scholarly journals A general sectional volume equation for classical geometries of tree stem

2016 ◽  
Vol 16 (2) ◽  
pp. 89-94
Author(s):  
Gildardo Cruz de León
Keyword(s):  
Positive Integer ◽  
Classical Theory ◽  
Arithmetic Mean ◽  
Statistical Nature ◽  
Stem Form ◽  
Geometric Means ◽  
Volume Equation ◽  
Forest Measurement ◽  
Volume Equations ◽  
Tree Stem

This work refers to the classical theory of tree stem form. It shows the derivation of a general sectional volume equation for frustums of solids of revolution generated by the function y2 = pnxn where, pn is a positive constant, and n any positive integer. The cylinder case presents a singular situation because of its sectional volume equation cannot be defined for n = 0 as it is known for the generating function. However, that geometry is implicit as a trivial solution of the derived equation. The known sectional volume equations for frustums of paraboloid, conoid and neiloid are particular cases of that equation for n =1, 2, and 3, respectively. The general sectional volume equation has an unexpected statistical nature. It is given as an arithmetic mean of geometric means The classical theory of tree stem form continue being present in the forest measurement teaching and research. This work could contribute to improve the understanding on that theory. 

Stem Form Changes in Unthinned Slash and Loblolly Pine Stands Following Midrotation Fertilization

1988 ◽  
Vol 12 (2) ◽  
pp. 90-97 ◽  
Author(s):  
Steven B. Jack ◽  
Earl L. Stone ◽  
Benee F. Swindel
Keyword(s):  
Loblolly Pine ◽  
Pinus Elliottii ◽  
Slash Pine ◽  
Stem Analysis ◽  
Stem Form ◽  
Cross Sectional ◽  
Pine Stands ◽  
Volume Equation ◽  
Volume Equations ◽  
Fertilization Experiments

Abstract Trees from fertilization experiments in four slash pine (Pinus elliottii Engelm. var. elliottii) and two loblolly pine (P. taeda L.) stands were subjected to stem analysis. The stands were unthinned and were between 13 and 25 years old at time of treatment. Profiles of radial width and cross-sectional area were examined to determine whether fertilization changed stem form. Proportionally greater growth on the upper stems of fertilized trees in the years immediately after treatment led to underestimating response with conventional volume equations. After 5 or more years, however, form was little changed and a single volume equation was appropriate for both fertilized and unfertilized trees.² South. J. Appl. For. 12(2):90-97.

An inequality relating means

1944 ◽  
Vol 40 (3) ◽  
pp. 253-255
Author(s):  
J. Bronowski
Keyword(s):  
Arithmetic Mean ◽  
Arithmetic Means ◽  
Geometric Means ◽  
Left Hand ◽  
Right Hand ◽  
Image Position ◽  
The Right

1. Let a, b be positive constants; and let y1, y2, …, yn be real exponents, not all equal, having arithmetic mean y defined by(here, and in what follows, the summation ∑ extends over the values i = 1, 2, …, n). Then it is clear thatsince the right-hand sides are the geometric means of the positive numbers whose arithmetic means stand on the left-hand sides. I know of no results, however, which relate the ratios and and I have had occasion recently to require such results. This note gives an inequality between these ratios, subject to certain restrictions on a and b.

scholarly journals Proofs of an Inequality

1905 ◽  
Vol 24 ◽  
pp. 45-50 ◽  
Author(s):  
R. F. Muirhead
Keyword(s):  
Finite Number ◽  
Present Article ◽  
General Type ◽  
Geometric Mean ◽  
Arithmetic Mean ◽  
Geometric Means ◽  
The Given

§ 1. The inequality of the Arithmetic and Geometric Means of n positive quantities has been proved by many different methods; of which a classified summary has been given in the Mathematical Gazette (Vol. II., p. 283). The present article may be looked on as supplementary to that summary. It deals with proofs that belong to a general type, of which the proof given in the Tutorial Algebra, §205, and that given by Mr G. E. Crawford in our Proceedings, Vol. XVIII., p. 2, are very special limiting cases. Proofs of the type in question consist of a finite number of steps, by which, starting from the n given quantities, and changing two at a time according to some law, we reach a new set of quantities whose arithmetic mean is not greater, and whose geometric mean is not less than the corresponding means of the given quantities.

Simultaneous total and merchantable volume equations and a compatible taper function for loblolly pine

1987 ◽  
Vol 17 (1) ◽  
pp. 87-92 ◽  
Author(s):  
John P. McTague ◽  
Robert L. Bailey
Keyword(s):  
Loblolly Pine ◽  
Forest Products ◽  
Raw Material ◽  
Forest Products Industry ◽  
Santa Catarina ◽  
Breast Height ◽  
Taper Function ◽  
Volume Equation ◽  
Volume Equations ◽  
Special Case

Loblolly pine (Pinustaeda L.) is an important source of raw material for the forest products industry of Santa Catarina, Brazil. Data from 159 trees were used to develop a simultaneously estimated total and merchantable volume equation, which treats total volume as a special case of merchantable volume with Dm, the diameter limit, equal to zero. By imposing a restriction on the parameters of the total and merchantable volume equation, a compatible taper function was derived that predicts diameter at breast height when merchantable height equals 1.3 m. The taper function possesses an analytic point of inflection in the lower portion of the stem.

