Form Factor Variability in Khaya grandifoliola Trees in Brazil: Implications for Accurate Volume Estimation

Abstract

Form factor is a key parameter for describing tree taper and provides a simple yet effective method for estimating wood volume. However, applying a single form factor across all tree sizes and ages may lead to substantial errors in volume estimation. This study aimed to determine form factors and their ability to estimate the wood volume of Khaya grandifoliola trees across a wide range of ages (1 to 18 years) and diameters at breast height (2 to 92 cm). Using an electronic dendrometer, a total of 733 trees were scaled across Brazil to derive total and stem form factors. Wood volume was computed using Smalian’s formula, and form factors were determined and stratified for 10 diameter and 7 age classes. The form factor values ranged from 0.30 to 1.75. Mean total and stem form factors were 0.42 and 0.83, respectively, when grouped by diameter class, and increased to 0.50 and 0.93 when grouped by age class. Results revealed a consistent decrease in form factor with increasing diameter and age, indicating a gradual change in tree shape as trees mature. These findings highlight that using diameter-class specific form factors enhances the accuracy of volume estimation while maintaining the easiness of traditional methods.

1. Introduction

African mahogany (Khaya spp.) comprehends several tree species within the genus Khaya, which are gaining commercial relevance due to their high-quality, durable, and aesthetically appealing wood [1], used in a variety of applications, such as for construction, veneer, interior and exterior furniture, boat building, and medicinal purposes [2]. Around the world, Khaya species are recognized for their economic value, particularly in Central and West African countries, which have historically been the main exporters of these species from its native forests [3]. In Brazil, the cultivation of African mahogany has expanded rapidly, with stands now covering over 50,000 hectares. The most widely planted species are Khaya grandifoliola C. DC. and Khaya senegalensis (Desr.) A. Juss. [4]. In addition to its desirable wood properties, African mahogany is considered a viable alternative to the Brazilian mahogany (Swietenia macrophylla King), whose large-scale cultivation is restricted due to its high susceptibility to the shoot borer (Hypsipyla grandella) [5,6]. The relative resistance of Khaya species to this pest has made them more attractive for sustainable and large-scale forestry production in tropical regions [2,7,8].

Despite the expansion of African mahogany stands, precise and efficient tools for estimating tree volume remain limited. Accurate volume estimates are critical for forest management, inventory, commercialization, and planning [9,10]. Over the past decades, a wide range of methodologies has been developed for estimating tree volume, from simple equations to more complex remote sensing techniques [11,12,13,14]. Given that most African mahogany producers are landowners operating on a small scale, they often lack access to specialized forest inventory expertise and advanced technologies, such as machine learning algorithms [12], terrestrial laser scanning [15], and data processing tools for accurate volume estimation [16]. Moreover, direct tree volume measurement (felling trees) is typically unfeasible in operational contexts due to labor and time constraints [17], underscoring the need for simple, cost-effective tools for reliable wood volume estimation.

Therefore, accessible methods, such as form factors, become essential for accurate wood volume estimation, aiding in the decision-making process. The form factor is a numerical ratio that relates a tree’s actual wood volume to a cylinder volume, with the cylinder volume calculated using the tree’s diameter at breast height (DBH) and height. Form factors are commonly used in tree and forest wood volume estimation [18,19]. While DBH and height are easily measured in the field, form factors require prior calibration through tree scaling, which consists of successive diameter measurements along the stem, which in turn are used to determine real wood volume. Tree scaling can be performed directly or indirectly, i.e., by taking measurements of felled trees or standing trees, using specialized equipment [20].

The form factor is known to vary across species, growing conditions, silvicultural treatments, and biological attributes, such as age and tree architecture [21,22,23,24]. Although volumetric equations for Khaya species have been developed in Brazil [13,25,26,27,28,29,30,31,32], Africa [33,34,35], Malaysia [36] and Australia [37,38], these models are often limited to their fitting range. More importantly, to date, no studies have addressed the estimation of form factors for Khaya species, nor have they evaluated how these factors may vary with age or diameter class.

