摘要: 目的开发一种伸缩式测高仪，以解决基于三角函数原理设计的测高仪器测量落点范围受限的问题，以及实现垂直生长和倾斜生长立木树高精确测量、�/sec> 方法基于拉绳传感器测高原理，以光电编码器、无刷直流电机、卷盘和钢绳为主要结构，研发了伸缩式测高仪。以皮尺为测量伐倒木树高为真值，利用伸缩式测高仪、布鲁莱斯测高器和森林罗盘仪，分别测量了20株垂直生长样木和11株倾斜生长样木树高精度结果，比较各仪器测高的准确度、方差和 t检验结果；�?种仪器分别连�?次测�?号样木（垂直生长样木）和26号样木树高（倾斜生长样木），比较各仪器测高的精密度、�/sec> 结果结果显示：伸缩式测高仪测量垂直生长林木树高和倾斜生长林木树高的精准度分别�?.034�?.028 m，方差分别为5.60�?.94，精密度分别�?.028�?.015 m。布鲁莱斯测高器测量垂直生长林木树高和倾斜生长林木树高的精准度分别�?.154�?.267 m，方差分别为5.76�?0.00，精密度分别�?.150�?.125 m。森林罗盘仪测量垂直生长林木树高和倾斜生长林木树高的精准度分别�?.059�?.183 m，方差分别为5.66�?0.02，精密度分别�?.056�?.066 m、�/sec> 结论伸缩式测高仪各项测量精度结果要优于布鲁莱斯测高器和森林罗盘仪，不仅解决外业调查与内业录入脱节的问题，还能够有效满足国家森林资源连续清查和森林资源规划设计调查等项目对立木测高的要求、�/sec>

关键诌�
• 林木树高/
• 立木测量/
• 三角函数/
• 拉绳传感�?/a>

Abstract: ObjectiveA scalable altimeter was developed to solve the limited landing range of measuring tree height based on trigonometric function and to realize accuracy measurement of vertical and inclined growth tree height. MethodBased on the principle of draw-wire sensor measuring tree height, the scalable altimeter was developed, of which main structure contained optical electricity encoder, brushless DC motor, coil and rope. The tree height measured by linen tape was taken as true value. A total of 20 vertical growth trees and 11 inclined growth trees were measured by scalable altimeter, Blume-Leiss altimeter and forest compass to compare the measurement precision, variance and tresult, respectively. We measured the height of sample wood No. 8 (vertically growing sample wood) and sample wood No. 26 (obliquely growing sample wood) six consecutive times using four instruments, and compared the precision of height measurement by various instruments. ResultThe accuracy of the scalable altimeter in measuring the height of vertically growing trees and obliquely growing trees was 0.034 and 0.028 m, respectively, with variances of 5.60 and 9.94, and precision of 0.028 and 0.015 m, respectively. The accuracy of measuring the height of vertically growing trees and obliquely growing trees using the Blume-Leiss altimeter was 0.154 and 0.267 m, respectively, with variances of 5.76 and 10.00, and precision of 0.150 and 0.125 m, respectively. The accuracy of measuring the height of vertically growing trees and obliquely growing trees with a forest compass was 0.059 and 0.183 m, respectively, with variances of 5.66 and 10.02, and precision of 0.056 and 0.066 m, respectively. ConclusionThe measurement accuracy results of scalable altimeter are superior to those of Blume-Leiss altimeter and forest compass. It not only solves the problem of disconnection between field surveys and indoor input, but also effectively meets the requirements of national forest resource continuous inventory and forest resource planning and design surveys for measuring the height of opposing trees.

Key words:
• tree height/
• standing tree measurement/
• trigonometric function/
• draw-wire sensor

�?nbsp; 1三角函数测量树高落点国�/p>

a.测高仪器距离目标树较近；b.测高仪器距离目标树适中；c.测高仪器距离目标树较� a, the altimeter is relatively close to the target tree; b, the altimeter is at a moderate distance from the target tree; c, the altimeter is far from the target tree

Figure 1.Landing points of tree height measurement using trigonometric functions

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�?nbsp; 2天然林中倾斜树体实物国�/p>

Figure 2.Physical view of leaning trees in natural forest

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�?nbsp; 3系统硬件框图

Figure 3.Hardware configuration diagram of the system

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�?nbsp; 4伸缩式测高仪实物国�/p>

Figure 4.Object picture of scalable altimeter

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�?nbsp; 5利用伸缩式测高仪测树髗�/p>

Figure 5.Application of scalable altimeter measuring tree height

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�?nbsp; 6伸缩式测高仪底座内部结构国�/p>

Figure 6.Internal structure picture of scalable altimeter base

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�?nbsp; 7Nidec无刷直流电机

Figure 7.Nidec brushless DC motor

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�?nbsp; 8光电编码器测距工作原琅�/p>

Figure 8.Operation principle of photoelectric encoder measuring distance

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�?nbsp; 9主程序和功能模块流程国�/p>

Figure 9.Flowcharts of main program and function modules

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�?nbsp; 10“林木信息采集管理V2.0� 软件界面

Figure 10.Forest information collection and management V2.0 interface

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�?nbsp; 11伸缩式测高仪测量树高原理

H.树高侧量真值；h.测杆在垂直方向上会产生倾斜长度：�i>h₁.测杆实际直立长度：�i>h₂.没有弹性形变的高度、�i>H, the true value of tree height;h, the length of the measuring rod that will be tilted in the vertical direction;h₁, the actual upright length of the measuring rod;h₂, the height without elastic deformation.

