**5. Differences in results**

Results of measurements and determination of the volume of logs obtained according to rules given in table 1 are compared with the value of a volume, which approaches most the geometrical volume of logs. Calculation of the "geometrical" volume of logs is based exclusively on values scanned on a regular basis according to present regulations. Thus,


By means of the same colour the same way of step realization at particular rules are indicated Table 1. The survey of rules and determined methods of the implementation of particular steps. Round Wood Measurement System 117

scanning is realizable at each equipment fulfilling requirements of given regulations. Evaluation of the "geometrical" volume results from a section method: the volume of a log is the sum of volumes of particular sections. Lengths of sections are 10 cm, which corresponds to the distance of particular measurements of the log diameter determined by present rules. The section diameter is equal to the average value from two measurements perpendicular at each other at the beginning and at the end of the section (four values), the section volume is determined as the volume of a cylinder. Thus, the determination of "geometrical volume" is realizable at any existing equipment after the adjustment of its program (software) equipment. Details are given in a table 1, where this method is termed

The comparative measurements were carried out on about 180 000 spruce logs. Dimensional and quality properties of logs correspond to logs for sawmill processing (quality class III, qualities A, B and C, classification according to Recommended rules for the measurement and grading of timber in the Czech Republic 2008, Tab. No. 13, p. 70). Supplies (deliveries) were created in 72% by logs in basic lengths 3 to 6 m with the predominance of lengths 4 and 5 m, 28% supplies were logs in combined lengths 7 to 14 m, however mainly 8 to 12 m (relatively uniform proportion). The average mid diameter of logs ranged about 27 cm. Parameters of each log (values of diameters taken horizontally and vertically at a length interval of 10 cm + measurement location + value of length) obtained by long-term operational measurements at 2 sawmills were stored and subsequently processed according to compared rules. In this way, the consistency of input data was provided. Values of particular comparative coefficients are obtained as medians of values of volumes of particular logs determined according to compared procedures but not as the comparison of total volumes of supplies (deliveries) defined according to compared rules. Values of medians differ from values of averages quite insignificantly, namely at the 4th to the 6th

The total comparison of log volume values determined according to particular rules with the comparative method of "geometrical volume" (not distinguishing properties of logs) is

The relationship between the log volume determined according to given rules and a "geometrical" volume determined according to a comparative method (i.e. coefficient) is, in the majority of procedures, substantially dependent on the log diameter and less on the log length (although not negligible). Thus, values given in the table 2 apply only to the considerable number of deliveries of saw logs (thousands logs). Dependencies on other parameters (e.g. taper, flattening) were not examined. Reasons consisted in the rather controversial practical efficiency of these dependences even in cases their effects would be proved. However, particular deliveries of logs (ordinarily 80 – 200 logs) differ in their properties and the mean value of their dimensions is often different from a long-term average. Therefore, for the practical use of given coefficients, it is necessary to specify their average values according to properties of actual deliveries. With respect to the "step character" of deviations at the determination of volume of the same log according to different procedures (mainly due to the conversion of mm to cm) standard statistical processing does not provide too objective image on actual properties of particular procedures. The graphic representation

of properties of particular procedures is well-arranged.

as "comparative".

decimal place.

given in table 2.

By means of the same colour the same way of step realization at particular rules are indicated

Table 1. The survey of rules and determined methods of the implementation of particular steps.

scanning is realizable at each equipment fulfilling requirements of given regulations. Evaluation of the "geometrical" volume results from a section method: the volume of a log is the sum of volumes of particular sections. Lengths of sections are 10 cm, which corresponds to the distance of particular measurements of the log diameter determined by present rules. The section diameter is equal to the average value from two measurements perpendicular at each other at the beginning and at the end of the section (four values), the section volume is determined as the volume of a cylinder. Thus, the determination of "geometrical volume" is realizable at any existing equipment after the adjustment of its program (software) equipment. Details are given in a table 1, where this method is termed as "comparative".

The comparative measurements were carried out on about 180 000 spruce logs. Dimensional and quality properties of logs correspond to logs for sawmill processing (quality class III, qualities A, B and C, classification according to Recommended rules for the measurement and grading of timber in the Czech Republic 2008, Tab. No. 13, p. 70). Supplies (deliveries) were created in 72% by logs in basic lengths 3 to 6 m with the predominance of lengths 4 and 5 m, 28% supplies were logs in combined lengths 7 to 14 m, however mainly 8 to 12 m (relatively uniform proportion). The average mid diameter of logs ranged about 27 cm. Parameters of each log (values of diameters taken horizontally and vertically at a length interval of 10 cm + measurement location + value of length) obtained by long-term operational measurements at 2 sawmills were stored and subsequently processed according to compared rules. In this way, the consistency of input data was provided. Values of particular comparative coefficients are obtained as medians of values of volumes of particular logs determined according to compared procedures but not as the comparison of total volumes of supplies (deliveries) defined according to compared rules. Values of medians differ from values of averages quite insignificantly, namely at the 4th to the 6th decimal place.

