The associations of selected technical parameters with discus throwing performance: A cross-sectional study
Leigh, S., & Yu, B. (2007). The associations of selected technical parameters with discus throwing performance: a cross-sectional study. Sports Biomechanics / International Society of Biomechanics in Sports, 6(January 2015), 269–284. https://doi.org/10.1080/14763140701489744
Abstract :
The aim of this study was to identify associations between discus
throwing performance and the technical parameters of: hip–shoulder and
shoulder–arm separation, trunk forward–backward tilt, and throwing-arm
elevation angles.
研究的目标是确定运动表现和技术参数的关系：髋-肩和肩-上臂分离，躯干前后倾以及投掷手臂的仰角。
----研究目的
Video data of male and female discus throwers’ competitive performances
were captured during major competitions. Real-life。Real-life
three-dimensional coordinates of 21 body landmarks, and the discus’s
centre, were obtained for 94 trials using the direct linear
transformation procedure.Each technical parameter was reduced at six
critical instants（关键帧）.The trend of each parameter
across four standards of performance was analysed separately for both
sexes.
----研究方法
For the female throwers, hip–shoulder and shoulder–arm separations after
the flight phase, as well as forward– backward trunk tilts at the
beginning and end of the throwing procedure were associated with
performance.
对于女性运动员，髋-肩和肩在腾空阶段分离和投掷过程中前后躯干倾斜角度与运动表现有联系。
For male throwers, only the hip–shoulder separation immediately before
the flight phase was associated with performance.
对于男性运动员，只有腾空阶段之前髋-肩立即分离与运动表现有联系。
These findings suggest that the relationships between technical
parameters and discus throwing performance are different for males and
females.
研究建议技术参数和铁饼投掷的运动表现的关系在男性和女性之间有区别。
----研究结果
Our results suggest that elite female discus throwers are reliant on effective technique throughout the throwing procedure to achieve long distances, whereas male discus throwers may have a relatively homogeneous technique, and a dependence on physical strength to achieve their long throws.我们的结果：优秀女子铁饼运动员在投掷过程中通过依靠有效的投掷技术来达到较好的成绩，而男子铁饼运动员可能具有相同的投掷技巧，通过身体力量来达到较好的成绩。
----研究结论
Introduction
The most important component of official distance is the vacuum
flight distance.
官方距离最重要的组成部分是真空飞行距离。
The vacuum flight distance of the discus is dependent on discus release
characteristics: the release speed, and the angle and height of
release.
铁饼的真空飞行距离取决于铁饼的出手特征：出手速度、出手角度和高度。
Among these release characteristics, release speed is the single most
important determinant of the difference in vacuum flight distance among
athletes (Bartlett, 1992; Hay and Yu, 1995).
整个出手特征中，出手速度最重要。
The official distance thrown determines the winner of each competition.
The most important component of official distance is the vacuum flight
distance, although the aerodynamic distance and the distance lost at
release also affect official distance(Hay and Yu, 1995).
官方成绩决定了运动员的名次。官方成绩最重要的组成部分是真空飞行距离。
The vacuum flight distance of the discus is dependent on discus release
characteristics: the release speed, and the angle and height of
release.
真空成绩取决于出手特征：出手速度，出手角度和出手高度。
Among these release characteristics, release speed is the single most
important determinant of the difference in vacuum flight distance among
athletes (Bartlett, 1992; Hay and Yu, 1995).
整个出手特征中，出手速度是一个重要特征。
To achieve the longest vacuum flight distance, athletesmust carefully
control their releases so that the discus is thrown at the maximum
height possible, combined with optimal release angles, and most
importantly with the maximum possible speed, which is the most important
factor contributing to the vacuum flight distance, and therefore long
throws (Bartlett, 1992; Hay and Yu, 1995).
为达到最长的真空飞行，运动员细心的控制出手特征。
All other release characteristics lie within a limited range of values,
and may only be important in the manner in which they affect release
speed (Hubbard, de Mestre, and Scott, 2001).
所有出手的特征都在一个有限的范围内，并且可能只在影响出手速度的方式中起重要作用。
From complex, high-speed movements made within the confined space of the
throwing circle, an athlete may be able to increase the release speed
above that possible with a standing throw alone (Hay, 1993).
在投掷圈的受限空间内，从复杂、高速的动作中，运动员可以通过单独投掷提高其速度。
Therefore, optimizing technique to achieve the largest release speed is
vital in discus throwing.
