3 Page references followed by "T" indicate illustrated figures or photographs, followed by "" indicates a table. 11-14, 68-69, 109, 132, 198, 210-213, 227, 229- 236, 240-244, 247, 252-255, 257, 260, 266-268, 270-271, 276-281, 290-291, 299-301, 319-322, 324-329, 336, 338-341, 346-348, 358-364, 371-373, 375, 386-387, 392-393, 395-398, 400, 462, 464-467, 485, 522, 541, 586-588, 590-591, 596-597, 608-610, 624-625, 653, 664, 666-668, 678, 680, 688-690, 702, 711, 715, 724-731, 803, 810, 817, 834-841, 844, 847-848, 855, 857, 863 3M, 196, 705, 726-727 A Abscissa, 194, 554 Accelerated, 6, 9 Accuracy, 353, 355, 408, 756, 804 Addition, 3, 141, 226, 265, 322, 602, 606, 622, 629, 702, 859 Adjustment, 370 Advanced, 4, 177, 352, 409 Air, 42, 85, 457,483, 579 Aircraft, 41, 47, 109, 248, 285, 578 Alloy, 101, 104-105, 108-109, 112-114, 119, 130-131, 151, 160, 164, 169, 174, 237, 244, 254, 257, 266, 273,277, 359, 374, 381, 578, 590, 742, 750, 754, 765-766, 776, 778-780, 783, 787-788, 828-829 Alloying, 107 mechanical, 107 Alloys, 115, 123 aluminum, 123 Aluminum, 59, 61, 65, 101, 109-110, 120, 122-123, 126, 130-131, 144-145, 148-149, 151, 158, 160, 164, 166-168, 171-175, 188, 194-195, 232-233, 237, 244, 247, 254-255, 261, 266, 276-277, 326, 330, 359, 361, 381, 442, 578, 718, 742, 747, 750, 754, 770, 772, 778-780, 782-783, 787-789, 802, 814, 819-820, 825, 828-830, 850 American Institute of Steel Construction (AISC), 605, 771 and, 2-11, 13-66, 70-72, 75-91, 94-132, 137-196, 198, 200-215, 217-271, 273-278, 280, 285-336, 338-388, 398, 403-425, 427-443, 445-449, 452-465, 468-484, 486, 490-494, 496-542, 545-585, 587-597, 599-634, 635-731, 735-791, 793, 796-818, 820-841, 844-865 Angle, 26, 42, 77, 79, 81-82, 84-85, 118-119, 124, 130-131, 150, 167, 200-203, 212, 224-238, 240- 244, 246-247, 250-255, 257, 261-263, 267-268, 270-274, 276-277, 313, 334-335, 337-338, 350, 387, 409, 440-441, 496-499, 506, 511-512, 516-520, 525, 531, 546-549, 553, 555-557, 559-560, 576-577, 595, 621, 640, 662, 672-675, 677-678, 689, 694, 781, 821, 844, 851 of twist, 118, 200-202, 224-238, 240-244, 246-247, 250-255, 257, 261-263, 267-268, 270-274, 276-277 Angles, 15, 76, 78, 83, 126, 201, 226, 230, 239, 409, 517, 552, 564-565, 584, 603, 605-606, 622, 674, 740, 750 bearings, 230 deflection, 126, 674, 740 measurements, 76, 564 Anisotropy, 24 normal, 24 Arc, 203, 640, 643, 656, 673, 678 area, 4, 7-11, 14, 22-28, 30-34, 37, 40, 43, 46-47, 49-53, 56, 58, 62, 64-65, 72, 96-97, 99, 101, 106-107, 109-113, 115, 122, 127-128, 140-141, 143-144, 146, 149-153, 159, 172-177, 179, 181, 186, 188-190, 194-195, 211, 225-226, 245-252, 257, 261, 265, 275-276, 285, 294-296, 299-300, 311, 314-322, 326-328, 330-334, 341-346, 348-351, 353-354, 356-358, 363, 365, 371-372, 375, 382-383, 386-387, 405-407, 410-415, 419, 421-422, 431-435, 439, 441, 460-461, 465, 467, 476, 482, 492-494, 496, 583-585, 590, 618-619, 622, 639, 672-680, 700-704, 721-723,740-741, 743, 750-752, 759, 776, 780-782, 804, 828, 840-844, 855-856, 859 units of, 23, 31, 144, 146, 241, 411, 663, 678, 680 ARM, 18, 20, 33, 50, 81, 84, 189, 221, 237, 249, 277, 304, 306, 438, 482 Assembly, 21, 46, 55, 144, 148-150, 158, 164-165, 167-168, 172-173, 175, 188, 194, 221, 235, 277, 362-363, 443, 719, 748, 811-812, 821, 829-830 flexible, 173 Assumptions, 22, 47, 203, 312, 314, 408, 618, 823 Atmospheric pressure, 453 Atoms, 105 Average, 24-32, 34-37, 39-45, 47, 49, 52, 54, 56-57, 62-65, 76, 80, 82, 84-89, 95-96, 103, 106, 119- 120, 122, 152, 158, 163-168, 170, 172-178, 192, 194, 221, 226, 248-252, 255-257, 275, 408-409, 413, 415, 503-505, 509-510, 513, 516-517, 520, 523-525, 530, 534, 559-561, 566-567, 582, 594-595, 741, 759, 773 Average shear stress, 32, 34-37, 40-45, 54, 56-57, 62, 64-65, 119, 221, 248-252, 255-257, 275, 408, 413, 415, 428, 430, 608 Average value, 226 Axial loads, 62, 140, 149, 195, 781 columns, 781 maximum, 781 Axis, 6-9, 14, 17, 24-27, 33, 65, 76, 80, 88, 97, 101, 122-123, 127, 201-208, 210-211, 223-225, 228, 230, 234, 238-239, 243, 246-247, 260, 264-265, 285-287, 295, 305, 311-323, 330, 332-346, 348-353, 355, 365, 367, 369-372, 374-375, 383-384, 386-387, 406-408, 410-414, 420, 422-426, 434-439, 441, 460-462, 465, 467-468, 472, 481-482, 494-498, 515-521, 529-531, 541, 552, 554-556, 563, 567, 570, 580, 602-603, 622-623, 637, 639-640, 645, 665, 673, 694, 712, 741-743, 746-748, 750, 753-755, 759, 761, 769, 774, 776-777, 779, 781-782, 784, 786-787, 791, 793, 844 B Back, 4, 98, 105, 116-118, 160-161, 169-171,252, 459, 474, 645, 753 Bakelite, 360 Ball, 85 Band, 75, 85, 116, 121, 385, 458, 481, 656 saw, 385, 656 Bar, 21, 24-28, 31-32, 38, 40, 53, 55, 62, 111, 115-117, 138-142, 144, 147, 150-151, 159, 161, 166-167, 170-171, 174-176, 178, 180-181, 183, 187-188, 190-192, 194, 202, 224-225,246, 254-255, 270, 308, 311-312, 356, 