The Metric System in New Zealand Forestry

NEW ZEALAND FOREST SERVICE 1972

THE METRIC SYSTEM IN NEW ZEALAND FORESTRY

think metric Oxford Decimal Classification 511

New Zealand Forest Service - Information Series No. 63

THE MEI1RIC SYSTEM IN NEW ZEALAND FORESTRY

New Zealand Forest Service Wellington, 1972 (ii)

CONTENTS Page What is the metric system? 1 What advantages does the metric system have? 1 What is the SI system? 1 What are the advantages of the SI? 2 Why has this system been adopted in N.Z.? 2 Does the change involve a:ny change in the handling of figures? 2 Are there a:ny rules for using metric symbols? 4 Are there a:ny reference publications describing the use of the metric system in N.Z.? 5 What degree of precision is required in converting information? 6 What metric units will be used in forestry practice in N.Z.? 6 Are a:ny changes to measuring equipment involved in this change to metric measurement? 11 How is this changeover to occur? 11

Appendices I Conversion Factors 13 II Metric Sizes for Sawn Timber 17 III Suggested Metric Plot Sizes 19 IV Precision in Conversion 20

(The material for this booklet was compiled by I. Trotman, Senior Forester, New Zealand Forest Service, Wellington) -1-

This booklet has been prepared as an introduction to the change from imperial to metric measurement in New Zealand as it affects forestry.

WHAT IS THE METRIC SYSTEM?

The metric system was introduced in France in the 18th century as a system of weights and measures based on the metre and gram units, smaller and larger units being decimals and multiples of the primary units.

The metre, the basic metric unit of length, was originally the distance, at the melting point of ice, between the ends of a platinum bar intended to be one-ten-millionth ( 1o,o6o,ooo) part of the earth's meridian quadrant based on Paris, i.e. that portion of an imaginary circle extending through the North and South Poles and passing through Paris. Later discoveries showed that errors occurred in the calculation for ascertaining the length of the quadrant. Since 1958 the distance between the waves of electromagnetic radiation emitted by the orange-red light ray in the spectrum of the gas krypton 86 has been adopted as the of the international unit of length. A gram is the mass of a cubic centimetre of water at 4° celsius; a litre is the volume of 1 cubic decimetre of water at 4° celsius.

HAT ADVANTAGES DOES THE METRIC SYSTEM HAVE?

The main advantage is the intrinsic simplicity of the decimal it easy to learn and use. This simplicity is ticularly useful in the application of mechanical and other aids to 'otmting and similar office practice.

JIS THE SI SYSTEM?

The "Syst~me International (SI) d'Unit~s", or "International of Units", was adopted by the Eleventh General Conference on 1960. It is essentially a standardisation and system's basic units, supplementary u.nits, -2- derived units, and the decimal multiples of these (see tables 1 and 2).

Only one multiplying prefix is applied at one time to a given unit. Thus one-thousandth of a millimetre is not referred to as 1 milli millimetre but as 1 micrometre. Similarly, 1 thousand kilowatts is referred to as 1 megawatt, not as 1 kilo kilowatt.

Derived and supplementary units together with more details of the international system are described in the Standards Association of New Zealand provisional publication NZS 6501P:1971, "The International System (SI) Units and Their Application".

WHAT ARE THE ADVANTAGES OF THE SI?

'Whilst retaining the simplicity of the metric system and its decimal relationship the SI has the additional advantages of standard systematic nomenclature, logical arrangement, and regulation by an international convent.ion.

WHY HAS THIS SYSTEM BEEN ADOPTED IN N.Z.?

Briefly the system should lead to simpler and more efficient handling of weights and measures, to a considerable reduction in the time taken to learn arithmetic, to rationalisation of varieties and sizes of materials and components in industry, to savings in purchases from a broadening metric market rather than a shrinking imperial market, and to benefits in recording information by a common internationally understood system.

DOES THE CHANGE INVOLVE ANY CHANGES IN THE HANDLING OF FIGURES?

Yes, particularly in regard to the grouping of digits and the expression of decimals.