While research specifically on Khaya genus is relatively scarce and geographically concentrated, the underlying methodologies for volume estimation and form factor determination are well established and globally applied across many commercial species, for example for Eucalyptus sp. [20,39], Pinus sp. [40], Fagus orientalis [41], and Shorea robusta [42]. By adapting these established principles to the context of African mahogany stands in Brazil, it is possible to address existing knowledge gaps with robust, transferable solutions to a broad type of forests, allowing for easy volume calculation. The aim of this study was to establish form factor values for Khaya grandifoliola trees and to determine their variation across age and diameter classes, as well as to compare volume estimations derived from these form factors with those obtained from published volume equations for the species. It was hypothesized that the form factor varies significantly with tree age and diameter, such that the use of a single average form factor or generic volumetric equations leads to biased and less accurate estimates of tree volume. Therefore, this research sought to provide precise, simple, and operational tools for estimating tree volume, supporting landowners in forest management decisions, resource assessment, and commercialization strategies for this high-value tropical timber species.

2. Materials and Methods

2.1. Study Sites

Data were collected from Khaya grandifoliola forest stands covering a broad range of Brazilian areas, in the states of Minas Gerais, Pará and Goiás (Figure 1). The field data obtention in this study were part of continuous forest inventory campaigns carried out to describe the growth and yield of this species in Brazil, and results of these studies can be found in [1,2,7,8]. Thus, the trees selected for scaling were located near the monitored forest inventory permanent plots, in which trees of good form and with different diameters were chosen, aiming to adequality represent the full diameter distribution of the different stands at their respective ages, which have been monitored by the authors since 2014 (Figure 1).

Forest management practices for these stands were similar, adopting wide spacings (4 × 5 m and 6 × 6 m in younger stands, and 12 × 12 m in older stands in Pará state). Unlike traditional crops for pulp or energy production, such as eucalyptus stands, African mahogany is planted at lower densities, with an average of 277 trees per hectare, aiming for larger diameters for sawlogs [7]. Intensive fertilization practices were carried out in all stands, and in certain cases, irrigation systems were implemented in dry zones (such as the stands located in the Cerrado biome, in the northern part of Minas Gerais state).

2.2. Data Collection and Analysis

While felling and measuring the tree is the most common approach in forestry, it is a demanding operation and less suitable for species with long rotation periods, and alternative methods have been developed over the years to allow for the accurate estimation of the wood volume of standing trees [43,44]. Indirect tree scaling was applied in the present study, measuring diameters at different height positions of the Khaya grandifoliola standing trees to calculate volume. This was carried out using a Criterion RD 1000 electronic dendrometer (Laser Technology, Centennial, CO, USA) coupled with a TruPulse hypsometer (Laser Technology, Centennial, CO, USA). On average, 9 diameter measurements (±3) were taken along the main stem on each tree, corresponding to approximately one measurement per meter of the stem, or adjusted according to variations in stem shape and visibility. Oliveira et al. [26] compared the volume estimates of felled African mahogany with those obtained using the Criterion RD 1000. The authors reported that differences between the two methods were not statistically significant. Thus, the dendrometer’s laser technology used in the present study supports indirect volume measurements and has been successfully applied in previous forest research [26,45,46].

Two distinct form factors were computed in this study, the artificial form factor for total volume (Equation (1)) and the stem form factor (Equation (2)) for stem volume. While the artificial form factor is used to estimate the total wood volume of the tree (including wood from the main stem and the tip of the tree), the stem form factor provides wood estimates considering only the tree’s main stem, i.e., the most valuable portion of the tree. Tree stem volume was estimated using Smalian’s method [18]. To estimate the tree’s total volume, the stem volume was added to the volume of the tip section (i.e., the wood section situated between the last measured diameter, usually at the stem height, and the tree’s total height), computed as the product of the cross-sectional area at the top of the last measured section and its length, divided by three [18].