358, 363-364, 380-381, 479, 482, 512, 576, 588-590, 691, 736-737, 753-755, 769, 779-780, 788, 802, 817, 828-830, 852 two materials, 404 Barrel, 103 Bars, 26, 41, 103, 115, 159, 166-167, 174, 190, 285, 348, 356, 686, 707, 736-737, 749, 754, 819-820, 864 base, 26, 45, 47, 58-59, 88, 146, 158, 259, 358, 481, 525, 627, 693-694, 744-745, 747, 750, 765-768, 780, 783, 785, 787 Basic, 23, 76, 212, 319, 461, 498 size, 212 Beams, 4, 151, 285-287, 298, 310-311, 341-342, 344-345, 349-350, 367, 370, 383-384, 402-403, 410, 437, 445, 599-634, 635-731, 773, 808-809, 818, 836, 844-845, 858 bearing plates, 602 bending stresses, 606, 618, 629 composite, 285, 342, 344, 370, 383, 445, 611,682, 773 concrete, 310, 345, 618, 637 continuous, 342, 644, 661, 695, 698, 720 cross sections, 311, 349-350, 410, 437, 605, 622, 640 deep, 606, 818 deflection and, 637, 659, 693 deflections, 604, 637, 641, 687, 694, 844 floor, 285, 341, 600, 604, 614, 631, 659, 699 function of, 287, 350, 437, 618-619, 626-627,630, 642, 645, 654, 663, 665, 720, 804, 818, 844 girders, 606 plastic moment, 367, 370 ponding, 643 shear, 285-287, 298, 310, 402-403, 410, 437, 445, 601-619, 623-625, 627-631, 639, 647, 662-663, 693, 698-700, 706, 711, 717, 723, 808-809, 818, 836, 844-845, 858 shear center, 403, 437 simply supported, 285, 287, 341, 613-614, 617, 615 626, 631, 648, 650, 658, 660, 669, 672, 681-682 684-685, 689, 692-694, 703, 705, 718-719 size of, 286, 605, 618, 623 stresses in, 384, 602, 618 sweep, 678 tapered, 621, 626, 804, 809 Bearing plates, 60-61, 602 beam, 60-61, 602 Bearings, 21, 210, 218, 222-223, 230, 233-235, 243 260, 304, 327-328, 330, 387, 513, 624, 627-62 669, 671, 682-684, 719, 722 Bed, 831 Bend, 8, 98, 370, 422, 436-438, 446, 638, 756, 760 length, 422, 438, 760 Bending, 8-9, 14, 16, 34, 62, 96, 283-400, 405, 410 429, 452-453, 460-462, 464-468, 479-480, 48 588-591, 601-604, 606-610, 613-618, 622-62 626-631, 636, 641, 654, 656, 672, 693, 722, 73 869 SAL - NO Mama L144SS 1-15-2426 21, 23, 244 132 379 M 47 24 - No 42 x L KARA 154, 226 2 RM42 37, 45-442 443 444 139-721 74, 750-75 Mus&277, 422-804 252 256 257 27 435, 454, 770 45, 101, 113, 114, 122, 170031 9, 101, 187 (25-425, 127, 879 M21 291, 404, M Md 25, 2-4 M 2943017121 391 392 422 40, 4 74, 772-721-414 A 121 i 177, 200, 25, 41-442 79, 71, 771, 781 745-467 402, 04-3, 49, 853 796-400, 516-7, 8-4 367 360-372 24-NO-M 204 4%, 4R 4644044 44 445 44, 467 541, 600-44, 606, 349-353 A 31-325, 300 10-15 345, 36, 367, 332 JN 175 383 384 387 406-40 40-4144204-06 415 430 440 445 46 46 47, 541, 42-600, LEK-64, 712, 142, 44, Newton 39,212 helige M Pa 134 446 41-422,153 320-32, 3, 42 44, 44 Pascal, Pomgen 40 Pulal 526 2449 Period 121, 102, 125 homas, 102, 105, 12, 124 126-128, 110 19.200-271,271-813 p12-31 54-15 94,445, 72 81, 113-114131, 1, 41-46, 745-258 776-7785-79, 8M Pipi 14.21.40, 41, 5, 1401 112 JA 44442M 748, 79, 121, X25 dations 114, 3, 2, 140, 175-174128 Pipes 189 194 Normal X 14 16 17,21-231, 38-459, 47. 4953-52, 54, 56-58 60 64-45, 75-89 95-96 118 117, 128, 125, 127, 130, 14 147 149 158, 143-168, 170, 172-178, 187, 343-325 317-318 321-322 113-1140 343-198865-366 30-371, 373-375-3 422, 456-415, 45-49 460 462 464-46 470 473-476, 480 482-48341-449-51 52-42, 4 523-527, 530, 534-533,540, 545-547, 353-555, 537-562 566-471, 584-586, 582-991, H2, 509, 614-419 420 421, 626-627, 714, 741, 79 804, 821 Plast m 545-547.356-554 256-561-6 34 Not al 316, 673 23, 142, 227, 672 640 Nylon 107 C 940,595 572-574 576 176, 182, 52, 588 621, 813 P, 21, 32, 34, 6284404 454 444 43015 M 5541 580-581,622 Plast 47 Plastic defienation, 1, 1, 12, 504-500, 50 10477,772 677 Modeling 264, 763, 804 Mf 104-109 111-014, 118, 120, 123-128, 131, 141, 143, 146, 149, 152-153, 183, 165, 167, 173-175 190 225 226 264 268, 276, 342, 364 17-571, 576 57 579 44 64, 655, 657 684-685692, 71, 72, 740 741, 142, 772, WIZ K00-42), 137, 544.855, 859 106-107, 109, 112-113, 128 day, 118, 123-124,640 11, 12, 124-125, 127, 131, 141, 143, 144 152-153, 163, 167, 173-175, 190, 225-226, 229 342, 376-471, 376-57,579, 594,640, 655,657 684-685, 92 700, 71, 723, 740-141, 72, 772 02 42-423,837, 844, 855, 859 Modula 106-107, 109 112-413, 128 nipdity, 118, 123-124 mptus, 254, 26, 308, 373 gh, 107, 109, 112-114, 128 ina 205-208, 210-211, 225, 228-229 317-323, 330, 334, 336, 138, 344, 146, 348,371, 407, 410-411,414,422, 424-426 433, 435,439, Objectives) Object 822 825 Observations, 201, 311-312, 569 Offer, 101, 107-108, 114, 121, 452 451-410.234.2 38. 