Number grouping: In many countries using the metric system the comma is used as a decimal marker instead of the decimal point. For this reason the comma will no longer be used to separate thousands.* * The comma will still be used in money transactions to avoid the possibility of forgery. -3-

TABLE 1: SI BASIC A.ND SUPPLEMENTARY UNITS* Name of unit Unit symbol

metre (length) m kilogram (mass) kg second !time) s Basic ampere electric current) A kelvin thermodynamic temperature) K candela (luminous intensity) cd mole (amount of substance) mol Supple- ( radian (plane angle) rad mentary ( steradian (solid angle) sr

* Other units related to base units and in use are: mass, tonne (103 kg) time, minute (min) hour (h) day (d) temperature, degree celsius (0 c)

TABLE 2: SI PREFIXES DENOTING DECIMAL MULTIPLES A.ND SUBMULTIPLES

Prefix Symbol Multiplication factor tera* T 1012 = 1 OOO OOO OOO OOO giga* G 109 = 1 OOO OOO OOO mega* M 106 = 1 OOO OOO kilo* k 103 = 1 OOO 2 hecto h 10 = 100 deca da 101 = 10 1 1 1 deci d 10- = 0.1 2 centi c 10- = 0.01 milli* m 10-3 = 0.001 6 micro* µ 10- = o.ooo 001 nano* n 10-9 = 0.000 OOO 001 pico* p 10-12 = 0.000 OOO OOO 001 femto* f 10-15 = 0.000 OOO OOO OOO 001 at to* a 10-18 = 0.000 OOO OOO OOO OOO 001

* Multiples and subrnultiples recommended for common use. -4-

To facilitate reading, however, numbers of more than four digits will be set out with one space between groups of three numbers:

Correct Incorrect 1000 or 1 OOO 1,000 10 OOO 10,000 or 10000 100 OOO 100,000 or 100000 Decimal notation: The point will. be retained as the decimal marker, and the following guides should be used:

(a) The decimal point is represented by the fullstop sign, e.g. 3. 3. (b) A decimal point opposite the middle of the figures, e.g. 5·5 is acceptable but not preferred.

Correct Incorrect 0.1 • 1 0.01 .01 0.001 .001

(d) The number of decimal places used conveys the degree of accuracy.

(e) It may be convenient to place the decimal point after the first digit and bring the number to its correct value by multiplying by 10n. Examples are: 8.752 x 103 instead of 8752 2.151 682 814 x 104 instead of 21 516.828 14.

ARE THERE ANY RULES FOR USING METRIC SYMBOLS?

There are several simple rules which should ensure uniformity in using the system's symbols:

(a) Capitals should generally not be used for any SI units written out in full. For a few symbols derived from peoples' names capitals are used, e.g. N for newton, Hz for hertz.

(b) Capitals are not used for the prefixes other than for the large quantities tera (T~ giga (G),and mega (M). An error in using M and m, respectively mega and milli, could be disastrous. -5-

(c) If more than one unit is referred to it is written in the plural, e.g. 2 litres, 7 grams; but note that the symbols are always the same for singular and plural, e.g. 1.72 g is the correct way of expressing 1.72 grams.

(d) Periods (fullstops) are not used after symbols except as customary at the end of a sentence.

(e) A space should be left between numbers and symbols, e.g. 15 kg not 15kg.

(f) No space is left between the prefix and symbol, e.g. cm not c m.

(g) When "per" is used, as in kilometres per hour, it should in abbreviated forms be shown by a solidus (/) not "p", e.g. km/h not kmph. 2 (h) Care should be taken when using powers, e.g. m or m3 to show square and cubic measure, as when a symbol is prefixed it is 2 the whole unit which is squared or cubed. For example, 1 cm 2 2 means (0.01 m) , i.e. 1 square centimetre, and not (0.01)(m ), which is square metre or 100 square centimetres. 160 (i) The symbol for litre is 1, but as this can easily be confused with the figure 1 it is best to write litre out in full.

ARE THERE ANY REFERENCE PUBLICATIONS DESCRIBING THE USE OF THE METRIC SYSTEM IN N.Z.?

