338:
20:
136:
306:
991:
Making history interactive: computer applications and quantitative methods in archaeology (CAA); proceedings of the 37th international conference, Williamsburg, Virginia, United States of
America, March 22−26,
194:
1041:
915:"Three presentations on geographical analysis and modeling: Non-isotropic geographic modeling speculations on the geometry of geography global spatial analysis"
64:
254:
237:
On flat terrain this formula works out to 5 km/h. For off-path travel, this value should be multiplied by 3/5, for horseback by 5/4.
987:"GPS-aided Walking Experiments and Data-driven Travel Cost Modeling on the Historical Road of Nakasendō-Kisoji (Central Highland Japan)"
1027:
956:
885:
880:
1103:
875:
234:
The velocity on the flat terrain is 5 km / h, the maximum speed of 6 km / h is achieved roughly at -2.86°.
144:
1074:
248:
is the reciprocal of speed. For Tobler's hiking function it can be calculated from the following conversion:
890:
1061:
870:
1056:
31:
8:
865:
1126:
1070:
131:{\displaystyle W=6e^{\displaystyle -3.5\left\vert {\frac {dh}{dx}}+0.05\right\vert }}
1118:
1066:
1028:
Analyzing Tobler's Hiking
Function and Naismith's Rule Using Crowd-Sourced GPS Data
337:
1157:
939:
914:
341:
245:
966:. Anul VI (2). Academia Romana − Filiala Cluj Colectivul de Geografie: 124–129
1151:
1130:
39:
19:
1122:
47:
43:
1104:"Pace and critical gradient for hill runners: an analysis of race records"
994:. BAR International Series. Oxford u.a.: Archaeopress. pp. 158–165
301:{\displaystyle p=0.6e^{\displaystyle 3.5\left\vert m+0.05\right\vert }}
349:
986:
345:
35:
23:
Tobler's hiking function – walking speed vs. slope angle chart.
1030:. Erik Irtenkauf. The Pennsylvania State University. May 2014
928:(1). National center for geographic information and analysis
353:
272:
257:
147:
82:
67:
46:. This function was estimated from empirical data of
954:
300:
188:
130:
1149:
189:{\displaystyle {\frac {dh}{dx}}=S=\tan \theta }
955:Magyari-Sáska, Zsolt; Dombay, Ştefan (2012).
356:vs. slope angle for Tobler's hiking function.
957:"Determining minimum hiking time using DEM"
950:
948:
1111:Journal of Quantitative Analysis in Sports
1021:
984:
908:
906:
1097:
1095:
1060:
945:
336:
18:
985:Kondo, Yasuhisa; Seino, Yoichi (2010).
903:
1150:
1092:
1033:
1006:
978:
912:
1012:
1101:
1039:
16:Formula for estimating hiking speed
13:
14:
1169:
876:Tobler hyperelliptical projection
1071:10.1111/j.1538-4632.2012.00838.x
886:Tobler's second law of geography
332:
1042:"Route Choice in Hilly Terrain"
913:Tobler, Waldo (February 1993).
881:Tobler's first law of geography
324:= gradient uphill or downhill (
230:= angle of slope (inclination).
38:speed, taking into account the
989:. In Frischer, Bernard (ed.).
1:
896:
42:angle. It was formulated by
7:
859:
10:
1174:
53:
1102:Kay, A. (November 2012).
891:Waldo Tobler bibliography
375:
372:
367:
362:
28:Tobler's hiking function
871:Preferred walking speed
240:
212:= elevation difference,
1123:10.1515/1559-0410.1456
1013:Imhof, Eduard (1950).
357:
302:
190:
132:
24:
964:Geographia Napocensis
340:
328:in Tobler's formula),
303:
191:
133:
22:
255:
145:
65:
32:exponential function
206:= walking velocity
1017:. Rentsch, Zurich.
1015:Gelaende und Karte
938:Available also in
358:
298:
295:
186:
128:
125:
58:Walking velocity:
25:
857:
856:
166:
112:
1165:
1142:
1141:
1139:
1137:
1108:
1099:
1090:
1089:
1087:
1085:
1079:
1073:. Archived from
1064:
1046:
1040:Kay, A. (2012).
