B. Determinations of length of roads
2. Determination of length of roads at the road inventory carried out by the National Forest Survey
a ) Methods
\Vhen information on the road-length in a certain area is required and when such data are lacking, there is near a t hand to measure t h e length of the roads on maps. However, no differentiation of the length can then be made regarding such factors as surface material, road width, carrying capacity and speed standards etc. When such a division is required t h e collection of data must be made in field. M a t h a t the Royal College of Forestry has advised on a collection of data by a method of random sampling t o determine the length of roads. The method may be used for work on maps as well as in field.
42 GUSTAF VON SEGEBADEN
Table 11. Total length (km) of the Swedish roads and streets as of January lst, 1963, distri- buted by the types of the roads and the surface material.
National road: road which is of great importance for t h e through long-distance traffic.
Provincial road: road other t h a n national road.
. .
Value n o t available.Road t y p e
Total length of
roads
Length f surfacec
roads
A. Public roads in rural areas
. . .
1. National roads
.
.2. Provincial r
. .
B. Roads a n d streets in towns a n d communi- ties with independ- e n t road mainte- nance
. . .
C. Private roads entitled t o financial support by subsidies . . .
Total
-
Surfaced roads per cent
96 027 1 2 102 8 3 925
1 0 8 7 9
55 223 162 129
Other
6 5 544 1 8 4 2 63 702
. .
. . Total
Icngth of gravelled
roads
Concerning t h e theoretical background of t h e method and its description Of which Oiled
reference is made t o t h e appendix "A method of estimating the total length of roads by means of a line survey" by Mafe'rn.
-
b ) Collection of data
During the current National Forest Survey, which started in 1953, the entire country is annually covered with a low percentage survey (8). Cf.
figures 19 and 20. Special problems with respect t o biology, geology or technology can then be considered and data on t h e problems can be gathered throughout t h e country in one single year. Precision desired in the total result is obtained by repeated collection for a number of years. An explora- tory collection of data on the roads called "road inventory" was made in 1956. On the basis of experiences gained a t this inventory, certain changes were made in t h e instruction for t h e field work after which the inventory has been repeated annually during t h e period 1957-1963. The recording of roads has then proceeded according to the following excerpt from t h e instruction (1 1):
s - - - special description shall be made according t o t h e following instruction for permanent roads and seasonal lorry roads t h e centre line of v h i c h is intersected by t h e survey line.
Permanent roads are trafficable all year (occasionally excluding the period of frost lift) with heavy d u t y lorries; where necessary trenched and gravelled or surfaced by some other material.
CROSS-COUNTRY T R A S S P O R T DISTAYCES AND ROAD K E T S 43 Seasonal lorry roods are planed main roads trafficable with heavy d u t y lorries or tractors in winter.
Main horse roads, roads under construction, a n d old roads no longer used for traffic due t o new roads being built are not reported.
Recording of permanent roads
The following characteristics are reported:
Ownership at intersection
Suture of road from a forestrg point of view Three different groups are reported:
S -roads v h i c h a t t h e intersection pass forest land or so near forest land t h a t timber can be hauled t o a n d piled on t h e road side. If t h e road passes land of some category other t h a n forest land, it is t o be considered as S-road provided t h e distance of t h e cross-country transport is shortened if t h e timber is piled on t h e road side. If t h e distance to t h e nearest stand margin exceeds 200 metres, however, T-road is recorded as follows.
T -roads on which timber is transported and t o which timber is n o t extracted directly.
I t is understood t h a t S-roads according t o above are also used for transport from t h e forest.
0 -other roads \\here transport of forest products does not occur.
P u b l i c or prluute roctds Ownership group
Width of t h e road
Recording of the seasonal lorry roads
Whcn there is doubt whether t h e main road is used for horse or lorry transport, t h e road is recorded ~ i i t h i n brackets.,
By "owner" is here meant t h e owner of t h e land (forest land or other land) served by the road and not the legal owner of the road.
I I I I '
II~EI rn
lmfl ID
1 12-50 krnI I I I I
Fig. 19. Approximate outline of t h e layout of t h e survey tracts.
Thin full line represents "survey line" a t t h e second National Forest Survey (1938-1952), now replaced b y "tracts" located along t h e former line
Thick 9 a H "tract"
Dashed r r boundary of "survey area" with one t r a c t surveyed per year
Tract surveyed in t h e first year - 121 )i
- ) i r second year
a. s. o.
G U S T A F VON S E G E B A D E N
Fig. 20. Division of t h e country into "regions" (I-V), the report areas of the road inventory and the tracts of one year of survey.