因此，优化技术以获得最大的出手速度是铁饼投掷的关键。
The flight of the discus after release has been thoroughly examined,
most often using a wind tunnel to investigate the aerodynamic properties
of the discus itself (Frohlich, 1981; Ganslen, 1964; Taylor,
1932;Terauds, 1978b)
出手后的铁饼飞行已经被完全验证了，最多的是调查铁饼在风洞中的空气动力学属性。
However, the relevance to the athlete from this line of study is
limited, since athletes are unable to control environmental conditions,
and studying the flight of the discus in isolation to the athlete’s
throwing technique does not allow for any cause and effect relationship
between technique and discus flight to be determined.
然而，这项研究与运动员的相关性有限，因为运动员是一种不可控制的环境条件，在要确定铁饼和运动技术关系中，任何原因和效果关系都不能孤立运动员的投掷技巧来研究铁饼的飞行。
Kinetic analyses of discus throwing during competition are difficult
because instrumentation of the circle with force plates during
competition is not often allowed.
动力学在比赛中分析铁饼的投掷非常困难，因为比赛中在投掷圈内放置测力台并不是经常允许。
Therefore, the extrapolation推断 of kinetic data obtained
in a laboratory setting, such as that from Yu and colleagues (Yu,
Broker, and Silvester, 2002), is most practical.
另外从实验室获得的运动学数据来推断是最实际的。
Kinematic analysis is probably best suited to use during competition, as
it causes minimal interference to the athletes.
因为最小的影响运动员，运动学分析可能是最适合运用分析比赛的。
Few kinematic analyses of discus throwing technique have been made, and
three-dimensional investigations are especially rare.
有一些铁饼投掷技术的运动学分析，然而三维研究非常罕见。
While discus release characteristics such as velocities, heights, and
angles have been reported (Ariel, 2000; Gregor, Whiting, andMcCoy, 1985;
HayandYu, 1995; Knicker, 1990; McCoy, Whiting, Rich, and Gregor,
1985;Terauds, 1978a, 1978b;Ward, 1969), these have rarely been linked to
variations in technique, and sample sizes have been small.
虽然有一些铁饼的出手特征已经被报道过，例如速度、高度和角度，但是这些极少的联系到各种技术并且样本量很小。
Hip–shoulder and shoulder–arm separation, trunk forward–backward tilt,
and throwing-arm elevation angles are important technical parameters
that are repeatedly emphasized in coaching literature (Burke, 1988;
Ecker, 1971; Hay, 1993; Johnson, 1985; Knicker, 1988; Maughan,
1964).
髋-肩和肩-肘角度，躯干前后倾角度以及投掷臂升高角度是非常重要的技术参数，它们经常在教练的书籍中反复强调。
A recent extensive literature review, however, failed to reveal any
scientific evidence to support the coaching literature.
最近大量的文献调查，都缺少科学的证据来证明教练的书籍。
Furthermore, the kinematic analyses performed by Susˇanka and colleagues
(Sus ˇanka, Dumbrovsky ˆ, Barak, S ˇtepa ´nek, and Nosek, 1988), Knicker
(1990), Lindsay (1991), and Hay and Yu (1995) did not identify an ideal
technique.
而且，运动学分析都没有识别出理想技术。
The selected technical parameters can clearly describe actions of a
discus thrower throughout自始自终 the throwing
procedure.
选择的技术参数可以清楚的描述整个投掷过程的铁饼投掷动作。
The angles between the hips and the shoulders and between the shoulders
and the throwing arm are representative of the amount of stretch
experienced by the trunk rotators and arm horizontal
adductors内收.
投掷臂的髋肩-肩肘角度代表总的躯干旋转和上肢水平内收的伸展经验。
The angles of trunk forward–backward tilt and of the elevation of the
throwing arm have been used in kinematic analyses of the shot put
(Alexander, Lindner, and Whalen, 1996; Young and Li, 2005) to describe
body orientation during the throwing procedure.
躯干的前倾-后仰角度和投掷臂的升高曾用于铅球的运动学分析，来描述投掷过程中身体的方向。
These technical parameters, together with anthropometric parameters of
the individual athlete, largely determine the height and angle of
release (Hay, 1993; Sˇtepa ´nek, 1990).