$${\mathrm{f}}_{1.3}={\displaystyle \frac{\mathrm{v}}{{\mathrm{v}}_{\mathrm{c}\mathrm{y}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{r}}}}={\displaystyle \frac{\sum \left(\frac{{\mathrm{g}}_1+{\mathrm{g}}_2}{2}\times \mathrm{l}\right)+\left({\mathrm{g}}_{\mathrm{x}}\times \mathrm{l}\times \frac{1}{3}\right)}{\frac{\mathsf{\pi }\left({\mathrm{D}\mathrm{B}\mathrm{H}}^2\right)}{40.000}\times \mathrm{H}}}$$

(1)

$${\mathrm{f}}_{\mathrm{s}}={\displaystyle \frac{{\mathrm{v}}_{\mathrm{s}}}{{\mathrm{v}}_{\mathrm{c}\mathrm{y}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{r}}}}={\displaystyle \frac{\sum \left(\frac{{\mathrm{g}}_1+{\mathrm{g}}_2}{2}\times \mathrm{l}\right)}{\frac{\mathsf{\pi }\left({\mathrm{D}\mathrm{B}\mathrm{H}}^2\right)}{40.000}\times \mathrm{H}\mathrm{s}}}$$

(2)

where $\mathrm{v}$ is the total wood volume (m³); ${\mathrm{v}}_{\mathrm{s}}$ is the stem volume (m³); ${\mathrm{f}}_{1.3}$ is the artificial form factor; ${\mathrm{f}}_{\mathrm{s}}$ is the stem form factor; g₁ and g₂ are the log’s cross-sectional areas (m²) of each section of the scaled tree; g_x (m²) is the cross-sectional area of the tip of the tree, obtained from the last measured diameter (in the crown insertion or main stem bifurcation); and l is the length of the section (m).

The productivity of African mahogany stands varies according to location and management, with more productive sites concentrated in the southeast of the country [7,8]. The range of variation in the data can be observed in Figure 2. The photos illustrate the trees’ characteristics according to three different stages of development (Figure 2).

Data were collected on 733 trees of different diameters sizes (ranging from 2 to 92 cm) and ages (ranging from 1 to 18 years, Figure 3), distributed in the different sites under study (Figure 1). The age of the scaled trees was determined using the planting date provided by the farmer and the date of data collection. The oldest stands are located in the north of the country, in the Amazon biome, and the youngest in the southeast, in the Cerrado biome. The measurements performed in each tree were: diameter at breast height (DBH), total height (H, measured as the vertical distance from ground level to the highest point of the crown), stem height (Hs, measured from ground level to the first major bifurcation of the main stem), as well as tree scaling for wood volume estimation.

The artificial and stem form factors were computed for each scaled tree, and its variation to the tree’s age and DBH was assessed. For this, diameter and age data were grouped into class intervals using Sturges rule [47] according to range of age and diameter for the 733 trees. The calculated form factor values were plotted against age and DBH to observe the pattern, and a regression analysis was fitted using an ordinary least squares method.

To evaluate the accuracy of using the calculated form factor values for estimating total and stem volume, in a comparative assessment, volumetric literature-based equations developed for Khaya genus [13,26,36,48] were applied to the database to estimate total and stem volumes. The mathematical structure of these equations is presented in

Table 1. Literature-based equations for volume estimative of Khaya spp. trees.

Equation *	Reference
$\mathrm{v}\mathrm{s}=0.0003299\times {\mathrm{D}\mathrm{B}\mathrm{H}}^{1.773}\times {\mathrm{H}\mathrm{s}}^{0.5723}$	Oliveira et al. (2018) [26]
$\mathrm{v}\mathrm{s}=0.0258+0.000056\times \left(\mathrm{D}\mathrm{B}{\mathrm{H}}^2\mathrm{H}\mathrm{s}\right)$	Gomes et al. (2024) [48]
$\mathrm{v}=0.00017\times ({\mathrm{D}\mathrm{B}\mathrm{H}}^2{\mathrm{H})}^{0.81925}$	Heryati et al. (2011) [36]
$\mathrm{v}=\mathrm{e}\mathrm{x}\mathrm{p}(-8.95236+0.86475\times \mathrm{l}\mathrm{n}\left(\mathrm{D}\mathrm{B}{\mathrm{H}}^2\mathrm{H}\right))$	Oliveira et al. (2018) [26]
$\mathrm{v}=0.001\times {\mathrm{D}\mathrm{B}\mathrm{H}}^{2.0038}\times {\mathrm{H}}^{0.5889}$	Santos et al. (2019) [13]

* vs = stem volume (m³); v = total volume (m³).