The Standards Association of New Zealand is coordinating information from various sectors of the country into three publications. The first of these, NZS 6501P, "The International System (SI) Units and Their Application", has been published and sets out as standards the units adopted in New Zealand for most purposes. It also covers many aspects of handling the system, some of which have been summarised here.

For the first few years of the changeover there will be a need for conversion factors and conversion tables to convert quantities. The Standards A$SOciation is preparing a booklet of factors and tables which can be used to convert most of the generally used units from imperial to metric. This publication will be given a standards number, NZS 6502, and the conversion factors included are likely to be used for settling any disputes. -6-

In addition to these fairly detailed publications the Standards Association also intends to produce a loose-leaf series publication, NZS 6503, dealing with specialised matters. Number 1 of the series will be a summary of the more general interest topics contained in NZS 6501 - including information on how to use the metric system. Subsequent issues in the series will cover standards and perhaps conversion factors peculiar to specialised industries or disciplines. Forestry is such a discipline, and tha standards determined by the Forestry Metrication Committee will be included as an addition, having full status as N.Z. Standards.

Among the appendices to this present booklet are:

Appendix I: Conversion Factors Appendix II: Metric Sizes for Sawn Timber Appendix III: Suggested Metric Plot Sizes

WHAT DEGREE OF PRECISION IS REQUIRED IN CONVERTING INFORMATION?

In converting there are three major factors to be considered as regards the precision necessary:

(a) The degree of precision that went into the preparation or measurement of the figures being converted.

(b) The degree of precision required in using the converted figures.

A number of examples are discussed in appendix IV to illustrate these concepts. They follow a rather general approach and various organisations may lay down more rigid criteria for converting in special instances, e.g. timber sales. Readers are urged to study and consider the examples and their implications.

WHAT METRIC UNITS WILL BE USED IN FORESTRY PRACTICE IN N.Z.?

The Forestry Metrication Committee has selected, or endorsed where other sector committees are involved, the following units for general forestry use: -7-

LAND AREA

square me t re (m2) 2 hectare (ha) = 10 OOO m square kilometre (km2)

Areas generally greater than 1 hectare will be measured and recorded in hectares; areas generally less than 1 hectare will be recorded in square metres. For very large areas square kilometres 6 2 (10 m = 1 knt) ma:y be used in lieu· of square miles. The explanation given to the use of the above units for land area will generally apply under the conditions outlined. However, for forestry purposes some flexibility must be allowed. For example, on stock maps or in stock books, where it will be standard practice to record areas in hectares, stands or subcompartments less than 1 ha should be recorded as decimals of a hectare rather than in square metres. Similarly where large numbers of small areas are being handled which collectively total several hectares there is freedom to use either square metres or decimals of a hectare.

Appendix III gives an indication of suitable metric plot sizes.

The following are some examples of area conversion equivalents:

Original (acres): 3 5 20 75 159 Exact equiv. (hectares): 1.214 058 2.023 430 8.093 720 30.351 450 64.345 074 Rounded equiv. (to nearest 0.5 ha): 1.0 2.0 '8.0 30.5 64.5

LENGTH

metre (m) millimetre (mm) centimetre (cm) kilometre (km) Kilometres should be used for longer distances on maps, for lengths of roads, etc. Metres should be used for shorter distances such as in surveying and for measuring tree heights and log lengths. Centimetres and millimetres should be used for small measurements such as height and diameter of seedlings or the dimensions of forest insects. -8-

For examples of length conversions refer to those under Tree Measurement on p. 9, covering height, diameter, and log length.

MASS (WEIGHT) kilogram (kg) tonne (Mg) gram (g)

The basic unit of mass is the kilogram, but a tonne or megagram., which equals 1000 kg, is more suitable for expressing the weights of loads of logs. A ton and a tonne are roughly equal. For small quantities grams may be used.

