A mechanical study on the mitigation of lodging in edible canna

Abstract Because edible canna is approximately 3-m tall in its latter growth stage, strong winds such as by typhoons can induce plant lodging and cause severe damage to it. To improve our previous estimations that the 1-m dwarfing of a plant mitigated 10–20% by strong wind (external force) and 50% by own weight (internal force), respectively, we re-examined these parameters in relation to rhizome yield for field-grown plants. From early middle growth stage (July–August) of edible canna, the perpendicularly projected area of above-ground biomass increased rapidly due to rapid shoot elongation. After the middle growth stage (September), the stock base radius increased and shoot inclination angle decreased until the latter growth stage (November) gradually, indicating a disturbed architecture and easy lodging. Throughout the growth period, we observed no radial, directional difference in the leaf area distribution. Increase in the distance between the ground surface and the center of gravity of shoot weight and decrease in the shoot inclination increased the components of the internal force. The easiness to fall down (percentage own-weight invasion moment) of plant became maximal in the latter growth stage. We conclude that approximately 50-cm dwarfing of the plant with minimal loss of rhizome yield (as low as approximately 20%) and the maintenance of lodging tolerance is optimal. In such a situation, both external and internal forces are mitigated by approximately 30%.


Introduction
Edible canna is a prospective plant resource that is domesticated in Andean Regions (Gade, 1966;Ugent et al., 1984). Presently, it is cultivated on a small scale at scattered locations in sub-tropical to tropical areas without intensive breeding, and it is used for several purposes such as direct food, animal food, a source material of starch, and local medicine (Imai, 2011(Imai, , 2014National Research Council, 1989;Roth & Lindorf, 2002). The net photosynthetic rate of edible canna is moderately high among C 3 species (Imai & Ichihashi, 1986;Kato & Imai, 1996), and its potential productivity is thought to be very high (Imai et al., 1993(Imai et al., , 1994Yamamoto et al., 2010).
Although the superior structure and physical characteristics of roots (Hosoi & Imai, 2002) and the mushroom shape of the root system well support its tall and heavy stand with a high leaf area index (Hosoi & Imai, 2003), edible canna is intolerant to strong winds and heavy rains when low-pressure systems (e.g. typhoons) pass through during its latter growth stage (Imai et al., 1994). Based on our mechanical studies, important causal factors of lodging were determined to be the large projected area (mostly composed of leaves), which is acted upon by external forces such as wind, and the own-weight moment, which is affected by the internal force of its heavy aerial weight (Hosoi & Imai, 2004). In edible canna, the types of lodging include fallen-down, stem-bending, and stem-breaking, as reported for rice (Miyasaka, 1970) and maize (Minami & Ujihara, 1991; Figure 1). Reduction of plant height is a practical strategy for protecting plants from lodging. We previously evaluated plant architecture in terms of leaf area, internal force by own shoot weight, and external force by wind. The results indicated that a desirable plant height at the latter growth stage was about 2 m (about 33% shorter than the original height), which mitigated about 10-20% of the external force by decreasing the projected area and internal force by about 50% (Hosoi & Imai, 2004). However, the results did not indicate how much decreased the rhizome yield. Moreover, from our experiences of edible canna cultivation at field sites, 1 m of shortening seemed too severe to maintain a high level of productivity.
In the present experiment, therefore, we re-evaluated the external and internal forces in relation to yield loss. By choosing related parameters and using regression equations with higher correlation coefficients, we calculated the appropriate plant height with minimum sacrifice of the expected rhizome yield. CLASSIFICATION agronomy & crop ecology of 75 g m −2 as a basal application. Plants were cultivated under rain-fed conditions with appropriate weeding by hand and without additional fertilizer. Meteorological data (solar radiation, air temperature, and rainfall) were recorded at the experimental site and expressed as 10-day averages, as shown in Figure 2.