46-48, 17, 61, 75, 77-7995-96, 106-102, 105, 121, 123, ET, LM 140-143, 152, 155, 157, 160-165, 174, 171, 184, 188-189, 192, 194 217, 223-226, 238, 240, 245 24, 251, 254 256, 261 268, 270-271 285-297 295-296 298, 31, 328, 333-335, 137, HC-144 346, 358 408, 422 434, 460-461, 494-495, 529 54, 554, 562, 570 582-585 590, 47, 613-614 695,647 698, 707, 130-721, 744-145, 75-752 754-755, 759, 765-766 769-771, 802-85, 809, 815-836,853 Open 436, 438, 446 457, 463, 481, K21 Optical Optimum, 459 Onder 4-7, 9, 15, 47, 59, 62, 76, 78-79, 89, 10, 116, 122, 155-156, 166, 17, 182, 185, 226 234-239, 24, 266, 272, 286-287 291-292348 322.343-345 391, 353, 371, 418 422, 431, 431, 453, 466, 547, 605-606, 618 622-623, 631, 641. 647, 661, 663, 64, 701, 71, 710, 734, 770, 773 833, 647-848 854 Ordiner, 194, 554 Play 126 Post 4-1,9-8, 12, 15-222- 0-4-SCHRAM 10-119, 112 116-119 126-128, 138, 14-12 145, 13, 14, 16 17 18 182, 134 1 190-196 398 214-218-216 28 28 288 246-34, 25, 261, 20-34, 290, 20-28 297-29 1 113-315317-334 1332-134 127, 334-375, 308 340-30 MM 383-355, 258 36C 364 371-17 J 407-410 414-418 437-42 443 444 4 43-467 49-471, 413-475 477-40 40 491-445, 500-301, 57-823, 525 539-542-345-546 950-362, 961-337D-STA 563, 585-5510-5, 64, 60-61 462 672-478 685 -4 0 2 18 TO 720-721, 7, 78, 70, 415-412, 6, 416-415 841-842 346-4118-AT MY Pom 3-4817-182 83, 97, 107, 125-131, 12, 288- 199, 17, 181, 208 230-211,211-852 24 218 245-24 20, 252 297 298 26-387 318, 326-321, 134, 136-127 318 34 36 38 362-363 370 382, 18409-41944 434-415, 48, 40-441 462 473-47, 48, 873 444 WA RANCHO LONAS from cent vertical c slopes of horizonta (Section slope). T 1:1.5. For 45°); for Wh For exar Side slo represen the slope Aft determi lated ve Fo are de section param profile FIGURE 16.34 (c) Perspective view of a DTM projected on a video screen. (Courtesy of Integraph Corporation.) superi necess stakes comp for su 002 A horizontal or geodetic datum consists of an ellipsoid of revolution approximating the figure of the earth and a set of constants or constraints that specify the size, position, and orientation of the ellipsoid. Two of the constants define the semimajor axis and the flattening of the ellipsoid. The position is often given indirectly by three constants E., Ma and N. at an origin point, O, where &, represents the deflection of the vertical in the meridian plane, n, represents the the deflection of the vertical in the prime vertical plane, and N represents the difference between the geoid and the ellipsoid, which is also called the geoid undulation. In addition to these three constants, an observed astronomic latitude and either an observed astronomic longitude or an astronomic azimuth would define the geodetic latitude and longitude of the origin point. More recent datums define the ellipsoid position by specifying that it coincide with the center of mass of the earth. An example of the earlier type of horizontal datum is the North American datum of 1927 (NAD 27), which was based on an origin point at Meades Ranch, Kansas, and used the Clarke 1866 ellipsoid with a = 6,378,206.4 meters and b = 6,356,583.8. This was the basis for most mapping done in the United States until recently. A general readjustment including satellite observations and very long base-line interferometry has resulted in the North American datum of 1983 (NAD 83), which is an example of the latter type of geodetic or horizontal datum. It is based on the geodetic reference system of 1980 (GRS 80) ellipsoid with a = 6,378,137.0 and 1/f = 1/298.257522101. The adoption of GRS 80 for the NAD 83 is a favorable circum- stance for users of the GPS system. The world geodetic system of 1984 (WGS 84), as used in GPS computations, essentially is the same as GRS 80. A vertical datum is the surface to which elevations or depths are referred. Prior to 1991, all surveys and mapping in the conterminous United States were based on the national geodetic vertical datum of 1929, formerly called the sea-level datum of 1929. This datum was based on a least-squares adjustment to 26 mean sea-level tide stations (Zilkosky, Richards, and Young, 1992) in the United States and Canada and was the result of a general adjustment of level networks in the United States and Canada in 1929. In 1991, the National Geodetic Survey completed incorporating new data into the existing survey network, result- ing in the North American vertical datum of 1988 (NAVD 88). Elevations used in topo- graphic mapping, geodetic surveys, engineering studies, engineering construction surveys, and geographic information systems should be referred to the current national vertical datum, NAVD 88. The NAVD 88 is not a mean sea-level datum and should not be confused with local mean sea-level datums. The national datum was determined by a minimal constraint adjustment, holding fixed the height of a primary tidal bench mark at Father Point (Pointe au Pere), Rimouski, Quebec, Canada. Canadian-Mexican-U.S. leveling observa- tions were included in this adjustment. Consequently, small differences exist between the national datum and local mean sea-level for a specific