The Risk Premium on Ordinary Shares

1995 ◽  
Vol 1 (2) ◽  
pp. 251-330 ◽  
Author(s):  
A.D. Wilkie
Keyword(s):  
Risk Premium ◽  
Geometric Mean ◽  
Arithmetic Mean ◽  
Short Term ◽  
Arithmetic Means ◽  
Price Inflation ◽  
Geometric Means ◽  
True Model ◽  
The Difference

ABSTRACTThe risk premium on ordinary shares is investigated, by studying the total returns on ordinary shares, and on both long-term and short-term fixed-interest investments over the period 1919 to 1994, and by analysing the various components of that return. The total returns on ordinary shares exceeded those on fixed-interest investments by over 5% p.a. on a geometric mean basis and by over 7% p.a. on an arithmetic mean basis, but it is argued that these figures are misleading, because most of the difference can be accounted for by the fact that price inflation turned out to be about 4.5% p.a. over the period, whereas investors had been expecting zero inflation.Quotations from contemporary authors are brought forward to demonstrate what contemporary attitudes were. Simulations are used along with the Wilkie stochastic asset model to show what the results would be if investors make various assumptions about the future, but the true model turns out to be different from what they expected. The differences between geometric means of the data and arithmetic means are shown to correspond to differences between using medians or means of the distribution of future returns, and it is suggested that, for discounting purposes, medians are the better measure.

A geometrical tree volume model based on the location of the centre of gravity of the bole

1982 ◽  
Vol 12 (2) ◽  
pp. 215-221 ◽  
Author(s):  
Robert R. Forslund
Keyword(s):  
Volume Estimation ◽  
Diameter Measurement ◽  
Stem Form ◽  
Total Height ◽  
Volume Model ◽  
Breast Height ◽  
Centre Of Gravity ◽  
Geometrical Form ◽  
Volume Equation ◽  
Diameter Outside Bark

A tree bole model describing a geometrical form in between a paraboloid and cone "paracone" has been developed. The model is based on empirical evidence that the average centre of gravity of aspen (Populustremuloides Michx.) boles without branches lies at 3/10 of the bole height from its base. Outside bark bole volume, V (cubic decimetres), can therefore be estimated nondestructively from the total height, H (metres), and the diameter outside bark, dK (centimetres), measured at a relative height, K, as follows:[Formula: see text]Based on a sample of 70 aspen stems, this equation estimates individual bole volume from total bole length or height and from a single diameter measurement, either at the 3/10 position or at the breast-height position, as accurately as Smalian's formula using seven diameter measurements. Based on the sample, the 3/10 position should be chosen over breast height wherever breast height lies below 20 or above 60% of the total height. It is important that care be taken in the measurement of the diameter due to the sensitivity of the volume equation to diameter variation. In addition to volume estimation, the paracone model provides a comparison profile around which stem form variation within and among species may be observed.

Cubic-Foot Volume for Yellow-Poplar in the Hilly Coastal Plain of Alabama

1982 ◽  
Vol 6 (3) ◽  
pp. 167-171 ◽  
Author(s):  
Michael S. Golden ◽  
Steven A. Knowe ◽  
Charles L. Tuttle
Keyword(s):  
Coastal Plain ◽  
Ratio Model ◽  
Yellow Poplar ◽  
Southern Appalachian ◽  
Volume Equation ◽  
Volume Equations

Abstract Volume equations of the form V = b0 + b1 D²H were developed to estimate total volume inside and outside bark for yellow-poplar (Liriodendron tulipfera L.) in the hilly Coastal Plain of Alabama. Volumes predicted using the outside-bark equation were determined to be different from those predicted by the comparable volume equation developed for southern Appalachian yellow-poplar. A nonlinear ratio model was developed to estimate the volume to any specified top diameter.

Constructing tree stem form from digitized surface measurements by a programming approach within discrete mathematics

Trees ◽  
2014 ◽  
Vol 28 (6) ◽  
pp. 1577-1588 ◽  
Author(s):  
Atsushi Yoshimoto ◽  
Peter Surový ◽  
Masashi Konoshima ◽  
Winfried Kurth
Keyword(s):  
Discrete Mathematics ◽  
Programming Approach ◽  
Stem Form ◽  
Surface Measurements ◽  
Tree Stem

scholarly journals Generalized stem taper and tree volume equations applied to eucalyptus of varying genetics in Brazil

2019 ◽  
Vol 49 (5) ◽  
pp. 447-462 ◽  
Author(s):  
Henrique Ferraco Scolforo ◽  
John Paul McTague ◽  
Harold Burkhart ◽  
Joseph Roise ◽  
Rafaela Lorenzato Carneiro ◽  
...  
Keyword(s):  
Model Performance ◽  
Volume Ratio ◽  
Forest Products ◽  
Single Product ◽  
Stem Taper ◽  
Volume Modeling ◽  
Volume Equation ◽  
Predictive Validation ◽  
Total Tree ◽  
Volume Equations

Lack of generalized equations has prevailed in Brazil, because it is assumed that localized or climate-specific equations are needed. This study aimed to develop generalized stem taper and volume equations applicable to 11 eucalyptus clones and evaluate if climate variation impacts the accuracy of the estimates. A total of 693 trees evenly distributed across 11 clones at 21 sites were used for model fittings and predictive validation. The penalized mixed spline (PMS) approach was developed for predicting stem taper and volume along the stem profile. The Schumacher and Hall (1933) equation was used to predict total tree volume, while volume ratio equations were applied to predict merchantable volume. For every fitted equation, an annual climatic variable was included to assess the improvement in model performance. The overall results highlighted that climatic variation does not need to be accounted for in stem taper and volume modeling. All of the equations displayed desirable accuracy, but the generalized PMS equation may be preferred when the forestry enterprise looks to furnish a range of multiple forest products. The generalized total tree volume equation, combined with the ratio equations, is highly recommended when the forestry enterprise produces a single product.

Sign in / Sign up

Export Citation Format

Share Document