The total comparison of log volume values determined according to particular rules with the comparative method of "geometrical volume" (not distinguishing properties of logs) is given in table 2.

The relationship between the log volume determined according to given rules and a "geometrical" volume determined according to a comparative method (i.e. coefficient) is, in the majority of procedures, substantially dependent on the log diameter and less on the log length (although not negligible). Thus, values given in the table 2 apply only to the considerable number of deliveries of saw logs (thousands logs). Dependencies on other parameters (e.g. taper, flattening) were not examined. Reasons consisted in the rather controversial practical efficiency of these dependences even in cases their effects would be proved. However, particular deliveries of logs (ordinarily 80 – 200 logs) differ in their properties and the mean value of their dimensions is often different from a long-term average. Therefore, for the practical use of given coefficients, it is necessary to specify their average values according to properties of actual deliveries. With respect to the "step character" of deviations at the determination of volume of the same log according to different procedures (mainly due to the conversion of mm to cm) standard statistical processing does not provide too objective image on actual properties of particular procedures. The graphic representation of properties of particular procedures is well-arranged.

*The ČSN 48 0050 Standard – Manual measurement* is not nearly used in practice. It is chosen as an example because its procedure is consistent with the original Huber method and the dependence of a coefficient on the log diameter and length is (as in Huber method) very marked. (Note: Values of coefficients at sets of logs the number of which did not reach 250 were not plotted – minimum for 0.5% accuracy for 95% results at 0.04 variability determined

Results of measurements demonstrate a well-known fact that the Huber method generally overvalues small-diameter top logs and undervalues large-diameter but logs (Kolektiv 1959). The different stem form and subsequently also different evaluation of the log volume becomes also evident in connection with the log length. Regardless of the log diameter the overvaluation of short logs is higher than the overvaluation of longer logs. Particularly visible differences occur between logs in basic and combined lengths. A next diagram, Fig. 10 is well-arranged. It contains only the course of the dependence of logs of length 3 – 6 m (altogether, red course) and 7 – 14 m (also altogether, blue course). In addition to this, the

whole group of logs is evaluated regardless of the log length (green course).

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 **log mid diameter**

On the basis of measurements it is possible to state that on average:

volume. The dependence very approaches linear dependence.

Fig. 10. The relationship between the volume of logs determined according to the ČSN 48 0050 Standard – Rough timber – manual measurement and a comparative method. The dependence of the relationship on the log mid diameter (x axis) and the length of logs (logs 3-6 m and logs 7-12 m). The total dependence (not distinguishing lengths) is expressed as a green line.

 with the decline of log mid diameter by about 8 cm the value of its volume (determined according to Huber method) increases roughly by 1% as compared with geometrical

3-6 m 7-12 m total linear 7-12 m linear 3-6 m linear total

according to a control sample).

0.94 0.95 0.96 0.97 0.98 0.99 1 1.01 1.02 1.03 1.04

**volum e relation**


Table 2. The total comparison of log volume values determined according to particular rules with the comparative method of "geometrical volume" (not distinguishing log properties). The average mid diameter of logs of the basic population ranged between 29 and 30 cm.

Fig. 9. The relationship between the volume of logs determined according to the ČSN 48 0050 Standard – Rough timber – manual measurement and a comparative method. The dependence of the relationship on the log diameter (x axis) and the log length (particular runs).

Measurement of dimensions - Part 2: Roudwood. 2006 0.981072 0.980692 0.981453

timber in the Czech Republic 2008. 0.941042 0.940679 0.941406

regulations. 1990 Manual measurement 1.000764 1.000394 1.001134

regulations. 1990 Automatic measurement 0.995303 0.995149 0.995457

(log diameter in cm) 0.936393 0.936037 0.936749

(log diameter in mm) 0.984777 0.984447 0.985107

Stammholz. 2005 (generally) 0.941534 0.941172 0.941896

Stammholz. 2005 (only a method up to a diameter of 20 cm) 0.958114 0.957753 0.958474

Table 2. The total comparison of log volume values determined according to particular rules with the comparative method of "geometrical volume" (not distinguishing log properties). The average mid diameter of logs of the basic population ranged between 29 and 30 cm.