location. and A Elevations used in boundary surveys are often referred to a tidal datum in tidal waters or the lake level in the Great Lakes regions. Tidal datums are defined by the phase of the tide, described as mean high water, mean low water, and mean lower low water. Caution always should be exercised to ensure that bench marks and control points refer to the same datum, particularly in areas where multiple datums are known to exist. Other horizontal and vertical datums are employed for Alaska (vertical datum), Puerto Rico, the Virgin Islands, Guam, and other oceanic islands. Specifications for these datums can be obtained by requesting information from the National Geodetic Survey. (X, Y) or eastings and northings (E, N). This is necessary both for preparing hard-copy maps and for representing map data digitally in a geographic information system. Eventu ally GIS systems may accommodate latitude and longitude, but at present they generally require Cartesian coordinates. As described in Chapter 11, map projections include the Lambert conformal conic and the transverse Mercator. The newer U.S.G.S. quadrangle maps are on the universal transverse Mercator (UTM) projection (Section 11.14). Older quadrangle maps employed the polyconic projection (Section 11.9). The state plane coor- dinate systems (SPCS), based on the Lambert conformal conic or the transverse Mercator projections, are widely used as reference coordinates for mapping and GIS. For regional or statewide projects that may cover multiple state plane zones, the UTM projection often is used. For special circumstances, a unique projection can be defined for a particular project, although data interchange is facilitated by using standard projections wherever possible. 14.4 TOPOGRAPHIC MAPS A topographic map shows, through the use of suitable symbols, (1) the spatial characteris- tics of the earth's surface, with such natural features as hills and valleys, vegetation and rivers; and (2) constructed features such as buildings, roads, canals, and cultivation. The distinguishing characteristics of a topographic map, as compared with other maps, is the representation of the terrain relief. Topographic maps are used in a variety of ways. They are necessary in the design of any engineering project that requires the consideration of elevations for gradients. They also are used for delineating the extent of a flood plain, planning for economic development, and managing natural resources. The preparation of general topographic maps traditionally has been a function of governmental agencies. However, the rapid development of computer-based tools for ter- rain modeling and the increasing availability of high-quality field data enable nearly any user of topographic information to create detailed, specialized topographic maps using a desktop computer. The principal source of topographic data in the United States remains the national map series of medium (1:24,000) to small (1:1 million) scale topographic maps prepared by the National Mapping Division of the U.S. Geological Survey (Figure 14.1). These maps cover the entire United States and its territories in quadrangle tiles from 7' x 7' in latitude and longitude at a map scale of 1:24,000 to tiles 4° x 12° in extent at a scale of 1:1 million. These topographic maps have been compiled using field survey data and photogrammetric compilation techniques. Recently, the U.S.G.S. also provided the same data contained in the printed map series in digital form as digital line graph (DLG) files. Although the printed maps are regularly photo revised, it is common for the latest quadrangle maps not to have been revised in several years. For engineering applications in rapidly developing areas, this time lag may not be acceptable. The U.S.G.S. currently is in the process of developing a new, large-scale digital orthophoto quadrangle (DOQ) and quarter-quad (DOQQ) map series for the entire coun- try. These new orthophoto maps will be generated at scales of 1:24,000 and 1:12,000, respectively. The DOQQ maps will have a 1-m ground sample (pixel) resolution and will be provided in a UTM system based on NAD 83. The status of the DOQ mapping program is shown graphically in Figure 14.2. The new map series combines the information content of a photograph and the geometric qualities of a standard map and will be uniquely suited for use in spatial information systems. More information on these products is available from the Earth Sciences Information Centers of the U.S.G.S. or by calling 1-800-USA-MAPS. 78 CH Ma M Sp Int Sy -3 m. Then two edges. In Figure 14.6b, the contours cross a paved road with curbs. Most curbs are 0.15 m high, so the contour crosses the curb at right angles and runs along the face of the curb until it reaches the contour