hr.ft.!') h M11q.m,..1, C (3.$ Btu/hr.sq.ft. F) Taira38C 1 rj Latitude Solar Absorptivity.9 FGUR 3 Calulated maximum pavement temperature as a funtion of solar absorptivity for various values of emissivity. of a large number of fators and their orresponding variations. These disrepanie.s are important to onsider for omparison purposes. One question onerns the auray of field temperature measurements at the surfae. A thermometer sitting on the pavement surfae will probably yield a different reading from a thermoouple implanted into the surfae. The wind veloity an influene the surfae temperature through its impat on onvetion heat transfer. ven though it may not be signifi- ant, onsidering the typial range of values for this parameter, the effet of wind veloity an make some slight ontribution to differenes between measured and predited values. Also a slightly loudy day versus a perfetly sunny ondition an ause small hanges. n many ases, the effet of loudiness and the perent sunshine are onsidered by applying a redution fator to solar radiation. Suh a redution fator is typially obtained from a regression equation for different loations. Obviously some probability and approximation are 8 h«= 11.4W/e q.m. (2.o Btu /hr. eq.ft, FJ Solar Abeorptivity =.9 missivity...9 Tair = 38 C (1 F) Latitude = Cl., :. :::J x 65 7 h.., 17. (J.O) 6 ---'----'.,... -'-... _.._..._"'-.L Condutivity K, W/(m. C) FGUR 4 Calulated maximum pavement temperature as a funtion of oeffiient of thermal ondutivity for various values of the surfae oeffiient of heat transfer.

6 6 TRANSPORTATON RSARCH RCORD 1417 involved in obtaining suh a redution fator. t also makes a differene whih part of the sky is loudy and at what time of the day loudiness ours. Another important fator is that the input parameters, es.,. peially thermal properties, are not exatly known for these field ases, and typial values reported for these parameters are used here for alulation purposes. These values are used on the basis of reasonable assumptions, previous measurements, or empirial formulas. Another fator is the inlination of the pavement surfae with respet to the diretion of the sun rays. Obviously a surfae inlined toward the sun rays reeives more radiation than a horizontal surfae, and a horizontal surfae reeives more radiation than a surfae inlined in the opposite diretion of the sun rays. n Figure 5 maximum hourly solar radiation of a horizontal surfae is ompared with that of a surfae normal to the sun rays. ven though suh inlinations may not be signifiant for asphalt pavements, they an reate disrepanies between measured and alulated values if the effet is not onsidered. Considering that there is a lot of unertainty with respet to the fators disussed earlier and their effets, one should not expet to math the measured values very losely. The alulated values should be onsidered as typial pavement temperatures for a ertain loation. The validity of the approah presented here is investigated by omparing the predited and measured surfae temperatures, taking into onsideration the preeding points. Using the equilibrium temperature disussed above and appropriate values for variables 'T, a, e, k, and he, the maximum surfae temperature was alulated for a number of ases for whih measured pavement surfae temperature was available. The ases investigated here inlude sites in Virginia, 112 Arizona, Saskathewan (Canada), daho, and Alabam nformation about these ases (exept Alabama) an be found in previous work (1,2,9,1). The results are shown in Table 1 and Figure 6. This equation predits the pavement temperature with reasonable auray, onsidering the previous disussion about the unertainties involved. The orrelation oeffiient and the R 2 value are.91 and.82, respetively. Ninety'-six perent of the measurements are within 4 C differene, and 83 perent are within 3 C differene. ffet of Latitude A useful feature of the present equation in prediting the maximum pavement temperature is that it takes advantage of the maximum hourly solar radiation rather than the total daily radiation. During the hot summer months, daily terrestrial radiation is almost the same for both northern and southern regions (Figure 7). However, the hourly radiations are different. Southern regions of the United States (lower latitudes) reeive more radiation per hour than do northern regions (Figure 8). Thus, higher radiation ontributes to larger differenes between air and pavement temperatures, as an be seen in Figures 9 and 1. Figue 1 indiates an almost linear relationship between the maximum air temperature and the alulated maximum pavement temperature. The figure implies that for the same latitude, the differene between air and pavement temperatures is almost onstant and is determined by heat transfer laws of radiation, ondution, and onvetion. However, a paraboli relationship is observed between _the latitude and the maximum pavement temperature for various air temperatures. Figure 11 shows the differene between air and pavement temperatures as a funtion 112 "' 18..._ 14 3: r: :g 1 Horizontal surfae,, ::... (/). "t: ::J :r: ::J x 88 ::!! '---'--l.'---'--1.'--_ , Latitude FGUR 5 Comparison of maximum hourly solar radiation reeived by a horizontal surfae versus a surfae normal to the sun rays.