> 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 **log mid diameter [cm]**

Fig. 9. The relationship between the volume of logs determined according to the ČSN 48 0050 Standard – Rough timber – manual measurement and a comparative method. The dependence

of the relationship on the log diameter (x axis) and the log length (particular runs).

<sup>1</sup>EN 1309-2 Standard Roundwood and sawn timber –

<sup>2</sup>Recommended rules for the measurement and grading of

<sup>3</sup>ČSN 48 0050 Standard Rough timber. Basic and common

<sup>4</sup>ČSN 48 0050 Standard Rough timber. Basic and common

<sup>7</sup>Rahmenvereinbarung für die Werksvermessung von

<sup>8</sup>Rahmenvereinbarung für die Werksvermessung von

<sup>5</sup>ÖN L 1021 Vermessung von Rundholz 2006

<sup>6</sup>ÖN L 1021 Vermessung von Rundholz 2006

0.94 0.95 0.96 0.97 0.98 0.99 1 1.01 1.02 1.03 1.04

**volume relation**

*Rule Coefficient Lower 95% Upper* 

*95%* 

4 m 5 m 6 m 7-8 m 9-10 m 11-12 m *The ČSN 48 0050 Standard – Manual measurement* is not nearly used in practice. It is chosen as an example because its procedure is consistent with the original Huber method and the dependence of a coefficient on the log diameter and length is (as in Huber method) very marked. (Note: Values of coefficients at sets of logs the number of which did not reach 250 were not plotted – minimum for 0.5% accuracy for 95% results at 0.04 variability determined according to a control sample).

Results of measurements demonstrate a well-known fact that the Huber method generally overvalues small-diameter top logs and undervalues large-diameter but logs (Kolektiv 1959).

The different stem form and subsequently also different evaluation of the log volume becomes also evident in connection with the log length. Regardless of the log diameter the overvaluation of short logs is higher than the overvaluation of longer logs. Particularly visible differences occur between logs in basic and combined lengths. A next diagram, Fig. 10 is well-arranged. It contains only the course of the dependence of logs of length 3 – 6 m (altogether, red course) and 7 – 14 m (also altogether, blue course). In addition to this, the whole group of logs is evaluated regardless of the log length (green course).

Fig. 10. The relationship between the volume of logs determined according to the ČSN 48 0050 Standard – Rough timber – manual measurement and a comparative method. The dependence of the relationship on the log mid diameter (x axis) and the length of logs (logs 3-6 m and logs 7-12 m). The total dependence (not distinguishing lengths) is expressed as a green line.

On the basis of measurements it is possible to state that on average:

 with the decline of log mid diameter by about 8 cm the value of its volume (determined according to Huber method) increases roughly by 1% as compared with geometrical volume. The dependence very approaches linear dependence.

*The EN 1309-2 Standard – Roundwood and sawn timber – "Methods of measuring dimensions"* is used only rarely at timber reception (ČSN 49 0018, EN 1309-2, 2006). In the CR, its use has

> 3-6 m 7-12 m total

polynomial 3-6 m polynomial 7-12 m polynomial total

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 **log mid diameter**

Fig. 12. The relationship between the volumes of logs determined according to the EN 1309- 2 Standard – Roundwood and sawn timber – Methods of measuring dimensions and a comparative method). The dependence of the relationship on a mid diameter (x axis) and the log length (logs 3-6 m and 7-12 m). The total dependence (not distinguishing lengths) is

Properties of the EN 1309 – 2 Standard are formed by two antagonistic effects – Huber method, which is a basis of the standard and the conversion of mm values of the log mid

The Huber method tends to undervalue large-diameter logs and to overvalue smalldiameter logs. The effect of Huber method prevails in total properties of the EN 1309 – 2 Standard in the field of large-diameter logs where it manifests itself by the fall of

At the conversion of millimetre values of the mid diameter to centimetres the standard combines i.e. mm are not taken into account (values of particular measurements) and mathematical rounding (values of the diameter in places of measurements and at the

The primary "cutting off" of measured diameter values causes the total marked decline of resulting values of log volumes. It becomes evident particularly at small-diameter logs where the decline of a value of a subsequently calculated volume as compared with

not been noted at all.

0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1

expressed as a green line.

characteristics.

diameter to cm ("cutting off" mm).

expression of a resulting mid diameter).

mathematical rounding can achieve even 5 – 7%.

**v o lu m e rela tio n**

 together with the geometrical volume, logs of mid diameters about 30 cm are evaluated. Logs in basic lengths are overvaluated already from 35 – 36 cm of a mid diameter while logs in combined lengths from about 27 – 28 cm.

F. X. Huber and also other sources (Šmelko, 2003) explain this fact by the different form of a stem in its butt (large diameter) or top (small diameter) part.