elevation in the gutter line. Therefore, if the grade (Sec. tion 3.8) of the road is 5 percent, the distance from where the contour crosses the top of the curb to the point where it meets the contour elevation in the gutter is 0.15/0.05 the contour crosses the pavement slightly convex down the slope to the gutter line on the other side, follows the face of the curb until the elevation at the top of the curb is reached, and crosses the curb and sidewalk at right angles (assuming that the sidewalk is horizontal), The contour interval in Figure 14.6a is 5 ft and that in Figure 14.6b is 2 m. 14.7 CHOICE OF MAP SCALE AND CONTOUR INTERVAL Formerly, when a hard-copy map was the archival data record used to present the results of a topographic survey, the choice of map scale and contour interval indeed was critical. Current engineering practice often dictates that map data be recorded digitally, usually in ground coordinate units. Thus, within limits, the hard-copy representation of the map can be plotted at any scale desired. This capability is well known to users of CAD systems and other computer graphics programs. Of course, such things as text annotation size and placement, point and line symbology, and feature generalization are scale specific and do not change with plot scale. So, for a map plotted at much smaller scale than intended, the text would be unreadable. A portion of the same map plotted at much larger scale than intended would be graphically unpleasing with the text too large. Likewise, the choice of contour interval was once a fixed parameter of the data collection process. Currently, the parameter that limits the fidelity of the representation of the ground surface often is the density of points in the digital terrain model (DTM, see Section 14.8). This might include the spacing of the points of known elevation or elevation "posts" in a grid layout, the density of points of known spatial position or mass points for construction of a triangular irregular network (TIN) (See Section 14.8), and the density and completeness of breaklines (Sec- tion 14.9) and other subordinate features. Having selected the sampling criteria of the terrain surface, a contour representation, again within limits, can be interpolated and plotted at any desired interval. Computer mapping programs, quite readily, and inappropriately. will produce 1-dm contours from data points 30-m apart and accurate to only 1 m. Therefore, sound judgment should be used in selecting the sampling density of the terrain points and a contour interval for interpolation and plotting. Hard-copy contour maps will continue to be used for the foreseeable future, and it therefore is useful to look at some of the design parameters used in their construction, in particular scale and contour interval. Accuracy standards for engineering maps, presented later in this chapter (Sec- tion 14.26), generally dictate that well-defined, plotted features should be located within 0.5 mm of their true position at the plotted map scale. Therefore, if a user needs point positions accurate to 2.5 m, a map scale of 1:5000 is indicated. With regard to elevations, accuracy standards generally require that interpolated heights be accurate to one-half contour interval. Therefore, if one needs 0.25-m elevation accuracy, the contour interval should be no greater than 0.5 m. Along with a given map scale, an implied level of detail is expected by the user. Other factors that influence the choice of map scale are (1) the clarity with which features can be shown. (2) the cost (the larger the scale, the higher is the cost). (3) the consistency of the map with other adjoining or overlapping maps, (4) the number and character of the features to be plotted, the nature of the terrain, and the contour interval. Typical map scales, map uses, and corresponding contour intervals are shown in Table 14.1. A horizontal or geodetic datum consists of an ellipsoid of revolution approximating the figure of the earth and a set of constants or constraints that specify the size, position, and orientation of the ellipsoid. Two of the constants define the semimajor axis and the flattening of the ellipsoid. The position is often given indirectly by three constants E., Mo and N. at an origin point, O, where &, represents the deflection of the vertical in the meridian plane, n, represents the the deflection of the vertical in the prime vertical plane, and N represents the difference between the geoid and the ellipsoid, which is also called the geoid undulation. In addition to these three constants, an observed astronomic latitude and either an observed astronomic longitude or an astronomic azimuth would define the geodetic latitude and longitude of the origin point. More recent datums define the ellipsoid