这些技术参数结合人体测量学的个体参数在很大程度上决定了运动员的出手高度和角度。
We believe the trunk forward–backward tilt and throwing-arm elevation
angles are associated with the vertical distance travelled by the discus
during the throwing procedure, which influences the vertical velocity at
release and, therefore, the speed and angle of release.
我们认为，躯干向前向后倾斜和投掷手臂仰角与铁饼投掷过程中的垂直距离有关，这影响了投掷时的垂直速度，因此影响了投掷的速度和角度。
We believe that the second single support phase is the most important
time to increase vertical velocity, since it is the phase that
immediately precedes优先 the release.
我们认为第二次单支撑阶段是提升垂直速度最重要的时间，因为这个阶段直接优先于出手。
Methods
paricipants
Altogether, 93 legal trials of 51 male and 42 female discus throwers
competing in the men’s and women’s discus throw finals of the 1990
Goodwill Games, the 1990 US Olympic Festival, and the USNationalOutdoor
Championships and OlympicTeamTrials from 1997 to 2005 were included in
this study. In the case of an athlete having multiple trials available
for analysis, his or her performance with the longest official distance
was selected. All throwers were right-handed. The official distances
ranged from 41.55m to 68.08m for female discus throwers, and from 48.91m
to 67.40m for male discus throwers. All trials were divided into four
groups for each sex according to the official distances recorded at the
meets: below 55m group, 55 to 60m group, 60 to 65m group, and over 65m
group. The numbers of throwers in each group are shown in Tables I and
II.
研究包含在1990年的Goodwill, the 1990 US Olympic Festival, and the
USNationalOutdoor Championships and OlympicTeamTrials from 1997 to 2005
男子51投和女子42投总共93投。
最好成绩：
女：41.5-68.08 男：48.9-67.4
男女分为四组分别成绩是
55以下 55-60 60-65 65以上
Data collection
两台S-VHS摄像机拍摄60HZ。一台在投掷圈的后面，另外一台在投掷圈的右边。主光轴约90°。使用24点标定框架标点，标定空间(2.5m
long × 2m wide × 2.5m high) 。
Five global reference markers were placed in the discus throwing circle
for establishing a global reference frame during data reduction (Figure
1).
5个球形参考点放置于投掷圈用于在数据平滑时建立一个球形参考框架。
Data reduction
直接线性变换(DLT)建立真实三维坐标。X轴指向投掷方向，Y轴指向面向投掷方向的左侧，Z轴指向上方。
视频从最大后摆的前5帧到铁饼出手的后4帧剪切。手工标记每一帧的人体标志点和铁饼重心。关键帧-右脚离地，左脚离地，右脚触地，左脚触地和出手从每一投的视频中识别。五个关键帧数用于同步两侧视频。三维坐标通过Butterworth
low-pass digital filter 过滤，截断频率7.14Hz。所用的解析软件是MSDLT
5.5版本(北卡chapel hill自己的软件)。
投掷中的6个关键时刻被识别：最大后摆，右脚离地，左脚离地，右脚着地，左脚着地和出手。(Bartlett,
1992; Hay and Yu, 1995)
6个关键时刻分离出5个阶段：第一次单支撑阶段，第一次双支撑阶段，腾空阶段，第二次单支撑阶段和第二次双支撑阶段或出手阶段。(Hay
and Yu, 1995)
一个躯干的参考框架建立在每一个关键时刻去计算髋-肩和肩-肘分离角。躯干的参考框架建立在这样一个相对于髋的直线上——X轴指向前方，Y轴指向左方，X轴从左右髋的中点到左右肩的中点较高的方向。
The global three-dimensional coordinates of the right and left hips and
shoulders and the centre of the discus at each critical instant were
transferred to the trunk reference frame.
