Aerodynamic Drag Reduction Effect of Drafting Formation in Race Walking Based on Wind Tunnel Tests
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摘要:目的 探讨不同编队位置对核心运动员气动阻力的影响以及与单人竞走情况相比的气动减阻效果，并量化评估不同编队策略对竞走成绩的影响。方法 选取由不同国家队竞走运动员人数组成的编队模拟不同竞走场景，通过风洞试验获取不同编队位置核心运动员的气动阻力。风洞试验内容包括核心运动员单人测试、双人编队测试、3人编队测试、4人编队测试。结果 与单人竞走情况相比，双人编队中核心运动员位于辅助运动员的正后方时气动阻力减小最为明显，减阻率可达64.9%，此编队站位为相对最佳双人编队；3人编队中核心运动员位于其他2名辅助运动员沿着运动方向连线的中间时气动阻力减小最为明显，减阻率可达79.9%，此编队站位为相对最佳3人编队；4人编队中核心运动员位于其他3名辅助运动员组成的V型编队的正后方时气动阻力减小最为明显，减阻率可达83.8%，此编队站位为相对最佳4人编队。在50 km竞走比赛中，与单人竞走成绩相比，若采用相对最佳双人编队策略，比赛成绩将至少提升约3.89%；若采用相对最佳3人编队策略，比赛成绩将至少提升约4.79%；若采用相对最佳4人编队策略，比赛成绩将至少提升约5.03%。结论 不同编队位置下竞走项目核心运动员的气动减阻效应存在一定差异，研究不同编队的气动减阻效应能为减小核心运动员气动阻力、优化能量分配、改进团队协作策略、提高运动成绩提供重要的科学指导。Abstract:Objectives To determine the influences of different drafting formations on the core athlete's aerodynamic drag as well as the drag reduction effects compared to individual race walking conditions, and to quantify the effects of different drafting formation strategies on race walking performance.Methods Drafting formations composed of different elite race walkers were used to simulate different race walking scenarios, and the core athlete's aerodynamic drag in different formations positions was obtained by wind tunnel tests, including individual, two-athlete, three-athlete and four-athlete drafting formation tests, respectively.Results Compared to individual race walking situations, when the core athlete was located directly behind the auxiliary athlete, his aerodynamic drag reduced most obviously with the reduction rate of 64.9%, which could be the optimal two-athlete drafting formation. When the core athlete was located in the middle part of the line while the other two auxiliary athletes moved along, his aerodynamic drag reduced most obviously with the reduction rate of 79.9%, the position of which is relatively optimal; While when the core athlete was located directly at the rear of the Type V formation of three other auxiliary athletes, his aerodynamic drag reduced most obviously with the reduction rate of 83.8% as the optimal four-athlete drafting formation. In the 50 km race walking, compared to the individual race walking, the two-athlete's result would be improved approximately by at least 3.89% with the optimal drafting formation strategy; similarly, the result for three-athlete drafting formation would be improved by 4.79%, and the result for four-athlete, 5.03%.Conclusions There exist differences of aerodynamic drag reduction effects for race walking core athletes in different drafting formation positions. Related research can provide important scientific guidance for reducing aerodynamic drag for core athletes, optimizing energy distribution, improving teamwork strategies and athletic performance.