The average value of mid diameters of coniferous logs delivered to sawmills in the Czech Republic ranges between 26 and 28 cm and it is possible to expect its gradual decline. It appears from this that the method mentioned above is inconvenient for consumers of the raw material (particularly logs) and, on the other hand, profitable for suppliers.

*Automatic measurement carried out according to the ČSN 48 0050 Standard* tries to express the exact actual (geometrical) volume of timber preserving the Huber method. The only possibility is to specify a mid diameter. It is calculated as the average value of all diameter measurements carried out within the nominal log length.

Results are given in Fig. 11. The course is rather balanced within the whole zone of monitored diameters. Thanks to the calculation of the log mid diameter from values taken within the whole (nominal) log length the overvaluation of small-diameter logs (typical of Huber method) is very limited. It becomes evident only at logs with a mid diameter up to about 18 cm, the volume of which is overvalued (on average) by 0.5%. The volume of logs within a mid diameter about 18 – 20 cm is evaluated according to the real volume. The volume of logs of larger diameters is evaluated similarly if they are in basic lengths (3 – 6 m). A lower than real volume (on average 0.5 to 0.7%) is evaluated only at logs of combined lengths and this deviation is rather balanced at all logs of mid diameters over 20 – 22 cm.

Fig. 11. The relationship between the volume of logs determined according to the ČSN 48 0050 Standard – Rough timber – automatic measurement and a comparable method. The dependence of the relationship on a mid diameter (x axis) and the log length (logs 3-6 m and logs 7-12 m). The total dependence (not distinguishing lengths) is expressed as a green line. The course of measured values is approximated to the polynomial of the 2nd degree.

 together with the geometrical volume, logs of mid diameters about 30 cm are evaluated. Logs in basic lengths are overvaluated already from 35 – 36 cm of a mid diameter while

F. X. Huber and also other sources (Šmelko, 2003) explain this fact by the different form of a

The average value of mid diameters of coniferous logs delivered to sawmills in the Czech Republic ranges between 26 and 28 cm and it is possible to expect its gradual decline. It appears from this that the method mentioned above is inconvenient for consumers of the

*Automatic measurement carried out according to the ČSN 48 0050 Standard* tries to express the exact actual (geometrical) volume of timber preserving the Huber method. The only possibility is to specify a mid diameter. It is calculated as the average value of all diameter

Results are given in Fig. 11. The course is rather balanced within the whole zone of monitored diameters. Thanks to the calculation of the log mid diameter from values taken within the whole (nominal) log length the overvaluation of small-diameter logs (typical of Huber method) is very limited. It becomes evident only at logs with a mid diameter up to about 18 cm, the volume of which is overvalued (on average) by 0.5%. The volume of logs within a mid diameter about 18 – 20 cm is evaluated according to the real volume. The volume of logs of larger diameters is evaluated similarly if they are in basic lengths (3 – 6 m). A lower than real volume (on average 0.5 to 0.7%) is evaluated only at logs of combined lengths and this deviation is rather balanced at all logs of mid diameters over 20 – 22 cm.

> 3-6 m 7-12 m total polynomial 3-6 m polynomial 7-12 m polynomial total

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 **log mid diameter**

Fig. 11. The relationship between the volume of logs determined according to the ČSN 48 0050 Standard – Rough timber – automatic measurement and a comparable method. The dependence of the relationship on a mid diameter (x axis) and the log length (logs 3-6 m and logs 7-12 m). The total dependence (not distinguishing lengths) is expressed as a green line. The course of measured values is approximated to the polynomial of the 2nd degree.

raw material (particularly logs) and, on the other hand, profitable for suppliers.

logs in combined lengths from about 27 – 28 cm.

measurements carried out within the nominal log length.

0.94 0.95 0.96 0.97 0.98 0.99 1 1.01 1.02 1.03 1.04

**volume relation**

stem in its butt (large diameter) or top (small diameter) part.

*The EN 1309-2 Standard – Roundwood and sawn timber – "Methods of measuring dimensions"* is used only rarely at timber reception (ČSN 49 0018, EN 1309-2, 2006). In the CR, its use has not been noted at all.

Fig. 12. The relationship between the volumes of logs determined according to the EN 1309- 2 Standard – Roundwood and sawn timber – Methods of measuring dimensions and a comparative method). The dependence of the relationship on a mid diameter (x axis) and the log length (logs 3-6 m and 7-12 m). The total dependence (not distinguishing lengths) is expressed as a green line.

Properties of the EN 1309 – 2 Standard are formed by two antagonistic effects – Huber method, which is a basis of the standard and the conversion of mm values of the log mid diameter to cm ("cutting off" mm).