Measurement and calculation of plant attributes
On 6-8 July, 17-19 August, 28-30 September, and 9-11 November in 2007 and 11-12 July, 18-19 August, 26-28 September, and 1-3 November in 2008, the 'external force' (the wind force on their shoots) and 'internal force' (generated by the plant's own weight) were measured for each of 10 medium-sized plants. , v is wind speed (unit: m s −1 ), C d is a resistance coefficient (reflecting the pliability of the plant depending on species, form, and wind speed), and S is the perpendicularly projected side-view area of the plant (units: m 2 ) that receives wind (Karizumi, 2010). As an important component of F, we investigated the role of S in the present experiment. In general, S has a three-dimensional structure (Shi-igai, 1993); however, we simplified it to two dimensions. The S values of the aboveground parts (leaves and stems), which show growth vigor, are very large during the latter growth stage of edible canna and are determined by three parameters (plant height, width of stock base, and stand angle). To proceed evaluations, we first compared the 'measured projected side-view area (S mea , units: m 2 )' and the 'calculated projected side-view area (S cal , units: m 2 ). ' Here, each of S mea and S cal is comparable to S by multiplying by 2.
(a) S mea : We took digital photographs from four directions (north [0 rad], northeast [.785 rad], east [1.571 rad], southeast [2.356 rad]) by arranging a scale (.3 m × .3 m styrene board) beside the plants. The photographs were uploaded to a computer and cutting of the plant images was conducted using graphic software (Adobe Photoshop 6.0, Adobe Systems Inc., San Jose, U.S.A.). The images were black-colored on a white background and divided into two portions at the center point of the stock base. Based on these images, S mea was obtained using area-estimation software (LIA for Win32, by K. Yamamoto, Nagoya Univ., Nagoya, Japan).

Plant materials
On 21    (b) S cal : As shown in Figure 3, the plant material tends to spread exterior and a sector (fan shape: S 1 + S 2 ) from the virtual point can be obtained: the fan shape begins underground and passes through the centerline of the stock to the terminal point of plant height (Hosoi & Imai, 2004). At first, we obtained S 1 (= temporary S cal ) by subtracting the area of a right triangle (S 2 ) from the sector. For the calculations, we measured the plant height (h, units: m), stock base radius (r, units: m), and inclination angle between the outmost shoot and the ground surface (θ out , units: rad, 0 ≤ θ out ≤ 2 ). After the calculation of the temporary S cal value on the right side of Equation (2) (without K), we plotted the temporary S cal and corresponding S mea values ( Figure  4). The linear regression coefficients K were regarded as correction coefficients. We applied these to Equation (2) and obtained S cal :

Evaluation of projected side-view area distribution.
The plant form develops vertically during July and August (early mid-growth stage) due to rapid shoot elongation, and it develops horizontally after September (mid-growth stage) due to the shoot inclination caused by its own weight increment and rhizome swelling. Especially after September, the plant form tends to be disturbed, and the distribution of the side-view area becomes unbalanced; thus, lodging is easily induced. In the present experiment, we examined the distribution of the projected side-view area during the four growth stages of edible canna (with reference to the quantitative evaluation of soybean form by image analysis; Ninomiya & Shigemori (1991)). (a) XD ( Figure 5(A)): This parameter shows the distance between main axis taken at the center point of stock width and mean position of vertically sectioned canopy frequency (unit: m). Converted plant images used for the measurement of the projected side-view area were vertically split into 20 sections (numbered 1-20 from left to right), and the number of section pixels fx(i) was counted using graphic software (Adobe Photoshop 6.0, Adobe Systems Inc., San Jose, U.S.A.). Thereafter, the frequency distributions of the proportion of pixels for individual to total sections Fx(i) were calculated as follows: The center point of a stock in the projected side-view was fixed as the main axis. The plant height (h, units: m), the stock breadth (b, units: m), and the distance between the main axis and the left side of the stock (AXS, units: m)  notes: h: plant height, r: stock base radius, θ out : inclination angle between outmost shoot and ground surface, S 1 + S 2 : area of fan shape, S 1 : temporary calculated projected side-view area, S 2 : area of right-angled triangle under ground surface.  Because h was fixed at 1 m, we calculated the mean position in terms of YM using the following equation:

Internal force
The internal force (units: N) exerted by the shoot weight can be expressed as where W a (units: N) is the static load of the above-ground parts, L is the distance (units: m) between the ground surface and the center of gravity of the shoot, and θ (units: rad) is the angle between the ground surface and shoot (i.e. the shoot inclination angle; Hozyo, 1976 were calculated using area estimation software (LIA for Win32, by K. Yamamoto, Nagoya Univ., Nagoya, Japan). Because XD (units: m) changes markedly during growth, we transformed b by fixing h to 1 m for all of the plants and normalized it as b*: Based on the calculated b*, the mean position (XM, units: m) was calculated by summing the products of each sectional Fx(i) and the distance between the left side of the stock and the center point of each section, as follows: XD was calculated by taking absolute values of (XM − AXS).
(b) YM ( Figure 5(B)): This shows the mean position of horizontally sectioned canopy frequency (unit: m). Converted plant images used for the measurement of the projected side-view area were horizontally divided into 20 sections (numbered 1 to 20 from bottom to top), and the number of section pixels fy(i) was counted using graphic software (Adobe Photoshop 6.0, Adobe Systems Inc., San Jose, U.S.A.). Thereafter, as in the case of XM, frequency distributions of the proportions Fy(i) of pixels in the individual sections to the total number of pixels were calculated as follows:

Statistical data analysis
Regression analysis between the plant parameters was conducted using software (Excel Statistics 2010 for Windows, Social Survey Research Information Co. Ltd., Tokyo, Japan). For each plant parameter in different growth stage of edible canna in 2007 and 2008, one-way ANOVA was conducted and afterward, Fisher's LSD tests were applied to determine the significant difference among each value as shown in Tables 1 and 2.