CROSS-COUPITTHY TRAYSPORT DISTANCES AND ROAD Y E T S 4 5 c) Computation
*kt computation t h e material collected in the field has first been checked with respect t o t h e formal correctness of t h e records. The material has also been supplemented with t h e public roads not included in the field work. According t o t h e instruction, distances over water and over large farm fields and over impediment may be obtained from the maps by means of ruler. Moreover, roads crossing over farm fields are to be reported only when t h e registration can be made wilhout great time consumption. In this case intersections between roads and the tract side may be lacking.
After this check the data have been punched on cards and sorted with respect to various factors. After sorting t h e number of intersections between roads and tract sides is obtained in each group of sorting. The road-length (Y) corresponding to the number of intersections (n) is obtained according t o formula (A 3)l:
Table 12. Theoretical land area factor at the third National Forest Survey and the actual land area factor at the surveys of 1956, 1957, and 1958.
Distance between lines a n d tracts a t Region tllc survey of
one year liln
Area per ltm of line surveyed, sq. k m Length
~ ~at tile tsurvey in ~ ~ l
one w a r * I956
1
1957I
1958*
After two years of survey t h e theoretical area per ltm of line surveyed is half t h a t pre- sented above etc.* *
From t h e 1958 survey t h e t r a c t slde in region I is 1.8 lrm and t h e area per k n ~ of line surveyed is theoretically 77.7777 ltm2.The length of the line system per unit area (t) depends on t h e length of t h e tract side and on t h e distances between lines and between tracts. These factors vary between the regions of t h e National Forest Survey (figure 19) according to table 12 where the corresponding area of land per unit of length on land surveyed in one year is presented for both t h e theoretical case (22) and the actual one. I t is assumed in t h e theoretical case t h a t t h e areas covered with water are evenly distributed over the total area and t h a t they
Formula (A 3) = formula (3) in appendix (p. 68).
46 G U S T A F VON S E G E B A D E N
are thus equally represented a t each annual survey and t h a t t h e line length surveyed is equally long each year. Actually, the representation of areas covered with water differs between years and hence t h e actual land area per unit of length surveyed on land. Moreover, t h e total line length per year varies since t h e number of survey tracts (or parts thereof on the area bound- aries) per year is not constant. A t repeated survey the actual land area factor approaches t h e theoretical one, nearly t o concur a t the end of the survey cycle. In the road inventory t h e theoretical factor has been chosen for use.
A t a division of t h e material by parts of regions (e.g. provinces) i t should be noted t h a t neither t h e nominal land area factor nor the actual one defi- nitely applies to t h e separate parts.
If t h e theoretical land area factor is used, an intersection between road and tract side corresponds t o t h e following road-length in kilometres.
Region Road inventory
1957-1960
d ) Results and accuracy
The results of 1957-1960 road inventories (denoted "road inventory 1957-60") are reported in tables 13, 14 and 15. The country has been divided into two areas (cf. figure 20):
a) North Sweden comprising t h e regions I, 11, and 111.
b) South Sweden comprising t h e regions IV and V.
The registration of t h e roads is made in four ownership groups:
State forests Other public forests Company forests Other private forests
Some data, however, are distributed b y individual regions without divi- sion into ownership groups.
B y means of t h e statistics on the area of forest land according to table 16, the road net density expressed in metres of road per hectare of forest land for various ownership groups has been computed in table 17.
CROSS-COUNTRY TRANSPORT DISTANCES AND ROAD NETS 4 7 Table 13. Public roads according to the road inventory.
Ownership group Total
1
Length of roads, k mXorth South
Sweden Sweden Sweden
. . .
State
Other public.. . . . . . .
Companies.
Other private. . . .
Total, road character S 1957-60. . . .
Total, road characters T and 0 1957-60.
Grand t o t a l 1957-60
. . .
Table 14. Private permanent roads with character S according to the road inventory.
State . . .
Other public.. . . . . . .
Companies.
. . .
Other private.
Total. road character S 1957-60.. . . .
Ownership group Total
Table 15. Seasonal lorry roads according to the road inventory.
Length of roads, k m
North South Whole of
Sweden Sweden Sweden
Ownership group Total
Length of roads, k m North Sweden
Table 18 gives a summary of the road-length and the road net density of public and private permanent S-roads distributed by regions.
To check the dependability of the method, adjustments have been made in accordance with statistics on the length of public roads from the Board of Roads and Waterways of January lst, 1960 (27).
State
. . .
Other p u b l i c . . . . . . . .
Companies.
Other p r i v a t e . . . .
Total1957-60 . . .