The Huber method tends to undervalue large-diameter logs and to overvalue smalldiameter logs. The effect of Huber method prevails in total properties of the EN 1309 – 2 Standard in the field of large-diameter logs where it manifests itself by the fall of characteristics.

At the conversion of millimetre values of the mid diameter to centimetres the standard combines i.e. mm are not taken into account (values of particular measurements) and mathematical rounding (values of the diameter in places of measurements and at the expression of a resulting mid diameter).

The primary "cutting off" of measured diameter values causes the total marked decline of resulting values of log volumes. It becomes evident particularly at small-diameter logs where the decline of a value of a subsequently calculated volume as compared with mathematical rounding can achieve even 5 – 7%.

Cutting off (millimetres are not taken into account) at the conversion of values of measurements given in mm to whole cm and subsequently also the conversion of an average value from these data in the same way becomes evident by the marked decline of values of the volume of all logs. This decline is particularly evident at small-diameter logs (up to 26 - 27 cm). Within the range of mid diameters (15 to 26 cm) the fall ranges from about 8.5% (to 91.5%) to about 5.5% (to 94.5%) as compared to the geometrical volume. The effect of the log length is not significant at small-diameter logs. At further increasing the log mid diameter the value of the difference does not increase. However, effects of the log length start to manifest. Logs in basic lengths keep their deviation from a geometric volume on a stable value about 5.3% (94.7% value of the log geometric volume). Logs in combined lengths slightly increase the value of their deviation (at 40 cm diameter, they reach the value

Comparing the courses with the previous "ČSN EN 1309-2 (49 0018) Standard – Roudwood and sawn timber" we can state that the double "cutting off" mm units at the determination of the log mid diameter becomes evident by more than double increasing the volume

> 3-6 m 7-12 m total

polynomial 7-12 m polynomial total polynomial 3-6 m

deviations (in percent) at logs of all diameters. The trend of decline is identical.

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 **log mid diameter**

Rahmenvereinbarung für die Werksvermessung von Stammholz 2005 and a comparative method. The dependence of the relationship on a mid diameter (x axis) and the length of logs (logs 3-6 m and 7-12 m). The total dependence (not distinguishing lengths) is expressed

*Rahmenvereinbarung für die Werksvermessung von Stammholz*, a general agreement for the measurement of round timber at sawmills used in Germany tries at least partly to balance the decline described below. Therefore, at logs up to 20 cm, the conversion of measured

Fig. 14. The relationship between the volumes of logs determined according to

of a deviation about 6.2%, i.e. 93.8% geometrical volume.

0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1

as a green line.

**volum e relation**

The size of the fall of total characteristics of the EN 1309 – 2 Standard in the area of smalldiameter and large-diameter logs is also dependent on the length of logs. Volumes of logs of basic lengths both the smallest (14 – 15 cm) and large (39 – 40 cm) diameters are evaluated by the method by about 2.5 to 3% lower than it corresponds to the geometrical volume. The volume of logs in combined lengths is (in the same comparison) lower by about 3.5%. Logs of medium diameters (between about 23 and 29 cm) are undervalued equally – by about 1.2 to 1.7%. Differences between evaluations of volumes in basic and combined lengths are small in the middle zone – the volume of logs in combined lengths is usually evaluated by 0.2 to 0.3% lower, than the volume of logs in basic lengths.

*Recommended rules for the measurement and grading of timber in the Czech Republic 2008*  determine for manual and electronic measurements virtually the same procedure. At manual measurements, the log mid diameter is an average from two values measured perpendicular each other in the centre of its nominal length. Only in case of anomaly in the log centre, two measurements are carried out near the anomaly in the same distance from the log centre, the mid diameter being the average value from four measurements. Electronic measurements determine the log mid diameter from these four values always.

Note: A German general agreement *Rahmenvereinbarung für die Werksvermessung von Stammholz (2005)* defines the mid diameter determination in the same way, however, only for log diameters 20 cm.

Fig. 13. The relationship between volumes of logs determined according to Recommended rules for the measurement and grading of timber in the Czech Republic 2008 and a comparative method. Dependence of the relationship on the log mid diameter (x axis) and the length of logs (logs 3-6 m and 7-12 m). The total dependence (not distinguishing lengths) is expressed as a green line.