Figure 11.Schematic principle of scalable altimeter measuring tree height

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�?nbsp; 12伸缩式测高仪、布鲁莱斯测高器和森林罗盘仪测量垂直生长林木树高误差分析

Figure 12.Error analysis of measuring vertical growth tree height by scalable altimeter, Blume-Leiss altimeter and forest compass

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�?nbsp; 13伸缩式测高仪、布鲁莱斯测高器和森林罗盘仪测量倾斜生长林木树高误差分析

Figure 13.Error analysis of measuring inclined growth tree height by scalable altimeter, Blume-Leiss altimeter and forest compass

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�?nbsp; 1伸缩式测高仪、布鲁莱斯测高器、森林罗盘仪和皮尺测量垂直生长林木树高结枛�/p>

Table 1.Results of measuring vertical growth tree height by scalable altimeter, Blume-Leiss altimeter, forest compass and linen tape m

树号Tree No.	伸缩式测高仪 Scalable altimeter	布鲁莱斯测高器Blume-Leiss altimeter	森林罗盘� Forest compass	皮尺 Linen tape
1	19.21	19.5	19.33	19.28
2	18.92	19.1	18.99	18.91
3	18.77	18.6	18.69	18.75
4	18.13	18.3	18.25	18.16
5	17.89	18.1	17.93	17.91
6	17.57	17.8	17.59	17.51
7	16.85	17.0	16.81	16.88
8	16.56	16.7	16.52	16.60
9	16.24	16.4	16.28	16.24
10	16.23	16.1	16.15	16.21
11	16.11	16.0	16.09	16.15
12	15.56	15.4	15.46	15.52
13	15.41	15.6	15.49	15.44
14	15.21	15.1	15.21	15.26
15	14.15	14.3	14.20	14.12
16	14.06	14.0	14.05	14.11
17	13.75	13.6	13.65	13.70
18	13.34	13.3	13.35	13.32
19	13.24	13.4	13.23	13.18
20	9.63	9.8	9.68	9.62
注：伸缩式测高仪测量均�?5.84 m，方�?.60＋�i>t�?.001，精准度0.034 m；布鲁莱斯测高器测量均�?5.91 m，方�?.76＋�i>t�?.034，精准度0.154 m；森林罗盘仪测量均�?5.85 m，方�?.66＋�i>t�?.002，精准度0.059 m。皮尺测量均�?5.84 m，方�?.66、�i>t0� = 1.96＇�i>α= 0.05）。Notes: the scalable altimeter: the average of measuring tree height is 15.84 m; the variance is 5.60; thetvalue is 0.001; the precision value is 0.034 m. The Blume-Leiss altimeter: the average of measuring tree height is 15.91 m; the variance is 5.76; thetvalue is 0.034; the precision value is 0.154 m. The forest compass: the average of measuring tree height is 15.85 m; the variance is 5.66; thetvalue is 0.002; the precision value is 0.059 m. The linen tape: the average of measuring tree height is 15.84 m; the variance is 5.66.t0= 1.96 (α= 0.05).

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�?nbsp; 2伸缩式测高仪、布鲁莱斯测高器和森林罗盘仪测量倾斜生长林木树高结果

Table 2.Results of measuring inclined growth tree height by scalable altimeter, Blume-Leiss altimeter, forest compass and linen tape m

树号 Tree No.	伸缩式测高仪 Scalable altimeter	布鲁莱斯测高� Blume-Leiss altimeter	森林罗盘� Forest compass	皮尺 Linen tape
21	17.69	17.4	17.58	17.78
22	16.74	16.4	16.47	16.71
23	16.29	16.1	16.18	16.32
24	14.19	14.0	14.08	14.16
25	12.85	12.6	12.58	12.87
26	11.48	11.3	11.36	11.51
27	11.27	11.1	11.05	11.23
28	10.54	10.2	10.34	10.54
29	9.74	9.4	9.51	9.73
30	9.23	9.0	9.11	9.25
31	8.95	8.6	8.77	8.94
注：伸缩式测高仪测量均�?2.63 m，方�?.94＋�i>t�?.001，精准度0.028 m；布鲁莱斯测高器测量均�?2.37 m，方�?0.00＋�i>t�?.063，精准度0.267 m；森林罗盘仪测量均�?2.46 m，方�?0.00＋�i>t�?.043，精准度0.183 m。皮尺测量均�?2.64 m，方�?0.02、�i>t0� = 1.96＇�i>α= 0.05）。Notes: the scalable altimeter: the average of measuring tree height is 12.63 m; the variance is 9.94; thetvalue is 0.001; the precision value is 0.028 m. The Blume-Leiss altimeter: the average of measuring tree height is 12.37 m; the variance is 10.00; thetvalue is 0.063; the precision value is 0.267 m. The forest compass: the average of measuring tree height is 12.46 m; the variance is 10.00; thetvalue is 0.043; the precision value is 0.183 m. The linen tape: the average of measuring tree height is 12.64 m; the variance is 10.02.t0= 1.96 (α= 0.05).

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