. It is important to note that the primary objective of this study is to simplify volume estimation. Therefore, it was opted to develop form factors rather than volume equations.

The performance of the most accurate volume estimation method, whether based on the average form factor, form factor by DBH class, form factor by age class, or literature-derived equations, was evaluated using traditional goodness-of-fit statistics: root mean square error (RMSE, Equation (3)), mean absolute error (MAE, Equation (4)) and the coefficient of determination (R², Equation (5)).

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{{\displaystyle \frac{{\sum ({\mathrm{v}}_{\mathrm{i}}-\widehat{{\mathrm{v}}_{\mathrm{i}}})}^2}{\mathrm{n}}}}$$

(3)

$$\mathrm{M}\mathrm{A}\mathrm{E}={\displaystyle \frac{1}{\mathrm{n}}}\sum \left|{\mathrm{v}}_{\mathrm{i}}-\right.\left.\widehat{{\mathrm{v}}_{\mathrm{i}}}\right|$$

(4)

$${\mathrm{R}}^2=1-{\displaystyle \frac{\sum {({\mathrm{v}}_{\mathrm{i}}-\widehat{{\mathrm{v}}_{\mathrm{i}}})}^2}{\sum {({\mathrm{v}}_{\mathrm{i}}-\overline{\mathrm{v}})}^2}}$$

(5)

where RMSE is the root mean square error (m³); MAE is the mean absolute error (m³), R² is the coefficient of determination (m³); ${\mathrm{v}}_{\mathrm{i}}$ is the observed volume (m³); $\widehat{{\mathrm{v}}_{\mathrm{i}}}$ is the estimated volume (m³); $\overline{\mathrm{v}}$ is the mean volume of observed trees (m³); and n is the number of trees.

3. Results

The mean form factor values and its standard deviations (SDs) were calculated by diameter class (

Table 2. Mean values of the total form factor at breast height (${\mathrm{f}}_{1.3}$) and stem form factor (${\mathrm{f}}_{\mathrm{s}}$) used for volume estimation, standard deviations (SDs) and sample sizes (n), across different diameter classes, based on measurements from 733 Khaya grandifoliola trees.

Diameter Class (cm)	n	Total		Stem
		${\mathbf{f}}_{1.3}$	SD	${\mathbf{f}}_{\mathbf{s}}$	SD
0–10	185	0.78	0.27	1.53	0.68
10–20	376	0.53	0.07	0.88	0.17
20–30	103	0.46	0.07	0.79	0.12
30–40	36	0.37	0.03	0.76	0.08
40–50	6	0.39	0.03	0.76	0.05
50–60	10	0.32	0.04	0.70	0.08
60–70	10	0.34	0.04	0.72	0.04
70–80	4	0.33	0.02	0.72	0.02
80–90	2	0.34	0.04	0.71	0.03
90–100	1	0.30	-	0.72	-
Mean		0.42	0.07	0.83	0.14

) and age class (

Table 3. Mean values of the total form factor at breast height (${\mathrm{f}}_{1.3}$) and stem form factor (${\mathrm{f}}_{\mathrm{s}}$) used for volume estimation, standard deviations (SDs) and sample sizes (n), across different age classes, based on measurements from 733 Khaya grandifoliola trees.

Age Class (Years)	n	Total		Stem
		${\mathbf{f}}_{1.3}$	SD	${\mathbf{f}}_{\mathbf{s}}$	SD
0–2	122	0.86	0.28	1.75	0.72
2–4	278	0.55	0.09	0.97	0.22
4–6	152	0.53	0.07	0.82	0.12
6–8	128	0.44	0.07	0.79	0.11
8–10	22	0.42	0.09	0.71	0.19
12–14	21	0.34	0.04	0.71	0.05
16–18	10	0.35	0.05	0.73	0.07
Mean		0.50	0.10	0.93	0.21

). The overall average form factor for total and stem volume was 0.42 and 0.83, respectively, when analyzed by diameter classes.