每个关键时刻左右髋、肩的球形三维坐标以及铁饼的中心被转化为躯干的参考框架中。
髋肩分离角α和肩肘分离角β计算的方式： \[
\alpha=\arccos \Big( \frac{\upsilon_s
\bullet\upsilon_h}{|\upsilon_s||\upsilon_h|}\Big)
\]
\[ \beta=\arccos \Big( \frac{\upsilon_d \bullet\upsilon_s}{|\upsilon_d||\upsilon_s|}\Big) \]
此公式是空间两直线求夹角的公式： 设两条直线的方向向量分别为S1=(m1,s1,p1）、S2=(m2,s2,p2),模分别为|S1|、|S2|, 两条直线的夹角a 则:
\[ \cos a=\frac{S1\bullet S2}{(|S1||S2|)} \] \[ a =\arccos \bigg( \frac{S1\bullet S2}{(|S1||S2|)}\bigg) \]
\(v_h,v_s,\)和\(v_d\)分别是右髋到左髋，右肩到左肩和铁饼中心到右肩的向量，在XY平面如图所示。
定义髋-肩和肩-肘分离角。髋-肩分离角是计算每个关键时刻XY平面身体框架左右宽关节中心向量与左右肩关节中心向量的夹角。The line of the hips leading the line of the shoulders is defined as a
positive angle正角. 由髋轴领导的肩轴组成的夹角定义为正角。每个关键时刻由左右肩关节中心向量和右肩中心与铁饼中心向量在躯干参考框架XY平面上所形成的夹角为肩肘分离角。肩轴领导投掷臂轴定义为正角。
The value of a was positive if the vector product of vs and vh was
pointing towards the superior direction, which meant that
the right hip was leading the right shoulder. The value of a was
negative if the vector product of vs and vh was pointing towards the
inferior direction, which meant that the right shoulder was
leading the right hip. The value of b was positive if the vector product
of vd and vs was pointing towards the superior direction, which meant
that the right shoulder was leading the right arm. The value of b was
negative if the vector product of vd and vs was pointing towards the
inferior direction, which meant that the right arm was leading the right
shoulder.
如果向量\(v_s\)和\(v_h\)的乘积指向向上的方向，α是正值，意味着右髋引导右肩。
如果向量\(v_s\)和\(v_h\)的乘积指向向下的方向，α的值是负值，意味着右肩引导右髋。
如果向量\(v_d\)和\(v_s\)的乘积指向向上的方向，β的值是正的，意味着右肩引导右臂。
如果向量\(v_d\)和\(v_s\)的乘积指向向下的方向，β的值是负的，意味着右臂引领右肩。
superior 和 inferior在解剖中是指上和下的关系 Now, there are more directional terms than just toward the front or the back of something. We also have the term superior, which means towards the head or above something, and the word inferior, which means towards the feet or below something1.
line of the hips, the y-axis was parallel to the horizontal plane and
pointing towards the left side of the trunk, and the z-axis was pointing
upwards and perpendicular to the horizontal plane. The trunk
forward–backward tilt angle, left–right tilt angle, and left–right
rotation angle were defined as the three Euler rotations of the trunk
reference frame relative to the ground reference frame with an x-y-z
rotation order. Trunk forward–backward tilt is reported as the first
rotation of the Euler angles. A positive value of x indicated a forward
trunk tilt, while a negative value of x indicated a backward trunk tilt
(Figure 3). This can be thought of as pure forward–backward trunk tilt.
Isolated trunk left–right tilt was not calculated.
为了确定躯干前倾后仰交（\(\chi\)），建立一个X轴方向指向髋轴前方，Y轴指向躯干左侧并且平行于水平面，Z轴指向上方并且垂直于水平面的大地坐标系。躯干前后倾角，左右倾角和左右旋转角度定义为相对于大地坐标系以躯干框架带有x-y-z旋转顺序的三个欧拉角。躯干前后倾角视为欧拉角的第一次旋转。\(\chi\)的正值表明躯干前倾，而负角表示躯干后仰（图3）。这样就可以认为是一个纯粹的躯干前倾后仰。独立躯干的左右倾斜而不计算。
投掷臂提升角(\(\delta\))为计算每个关键时刻： \[
\delta= \arctan\Bigg[ \frac
{z_d-z_{s,r}}{\sqrt{(x_d-x_{s,r})^2+(y_d-y_{s,r})^2}}\Bigg]
\] where xs,r, ys,r, and zs,r,and xd, yd, and zd, are the
three-dimensional coordinates measured in the global reference frame of
the right shoulder joint centre and the centre of the discus,
respectively. A positive value of d indicated that the position of the
discus was higher than that of the right shoulder, whereas a negative
value of d indicated that the position of the discus was lower than that
of the right shoulder (Figure 4).
