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Federal Highway Administration Research and Technology
Coordinating, Developing, and Delivering Highway Transportation Innovations

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This report is an archived publication and may contain dated technical, contact, and link information
Publication Number: FHWA-RD-98-085

LTPP Guide to Asphalt Temperature Prediction and Correction

Sample Data for Bells Equations

Surf. Temp., °C Time Depth, mm Prev. Days Avg.
Air Temp., °C		 BELLS2, °C BELLS3, °C
10 14:10 75 23 16.5 15.6
12 14:10 75 23 17.8 16.8
14 14:10 75 23 19.1 18.1
16 14:10 75 23 20.4 19.3
18 14:10 75 23 21.7 20.6
20 14:10 75 23 23 21.8
22 14:10 75 23 24.3 23
24 14:10 75 23 25.6 24.3
26 14:10 75 23 26.9 25.5
28 14:10 75 23 28.2 26.8
30 14:10 75 23 29.5 28
32 14:10 75 23 30.8 29.3
34 14:10 75 23 32.1 30.5
36 14:10 75 23 33.4 31.7
38 14:10 75 23 34.7 33
20 8:00 75 23 21.4 20.1
20 9:00 75 23 21.4 20.1
20 10:00 75 23 21.5 20.2
20 11:00 75 23 21.6 20.3
20 12:00 75 23 21.8 20.6
20 13:00 75 23 22.3 21.1
20 14:00 75 23 22.9 21.7
20 15:00 75 23 23.6 22.3
20 16:00 75 23 24.3 23
20 17:00 75 23 24.9 23.5
20 18:00 75 23 25.4 23.8
20 19:00 75 23 25.7 24
20 20:00 75 23 25.7 23.9
20 21:00 75 23 25.4 23.6
20 22:00 75 23 25 23.1
20 23:00 75 23 24.3 22.5
20 0:00 75 23 23.6 21.9

Sample Data for ATAF Equation

Tm, °C Tr, °C ATAFDefault
0 21 0.362
5 21 0.461
10 21 0.587
15 21 0.748
20 21 0.953
25 21 1.213
30 21 1.545
35 21 1.968
40 21 2.506

Sample Data for AREA Equation

Tm, °C Tr, °C ac Defl36 theta AREA BAFAREA
5 21 75 50 30 20.156 0.91
5 21 75 50 45 18.127 0.9
5 21 75 130 30 22.044 0.918
5 21 75 130 45 19.518 0.908
5 21 150 50 30 23.956 0.901
5 21 150 50 45 21.926 0.892
5 21 150 130 30 26.814 0.912
5 21 150 130 45 24.289 0.903
30 21 75 50 30 17.336 1.059
30 21 75 50 45 15.306 1.066
30 21 75 130 30 19.224 1.053
30 21 75 130 45 16.698 1.061
30 21 150 50 30 20.262 1.066
30 21 150 50 45 18.233 1.073
30 21 150 130 30 23.121 1.058
30 21 150 130 45 20.595 1.065

Sample Data for the F1 Equation

Tm, °C Tr, °C ac Defl36 theta LogF1 F-1 BAFF-1
5 21 75 50 30 -0.0422 0.9075 1.244
5 21 75 50 45 0.0557 1.1367 1.244
5 21 75 130 30 -0.1393 0.7256 1.244
5 21 75 130 45 -0.0176 0.9603 1.244
5 21 150 50 30 -0.2294 0.5896 1.323
5 21 150 50 45 -0.1316 0.7386 1.323
5 21 150 130 30 -0.3743 0.4223 1.323
5 21 150 130 45 -0.2526 0.559 1.323
30 21 75 50 30 0.1061 1.2767 0.884
30 21 75 50 45 0.2039 1.5993 0.884
30 21 75 130 30 0.0089 1.0208 0.884
30 21 75 130 45 0.1307 1.351 0.884
30 21 150 50 30 -0.0394 0.9132 0.854
30 21 150 50 45 0.0584 1.144 0.854
30 21 150 130 30 -0.1843 0.6541 0.854
30 21 150 130 45 -0.0626 0.8657 0.854