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Keywords:
- race walking /
- wind tunnel test /
- drafting formation /
- aerodynamic drag /
- drag reduction
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拉格朗日函数（Lagrange Function）是描述约束条件下优化问题的解析表达式，包含目标函数与约束条件，能有效应对约束最优化、强对偶性等问题。它在经济学理论领域的贡献是寻找多元函数在变量约束下的极值并提供最优解，在实践领域主要用于解决资源最优化问题。我国现有公共体育服务供给评价多采用指标体系构建方法，如层次分析法、熵值法、德尔菲法及模糊综合评价法等，缺乏引入经济模型进行评价的尝试。基于拉格朗日函数的特性与功能，将其应用于公共体育服务供给评价，可增加公共体育服务供给评价方法的选择范围，并提升决策部门优化公共体育服务供给方案的科学性。公共体育服务供给是一个复杂且不稳定的系统。基于双重属性的公共体育服务可细分为有形性公共体育服务与无形性公共体育服务。有形性公共体育服务主要针对基础设施的优化及资源配置效率的提升来补齐供给短板，如健身场地设施等；而无形性公共体育服务更强调公共体育服务的公益性，如公共体育服务政策等。为了实现帕累托最优，需要合理配置有形性公共体育服务和无形性公共体育服务的份额，使资源利用效率和投放效果达到最大化。因此，构建公共体育服务供给效用最大化的函数模型，需要先厘清公共体育服务供给结构，再建立带约束的拉格朗日函数，给出政府决策的最优条件，从而获取达到一般均衡的最佳比例。评价最优解要求有形性公共体育服务与无形性公共体育服务的边际替代率（MRS）相等，即有形性公共体育服务的边际效用（MU）要等于无形性公共体育服务的边际效用，此时公共体育服务的供给结构在理论上达到最佳状态。该函数模型的应用难点在于能否获得完整可靠的数据，从而保证有形性公共体育服务和无形性公共体育服务的量化标准统一。此外，拉格朗日函数解决的是带约束条件的最值问题，因此，不能用于衡量具体的公共体育服务供给水平与质量。
胡齐：提出论文主题，设计论文框架，撰写论文；李波：提供技术参考，处理数据；沈梦：核实数据，修改论文；洪平：提出论文主题，指导修改论文。 -
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图 2 二七厂体育综合风洞试验室
Figure 2. Sports comprehensive wind tunnel laboratory at Erqi factory
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图 3 双人编队竞走场景模拟
Figure 3. Simulation of race walking scene of two-athlete drafting formations
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图 4 3人编队竞走场景模拟
Figure 4. Simulation of race walking scene of three-athlete drafting formations
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图 5 4人编队竞走场景模拟
Figure 5. Simulation of race walking scene of four-athlete drafting formations
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图 6 双人编队不同站位下核心运动员的气动阻力
注：括号内百分比为核心运动员在该编队站位状态下与单人状态下气动阻力的比值百分比。
Figure 6. Aerodynamic drag of the core athlete in different formations of two-athlete drafting
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图 7 3人编队不同站位下核心运动员的气动阻力
注：括号内百分比为核心运动员在该编队站位状态下与单人状态下气动阻力的比值百分比。
Figure 7. Aerodynamic drag of the core athlete in different formations of three-athlete drafting
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图 8 4人编队不同站位下核心运动员的气动阻力
注：括号内百分比为核心运动员在该编队站位状态下与单人状态下气动阻力的比值百分比。
Figure 8. Aerodynamic drag of the core athlete in different formations of four-athlete drafting
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图 9 双人编队不同站位下核心运动员的气动减阻率
注：负值表示在某一编队站位状态下核心运动员的气动阻力相较单人状态并未减小，反而增大。
Figure 9. Aerodynamic drag reduction ratio of the core athlete in different formations of two-athlete drafting
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图 10 3人编队不同站位下核心运动员的气动减阻率
Figure 10. Aerodynamic drag reduction ratio of the core athlete in different formations of three-athlete drafting
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图 11 4人编队不同站位下核心运动员的气动减阻率
Figure 11. Aerodynamic drag reduction ratio of the core athlete in different formations of four-athlete drafting
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图 12 男子2组在4人编队站位3下试验现场
Figure 12. Field test of the second men's group in the third four-athlete drafting formation
表 1 盒式六分量天平技术参数（精度0.2%）
Table 1 Technical parameters of the box-type six-component balance
分量 阻力
（Fx）/N升力
（Fy）/N侧向力
（Fz）/N滚转力矩
（Mx）/（N·m）偏航力矩
（My）/（N·m）俯仰力矩
（Mz）/（N·m）量程 ±400 ±2000 ±400 ±500 ±500 ±500 
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表 2 编队气动减阻效应对运动成绩的影响
Table 2 Influence of aerodynamic drag reduction effect of drafting formation on sport performance
排名 运动成绩/（h:min:s） 与冠军成绩的差距/（h:min:s） 若夺冠成绩须提升百分比/% 若夺冠编队减阻率应达到值/% 1 4:04:20（14660 s） 0 0 0 2 4:04:59（14699 s） 0:00:39（39 s） 0.27 4.42 3 4:05:02（14703 s） 0:00:42（42 s） 0.29 4.76 4 4:05:36（14736 s） 0:01:16（76 s） 0.52 8.60 5 4:06:49（14809 s） 0:02:29（149 s） 1.01 16.77 6 4:07:46（14866 s） 0:03:26（206 s） 1.39 23.10 7 4:10:22（15022 s） 0:06:02（362 s） 2.41 40.16 8 4:11:28（15088 s） 0:07:08（428 s） 2.84 47.28 9 4:12:28（15148 s） 0:08:08（488 s） 3.22 53.69 10 4:13:56（15236 s） 0:09:36（576 s） 3.78 63.01
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