position by specifying that it coincide with the center of mass of the earth. An example of the earlier type of horizontal datum is the North American datum of 1927 (NAD 27), which was based on an origin point at Meades Ranch, Kansas, and used the Clarke 1866 ellipsoid with a = 6,378,206.4 meters and b = 6,356,583.8. This was the basis for most mapping done in the United States until recently. A general readjustment including satellite observations and very long base-line interferometry has resulted in the North American datum of 1983 (NAD 83), which is an example of the latter type of geodetic or horizontal datum. It is based on the geodetic reference system of 1980 (GRS 80) ellipsoid with a = 6,378,137.0 and V/f = 1/298.257522101. The adoption of GRS 80 for the NAD 83 is a favorable circum- stance for users of the GPS system. The world geodetic system of 1984 (WGS 84), as used in GPS computations, essentially is the same as GRS 80. A vertical datum is the surface to which elevations or depths are referred. Prior to 1991, all surveys and mapping in the conterminous United States were based on the national geodetic vertical datum of 1929, formerly called the sea-level datum of 1929. This datum was based on a least-squares adjustment to 26 mean sea-level tide stations (Zilkosky, Richards, and Young, 1992) in the United States and Canada and was the result of a general adjustment of level networks in the United States and Canada in 1929. In 1991, the National Geodetic Survey completed incorporating new data into the existing survey network, result- ing in the North American vertical datum of 1988 (NAVD 88). Elevations used in topo- graphic mapping, geodetic surveys, engineering studies, engineering construction surveys, and geographic information systems should be referred to the current national vertical datum, NAVD 88. The NAVD 88 is not a mean sea-level datum and should not be confused with local mean sea-level datums. The national datum was determined by a minimal constraint adjustment, holding fixed the height of a primary tidal bench mark at Father Point (Pointe au Pere), Rimouski, Quebec, Canada. Canadian-Mexican-U.S. leveling observa- tions were included in this adjustment. Consequently, small differences exist between the national datum and local mean sea-level for a specific location. and A Elevations used in boundary surveys are often referred to a tidal datum in tidal waters or the lake level in the Great Lakes regions. Tidal datums are defined by the phase of the tide, described as mean high water, mean low water, and mean lower low water. Caution always Radius of a curve is 230 m. What is the degree of the curve. datum, particularly in areas where multiple datums are known to exist. Other horizontal and vertical datums are employed for Alaska (vertical datum), Puerto Rico, the Virgin Islands, Guam, and other oceanic islands. Specifications for these datums can be obtained by requesting information from the National Geodetic Survey. по derivative of the terrain surface is not continuous; for example, along a ridge line or a drain line. These data are not tied to a particular graphic representation. Implicitly associated with the terrain data in a DTM is the interpolation algorithm used to reconstruct the terrain surface. Second, the archival record is the digital coordinate file itself rather than a par- ticular graphic depiction. Such graphical depictions as contours, profiles, or wire frame perspective views can be generated as needed, but only the original terrain points and features are considered to be archival data. DTMs generally are organized such that the "mass points" lie in a regular grid pattern or they represent vertices of local triangular patches in an array referred to as a triangulated irregular network. Companies and government agencies seem to have developed institu- tional preferences for one method or the other. Just as there are engineering design criteria for selecting a contour interval to represent terrain for a given application, so too similar criteria are used to select a point spacing so that the DTM adequately represents the terrain. These criteria depend on the potential uses for the data, accuracy requirements, the terrain character, and other factors. The advantages of a regular grid layout are a simplified data collection routine, and ease of data access by subsequent programs. The disadvantages are related mostly to the necessity to select a single grid interval, sufficient to define the terrain in the roughest areas although likely to be oversampled in regions where the terrain is smooth and featureless. Conversely, the merits of the irregular point approach are the mirror image of those for the regular grid. The sampling interval can change to match the local terrain