External force
We plotted the relationships between r and h, rhizome FW and mean θ, r and θ out , and h and θ out as bases to compose Tables 1 and 2 Table 1. S mea increased markedly from July to August in 2007 and from August to September in 2008, which was in accordance with a concurrent increase in h. It then (M max-shoot/stock , units: N m) was calculated by examining the maximum load tolerable by the shoot (after Matsuo et al., 1986). The load value was read when the relevant shoot completely fell down. The reading was achieved using a string connected to a pulley, with one side connected to the shoot's center of gravity and the other side connected to the hook of a spring balancer. The percentage internal force due to the shoot's own weight (percentage M shoot/ stock ) was calculated by M shoot/stock / (M shoot/stock + M max-shoot/ stock ) × 100 (after Hosoi & Imai, 2004). The rhizome fresh weights (FW, units: kg) of the fallen-down plants were also measured.

Mitigation effects
In the present experiment, we compared the mitigation effects of the external and internal forces and the degree of yield loss using regression equations and choosing the largest coefficient of determination. Initially, we calculated the correlations between h and shoot FW in November (Figure 8(A)). Using these, we converted all shoots longer than the target plant length to the target plant length and their expected shoot FW values; thus, we calculated M and %M. Next, using the regression equations between aboveground FW and rhizome FW (Figure 8(B)), we obtained the rhizome FW values expected after shortening of aboveground parts (using the corresponding above-ground FW). Finally, we calculated S cal with changes of .1 m in h and without changing r, θ, or K. notes: S mea : measured projected side-view area. S cal : calculated projected side-view area. h: plant height. r: radius of stock base. θ out : inclination angle between outmost shoot and ground surface. XD: distance between main axis and mean position of canopy frequency obtained by vertical sections of S mea (Figure 5(a)). YM: mean position of canopy frequency obtained by horizontal sections of S mea (Figure 5(B)). in each item, values with the same letter are not significantly different at 5% level of probability (n = 10).  is the distance from the top of the canopy). In their experimental plants (soybean), YM ranged from .3068 to .46 m, and the average was .3898 m. In our plants (edible canna), YM (.5122 m to .6221 m) was higher than was reported for soybean plants; therefore, our values did not so strongly affect lodging.

Internal force
Equation (8) indicates that the internal force (M) is influenced by above-ground shoot FW, L, and θ. There were high correlations between the shoot length and L in July to November (Figure 7). L was approximately one-third of shoot length in July and August and after September, it had slightly higher regression coefficient, indicating that L expanded to upper portion because the larger size of upper leaves and the loss of dead lower leaves tended to increase the height of the plant mass concentration. Also, M shoot and M max-shoot increased with growth because of increases in shoot FW and L (data not shown), and θ out decreased in the latter growth stages (Table 1). These suggest plants are getting easy to lodge with progressing growth stage. Table 2 (Table 2).