\(x_{s,r}\) ,\(y_{s,r}\),\(z_{s,r}\)和\(x_d\)，\(y_d\)，\(z_d\)是以右肩中心与铁饼中心的球形坐标系的各自三维坐标。\(\delta\)正值表示铁饼的位置高于右肩，当\(\delta\)值为负值表示铁饼的位置低于右肩(图4)。
Data analysis
The male and female throwers were analysed separately in an attempt
to control for confounding factors that were not controlled for in this
study.
分别分析男性和女性的投掷者，试图控制在本研究中未被控制的混杂因素。
The four groups based on official distance for each sex were coded as
groups 1 to 4, where grouping generally represented performance, and was
used as the dependent variable for statistical analyses.
根据每个性别的官方距离的四组被编码为组1至4，其中分组通常代表表现，并且被用作统计分析的因变量。
The difference in sample size of the groups was accounted for by
weighting the means for each group with respect to sample size.
组间样本量的差异是通过对每个组的样本量进行加权平均来解释的。
Linear trend analyses were performed to determine the trend of the mean
hip–shoulder and shoulder–arm separation angles, and the mean trunk
forward–backward tilt and throwing-arm elevation angles at each critical
instant with group, as well as the trend of the maximum angles of trunk
forward–backward tilt and throwing-arm elevation during the second
single support phase with group.
进行线性趋势分析，以确定平均髋-肩和肩-臂分离角度的趋势，每组关键时刻的平均躯干前后倾角和投掷臂仰角以及在第二次单支撑阶段躯干前后倾角和投掷臂抬高的最大角度。
A linear trend analysis assesses whether the slope of the standardized
regression line is equal to zero, and so if the dependent variable is
significantly related to the independent variable.
线性趋势分析评估标准化回归线的斜率是否等于零，如果等于零则因变量与自变量显着相关。
A linear trend analysis is a more sophisticated version of a simple
correlation, because the F-ratio directly reflects the strength of the
association between the two variables.
线性趋势分析是一个简单相关的更复杂的版本，因为F比率直接反映了两个变量之间关联的强度。
The significance level for the F-test and t-test of a linear trend
analysis is the same (since the square of the t is the same as the
F-ratio); however, both statistics will be reported since the sign of
the t indicates the direction of the relationship (Elston and Johnson,
1994; Myers andWell, 1991). An a priori type I error rate of α= 0.05 per
comparison was chosen to indicate statistical significance. The alpha
level for each individual test was not adjusted because the trend of
each technical parameter with discus throwing performance was analysed
in isolation.We did not consider the associations of combinations of
technical parameters with performance, or the inter- relationships
between technical parameters. All statistical analyses were performed
with SPSS version 11.5 statistical software (SPSS Inc., Chicago, IL.).
写的啥，看不懂，google翻译的
线性趋势分析的F检验和t检验的显着性水平相同（因为t的平方与F比率相同）。
然而，这两个统计数据将被报告，因为t的符号表明了关系的方向（Elston and
Johnson，1994; Myers and Well，1991）。 选择每个比较a =
0.05的先验I型错误率来表示统计学显着性。
由于各项技术参数对铁饼投掷性能的影响是单独进行分析的，我们没有考虑到每个单项测试的α水平。我们没有考虑技术参数组合与性能的关系，或者技术参数之间的相互关系。
所有统计分析均采用SPSS 11.5版统计软件（SPSS
Inc.，Chicago，IL）进行。
Result
Discussion and implication
Conclusion
Although the results of this study may not be applicable to a
different population of discus throwers, they provide important
information to coaches and elite discus throwers and the following
conclusions appear warranted:
虽然这项研究的结果可能不适用于不同人群的铁饼运动员，但他们为教练员和铁饼运动员提供了重要的信息，并得出如下结论：
- Large hip–shoulder and shoulder–arm separations after the flight
phase, and more forward trunk tilt at the beginning and more backward
trunk tilt at the end of the end of the throwing procedure, are
important technical characteristics of elite female discus throwers with
long official distances.
-
飞行阶段后较大的髋-肩和肩-臂分离，开始阶段过多的前倾，以及出手阶段后期过多的后倾是官方成绩较好的优秀女子铁饼运动员的重要技术特征。
- Hip–shoulder and shoulder–arm separations, trunk forward–backward
tilts, and throwing-arm elevations may not be important technical
parameters that differentiate the performances of elite male discus
throwers.