The size of the fall of total characteristics of the EN 1309 – 2 Standard in the area of smalldiameter and large-diameter logs is also dependent on the length of logs. Volumes of logs of basic lengths both the smallest (14 – 15 cm) and large (39 – 40 cm) diameters are evaluated by the method by about 2.5 to 3% lower than it corresponds to the geometrical volume. The volume of logs in combined lengths is (in the same comparison) lower by about 3.5%. Logs of medium diameters (between about 23 and 29 cm) are undervalued equally – by about 1.2 to 1.7%. Differences between evaluations of volumes in basic and combined lengths are small in the middle zone – the volume of logs in combined lengths is usually evaluated by

*Recommended rules for the measurement and grading of timber in the Czech Republic 2008*  determine for manual and electronic measurements virtually the same procedure. At manual measurements, the log mid diameter is an average from two values measured perpendicular each other in the centre of its nominal length. Only in case of anomaly in the log centre, two measurements are carried out near the anomaly in the same distance from the log centre, the mid diameter being the average value from four measurements. Electronic measurements determine the log mid diameter from these four values always.

Note: A German general agreement *Rahmenvereinbarung für die Werksvermessung von Stammholz (2005)* defines the mid diameter determination in the same way, however, only

> 3-6 m 7-12 m total

polynomial 3-6 m polynomial 7-12 m polynomial total

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 **log mid diameter**

rules for the measurement and grading of timber in the Czech Republic 2008 and a

Fig. 13. The relationship between volumes of logs determined according to Recommended

comparative method. Dependence of the relationship on the log mid diameter (x axis) and the length of logs (logs 3-6 m and 7-12 m). The total dependence (not distinguishing lengths)

0.2 to 0.3% lower, than the volume of logs in basic lengths.

for log diameters 20 cm.

0.9 0.91

is expressed as a green line.

0.92 0.93 0.94

0.95 0.96 0.97 0.98

**volume relation**

0.99

1

Cutting off (millimetres are not taken into account) at the conversion of values of measurements given in mm to whole cm and subsequently also the conversion of an average value from these data in the same way becomes evident by the marked decline of values of the volume of all logs. This decline is particularly evident at small-diameter logs (up to 26 - 27 cm). Within the range of mid diameters (15 to 26 cm) the fall ranges from about 8.5% (to 91.5%) to about 5.5% (to 94.5%) as compared to the geometrical volume. The effect of the log length is not significant at small-diameter logs. At further increasing the log mid diameter the value of the difference does not increase. However, effects of the log length start to manifest. Logs in basic lengths keep their deviation from a geometric volume on a stable value about 5.3% (94.7% value of the log geometric volume). Logs in combined lengths slightly increase the value of their deviation (at 40 cm diameter, they reach the value of a deviation about 6.2%, i.e. 93.8% geometrical volume.

Comparing the courses with the previous "ČSN EN 1309-2 (49 0018) Standard – Roudwood and sawn timber" we can state that the double "cutting off" mm units at the determination of the log mid diameter becomes evident by more than double increasing the volume deviations (in percent) at logs of all diameters. The trend of decline is identical.

Fig. 14. The relationship between the volumes of logs determined according to Rahmenvereinbarung für die Werksvermessung von Stammholz 2005 and a comparative method. The dependence of the relationship on a mid diameter (x axis) and the length of logs (logs 3-6 m and 7-12 m). The total dependence (not distinguishing lengths) is expressed as a green line.

*Rahmenvereinbarung für die Werksvermessung von Stammholz*, a general agreement for the measurement of round timber at sawmills used in Germany tries at least partly to balance the decline described below. Therefore, at logs up to 20 cm, the conversion of measured

cm/) by the total decline of evaluated volumes only very little – by about 0.2%. This value determined by a separate analysis is significant only at the total delivered volume of timber for a certain period (e.g. a month) or at least of whole supplies (deliveries). At particular logs, it virtually coincides with the accuracy of measurement. The practical result of the effect of allowances is different at logs in basic lengths and combined lengths. Logs in basic lengths have allowances rather exact in length (up to 2.5%) and their effect on decreasing the calculated value of the log volume ranges at a level of 0.1 – 0.2%, however, often only in hundredths percent. The effect can be statistically specified, however, it is not possible to prove it virtually by measurements at particular logs (contrary to calculations). At logs in combined lengths, larger (longer) allowances are usually left for the purpose of subsequent cross-cutting. It results in higher values of the decline of evaluated volume by 0.2 to 1.0%. Note: For the purpose of cross-cutting longer allowances than generally accepted 2 or 1.5% are locally negotiated at logs in combined lengths. In order this step to have no negative impacts on roundwood suppliers additional charges are also usually negotiated for these allowances. *ÖN L 1021 Vermessung von Rundholz* makes possible to evaluate mid diameters and subsequently also the volume of logs from values given in mm without conversion to whole

This alternative markedly approaches evaluated diameters and thus also volumes of all logs to their real geometrical values and, at the same time, avoids the decline of evaluated volumes of logs of small diameters. However, undervaluation of large-diameter logs

> 3-6 m 7-12 m total

polynomial 3-6 m polynomial (7-12 m) polynomial total

cm. Otherwise, the procedure is consistent with the previous procedure.