Sample Data for the Delta Equations

Tm, °C Tr, °C ac Defl36 theta LogDelta8 Delta8 BAFDelta8 LogDelta12 Delta12 BAFDelta12 LogDelta18 Delta18 BAFDelta18 LogDelta24 Delta24 BAFDelta24 LogDelta36 Delta36 BAFDelta36 LogDelta60 Delta60 BAFDelta60
5 21 75 50 30 1.7288 53.6 1.326 1.9822 96 1.239 2.1482 140.7 1.187 2.15 141.3 1.323 2.2299 169.8 1.272 2.3567 227.3 1.222
5 21 75 50 45 1.8424 69.6 1.517 2.0881 122.5 1.434 2.2617 182.7 1.362 2.3083 203.4 1.368 2.3841 242.1 1.309 2.3567 227.3 1.222
5 21 75 130 30 1.8922 78 1.326 2.1685 147.4 1.239 2.3426 220.1 1.187 2.4459 279.2 1.149 2.5229 333.4 1.14 2.6265 423.1 1.222
5 21 75 130 45 2.0057 101.3 1.517 2.2744 188.1 1.434 2.4793 301.5 1.362 2.6395 436 1.169 2.7121 515.3 1.158 2.6265 423.1 1.222
5 21 150 50 30 1.3037 20.1 1.589 1.5302 33.9 1.508 1.7162 52 1.428 1.7708 59 1.517 1.9043 80.2 1.422 2.1294 134.7 1.262
5 21 150 50 45 1.4201 26.3 1.858 1.6393 43.6 1.787 1.8326 68 1.673 1.9313 85.4 1.595 2.0603 114.9 1.483 2.1294 134.7 1.262
5 21 150 130 30 1.467 29.3 1.589 1.7165 52.1 1.508 1.9106 81.4 1.428 2.0667 116.6 1.318 2.1974 157.5 1.274 2.3992 250.7 1.262
5 21 150 130 45 1.5835 38.3 1.858 1.8256 66.9 1.787 2.0503 112.3 1.673 2.2625 183 1.363 2.3883 244.5 1.311 2.3992 250.7 1.262
30 21 75 50 30 1.9202 83.2 0.853 2.1274 134.1 0.887 2.2648 184 0.908 2.3398 218.7 0.854 2.3933 247.3 0.873 2.4928 311 0.893
30 21 75 50 45 2.1251 133.4 0.791 2.3325 215 0.817 2.4711 295.9 0.841 2.5207 331.7 0.839 2.567 369 0.859 2.4928 311 0.893
30 21 75 130 30 2.0835 121.2 0.853 2.3137 205.9 0.887 2.4592 287.9 0.908 2.5404 347 0.925 2.6117 409 0.929 2.7625 578.8 0.893
30 21 75 130 45 2.2885 194.3 0.791 2.5189 330.3 0.817 2.6888 488.4 0.841 2.7452 556.1 0.916 2.8114 647.8 0.921 2.7625 578.8 0.893
30 21 150 50 30 1.618 41.5 0.771 1.809 64.4 0.794 1.9578 90.7 0.818 2.0537 113.2 0.791 2.1431 139 0.82 2.2873 193.8 0.877
30 21 150 50 45 1.8406 69.3 0.706 2.0333 108 0.721 2.182 152.1 0.749 2.248 177 0.769 2.3276 212.6 0.801 2.2873 193.8 0.877
30 21 150 130 30 1.7814 60.5 0.771 1.9954 98.9 0.794 2.1523 142 0.818 2.2543 179.6 0.856 2.3615 229.9 0.873 2.5571 360.7 0.877
30 21 150 130 45 2.004 100.9 0.706 2.2196 165.8 0.721 2.3997 251 0.749 2.4724 296.8 0.84 2.572 373.2 0.859 2.5571 360.7 0.877