9 850 1 750 1 3 010 27 030 51 640
GUSTAF \.OX S E G E B A D E S
Region I 103 950
Total I1 48 621 203 882 Region 0°7
, 13 604} 92 611 296 493 r I11 51 311
Table 16. Forest land according to the National Forest Survey 1953-57.
All land except mountains, farm fields a n d roads, is considered forest land.
Table 17. Road net density expressed in metres of road per hectare of forest land according to the road inventory pertaining to public and private permanent roads with character S,
and seasonal lorry roads.
Ownership group Total
S t a t e . . . .
Other p u b l i c . . . . .
Companies.. . . .
Other private. . . .
The standard errors of t h e deterrnhations are reported in table 20.
North Sweden
Forest land area, sq. Bm
South Sweden North
Sweden
53 575 11 616 56 053 82 638
- Total
all roads Private
roads
South Sweden
5 843 5 763 1 3 976 67 029
- Total perm.
roads
-
2.2 2.6 4.3 5.1
Whole of Sweden
59 418 17 379 70 029 149 667
Seasonal lorry roads Ownership group
Public roads
S t a t e . . . . 0.7 Other public.
. . .
0.7 Companies.. . .
I .4 Other private. . . . . 2.1 Average 1957-60(
1 . 5Table 18. Permanent roads with character S distributed by regions according to the road inventory.
1
RegionI-V
64 600 150 750 215 350 296 493
2.2 5.1 7.3 Length of roads, k m
Public r o a d s . . . . .
Private roads . . .
Total, S-roads.. . . .
Forest land area, sq. linl. . . .
Road n e t density, m h e c t a r e Public roads. . . .
Private roads.
. . .
Total, S-roads.. . . . 1 3 730 17 930 31 660 103 950 1.3 1.7 3.0
9 450 1 0 860 20 310 48 621 2.0 2.2 4.2
CROSS-COUXTRY TRAXSPORT DISTANCES AND ROAD X E T S 49
The length of the roads according to the road inventories of 1956 and 1960 for four province groups and for the entire country, and the mean value of the five inventories 1956-1960 put in relation to the values of t h e official statistics have been compiled below.
I
Length of roads according t o Official R o a d inventorystatistics 1956
1
1960/
1956-1960Province groups. . . .
.
. 100.0 95.6-109.4 93.6-120.0 100.2-106.E (range of variation)o l e of d e n . .
.
. . . , . 1 0 0 0 103.8 105.7 101.2A comparison between the values of separate provinces naturally gives considerably greater deviations, especially when only one year survey is used, e.g. province of Ostergotland 1956 (65 intersections)
+
32.9 :lo;1956-1960 (65 1 59
+
45+
42+
39 intersections)+
1.5%.
This adjustment of t h e length of public roads obtained a t t h e road in- ventories to t h e length according to official statistics shows t h a t the material from t h e road inventory on the survey tracts of one year provides usable values of road-length for large areas.
The precision of the estimate of t h e length of permanent roads with t h e character S has been investigated by computations of t h e relative standard errors of the estimates. At the computations i t has been assumed t h a t the length of a road net within a region estimated by means of x intersections has a relative standard error t h a t amounts to 1 3 0 / ~ ; per cent. The formula has been obtained in a numerical n a y by means of tract systems placed on maps.
A system of tracts from the area concerned in one year has then been placed in various positions on t h e map b y parallel translations corresponding t o a certain number of replications of one year survey.
A t t h e computation of t h e relative standard error E (= standard error expressed in per cent) of the length of roads estimated of one year, the following computations have been carried out.
5
= n 1 - (xl+ x2 + . . . + x,,)
50 GUSTAF VON SEGEBADEN
where 11 = no. positions (= no. surveys) and
xl,
x,,. . . . xn
= no. inter- sections between tract sides and roads in the n positions.Table 19. Compilation for the computation of an approximate formula for the relative standard errors of the road-length estimates.
Area Region
P a r t of t h e province of Norrbotten
P a r t s of t h e units of Dalar- na, Jamtland and Halsing- land
Unit of a n g e r m a n l a n d Unit of hledelpad Province of Ostergotland Province of Kronoberg
20 Public Private All 20 Public
Private
Public Public Total
Table 19 shows a compilation for determination of E . The following ap- proximate formula for E is obtained.
'Table 20 presents t h e computed relative standard errors for the length of the permanent roads with character S , which are reported in tables 13 and 14.
Table 20. Calculated relative standard errors for permanent roads with character S according to the road inventory.
I
Xorth Sweden/
South Sweden/
Total perm.
roads
6 6 5 2 2 Ownership group
Total Public
roads
Private roads
Private roads perm.
roads
S t a t e . . .