1037:
1031:
1025:
1019:
1018:
1010:
1004:
1003:
1001:
999:
982:
976:
975:
973:
971:
961:
952:
943:
937:
935:
933:
922:Technical Report
919:
910:
360:
359:
307:
305:
304:
299:
297:
296:
294:
290:
195:
193:
192:
187:
167:
165:
157:
149:
137:
135:
134:
129:
127:
126:
124:
120:
113:
111:
103:
95:
34:determining the
1173:
1172:
1168:
1167:
1166:
1164:
1163:
1162:
1148:
1147:
1146:
1145:
1135:
1133:
1106:
1100:
1093:
1083:
1081:
1077:
1062:10.1.1.391.1203
1044:
1038:
1034:
1026:
1022:
1011:
1007:
997:
995:
983:
979:
969:
967:
959:
953:
946:
931:
929:
917:
911:
904:
899:
866:Naismith's rule
862:
369:
364:
335:
280:
276:
271:
267:
256:
253:
252:
243:
158:
150:
148:
146:
143:
142:
104:
96:
94:
93:
89:
81:
77:
66:
63:
62:
56:
17:
12:
11:
5:
1171:
1161:
1160:
1144:
1143:
1091:
1032:
1020:
1005:
977:
944:
901:
900:
898:
895:
894:
893:
888:
883:
878:
873:
868:
861:
858:
855:
854:
851:
848:
845:
842:
839:
836:
832:
831:
828:
825:
822:
819:
816:
813:
809:
808:
805:
802:
799:
796:
793:
790:
786:
785:
782:
779:
776:
773:
770:
767:
763:
762:
759:
756:
753:
750:
747:
744:
740:
739:
736:
733:
730:
727:
724:
721:
717:
716:
713:
710:
707:
704:
701:
698:
694:
693:
690:
687:
684:
681:
678:
675:
671:
670:
667:
664:
661:
658:
655:
652:
648:
647:
644:
641:
638:
635:
632:
629:
625:
624:
621:
618:
615:
612:
609:
606:
602:
601:
598:
595:
592:
589:
586:
583:
579:
578:
575:
572:
569:
566:
563:
560:
556:
555:
552:
549:
546:
543:
540:
537:
533:
532:
529:
526:
523:
520:
517:
514:
510:
509:
506:
503:
500:
497:
494:
491:
487:
486:
483:
480:
477:
474:
471:
468:
464:
463:
460:
457:
454:
451:
448:
445:
441:
440:
437:
434:
431:
428:
425:
422:
418:
417:
414:
411:
408:
405:
402:
399:
395:
394:
391:
388:
385:
382:
378:
377:
374:
371:
366:
334:
331:
330:
329:
319:
309:
308:
293:
289:
286:
283:
279:
275:
270:
266:
263:
260:
242:
239:
232:
231:
225:
219:
213:
207:
197:
196:
185:
182:
179:
176:
173:
170:
164:
161:
156:
153:
139:
138:
123:
119:
116:
110:
107:
102:
99:
92:
88:
85:
80:
76:
73:
70:
55:
52:
15:
9:
6:
4:
3:
2:
1170:
1159:
1156:
1155:
1153:
1132:
1128:
1124:
1120:
1116:
1112:
1105:
1098:
1096:
1080:on 2012-11-14
1076:
1072:
1068:
1063:
1058:
1055:(2): 87–108.
1054:
1050:
1043:
1036:
1029:
1024:
1016:
1009:
993:
988:
981:
965:
958:
951:
949:
941:
927:
923:
916:
909:
907:
902:
892:
889:
887:
884:
882:
879:
877:
874:
872:
869:
867:
864:
863:
852:
849:
846:
843:
840:
837:
834:
833:
829:
826:
823:
820:
817:
814:
811:
810:
806:
803:
800:
797:
794:
791:
788:
787:
783:
780:
777:
774:
771:
768:
765:
764:
760:
757:
754:
751:
748:
745:
742:
741:
737:
734:
731:
728:
725:
722:
719:
718:
714:
711:
708:
705:
702:
699:
696:
695:
691:
688:
685:
682:
679:
676:
673:
672:
668:
665:
662:
659:
656:
653:
650:
649:
645:
642:
639:
636:
633:
630:
627:
626:
622:
619:
616:
613:
610:
607:
604:
603:
599:
596:
593:
590:
587:
584:
581:
580:
576:
573:
570:
567:
564:
561:
558:
557:
553:
550:
547:
544:
541:
538:
535:
534:
530:
527:
524:
521:
518:
515:
512:
511:
507:
504:
501:
498:
495:
492:
489:
488:
484:
481:
478:
475:
472:
469:
466:
465:
461:
458:
455:
452:
449:
446:
443:
442:
438:
435:
432:
429:
426:
423:
420:
419:
415:
412:
409:
406:
403:
400:
397:
396:
392:
389:
386:
383:
380:
379:
361:
355:
351:
347:
343:
339:
333:Sample values
327:
323:
320:
317:
314:
313:
312:
291:
287:
284:
281:
277:
273:
268:
264:
261:
258:
251:
250:
249:
247:
238:
235:
229:
226:
223:
220:
217:
214:
211:
208:
205:
202:
201:
200:
183:
180:
177:
174:
171:
168:
162:
159:
154:
151:
141:
140:
121:
117:
114:
108:
105:
100:
97:
90:
86:
83:
78:
74:
71:
68:
61:
60:
59:
51:
49:
45:
41:
37:
33:
29:
21:
1134:. Retrieved
1114:
1110:
1082:. Retrieved
1075:the original
1052:
1048:
1035:
1023:
1014:
1008:
996:. Retrieved
990:
980:
968:. Retrieved
963:
930:. Retrieved
925:
921:
325:
321:
315:
310:
244:
236:
233:
227:
221:
215:
209:
203:
198:
57:
48:Eduard Imhof
44:Waldo Tobler
27:
26:
218:= distance,
1136:19 January
1084:19 January
1049:Geogr Anal
897:References
1131:1559-0410
1057:CiteSeerX
350:kilometer
326:dh/dx = S
184:θ
181:
84:−
1152:Category
998:21 March
970:21 March
932:21 March
860:See also
390:min / mi
387:min / km
368:Gradient
224:= slope,
942:format.