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 **log mid diameter**

Fig. 16. The relationship between the volume of logs determined according to the Austrian Ö-Norm L 1021 (2006) Standard and a comparative method. Values of a mid diameter are given in mm. The dependence of the relationship on a mid diameter (x axis) and the length of logs (logs 3-6 m and 7-12 m). The total dependence (not distinguishing lengths) is

characteristic of Huber method remains.

0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1

expressed as a green line.

**volum e relation**

values is not carried out. Only the calculated value of the mid diameter is converted. Thus, "only" one cutting off mm is carried out.

The described adjustment gradually balances the general characteristics of the procedure and the evaluated volume is generally approached to reality (it evaluates on average 94% geometrical volume, average deviation is 6%). However, this value is only of orientation character. In reality, it substantially depends on the diameter structure of logs in the actual delivery.

The Austrian standard *Ö-Norm L 1021 Vermessung von Rundholz* (2006) approaches Recommended rules for the measurement and grading of timber in the Czech Republic 2008 as for the determination of the log mid diameter and calculation of its volume. The log mid diameter is not determined as an average diameter but as the smaller one from diameters in both places of measurement and the position of a mid diameter is derived from a geometric and not nominal length. Thus, the place of measurement is shifted by half the length of an actual allowance towards the top end. The value of mid diameter and subsequently the log volume are thus slightly lower. The higher value of allowances (the volume of these allowances is not included into the log volume) results paradoxically in the lower evaluated diameter and volume of logs.

Fig. 15. The relationship between the volumes of logs determined according to the Austrian Ö-Norm L 1021 (2006) Standard and a comparative method. Values of a mid diameter are given in cm. The dependence of the relationship on a mid diameter (x axis) and the length of logs (logs 3-6 m and 7-12 m). The total dependence (not distinguishing lengths) is expressed as a green line.

The determination of a mid diameter as a smaller but not average value from both places of measurements becomes evident (thanks to a very small distance of both measurements /10

values is not carried out. Only the calculated value of the mid diameter is converted. Thus,

The described adjustment gradually balances the general characteristics of the procedure and the evaluated volume is generally approached to reality (it evaluates on average 94% geometrical volume, average deviation is 6%). However, this value is only of orientation character. In reality, it substantially depends on the diameter structure of logs in the actual

The Austrian standard *Ö-Norm L 1021 Vermessung von Rundholz* (2006) approaches Recommended rules for the measurement and grading of timber in the Czech Republic 2008 as for the determination of the log mid diameter and calculation of its volume. The log mid diameter is not determined as an average diameter but as the smaller one from diameters in both places of measurement and the position of a mid diameter is derived from a geometric and not nominal length. Thus, the place of measurement is shifted by half the length of an actual allowance towards the top end. The value of mid diameter and subsequently the log volume are thus slightly lower. The higher value of allowances (the volume of these allowances is not included into the log volume) results paradoxically in the lower evaluated

> 3-6 m 7-12 m total

polynomial 3-6 m polynomial total polynomial 7-12 m

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 **log mid diameter**

Fig. 15. The relationship between the volumes of logs determined according to the Austrian Ö-Norm L 1021 (2006) Standard and a comparative method. Values of a mid diameter are given in cm. The dependence of the relationship on a mid diameter (x axis) and the length of logs (logs 3-6 m and 7-12 m). The total dependence (not distinguishing lengths) is expressed

The determination of a mid diameter as a smaller but not average value from both places of measurements becomes evident (thanks to a very small distance of both measurements /10

"only" one cutting off mm is carried out.

diameter and volume of logs.

delivery.

0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1

as a green line.

**vvolume relation**

cm/) by the total decline of evaluated volumes only very little – by about 0.2%. This value determined by a separate analysis is significant only at the total delivered volume of timber for a certain period (e.g. a month) or at least of whole supplies (deliveries). At particular logs, it virtually coincides with the accuracy of measurement. The practical result of the effect of allowances is different at logs in basic lengths and combined lengths. Logs in basic lengths have allowances rather exact in length (up to 2.5%) and their effect on decreasing the calculated value of the log volume ranges at a level of 0.1 – 0.2%, however, often only in hundredths percent. The effect can be statistically specified, however, it is not possible to prove it virtually by measurements at particular logs (contrary to calculations). At logs in combined lengths, larger (longer) allowances are usually left for the purpose of subsequent cross-cutting. It results in higher values of the decline of evaluated volume by 0.2 to 1.0%.