The average values of form factors by age class were 0.50 and 0.93 for total and stem volume, respectively, both decreasing as the tree ages, with the exception of the older trees (Table 3).

Form factor values drop as the trees get bigger and older (Figure 4), indicating that the cylindrical shape of Khaya grandifoliola trees tends to diminish with increasing age and diameter. Regression analyses showed that age is a less significant predictor for explaining the form factor trends compared to diameter, as evidenced by the coefficient of determination (R²) values from the regressions fitted for both total and stem form factors.

Methods Performance for Volume Estimation

Figure 5 illustrates the volume estimative behavior comparing estimations derived from the form factors found in this study with methods obtained from published volume equations for the genus, using data from representative trees distributed in different diameter and age classes.

Few volumetric models for African mahogany are found in the literature, and the selected volumetric models for comparative purposes (Figure 6) were not generalist, being developed for specific forest conditions. The model by [48] was fit for 9.5-year-old Khaya grandifoliola trees, with an average DBH of 21.3 cm. For [26], the fitting database included 7- and 14-year-old forests, while [13,36] fitted models for young trees of the species Khaya ivorensis, up to 5 years of age, in Malaysia and in an agroforestry system in northeastern Brazil, respectively. Those differences in the fitting environment impacted both error metrics and fitting criteria for volume estimation (

Table 4. Statistical metrics calculated for different volume estimation methodologies for total and stem volume of Khaya grandifoliola trees.

Total Volume	RMSE	MAE	R2
Oliveira et al. (2018) [26]	0.080	0.031	0.987
Santos et al. (2019) [13]	0.085	0.030	0.987
Heryati et al. (2011) [36]	0.191	0.048	0.984
Average form factor—DBH	0.188	0.053	0.986
Form factor by DBH class	0.062	0.022	0.992
Average form factor—Age	0.248	0.063	0.986
Form factor by Age class	0.086	0.033	0.987
Stem volume	RMSE	MAE	R2
Oliveira et al. (2018) [26]	0.060	0.025	0.984
Gomes et al. (2024) [48]	0.035	0.024	0.993
Average form factor—DBH	0.071	0.027	0.993
Form factor by DBH class	0.033	0.018	0.993
Average form factor—Age	0.037	0.021	0.992
Form factor by Age class	0.558	0.135	0.943

).

For both stem and total volume estimation of the present database, the best method consisted of using the form factor stratified by diameter class, providing a simple strategy of obtaining accurate estimates (Table 4 and Figure 6).

4. Discussion

The form factor plays a crucial role in accurately capturing the shape of a tree, and facilitating precise volume estimation, which is key for sustainable forest management and planning. Despite its simplicity, flexibility, and advantages in volume estimation, the form factor has received less attention compared to other methods, such as taper equations, volume equations, and form quotients [19]. As far as it is known, no published studies have yet assessed form factor of African mahogany forests with the level of detail presented here, particularly assessing the impact of tree taper over a range of ages and DBH translated into form factor values. This study is the first to describe variations in tree shape quantified by the form factor, across different tree sizes and stand development phases. As such, it offers a novel and detailed analysis that enhances the accuracy and simplicity of wood volume estimation for this species.

The form factor is a key indicator in forest measurement, working as a proxy to tree architecture, assortments and volume, correlated to height and diameter over the stem. In this study, it was observed that as trees age, they tend to assume a less cylindrical and more conical shape. Several factors, such as tree age, genetic material, spacing, and thinning regimes, trigger substantial changes in tree shape throughout its life cycle [21]. Environmental conditions, such as soil, climate, and water availability, also play a role in shaping tree form [11,49,50]. Even the scaling method can impact the form factor [51].