Other p u b l i c . . . . .
. . .
Companies.
Other private. . . . Total, S-roads.. . . .
Public
'Oads
CROSS-COUXTRY TRANSPORT DISTANCES AND ROAD S E T S 51
I t appears a t a division of t h e material into small areas or ownership groups of small extent such as "other public forests" in North Sweden t h a t the separate values become rather inaccurate.
The relative standard errors computed for the length of S-roads presented in table 18 are reported in table 21.
Table 21. Calculated relative standard errors for nermanent roads with character S distributed by regions according to the road inventory.
Road t5-pe Total
The road-length obtained for each of t h e two report areas North Sweden and South Sweden shows rather good agreement between the various in- ventories as regards the total length of public roads while t h e length of private permanent roads with the character S displays a considerably greater variation. I t has therefore been considered of value t o analyze further these variations.
The relative standard error of the mean value has therefore been primarily computed for the length of public, respectively, private permanent roads with character S a t the four inventories 19.57-1960. The standard error has been computed on the basis of t h e actual results from the inventories of the separate years. Below this "standard error obtained" has been compared with the standard error computed b y means of formula (11) reported in
Region
I
/
I1/
1111
IVI
V 1 1 - YPublic r o a d s . . . . .
Private r o a d s . . . . .
1
Tota1.S-rordr . . .table 20.
" ; I 1 1 ;
5
4
1
51
41
21
31
1Public S-roads
. . .
Standard error obtained.
. . .
i) )) c o m p u t e d . . Private S-roads
. . .
Standard error obtained.
) u c o m o u t e d . . . . .
I
North Sweden/
South SwedenA t tests of significance of t h e standard errors no significant difference is obtained between t h e errors obtained and those calculated for the public roads, b u t a significant difference on t h e 0.001-level for the private roads.
The differences between t h e results of t h e various years for t h e private permanent S-roads may not be randomly conditioned only. The extension
52 GUSTXF YON SEGEBXDEN
carried out during the period for such roads, which for the years 1957-1960 is reported a t between 2 400 and 3 300 km per annum @I), cannot have any influence of importance in this context. The variations are likely caused by the difficulties a t the field work to malie a correct judgement of the carrying capacity of the roads, i.e. to make a correct distinction between permanent roads and other types of roads (e.g. cart roads and main seasonal roads).
I t may be a matter of differences in the judgement between various team leaders, as vell as between judgements made by the same team leader a t different occasions. This situation is to be expected since the judgement is subjective. The members of the survey teams generally lack the local in- formation t h a t would enable a more correct classification of the carrying capacity. The difficulty of making a correct classification of the carrying capacity has been elucidated by Hjelmstrom (10).
Differences in the classification of roads nit11 respect to the road-character should not have had any decisive influence on the variations between the inventory results of the various years for the p r i ~ a t e permanent S-roads.
This statement is vindicated by the good agreement between the obtained and the computed precision of the inventory results for the public roads with character S. Since the public roads h a r e been classified as permanent with extremely few exceptions, the judgement of the carrying capacity in this case has no influence on the variations between the various yearly inventory results.
Uniformity in the judgements made a t the road inventory, as in the other registrations in field made by the National Forest Survey, is airned a t by excursions v i t h the team leaders before the beginning of the field work season and by inspections of the field work.
The length of private permanent roads with character S presented in table 14 also includes such roads which have been subject to doubts whether they are trafficable with heavy lorries even in rainy periods (autumn). The share of "doubtful" roads reported in table 14 is 14-15 per cent of the total length.
The standard of the private permanent roads may also be elucidated t o
Table 22. Hard surfaced width of private roads with character S according to the road inven- tory.
P a r t of t h e country
Total length of roads percentage distributed by various widths (metres) of h a r d surfaced roads
Xorth Sweden..
. .
. . . ..
. .South S v e d e n . .
.
. .. .
..
. .1 1 b 1 %
CROSS-COUSTRY T R A S S P O R T DISTASCES XXD ROAD NETS 53 some extent by t h e surfaced width of t h e roads which is reported in table 22.
The table shows for t h e private permanent roads with character S t h a t about 70 per cent of such roads in North Sweden and about 90 per cent in South Sweden have a surfaced width less than 3.25 metres.
According to t h e instruction, permanent roads with character S are roads "which a t the intersection pass over forest land or so near forest land t h a t timber can be hauled t o and piled by the road". These roads thus affect directly t h e transport distance from t h e stump to the road.