Countermeasures for lodging
In edible canna, S mea (i.e. comparable to S by multiplying by 2) in November sometimes exceeds 2 m 2 , which is far increased gradually from September to November in both years due to the stagnation of h, increased r, and decreased θ out , in parallel with rhizome thickening. S, h, and r values in August 2007 were greater than those in 2008, because greater solar radiation and higher temperatures during May and June (Figure 2) promoted the initial growth of the edible canna. After September, these values reversed due to the typhoon strike in 2007. The trends in S, h, and r were similar to the ontogenetic change in above-ground growth of edible canna previously observed with and without typhoon attack (Imai et al., 1993(Imai et al., , 1994. Both in 2007 and 2008, the K (regression coefficient shown in Figure 4) value of S cal decreased during September to November. K < 1.0 indicates that the standing crop has scarce mutual shading by leaves and stems. In contrast, K > 1.0 indicates that many of the plant parts are located outside the projected side-view area. Therefore, in the present study, the mutual shading by leaves and stems of a stock was larger during July and August than during September and November, when K declined due to an increased number of ruptured and dead leaves and an increased inclination of shoots. Furthermore, K in November 2007 was smaller (.609) to that in November 2008 (.647) because the plant architecture was disturbed for a substantial period by the typhoon strike in September 2007.
The plant form disturbance by the typhoon greatly affected XD; in September 2007, it increased to its maximum value of .1306 m. Among all of the edible canna growth stages, this value was the largest, and most of the plants were affected by lodging. XD of the edible canna decreased to .0707 m in November 2007, probably because the fallen-down shoots somewhat recovered their architectures and reduced the horizontal canopy form distributions. Also, after September 2008, several shoots fell to the ground; however, XM was not affected, and hence, XD was also not affected markedly (data not shown). Once a plant lodges, its canopy architecture is greatly disturbed and XD sustains high values; thus, the plant lodges with increased ease. In the case of soybean plants, Ninomiya & Shigemori (1991) reported that XD ranged from .0115 m to .2756 m, with a mean value of .0982 m.
YM attained its maximum in November, both in 2007 and 2008 (Table 1), which suggests that the projected area occupied by flower clusters was very small; thus, the frequency of plots including flower clusters was small (data not shown). YM after September 2007 was larger than that in 2008 because the upper part of the canopy was broken and/or lost due to the typhoon and the S value of the upper part of the canopy was decreased. Ninomiya & Shigemori (1991) emphasized that soybean plants are tolerant to lodging, i.e. that with larger YM, plants are more tolerant to lodging due to the location of the projected area becoming converged in the lower canopy (since YM canna forms many rhizomes, and these become thick by pushing aside the stems. However, the decline of θ is necessary for the formation and swelling of rhizomes. h is correlated with the leaf area, and if h is too low, a yield decline is induced due to decreased whole-plant photosynthesis. On the other hand, if h is too high, lodging is triggered by way of large L and shoot FW. Therefore, it is necessary, to a certain degree, to shorten h from the current value after the middle growth stage. Shortening h induces the lowering of S, L, and above-ground FW; thereby reducing M. The above-ground parts of edible canna are prone to over-luxuriant growth because solar energy absorption in the canopy of this plant attains equilibrium during the middle growth stage (120 days after planting; Yajima et al., 1988) and partial shoot cutting increases the root/top ratio by improving the light-interception characteristics (Toyohara & Nishiyama, 1985). The number of shoots is an important component in the smooth formation of yield via stock base enlargement and new rhizome thickening. Hosoi & Imai (2004) calculated S cal and M; by considering the solar energy absorption in the canopy and the leaf area index, they concluded that the optimal h of edible canna was about 2 m. Table 3 shows results of the calculation of parameters in relation to lodging mitigation effect by changing potential plant height from 2.0 to 3.0 m. In 2007, there was no mitigation effect on M stock or %M stock at h = 2.6 m. Negative values were obtained above 2.7 m, probably because of the lodging induced by the typhoon. The results of the calculation in 2008 seemed to be more reliable than those in 2007. All of the parameters in 2008 decreased linearly with increasing h. The optimal plant height in this case (h and shoot FW were changed; r and θ out were unchanged) was 2.4 m, and the mitigations of S cal , M stock , %M stock , and rhizome FW reduction were 35.55, 36.81, 31.76, and 11.28%, respectively. To improve accuracy of the results, we varied r and θ out . Accordingly, we examined the correlations of not only the November data, but also those of four growth periods (July−November). However, there were low negative correlations between r and θ out (Figure 6(C)), and between h and θ out (Figure 6(D)). Also, there were very poor correlations between h and r in the November data (Figure 8(C)), although high correlations were obtained between these parameters when data from four growth periods (July−November) were included in the equation (2008> 2007Figure 8(D)). Thereafter, we calculated r at various values of h. We converted individual plants with r values larger than the calculated r value to the