Sample Data for the Ratio Equation

Tm, °C Tr, °C ac Defl36 theta LogRatio8 Ratio8 BAFRatio8 LogRatio12 Ratio12 BAFRatio12 LogRatio18 Ratio18 BAFRatio18 LogRatio24 Ratio24 BAFRatio24 LogRatio36 Ratio36 BAFRatio36 LogRatio60 Ratio60 BAFRatio60
5 21 75 50 30 0.0872 1.222 1.106 0.1628 1.455 1.159 0.3241 2.109 1.157 0.4432 2.774 1.194 0.6172 4.142 1.229 0.8812 7.607 1.185
5 21 75 50 45 0.0995 1.257 1.106 0.1979 1.577 1.136 0.3817 2.408 1.157 0.5279 3.372 1.194 0.7388 5.48 1.229 1.0348 10.834 1.185
5 21 75 130 30 0.0878 1.224 1.037 0.1433 1.391 1.112 0.254 1.795 1.157 0.3562 2.271 1.194 0.5342 3.421 1.229 0.7585 5.735 1.185
5 21 75 130 45 0.1 1.259 1.037 0.1869 1.538 1.085 0.3116 2.049 1.157 0.4409 2.76 1.194 0.6558 4.527 1.229 0.9121 8.167 1.185
5 21 150 50 30 0.0531 1.13 1.106 0.1028 1.267 1.159 0.1918 1.555 1.185 0.2704 1.864 1.229 0.4338 2.715 1.27 0.7131 5.165 1.218
5 21 150 50 45 0.0653 1.162 1.106 0.1379 1.374 1.136 0.2494 1.776 1.185 0.3551 2.265 1.229 0.5555 3.593 1.27 0.8666 7.356 1.218
5 21 150 130 30 0.0551 1.135 1.037 0.0687 1.171 1.112 0.1217 1.323 1.185 0.1834 1.525 1.229 0.305 2.018 1.27 0.5484 3.535 1.218
5 21 150 130 45 0.0674 1.168 1.037 0.1122 1.295 1.085 0.1793 1.511 1.185 0.2681 1.854 1.229 0.4266 2.67 1.27 0.702 5.035 1.218
30 21 75 50 30 0.1553 1.43 0.945 0.2631 1.833 0.92 0.4233 2.65 0.921 0.5635 3.66 0.905 0.757 5.715 0.891 0.9963 9.915 0.909
30 21 75 50 45 0.1675 1.471 0.945 0.2844 1.925 0.931 0.4809 3.026 0.921 0.6483 4.449 0.905 0.8787 7.562 0.891 1.1499 14.121 0.909
30 21 75 130 30 0.1127 1.296 0.98 0.2155 1.642 0.942 0.3532 2.255 0.921 0.4765 2.996 0.905 0.674 4.721 0.891 0.8736 7.475 0.909
30 21 75 130 45 0.1249 1.333 0.98 0.242 1.746 0.955 0.4108 2.575 0.921 0.5613 3.641 0.905 0.7957 6.247 0.891 1.0271 10.645 0.909
30 21 150 50 30 0.1212 1.322 0.945 0.2031 1.596 0.92 0.3069 2.027 0.909 0.4101 2.571 0.891 0.5962 3.946 0.874 0.8467 7.025 0.895
30 21 150 50 45 0.1334 1.36 0.945 0.2244 1.677 0.931 0.3645 2.315 0.909 0.4948 3.125 0.891 0.7178 5.221 0.874 1.0002 10.005 0.895
30 21 150 130 30 0.08 1.202 0.98 0.1408 1.383 0.942 0.2368 1.725 0.909 0.3231 2.104 0.891 0.4673 2.933 0.874 0.682 4.808 0.895
30 21 150 130 45 0.0923 1.237 0.98 0.1674 1.47 0.955 0.2944 1.97 0.909 0.4078 2.558 0.891 0.5889 3.881 0.874 0.8355 6.847 0.895

Sample Data for the Defl0 Equation

Tm, °C Tr, °C ac Defl36 theta TAFDefl0
21 5 75 50 30 1.21
21 5 75 50 45 1.256
21 5 75 130 30 1.101
21 5 75 130 45 1.126
21 5 150 50 30 1.26
21 5 150 50 45 1.336
21 5 150 130 30 1.15
21 5 150 130 45 1.203
21 30 75 50 30 0.895
21 30 75 50 45 0.876
21 30 75 130 30 0.946
21 30 75 130 45 0.934
21 30 150 50 30 0.868
21 30 150 50 45 0.839
21 30 150 130 30 0.919
21 30 150 130 45 0.895

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