605:-2.8624
416:216.23
370:(dh/dx)
346:minutes
318:= pace
54:Formula
1158:Hiking
1129:
1059:
853:46.31
850:1242.1
830:13.48
439:32.63
413:5799.9
410:3603.9
393:s / m
384:mi / h
381:km / h
311:where
228:θ
199:where
36:hiking
30:is an
1117:(4).
1107:(PDF)
1078:(PDF)
1045:(PDF)
960:(PDF)
918:(PDF)
847:771.8
827:361.5
824:224.6
807:5.39
804:144.6
784:3.66
761:2.56
738:1.83
715:1.32
692:0.97
669:0.76
646:0.71
623:0.60
608:-0.05
600:0.68
585:-0.09
577:0.93
562:-0.18
554:1.29
539:-0.27
531:1.80
516:-0.36
508:2.58
493:-0.47
485:3.80
482:101.9
470:-0.58
462:9.50
459:254.7
456:158.3
447:-0.84
436:875.3
433:543.9
424:-1.19
401:-1.73
376:Pace
373:Speed
365:(deg)
363:Slope
40:slope
1138:2017
1127:ISSN
1086:2017
1000:2013
992:2009
972:2013
940:HTML
934:2013
844:0.05
841:0.08
838:1.19
821:0.17
818:0.27
815:0.84
801:89.9
798:0.41
795:0.67
792:0.58
781:98.1
778:60.9
775:0.61
772:0.98
769:0.47
758:68.5
755:42.6
752:0.88
749:1.41
746:0.36
735:49.0
732:30.4
729:1.23
726:1.97
723:0.27
712:35.5
709:22.1
706:1.69
703:2.72
700:0.18
689:26.0
686:16.2
683:2.30
680:3.71
677:0.09
666:20.4
663:12.7
660:2.94
657:4.74
654:0.02
643:19.2
640:11.9
637:3.13
634:5.04
620:16.1
617:10.0
614:3.73
611:6.00
597:18.3
594:11.4
591:3.27
588:5.26
574:25.0
571:15.6
568:2.40
565:3.86
551:34.5
548:21.4
545:1.74
542:2.80
528:48.3
525:30.0
522:1.24
519:2.00
505:69.1
502:42.9
499:0.87
496:1.40
479:63.3
476:0.59
473:0.95
453:0.24
450:0.38
430:0.07
427:0.11
407:0.01
404:0.02
354:mile
348:per
342:Pace
288:0.05
246:Pace
241:Pace
118:0.05
1119:doi
1067:doi
559:-10
536:-15
513:-20
490:-25
467:-30
444:-40
421:-50
398:-60
352:or
344:in
274:3.5
265:0.6
178:tan
87:3.5
1154::
1125:.
1113:.
1109:.
1094:^
1065:.
1053:44
1051:.
1047:.
962:.
947:^
926:93
924:.
920:.
905:^
835:50
812:40
789:30
766:25
743:20
720:15
697:10
582:-5
216:dx
210:dh
50:.
1140:.
1121::
1115:8
1088:.
1069::
1002:.
974:.
936:.
674:5
651:1
631:0
628:0
322:m
316:p
292:|
285:+
282:m
278:|
269:e
262:=
259:p
222:S
204:W
175:=
172:S
169:=
163:x
160:d
155:h
152:d
122:|
115:+
109:x
106:d
101:h
98:d
91:|
79:e
75:6
72:=
69:W
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