calculated r value and obtained S cal without changing θ out or K (Table  4). In response to the lowering of h, the absolute value and mitigation effect of S cal were larger than those presented in Table 3. greater than for other reported crop species [e.g. 65 cm 2 in barley (Hordeum vulgare L. cv. Haganemugi; Udagawa & Oda, 1967), 42 cm 2 in wheat (Triticum aestivum L. cv. Norin 61; Udagawa & Oda, 1967), and 1,424 cm 2 in soybean (Glycine max (L.) Merr.; Ninomiya & Shigemori, 1991)]. The parameters largely influencing S are h, r, and θ. These increased rapidly during July and August. However, this period saw typhoon strike as we met in 2007. The expansion of r correlates with rhizome thickening and is necessary for horizontal expansion because of an increased number of rhizomes in the latter growth stage. A larger θ is desirable for M; however, in the latter growth stage, edible poor above-ground growth); therefore, the rhizome FW was underestimated. Therefore, Figure 8(E) was not suitable for estimating rhizome FW, even though the correlation was high.
Finally, we examined the results of regression analysis (Figure 8(F)). Although the correlation coefficient of Figure  8(F) was determined to be lower than that of Figure 8(E), the rhizome FW reduction rates at h = 2.5 m in 2007 and h = 3.0 m in 2008 were, 5.27 and 5.97%, respectively. These are closer to 0% than those obtained by the regression equation in Figure 8(E); therefore, we decided that use of the regression equation in Figure 8(F) was reasonable. To obtain Figure 8(F), we referred to the regression equation in 2008 because it was more reliable than that in 2007. At h = 2.0 m in 2008, the decreasing rate of rhizome FW was large (40.27%), but smaller than that obtained using the regression equation in Figure 8(E). At h = 2.5 m, which was the optimal value of h in Table 4, the decreasing rate of rhizome FW was 23.33%, more than 10% larger than that in Table 3. To accord with the decreasing rate of rhizome FW at the same level in Table  3, h should be 2.9 m; however, this value would not protect plants from lodging. Similarly, at h ≧ 2.7 m, the mitigation effect of the internal force was lower than 20%, and strong wind would induce lodging. Therefore, we concluded that the mitigation effects caused by external and internal forces constrained to about 30% (h ≈ 2.5 m) and the sacrifice of about 20% rhizome FW was reasonable (Table 4). In this trial, we obtained more specific and accurate S cal values than those from our previous work (Hosoi & Imai, 2004) because we changed not only h, but also r.
To improve validity of the results, it is necessary to conduct this type of experiments under diverse growth We have obtained strong correlations between r and rhizome FW in both years (2007: R 2 = .967, 2008: R 2 = .929) (Figure 8(E)). Furthermore, we examined these for November only (Figure 8(F)) because rhizome FW increased rapidly during the latter growth stage (after October). However, the correlations were comparable to those in Figure 8(E) only for 2008 (R 2 = .844), probably because of a lower amount of data. Therefore, in Table 4, we show two patterns of the simulation results, those for the absolute value and for the mitigation rate of rhizome FW after shoot shortening. In these results, we do not show the components of internal force because their calculation methods were the same as those in Table 3. The mitigation rates of S cal were adopted based on the 2008 data because these were more reliable than those in 2007. At h = 2.5 m, the mitigation rate of S cal was 35.83% and was equivalent to that at h = 2.4 m in Table 3. Therefore, we considered that the mitigation effect of S cal at h = 2.5 m could be obtained when the desired outcome was only lodging mitigation. However, when we considered the rhizome yield (Figure 8(E)), the % mitigation of rhizome FW reduction was high: 37. 35% and 73.79% in 2007 and 2008, respectively, at h = 2.5 m. At h = 2.0 m, these values were 66.53% and 88%, respectively, and indicated low rhizome yield. By referring to Table 1, h in November reached 2.5 m in 2007 and 3.07 m in 2008; thus, the decreasing rate of rhizome FW would move closer to 0%. However, the results of the simulation were different (2007: 37.35% at h = 2.5 m, 2008: 41.33% at h = 3 m). In Figure 8(E), the data between July and September (the stage of vigorous above-ground growth) were more dominant than those in November (the stage of vigorous rhizome growth with  Figure 8(a) and calculated. d Means calculated by M stock without changing maximum inversion moment. e Shoots longer than objective plant height were converted to shoot FW of objective shoot length by the equation in Figure 8(a) and calculated rhizome FW by the equation in Figure 8(B). to wind. Examples of C d measurement are few: an equation for Japanese cedar that includes natural frequency and external force (Shi-igai, 1993) and the use of the six-component force transducer for a conifer (Ishikawa, 2005). The measurement of C d may be equally important to that of S because C d fluctuates greatly in response to wind (Shi-igai, 1993). Furthermore, the effect of planting conditions in the future. In addition, increasing numbers of parameter such that related to θ may be worthy. We also plan to examine edible canna with a reduced shoot length caused by the application of growth retardant (Sumioka & Imai, 2010). One remaining, and important, subject is to clarify the hydrodynamical drag coefficient (C d ), which indicates the pliability of above-ground parts data of 8a, 8B, 8c, and 8F were obtained in november and those of 8d and 8e, in July-november.   Figure 8F. e calculated by the method of (c) using values obtained from (d). f calculated by the method of (c) using values obtained from (e).