-
髋-肩，肩-臂分离，躯干前后倾，投掷臂抬高可能不是区分男子铁饼优秀运动员表现的重要技术参数。
- Female discus throwers should concentrate on increasing their
hip–shoulder and shoulder–arm separations after the flight phase, and
releasing the discus when the lines of the hips, shoulders, and throwing
arm are parallel. They should also increase their backward trunk tilt
during the delivery phase.
-
女子铁饼运动员应该集中精力在飞行阶段之后增加他们的髋-肩和肩-臂分离，并且在髋轴，肩轴和投掷臂轴的线条平行时释放铁饼。
在出手阶段，他们也应该增加躯干后倾的角度。
Further investigations are needed to determine which other technical
parameters can help differentiate between the performances of male
discus throwers and which combinations of technical parameters may
differentiate the performances of both male and female discus
throwers.
还需要进一步调查，以确定哪些其他技术参数可以帮助区分男性铁饼运动员的表现以及哪些技术参数的组合可以区分男性和女性铁饼运动员的表现。
国内、外优秀女子铁饼运动员掷铁饼技术的比较研究
林辉杰,梁海丹,严波涛,许崇高,张勇. 国内、外优秀女子铁饼运动员掷铁饼技术的比较研究[J]. 中国体育科技,2013,49(01):71-77. 国家体育总局重点实验室项目（２０１１Ｂ０２５）； 上海体育学院研究生教育创新基金项目（ｙｊｓｃｘ２０１２０１３）。
前 言
对 国
内、外优秀女子铁饼运动员掷铁饼技术特征的比较，有助于掌握与克服我国与国外运动员技术的优势与劣势，为我国运动员备战世界大赛提供科学训练依据。
目前，对于我国优秀女子铁饼运动员掷铁饼技术运动学特征的研究还是较多的，但
是，由 于 条 件
的限制，对于国内、外优秀女子铁饼运动员技术直接比较的文献还未曾发现。
在本研究中，将我国重点运动员李艳凤（２０１１年大邱世界锦标赛冠军）、谭
建（２０１１年 大 邱 世 界 锦标 赛
第６名）与多名国外优秀女子铁饼运动员技术的运动学特征进行比较，旨在探索我国运动员技术的优、缺点以及国外运动员的技术特点，从而揭示优秀女子铁饼运动员的一些重要技术特征，为我国女子铁饼运动员的科学训练提供参考。
## 研究对象与方法
测试对象
本研究选取了２名国内与５名国外优秀女子铁饼运动员作为研究样本，这些运动员个人最好成绩均在奥运会Ａ标（６２ｍ）之 上，本 次 测 量 成 绩（２０１１年 国 际 田 径 钻 石 联赛 上 海 站）均 在奥运会Ｂ标（５９．５ ｍ）之上，基本上代表了目前世界女子铁饼项目的最高水平（表１）。 >要对运动员的水平进行分析，在国内的水平如何，在国外的水平如何。
研究方法
本研究将铁饼技术分为５个 时 相，分别为第1双支撑阶段、第１单支撑阶段、腾空阶段、第 ２ 单支 撑阶段（过 渡阶 段）以及第２双支撑阶段（最 后 用 力 阶 段）。以 右手持饼为例，第１双支撑阶段是指从预摆结束至右脚离地时刻；第１单支撑阶段是指从右脚离地至左脚离地时刻；腾空阶段是指从左脚离地至右脚着地时刻；第２单支撑阶段是指从右脚着地至左脚着地时刻；第２双支撑是指从左脚着地至铁饼出手时刻。 >同样是将投掷动作划分为5个阶段。第一次双支撑，第一次单支撑，腾空阶段、第二次单支撑，第二次单支撑(出手阶段)。
采用2台casio
fh25摄像机，主光轴90°夹角，拍摄频率120fps。机高1.2m。
用simi解析。选 择 左 右 侧 手、肘、肩、髋、膝、踝、脚 尖 以 及 头、肩
轴中 点、髋轴中点以及铁饼点等 ２０ 个 点 进 行 解 析。
人体以及环节重心等人体惯性参数依据
dempster人体参数模型计算获得，采用数字滤波进行噪音处理，截止频率选择为８Ｈｚ。
技术指标
真空距离：铁饼飞行的真空距离是去除了流体的影响后铁饼在理论飞行的距离2，计算公式如下： \[ d= \frac{S_R^2\sin\theta_R \cos\theta_R+S_R\cos\theta_R\sqrt{[(S_R\sin\theta_R)^2+2gh_R]}}{g} \]