Similarly, it was observed that form factor values decreased with increasing tree diameter, especially the artificial form factor for total volume estimation (Table 1). This indicates that as trees grow in diameter, the shape of the trunk becomes less cylindrical and more conical, which was also described by [19,52]. In fact, form factor by diameter class for Eucalyptus saligna have already reported in the literature [39], and the results pointed out that calculating volume using form factors stratified by diameter class improved the accuracy of volume estimation, with resulting estimates closer to the actual measurements.

Studies conducted by [49,53,54,55] also estimated volume across diameter classes for other tree species in Brazil and found similar patterns to those presented in this study, with form factor values decreasing with the development of the forest. Additionally, ref. [19] presented a global literature review on form factors encompassing tropical timber and concluded that form factors decreased with DBH and age in most cases. There was a gradual decrease in the form factors, with the large trees having the lowest values. In this case, the form factor reduction from small to large trees in the stand remains constant at a certain DBH or age point, but varies with tree and site attributes [19].

As African mahogany trees can reach high volumes, any bias introduced from inaccurate volume calculations can result in large impacts. For example, ref. [56] applied the equation developed by [26] in Minas Gerais state, Brazil, to estimate volume in Nigeria. According to [57], in Benin, the lack of appropriate volume tables compels forest managers to rely on formulas established by Dawkins in 1961. As a result, they commonly adopt fixed form factor values of 0.55 for total volume and 0.70 for stem volume, regardless of tree diameter or age class and morphology of the trees. Reference [58] noted an underestimation of about 10% of the volume estimated with the form factor proposed by Dawkins for four species (Isoberlinia doka, Isoberlinia tomentosa, Anogeissus leiocarpa and Daniellia oliveri), highlighting the importance of accessing a range of form factor values according to the tree diameter size and age.

Form factors typically take a value within the range of 0–1, but exceptions can occur. Examining the form factors found in this study (Table 1 and Table 2), the highest values for stem form factor reached 1.75 in the early years. Reference [59] reported that artificial form factors for the estimation of total wood volume of Araucaria angustifolia stands only reached values lower than 1 when the stands were older than 4 years of age. Thus, the form factor of young and short trees may be greater than 1, as the cylindrical volume used as a reference is smaller than the actual wood volume. A key reason for this is that the cylindrical volume is based on the basal area at 1.3 m, with small values calculated from a relatively high position on the tree, distorting the relationship between the tree’s actual volume and the cylindrical volume [11]. However, this does not mean that the trees have a shape or volume closer to that of a cylinder, but rather that the growth of the tree’s actual volume and shape occurs out of proportion to the cylinder, especially when the trees are young and thin.

The form factors obtained for Khaya grandifoliola are consistent with those reported for other species with similar characteristics and uses. References [60,61] reported values ranging from 0.32 a 0.65 to estimate the total volume of Tectona grandis trees with different ages (1 to 36 years old), 0.54 for Toona ciliata [62], and 0.47 for Pinus taeda [52]. Regarding Brazilian native species, ref. [50] reported an average form factor for Araucaria of 0.59. Reference [63] studied twenty Amazonian species and found an average form factor of 0.87 for stem volume, close to the average value found in this study (0.83–0.93). It is noteworthy that, as African mahogany trees age and increase in size, their stem form factors reach values up to 0.70 (Table 1 and Table 2). These values align closely with the stem form factor of 0.70 recommended by the Brazilian Institute of the Environment and Renewable Natural Resources [64] for Swietenia macrophylla (native mahogany) and commonly applied in the region for volume estimation [64]. This similarity underscores the comparable stem form of the trees in this study to that of the highly valued individuals harvested under sustainable forest management plans in the Amazon [65], highlighting the potential of plantation grown Khaya spp. to serve as a sustainable substitute.