Examples of imperial measurements of mass with their rounded-off metric equivalents are tabulated below:

tons 20 35 50 tonnes 20 36 51

cwt '2 5 7 kg 102 254 356

lb 2 5 kg 0.9 2.3

oz 2 5 g 57 142

LIQUID MEASURE litre (1)

millilitre (ml)

Liquid measure will normally be in litres, but in experiments millilitres (ml) may be used. Note that 1 millilitre equals 1 cubic centimetre (1 cm3). Examples of rounded-off metric equivalents of imperial liquid measures are tabulated below:

pints 0.5 2 litres 0.3 1.1

gal 2 5 litres 9 23 -9-

gal/ac 5 20 30 litres/ha 60 220 340

PRESSURE kilopascal (kPa) Pressure will be measured in kilopascals.

TREE MEASOREMENT Precision of conversion in tree measurement will depend on circumstances. (For considerations in relation to precision, turn to appendix IV. ) Height of trees will normally be expressed in metres (m), but where greater precision is required for special purposes (e.g. research) or where small seedlings are being measured centimetres or millimetres can be used. Examples of metric equivalents, rounded to the nearest 0.5 m, are:

feet 20 35 90 130 metres 6.o 10.5 27.5 39.5 Diameter of trees will normally be expressed in centimetres (cm), but again for greater precision or for measuring small dimensions millimetres may be used, e.g. seedling diameter, increment cores. Examples of conversions are:

inches 4 12 17 25 40 centimetres 10 30 43 64 102 2 Sectional area will be expressed in square metres (m ) for individual trees and for stands. In special cases, such as diameters measured in millimetres, square millimetres may be used. The diameters given in the preceding paragraph in centimetres would respectively equate to basal areas (m2) of: 0.00785 0.07069 0.14522 0.32170 0.81713 which can be restated in terms of m2 x 10-2 as: 0.785 1.069 14.522 32.110 81.713 -10-

Other examples of basal area conversions are: sq ft 2 5 10 30 2 m 0.2 0.5 0.9 2.8

sq ft/ac 35 80 200 350 2 m /ha 8.0 18.5 46.0 80.5

Volume of wood will be expressed in cubic metres (m3). It is recognised that to obtain a measure of absolute volume, measurement must normally be made over bark. Various allowances (e.g. for bark, to top diameter, etc.) are then normally applied to this absolute volume to reduce it to a realisable volume. All volume and yield tables should state what allowances have been made. Examples of conversions are:

CU ft 12 30 100 m3 0.34 0.85 2.83

cu ft/ac 700 2000 9000 m3/ha 50 140 630

Breast height point for tree diameter measurement will be 1.4 m from ground level, on the uphill side of trees on sloping ground.

LOG MEASUREMENT

Length of logs will be in metres (m). Examples of conversions:

ft 10 12 18 26 39 m 3.0 3.5 5.5 8.0 12.0 Girth will not be used. This means that indigenous logs will be scaled by diameter from the time conversion to metric measurement occurs in timber sales.

Diameter will be in centimetres (cm), stating whether over or under bark.

Volume of logs will be in cubic metres (m3), stating whether over or under bark. The general practice of selling under bark volume will continue in most areas. -11-

SAWN TIMBER MEASUREMENT

Final decisions have at present (August 1972) not been made on timber measurements, but an indication of proposed dimensions is given in appendix II.

ARE THERE ANY CHANGES TO THE MEASURING EQUIPMENT INVOLVED IN THIS CHANGE TO METRIC MEASUREMENT?

Arrangements have been made for the purchase of metallic diameter tapes and for the provision of new variable staffs for use in operating Blume Leiss and Suunto clinometers. Tables required in using these staffs are being prepared by the Forest Research Institute.

The new diameter tape has on one side markings in millimetres for linear measurements up to 6.00 metres. On the reverse markings are adjusted by a factor of pi (n) to read directly in centimetres. Directions for use will be prepared for issue with tapes and staffs should this be necessary.

Weight scales, liquid containers, surveying chains, and other requirements will gradually become available as other sectors change over to metric equipment.

HOW IS THIS CHANGEOVER GOING TO OCCUR?

The steps to be ta...~en in changing to metric measurement in forestry are:

(a) Preparation of Reference Material By the end of 1972 (Tables, conversion factors, training publications)

(b) Acquisition of Measuring By the end of 1972 Equipment (Tapes, hypsometers, etc.)