7 Solaimanian and Kennedy 7 TABL. 1 Measured and Calulated Pavement Temperatures Case College Park,MD Hybla,VA Tuson,AZ Tuson,AZ Tuson,AZ Tuson,AZ us 84, AL daho Cale. Temp., C 61.l i Measured Temp., Diff. Cal.-Meas of latitude. The maximum differene that ours at lower latitudes varies between 25.5 C and 26.5 C (46 F and 48 F) when the maximum air temperature varies between 24.5 C and 42 C (76 F and 18 F). The differene at 6-degree latitude varies between l5 C and l6 C (27 F and 29 F). This figure shows that the differene between air and pavement temperatures as a funtion of latitude is almost independent of the air temperature (or at least the effet of air temperature an be negleted). A parabola fits the average differene data perfetly. The equation of the parabola is 6.T = -.62 < < , < is the latitude and 6.T is the differene between the maximum air temperature and the maximum pavement temperature in degrees Celsius. Therefore, one latitude of a loation is known, 6.T an be approximately estimated using this simple equation. Also, in southern parts, the differene between air and alulated maximum pavement temperature is 25 C to 28 C (45 F to 5 F), as in northern regions it is 19.5 C to 22 C (35 C to 4 F). Moreover, the differene between air and maximum pavement temperature hanges more rapidly as one moves farther north. Count Average Std. Dev. Maximum Minimum Temperature Variation with Depth t is possible to approximate the temperature variation with depth one the surfae temperature is known. A number of () e '... :J x "O :J f/) k h 8 =.9 =.9 = 1.38 W/m C (.8 Btu/hr.ft.F) = W/m2. C (3.5 Btu/hr.ft2.F) = Calulated Maximum Pavement Temperature, C FGUR 6 Calulated maximum pavement temperature versus measured maximum pavement temperature for various sites. 8

8 8 TRANSPORTATON RSARCH RCORD ) Cl) "5 "J 29 O Cl) ::!: " 24 :p ;:; ::: 19 :5 ) ' x 9 w Day of the Year FGUR 7 xtraterrestrial solar radiation as a funtion of time of year for various latitudes. ases from Hybla, Virginia; Tuson, Arizona; and Saskathewan, Canada, were investigated to find the best urve fitting the measured temperature profile. t was found that a ubi funtion of the form T = C + C 1 d + C 2 d 2 + C 3 d 3 fits the measured data best. n this equation, oeffiients C, C 1, C 2, and C 3 were determined for eah ase. These oeffiients were then normalized with respet to the surfae temperature, whih is presented by C in the preeding equation. The equation an be rewritten as C 1 /C, C 2 /C, and C 3 /C are normalized oeffiients. Using n 1, n 2, and n 3 for these oeffiients, respetively, the equation an be written in the following form: One oeffiients n 1, n 2, and n 3 were determined for eah ase, the average values were-' alulated. The overall ubi funtion was found to be in the following form: T = Ts(l -.63d +.7d2 -.4d 3 ) '- ::... ) 27 Cl) "5 22 :p ;:; 17 ::: :s ) 2..., e Cl) O '- Cl) 12 7 l l Doy of the Year FGUR 8 Average extraterrestrial radiation as a funtion of time of year for various latitudes.

9 u f! 6 6.a e G i!.oj G G. ::J 5 5 x :::!! Maximum Air Temperature, C FGUR 9 Calulated maximum pavement temperature as a funtion of air temperature for various latitudes. r (..) e 6 6 e G a G n ::J x :::! Latitude FGUR 1 Calulated maximum pavement temperature as a funtion of latitude for various air temperatures.