For young Khaya grandifoliola trees, up to 8 years old and with diameters up to 50 cm, the volume estimation methods assessed do not differ significantly, except for the equation of [48], which overestimated volume for small trees (Figure 5). For older and larger trees, the use of form factors stratified by DBH class significantly improved volumetric estimation, suggesting that the use of form factors by diameter class estimated volume values more accurately. Reference [49] investigated form factors for Araucaria angustifolia and found that volumetric models do not always provide superior estimation; in some cases, using an overall mean form factor can yield greater accuracy. Even so, the most precise volume estimates were obtained when form factors were stratified by diameter class. Reference [54] studied different native Brazilian trees in a transition area between the Caatinga and Cerrado biomes and concluded that the best application of form factors occurred when the trees were stratified into diameter classes. Both studies corroborate the results found in the present research, which indicated better volume estimates with the use of form factors by diameter class.

The lowest error obtained was when using the form factor by diameter class, both for total volume and stem volume estimates (Table 3). For both total volume and stem volume, the second best estimation method was through literature volumetric equations, with [26] for total volume and [48] for stem volume. This suggests that when variation in form factor is not adequately captured (in this study, by diameter class), the use of published volumetric equations may be preferable to using a single average form factor, since these equations incorporate individual tree diameter and height values. Although the literature recommends using specific form factors according to age and tree size to estimate volumes, there are still few studies published on the topic [19], especially for recent crops such as African mahogany.

The form factor method has been recommended for tree volume estimation for its simplicity, flexibility, and analytical advantages, at least, over the least-squares volume regression techniques. It is true that the sampling effort of the present study presents a lack of representative ages and diameter size, since studies have pointed out a need for 3 trees per 2.5 cm diameter class for reliable tree scaling [66], and the present study adopted an interval of 8 cm, resulting in large sample sizes in smaller classes (see Table 1 and Table 2). Above 41.4 cm, the reduced number of trees may compromise the representativeness of the estimates. Since African mahogany cultivation in Brazil is recent [4], older and large-tree stands were scarce in the database, indicating the need for future studies to refine conclusions for such trees and to improve the volume prediction for the species. Even if underrepresented, we opted for not combining the larger/older diameter/age classes, considering that the maintenance of these classes shows important trends in the data, given that these trees are close to harvesting ages, providing a better understanding of patterns in the data. Therefore, this study demonstrates that form factors significantly differ according to age and tree diameter size for Khaya grandifoliola trees, and this should be considered when estimating tree volume to improve forest management practices.

Despite the robustness of the dataset, this study presents some limitations related to data resolution and temporal scope. Although trees were stratified into diameter and age classes, the use of discrete classes may mask fine-scale variation in form factor within classes, particularly in transitional growth stages where stem form can change rapidly. In addition, while the age range (1 to 18 years) encompasses early to mid-rotation development of Khaya grandifoliola, it does not capture form factor dynamics in older stands, limiting the extrapolation of results to later maturity or long-rotation management scenarios. The cross-sectional nature of the data, obtained from trees measured at a single point in time, also restricts the ability to track individual tree form changes over time, potentially overlooking short-term growth responses to site conditions or management practices. Consequently, future studies incorporating higher-resolution measurements and long-term monitoring would improve the understanding of temporal variability in form factor and further refine volume estimation accuracy.

5. Conclusions

This study demonstrated that form factor is a valuable and practical parameter for estimating wood volume of Khaya grandifoliola, but its accuracy strongly depends on accounting for tree size and age. The observed decline in form factor with increasing diameter and age reflects progressive changes in stem shape as trees mature, emphasizing the limitations of applying a single, generalized form factor across heterogeneous stands. Using published volumetric equations requires a preliminary assessment of whether the fitting database is compatible with the estimation data. Consequently, tree-specific local form factors, volume tables, or taper equations can be applied to improve volume prediction accuracy across different ecological regions. In this study, we found that the use of locally obtained form factors by DBH class produced the most accurate volume estimates for both total and stem volume, outperforming all previously published equations tested.

By stratifying form factors by diameter and age classes, particularly by diameter, volume estimates were substantially improved while preserving the simplicity of traditional inventory methods. These findings provide important insights for forest managers and researchers seeking reliable yet operationally efficient approaches to volume estimation and support the adoption of class-specific form factors for young and developing Khaya grandifoliola stands.