(d) Change by Forest Owners to the Metric §ystem (i) For forest statistics and From late 1972 records this change should begin as soon as convenient to the organisation. (The Forest Service will be using a dual system in all correspondence and reports during 1973.) (ii) Full implementation of the From 1 January 1974 metric system except for valuation and sales of round and sawn produce. (iii) Valuation and sale of From 1 January 1975 round and sawn produce to coincide with conversion in timber and building industries. APPENDIX I: CONVERSION FACTORS To Convert !2. Multiply By (For accurate result) (For approx. result) acre hectare _.! 0.404 686 10 acre square metres 4 046.86 centimetre inch _.! 0.393 701 10 chain (66 feet) metres (exactly) 20.116 8 20 . 2 2 ch am metres 404.686 400 -2. foot metre (exactly) 0.304 8 I 10 I-' 2 2 1 \.>I foot metre 0.092 903 0 IT I 2 2 foot /acre metre /hectare 0.229 568 1 5 f~ot3 metre3 0.028 316 9 1 35 3 3 7 foot /acre metre /hectare 0.069 972 2 TOO gallon (imperial)* litres (cubic decimetres) 4.546 09 gallon*/acre litres/hectare 11.233 6

gram ounce 0.035 274 *Note that the gallons in this appendix are imperial gallons only. Different conversion factors will be required for any quantities involving the U.S. dry gallon or the U.S. wet gallon. (Appendix I continued)

To Convert To Multiply By (For accurate result) (For approx. result) hectare acres 2.471 05 lQ 4 hundredweight tonne (=50.802 3 kg) 0.050 802 3 hundredweight/acre kilograms/hectare 125.535 inch centimetre (exactly) 2.54 lQ 4 inch metre (exactly) 0.025 4 11 kilogram pounds 2.204 62 I 5 ~ kilogram/hectare hundredweight/acre 0.007 965 89 kilogram/hectare pounds/acre 0.892 179 8 kilometre mile 0.621 371 2 8 kilometre/Ii tre mile per gallon 2.824 81 kilometre2 mi·1 e 2 0.386 102 kilopascal pound/ square inch 0.145 link metre 0.201 168 (Appendix I continued) Multiply By To Convert To (For accurate result) (For approx. result) litre (cubic decimetre) gallon (imperial)* 0.219 969 litre pints 1. 759 76 litre/hectare gallon*/acre 0.089 018 metre yards 1.09361 1 metre links 4.970 97 metre feet 3.280 84 ..1Q 3 I I-' metre inches 39.370 1 \J'I I 2 2 metre f eet 1o.763 910 11 2 2 metre yard 1.195 99 .§. 5 2 2 metre /ha feet /acre 4. 356 01 .9. 2 3 3 metre feet 35.314 7 35 metre3 yard3 1.307 95 3 metre3/ha feet /acre 14.291 4 14 mile kilometres 1.609 34 8 5 *Note that the gallons in this appendix are imperial gallons only. Different conversion factors

.~ill be required for any quantities involving the U.S. dry gallon or the U.S. wet gallon. (Appendix I continued)

To Convert To Multiplt By (For accurate result)For approx. result) mile per gallon kilometres/litre 0.354 006 2 mi·1 e 2 kilometres 2.589 99 ounce grams 28.349 5 pint litre 0.568 261 -2. pound kilogram 0.453 592 11 pound/acre kilograms/hectare 1.120 85 I I-' pound/cubic foot kilograms/cubic metre 16.018 5 7' pound/square inch kilopascals 6.89 stem/acre stems/hectare 2.471 05 stem/hectare stem/acre 0.404 686 ton (imperial) tonnes 1.016 05 tonne ton 0.984 207 yard metre (exactly) 0.914 4 2 2 metre 0.836 127 2. yard 6 yard3 metre3 0.,764 555 APPENDIX II: METRIC SIZES FOR SAWN TIMBER (Dimensions proposed for adoption by the Standards Association of New Zealand)