10 1 TRANSPORTATON RSARCH RCORD 1417 (.) i L. <( x :::!: - : i....., : x :::!: : , ;::. : f :;: 14.._ _...., Latitude FGUR 11 Differene between maximum pavement and maximum air temperatures as a funtion of latitude for various air temperatures. d = depth (in.), Td = temperature at depth d ( F), and Ts = the surfae temperature ( F). Note that this equation was developed for degree Fahrenheit and a onversion is needed to get the result in degrees Celsius. This equation was applied to eah ase. Comparison of measured and estimated temperatures at various depths indiates that within the top 2 m (8 in.) of the pavement, the differenes are 2.8 C to 3.4 C (5 F to 6 F). At higher depths, the differenes are signifiantly larger. t may be reasonable to assume that the design temperature will be seleted on the basis of the temperature distribution in the top 8 in. of the pavement, the largest impats on performane are observed. Minimum Pavement Temperature The minimum pavement temperature ours mostly during very early morning. An analysis of a number of field ases indiates that the minimum pavement temperature during the winter is in most ases 1 C or 2 C higher than the minimum air temperature. Therefore, it seems reasonable and safe to assume that the lowest pavement temperature is the same as the lowest air temperature. CONCLUSONS The following onlusions an be drawn on the basis of the results and analysis proposed in this study. 1. The proposed simple method is apable of prediting the maximum pavement surfae temperature within a reasonable level of auray. 2. The relationship between maximum pavement temperature and maximum air temperature is essentially linear. 3. The effet of maximum hourly solar radiation in regions with the same total daily radiation is signifiant and annot be ignored. This effet is onsidered on the basis of the latitude of the loation. 4. The differene between maximum pavement temperature and maximum air temperature is expeted to be lower at higher latitudes. 5. A quadrati equation perfetly fits the data representing the average differene between maximum air and maximum pavement temperatures as a funtion of latitude. 6. A hange in absorptivity from.7 to.8 or from.8 to.9 inreases the predited maximum pavement temperature about 7 F. 7. A hange in emissivity from.7 to.8 or from.8 to.9 inreases the predited maximum pavement temperature about 5 F. 8. As expeted, a lower thermal ondutivity results in a higher surfae temperature. RFRNCS 1. Barber,. S. Calulation of Maximum Pavement Temperatures from Weather Reports. Bulletin 168, HRB, National Researh Counil, Washington, D.C., 1957, pp Rumney, T. N., and R. A. Jimenez. Pavement Temperatures in the Southwest. n Highway Researh Reord 361, HRB, National Researh Counil, Washington, D.C., 1969, pp Dempsey, B. J. A Heat Transfer Model for valuating Frost Ation and Temperature Related ffets in Multilayered Pave- /

11 Solaimanian and Kennedy ment Systems. n Highway Researh Reord 342, HRB, National Researh Counil, Washington, D.C., 197, pp Kreith, F. Priniples of Heat Transfer, 3rd ed. Harper and Row Publishers, New York, Brown, A.., and S. M. Maro. ntrodution to Heat Transfer, 2nd ed. MGraw Hill Book Company, n., New York, Geiger, R. The Climate Near the Ground. Harvard University Press, Cambridge, Mass., Highter, W. H., and D. J. Wall. Thermal Properties of Some Asphalti Conrete Mixes. n Transportation Researh Reord 968, TRB, National Researh Counil, Washington, D.C., Vehrenamp, J.. xperimental nvestigation of Heat Transfer at an Air-arth nterfae. Transations, Amerian Geophysial Union, Vol. 34, No. 1, 1953, pp Kallas, B. F. Asphalt Pavement Temperatures. n Highway Researh Reord 15, HRB, National Researh Counil, Washington, D.C., 1966, pp Huber, G. A., G. H. Heiman, and R. W. Chursinoff. Predition of Pavement Layer Temperature during Winter Months Using a Computer Model. Canadian Tehnial Asphalt Assoiation, Nov Publiation of this paper sponsored by Committee on Charateristis of Bituminous Materials. 11