By means of t h e road net densities reported in table 17 summary com- putations of t h e mean cross-country transport distance can thus be made for the various areas of registration. More accurate results are then obtained if t h e position of t h e roads in relation t o t h e forest land they serve is taken into consideration. The land category on which t h e intersection between road and tract side is situated can then give some information.
The registration of the land category a t the field work is sl~own below.
Locatjon of t h e intersection (Symbol in table 23)
011forestland
. . . (9
. . .
farm fields. (1)
. . .
other land ( 0 )
In the border line between
forest land and farm fields..
. . .
(S/I)forest land and other l a n d .
. . .
( s / 0 >farm fields and other l a n d .
. . .
(110)The division by land categories between the public and t h e p r i n t e roads with character S is presented in table 23.
Table 23. Public and private permanent roads with character S distributed by land categories according to the road inventory.
Area Road t y p e
Total
North S ~ ~ e d e n Public r o a d s . . Private r o a d s . . . .
T o t a l . . . . .
P e r c e n t . . .
/
sI
r1 o 1
s11(
S I O1
110Length of roads, km
20 730 3 560
1 i:: 1
1 7401
2.5:1
30 18040 910 4 200 4 100 1 580 51 720
61 640 7 760 1 710 7 200 3 320 270 81 900 75.3
/
9.5I
2.11
8.8 4.01
0.31
100.0South Swedcn
. . . P i c o a .
Private roads. . . . T o t a l . . . . . P e r c e n t . . .
Land category
1 7 1 0 0 9 000 340 6 9 9 0 690
1
3001
34 42063 140 17 510 540 1 6 340 1 160 340 99 030 80 240 26 510 880 23 330 1 8 5 0 640 1 3 3 450 60.1
I
19.91
0.61
17.31
1.41
0.51
100.0Total
5 2 GUSTAF YON SEGEBADEX
A t t h e continued computations i t has been assumed t h a t roads on forest land are fed with timber from both sides while roads in t h e boundary between, or on, other land categories are fed with timber from one side only; of the latter roads is therefore counted half the length. Furthermore, i t has been assumed t h a t t h e mean cross-country transport distance to roads on farm land and in t h e boundary between farm land and other kinds of land is extended by 100 metres in relation to t h a t on forest land.
A t t h e computation t h e road net adjustment has been given the limit values 1.35 and 2.00. The cross-country transport distance adjustment has been assumed to amount to 1.20.
The computation of the mean cross-country transport distance is:
. . .
S-roads, total length, k m
deduction for one-sided cross-country transport, k m . . . . .
. . .
"Adjusted length", krn.
Forest land area, sq.lim
. . .
"Adjusted road n e t density", m / h a . . .
Cross-country transport adjustment.
. . .
Road net adjustment . . .
Mean distance o n forest land, k m .
. . .
allowance 100 m for t h e land categories and 110, km . . .
Mean cross-countrv t r a n s ~ o r t distance. k m
Xorlh Sweden South Sweden
Under t h e conditions given above t h e mean cross-country transport distance from the stump t o the permanent road in North Sweden is cited a t about 1.5 k m and for South Sweden a t about 0.5 km.
Based on i.a. information in table 18 an analogous computation (however, only for V-corr = 1.60, T-corr = 1.20) of t h e mean cross-country transport distance has been made for the various regions. The result of this computation is:
1 1
RegionI
I
1
I1I
111I
IV1 v /
I-V1
I I I I II
Mean cross-country transport distance, kml 1.81
1.41
0.9/
0.41
0.4/
0.8I
In the northern area t h e permanent road net is supplemented by the sea- sonal lorry roads trafficable in winter. If the computation of the mean cross- country haulage is made with consideration taken to t h e 2.5 metres of seasonal lorry road per hectare of forest land reported in table 17, a mean
CROSS-COUXTRY T R A K S P O R T D I S T A N C E S A S D R O A D N E T S 5 5 cross-country haulage to this combined road net of 0.7-1.0 k m is obtained under conditions equal otherwise.
Primarily in t h e northern area some transport occurs in the form of cross- country transport direct t o waterways. When t h e mean cross-country trans- port distance is sought for such a combined net of permanent roads and waterways, i t should be noted when a permanent road is built within a short distance from t h e waterway and along the same t h a t t h e length of one of these transport ways only should be included in the computations.
The registration of seasonal lorry roads has also been made in the southern parts of t h e country. The results show a very great variation between t h e years, the variation being so great as to make the inventory a failure in this respect. Objective standards of classification for t h e seasonal lorry roads as- well as the private permanent roads might be required to obtain greater accuracy in the estimates.
3. Determination of length of main roads within small areas in the prov-