character, introducing a kind of stratified sampling, optimizing the quantity of data necessary to define the terrain. Data access for subsequent software analysis is considerably more involved than when using the simple grid structure. Ideally, during the design of a DTM database, a quantitative analysis is done to deter- mine the magnitude of the errors expected during reconstruction of the terrain surface. The magnitude of these errors should be within the error budget of potential user or client applications. Interpolation methods for generating intermediate points can include patch- wise polynomials, b-splines, moving surface methods, linear prediction with trend surfaces and covariance functions (sometimes called summation of surfaces), bilinear methods, plane triangle methods, and ideal reconstruction functions from signal theory. Given a DTM database and an interpolation function, one should be able to construct a profile or cross section along any arbitrary path within the area covered by the DTM. Likewise, one should be able to interpolate heights at arbitrary points within the area covered. This capability would permit one to interpolate heights at regular grid points from an irregular grid as well as interpolate irregular points from a regular grid. Thus, with possibly some cost to accuracy, one could convert between these two popular storage conventions. Converting from irregular points to regular points is straightforward. Converting from regular gridded points to irregular points often is more difficult, especially when there is a desire to reduce drastically the number of points. Another issue to consider when constructing or using DTM databases is the matter of consistency between the terrain, as defined by the DTM, and the feature data, such as roads, streams, and buildings. On a hard-copy map, these two classes of data always are implicitly consistent. However, if they are collected and stored independently as 3D or 2.5D, then they may be inconsistent or conflicting. This could occur if, for example, a road were above the terrain surface or if a stream were placed so as apparently to flow uphill. 14.9 BREAKLINES AND OTHER TERRAIN FEATURES Terrain data points, whether in a grid pattern or an arbitrary pattern, always will fail to represent terrain fully in areas where there are sharp breaks or, more properly, discontinu- ities in slope. Such discontinuities occur along ridge lines, at the upper and lower edges of 79 CH M M Sp In Sy TABLE 14.1 Typical map scales Map scale Typical uses Contour interval for nonmountainous terrain 1:1,000 Design 1:2,000 Design 1:5,000 Planning 0.25 m 0.5 m Im 1:10,000 Planning 2 m 1:25,000 Regional planning 2.5 m 1:50,000 Regional planning 5 m 1:100,000 Regional planning 5 or 10 m 1:250,000 Regional planning 10 m 1:500,000 1:500,000 State planning 20 m National planning 20 or 50 m with The choice of a proper contour interval for a topographic survey and map is based on our principal considerations: (1) the desired accuracy of elevations to be determined from he map, (2) the characteristic features of the terrain, (3) the legibility of the map, and 4) the cost. Assuming that heights can be interpolated to one-half of the contour interval, then a map with a 1-m contour interval should yield more accurate heights than a map a 2-m contour interval. Terrain areas with a fine-textured surface may require a smaller contour interval to represent it than otherwise would be necessary. Contours should not be so close together as to obscure other important map features, although cartographic design and selection of colors, saturations, and line weights can significantly influence the map legibility. Smaller contour intervals, in general, cost more assuming that the conventional accuracy levels are maintained. As shown in Table 14.1, smaller map scales generally are associated with larger contour intervals. Traditionally, maps have been classified according to scale as large, medium, and small, with these categories generally as in Table 14.2. The American Society of Civil Engineers' (ASCE) Surveying and Mapping Division has a more detailed classification for map scales and contour intervals. 1. Design maps. These maps are used in the design and construction of specific engineering work of all kinds. Scales vary from 1:100 to 1:2000, with contour intervals from 0.1 to 1 m, depending on the type of project, land use, and terrain characteristics. Two subcat- egories are given within this group. Critical design maps are used on projects having critical space, orientation, position, or elevation restrictions; for example, a highway interchange in an urban area. General design maps are prepared for projects that have no such rigid restrictions with respect to location; for example, a map prepared for a rural water distribution system. 