Minimum Cross-Section Sizes for Sawn Timber Thickness (Green) Green Width Thickness (Dry) (mm) (mm) (mm)

50 75 100 125 150 200 225 250 300

25 x x :x x x :x x x :x 19

30 x :x 25

40 :x :x x x x x x x x 35 I 50 x x x x x :x x x :x: I-' 45 -J 75 x x x :x :x: x 65 ' 100 x x x x x 90 125 115 150 140 200 180

225 205

250 230 300 280

(Note: In accordance with convention millimetres will be used for all widths and thicknesses ~ rather than centimetres.) (Appendix II continued) Standard Lengths for Sawn Timber (metres)

1.8

2.1 2.4 2.7 3.0 3.3 I t-' 3.6 (l) I 3.9 4.2 4.5 4.8 5.1 5.4 5.7 6.0 .APPENDIX III: SUGGESTED Ml!,'"'TRIC PLOT SIZES

Imperial Plot Size Metric Equivalent Suggested Metric Plot Size (ac) (m2) (m2)

0.001 4.047 4

0.003 1.2.11,.l 12

0.025 101.172 100

0.050 202.343 200

0.100 404.686 400 1 ~...J 809. ?f{2 \0 0.200 800 ! 0.250 1 011 • 715 OOO

0.500 2 023.430 2 OOO 1.000 4 046.860 4 OOO -20-

APPENDIX IV: PRECISION IN CONVERSION

The five examples in this appendix are given to show considerations to be taken into account when making conversions. . The conversion factors are taken from those listed in appendix I. -21-

(Appendix IV continued) EXAMPLE 1 AREA

A compartment is 153 acres in area. Using the factor 0.404 686 for accurate conversion of acres to hectares, obtained from Appendix I, this acreage converts to 61.9169 ha. The precision here is in all likelihood spurious, because the original acreage measure was itself probably rounded off from somewhere within the range of 152i to 153i acres. If the conversion is ta.ken to three significant figures it becomes 61.9. This is still unnecessarily precise, since 1 ha equals approximately 2.5 acres, 0.1 ha is about 0.25 acre. If instead the figure is rounded to the nearest 0.5 ha (which equals 1.25 acres) comparable accuracy is obtained. Therefore 153 acres converts to 62.0 ha. Should the original acreage have been measured to say tenths it would be in order to quote the accuracy of the conversion to 0.1 ha, e.g. 41.7 acres converts to 16.9 ha. On the other hand, when dealing with large rounded-off numbers less precision is required. For example, using the factor for accurate conversion of acres to hectares to six significant figures, 5,000 acres converts to 2023.43 ha. To give comparable accuracy 2000 ha should suffice. A point to watch is instances where the parts and the whole of an overall quantity are dealt with. Let us say that a 59 acre forest compartment has three subcompartments, A 19 acres, B 17 acres, C 23 acres.

Original Converts to Rounded to nearest o.~ ha Subcomp A 19 acres 7.689 034 ha 8.0 ha Sub comp B 17 acres 6.879 662 ha 7.0 ha Sub comp c 23 acres 9.307 778 ha 9.5 ha

Adding the rounded-off hectare equivalents we get a total area of 24.5. But if we convert the original total compartment area of 59 acres directly we get 23.876 474, which rounded to the nearest 0.5 ha is 24.0. -22-

(Appendix IV continued)

EXAMPLE 2 HEIGHT

A tree is 24 ft high. To convert accurately from ft to metres we need to multiply by 0.3048, which gives us 7.3152 m. The conversion to five significant figures is probably spurious as the original 24 ft is likely to have been a rounded-off measurement. It ma:y be thought that since 0.3 m approximates 1 ft figures could be rounded to the nearest 0.3, i.e. 0.3, 0.6, 0.9. However, 0.3 is not an exact submultiple of 1 m and would involve rounding to the following special series: feet 1 2 3 4 5 6 1 8 9 10 11 12 metres 0.3 o.6 0.9 1. 2 1. 5 1.8 2.1 2.4 2.7 3.0 3.3 3.6 (approx.)