Note: For the purpose of cross-cutting longer allowances than generally accepted 2 or 1.5% are locally negotiated at logs in combined lengths. In order this step to have no negative impacts on roundwood suppliers additional charges are also usually negotiated for these allowances.

*ÖN L 1021 Vermessung von Rundholz* makes possible to evaluate mid diameters and subsequently also the volume of logs from values given in mm without conversion to whole cm. Otherwise, the procedure is consistent with the previous procedure.

This alternative markedly approaches evaluated diameters and thus also volumes of all logs to their real geometrical values and, at the same time, avoids the decline of evaluated volumes of logs of small diameters. However, undervaluation of large-diameter logs characteristic of Huber method remains.

Fig. 16. The relationship between the volume of logs determined according to the Austrian Ö-Norm L 1021 (2006) Standard and a comparative method. Values of a mid diameter are given in mm. The dependence of the relationship on a mid diameter (x axis) and the length of logs (logs 3-6 m and 7-12 m). The total dependence (not distinguishing lengths) is expressed as a green line.

The result of different interpretation consists in using 2D and 3D measurement the

 The inspection of measuring devices (setting and accuracy of measurements) is also derived from the inspection of traditional mechanical means of measurement. It is carried out by a tape and circular measurement standards (etalons) in the static condition of a line. By means of such checking it is possible to reveal possible inaccuracies of sensing but not the effect of filtration and subsequent evaluation of the

If we suppose the use of more methods in the future, the value of the log volume (reached at the electronic measurement of timber) will correspond rather to commercial needs than to the geometrical volume. Thus, it is necessary to understand it as a "commercial volume". Following steps are derived to increase the stability of measurements (repeatability with the

It is inevitable to determine unambiguously the method of assessment and implementation of particular steps of the algorithm of data processing. Without these conditions it is not possible to determine more exactly properties of the given procedure (regulations,

 To determine exactly the method of filtration of scanned data. For the central part of a log a combined procedure is recommended removing extreme values in the first part and in the following part slightly balancing the course not fundamentally affecting or eliminating values of local roughness (e.g. stem curvature, burls, root swelling). "Sliding" conditions tend to increase total values (effects of extreme values). For end parts (butt end, top end), it is suitable to start from the regression analysis of the course

 To define particular directions where the log diameter is to be evaluated. The determination of only two measurements perpendicular at each other not determining their directions (e.g. horizontally and vertically) or without the assessment of the direction equability of the evaluated measurement at a measured log makes possible to find out minima and thus to decline the resulting value. On the contrary, the determination of searching for a minimum value right in the rule disadvantages or even

It is suitable to determine the quality of roudwood where results of measurements are still valid. The worst quality of saw logs is supposed. At the worse quality of logs (sweep, stem curvature, knots, buttress) it is possible to suppose higher misrepresenting effects of data

Properties of used procedures (mainly dependences of the value of the calculated log volume) have to be determined with respect to a reference method. The comparison of two methods is suitable only for particular cases and cannot be used for the determination of actual properties of procedures. The volume of logs determined by a reference method has to approach geometrical volume. Comparison with a geometrical volume determined e.g. by a volumetric method (Hauffe, P. & Müller, L, 2002) is ideal however laborious, time

application of which and differences in results are not affected by the rules.

specified.

mid diameter and volume.

standards). It represents:

same or near results) by any method and to reduce deviations.

of diameters in the related log part (Hunková, 2011).

filtration and thus the decline of measurement accuracy.

forbids the use of 2D sensors common at present (Janák, 2007).

defined at all) and directions where the mid diameter is evaluated. In some rules, these are determined only as "perpendicular at each other" and concrete directions are not

By its results, the procedure is comparable with the EN 1309 – 2 Standard. The higher value of the evaluated volume of logs according to the Ö-Norm L 1021 Standard by about 1% in the area of log diameters over 24 cm is caused mainly by removing the conversion of mm values of the mid diameter to whole cm not taking mm units into account. A fact that a difference obvious in the diagram is lower than a difference mentioned here causes the reduction of the log volume value at ÖN L 1021 placing the mid diameter measurement into the centre of a geometrical length and determination of the mid diameter as a lower but not average value from measurements in both places of the measuring area.

The advantage of the ÖN L 1021 Standard at the evaluation of the mm values of measurements consists in the even course of characteristics in the zone of log diameters below about 24 cm. Methods using "cutting off " mm units (although "only" once, such as EN 1309-2) show an appreciable decline in this area. However, no sawmill was found, which would virtually use the given version of Ö-Norm L 1021.