2. Planning maps. These maps include a large group of maps used in planning engineering work or in overall planning at the urban, regional, national, and international levels. These maps may be used as a foundation for GIS, geological studies, land use, agricul- tural production, population studies, public service planning, and atlases. These maps generally fall in the medium- to small-scale range. TABLE 14.2 Map-scale categories Large scale Medium scale Small scale 1:20,000 and larger 1:20,000-1:50,000 1:50,000 and smaller 784 Greek 50 Slatt 20 ALTA HILL YER The Oaks Glenbrook 23 Hills Flat Cardon GRASSANES South 13107 Union Hill 35 STATE ISTORIC Puk Cedar Ridge 972 1213700 Nevada City FIGURE 14.1 Typical topographic map of the U.S. Geological Survey. Scale is 1:24,000 (2000 ft/in.). Contour Interval 20 ft. (U.S. Geological Survey.) Peardale 43 GQ (X, Y) or eastings and northings (E, N). This is necessary both for preparing hard-copy maps and for representing map data digitally in a geographic information system. Eventu ally GIS systems may accommodate latitude and longitude, but at present they generally require Cartesian coordinates. As described in Chapter 11, map projections include the Lambert conformal conic and the transverse Mercator. The newer U.S.G.S. quadrangle maps are on the universal transverse Mercator (UTM) projection (Section 11.14). Older quadrangle maps employed the polyconic projection (Section 11.9). The state plane coor- dinate systems (SPCS), based on the Lambert conformal conic or the transverse Mercator projections, are widely used as reference coordinates for mapping and GIS. For regional or statewide projects that may cover multiple state plane zones, the UTM projection often is used. For special circumstances, a unique projection can be defined for a particular project, although data interchange is facilitated by using standard projections wherever possible. 14.4 TOPOGRAPHIC MAPS A topographic map shows, through the use of suitable symbols, (1) the spatial characteris- tics of the earth's surface, with such natural features as hills and valleys, vegetation and rivers; and (2) constructed features such as buildings, roads, canals, and cultivation. The distinguishing characteristics of a topographic map, as compared with other maps, is the representation of the terrain relief. Topographic maps are used in a variety of ways. They are necessary in the design of any engineering project that requires the consideration of elevations for gradients. They also are used for delineating the extent of a flood plain, planning for economic development, and managing natural resources. The preparation of general topographic maps traditionally has been a function of governmental agencies. However, the rapid development of computer-based tools for ter- rain modeling and the increasing availability of high-quality field data enable nearly any user of topographic information to create detailed, specialized topographic maps using a desktop computer. The principal source of topographic data in the United States remains the national map series of medium (1:24,000) to small (1:1 million) scale topographic maps prepared by the National Mapping Division of the U.S. Geological Survey (Figure 14.1). These maps cover the entire United States and its territories in quadrangle tiles from 7' x 7' in latitude and longitude at a map scale of 1:24,000 to tiles 4° x 12° in extent at a scale of 1:1 million. These topographic maps have been compiled using field survey data and photogrammetric compilation techniques. Recently, the U.S.G.S. also provided the same data contained in the printed map series in digital form as digital line graph (DLG) files. Although the printed maps are regularly photo revised, it is common for the latest quadrangle maps not to have been revised in several years. For engineering applications in rapidly developing areas, this time lag may not be acceptable. The U.S.G.S. currently is in the process of developing a new, large-scale digital orthophoto quadrangle (DOQ) and quarter-quad (DOQQ) map series for the entire coun- try. These new orthophoto maps will be generated at scales of 1:24,000 and 1:12,000, respectively. The DOQQ maps will have a 1-m ground sample (pixel) resolution and will be provided in a UTM system based on NAD 83. The status of the DOQ mapping program is shown graphically in Figure 14.2. The new map series combines the information content of a photograph and the geometric qualities of a standard map and will be uniquely suited for use in spatial information systems. More information on these products is available from the Earth Sciences Information Centers of the U.S.G.S. or by calling 1-800-USA-MAPS. 78 CH Ma M Sp Int Sy