This would involve complication rather than the simplification at which metrication is aimed.

Again, if rounded to the nearest 0.2 ma degree of accuracy greater than the original figure is implied.

Rounding to the nearest 0.5 m is therefore suggested, even though this means a small loss of precision. On this basis a tree 24 ft'high converts to 7.5 m. Should the original data be available to the nearest 0.5 ft or less it would be all right to round to the nearest 0.2 m, which is likely to be the degree of precision used in metric measurement of tree height. -23-

(Appendix IV continued)

EXAMPLE 3 VOLUME

The conversion factor for cubic feet to cubic metres is 0.028 316 9. Conversely 1 m3 = approximately 35 cu ft, which means that 0.1 m3 approximates 3.5 cu ft. In this case the conversion factor is large so that for small logs, the volume of which is currently recorded to 0.1 cu ft, it will be necessary to convert to two decimals, i.e. 0.01 m3 = 0.4 cu ft. For example, 4.5 cu ft (a 10 ft log with 8 in. small-end diameter) converts to 0.12743 m3 with five sign,ificant figures, and should be rounded to 0.13 m.3 This is somewhat more coarse than the original measurement so that in preparing volume tables original data with more precise measurements will be used to produce volumes to three decimals for small logs.

· A log volume of 42 cu ft (a 10 ft log with 19 in. small-end diameter) converts to 1.19 m3. This implies a degree of precision greater than the original measurement (i.e. 0.01 m3 approximates 0.4 cu ft), but should only one decimal (i.e. to 3.5 cu ft) be used in this case there would be an unacceptable loss of precision. -24-

(Appendix IV continued)

EXAMPLE 4 VOLUME/AREA The conversion factor for cubic feet per acre to cubic metres per hectare is 0.069 972 2. Conversely, 1 m3/ha equals approximately 14 cu ft/acre, and 0.1 m3/ha equals approximately 1.4 cu ft/acre.

In using volume to unit area measure one normally refers to large quantities which a.re well rounded, e.g.:

(a) 500 cu ft/ac probably implies ::!: 50 cu ft/ac

(b) 2,500 CU ft/ac II " ::!: 250 CU ft/ac (c) 10,000 cu ft/ac " II ::!: 500 cu ft/ac (a) converts to 34.9861 m3/ha. The decimals a.re obviously spurious but so is the precision to 4 m3/ha (57 cu ft/ac) when the original figure implies+ 50. Rounding to the nearest 10 m3/ha + 5 implies a precision to +-70 cu ft/ac, while rounding to 5 m3/ha m~ans + 2.5 m3/ha and implies-+ 35 cu ft/ac. The conversion could therefore ~e quoted as 30 or 35 m3Jha, depending on the degree of precision required.

(b) converts to 174.931 m3/ha. This situation is a little more difficult as neither 170 m3/ha (+ 5), which implies a precision of 2 approx. ::!: 70 cu ft/ac, nor 200 m /ha (± 50), which implies a precision of approx. 700 cu ft/ac, is suitable. In this case rounding to the nearest 20 m3/ha (;t 10) is probably the best approach, i.e. 180 m3/ha. (c) converts to 699.722 m3/ha. Rounding to the nearest 100 is still too coarse so round to 50, i.e. 700 m3/ha. -25-

(Appendix IV continued)

EXAMPLE 5 SECTIONAL AREA/AREA

The conversion factor for square feet per acre to square metres 2 per hectare is 0.229 568. Conversely 1 m /ha equals approximately 2 4 sq ft/acre and 0.1 m /ha approximates 0.4 sq ft/acre. 2 For example, 45 sq ft/ac (± 2.5) converts to 10.3306 m /ha. 2 With small basal areas it may be desirable to round to 0.5 m /ha, so that if this example assumes + 2.5 sq ft/ac, the metric equivalent 2 2 becomes 10.5 m /ha. Otherwi~e it would round to 10 m /ha. As 2 another example, 180 sq ft/ac converts to 41.3222 m /ha, which is 2 rounded to 41 m /ha.

A.R. Shearer, Government Printer, Wellington, New Zealand - 1972