滑翔伞转弯的原理

Paraglider pilot since 1991, I design and build my own canopy since 1996. The few thoughts have been needed to determine the design drivers of the canopy Elisa (VL 280) and Bionic (VL 299).A great adventure !

我从1991年开始飞伞，1996年开始设计和制作自己的滑翔伞。有一些理念必须要理解，才能进行很好的设计，这些理念影响到了Elisa V280 和Bionic VL299的设计

Compromises and questions

Any aircraft, being a fighter jet or a paraglider, is the result of a compromise. Therefore it is important, before making any decisions, to understand the effects and consequences of one characteristic or an other on the final product to prevent a disappointing result: a high performance wing that does not turn, a good handling or very solid wing impossible to collapse but that flies like a pave stone etc…

妥协和需要回答的问题

任何航空器，无论是一架喷气式战斗机还是一顶滑翔伞，都是（一系列设计参数）妥协的结果；因此理解各种设计特点所产生的效果和后果是非常重要的，以避免产生令人不满意的结果，比如：滑翔比很大但是转弯差操控性能差，或者非常稳定的伞，很难塌陷但是飞起来像块石头。

One of the most important questions to answer to avoid failure when designing a canopy is the following:

在设计滑翔伞的时候需要考虑以避免设计失败的重要问题之一是：

How does a paraglider turn and what are the parameters that influence the

characteristics of the turn?

一顶滑翔伞是如何转弯的，哪些设计参数会影响到转弯的特性

My intention is to try to answer to this question simply but in details. I will try to highlight the basic principles of the mechanic of flight that applies to any type of aircraft (plane, hang-glider or paraglider) and demystify the misunderstanding on how a paraglider turn is initiated. At least once you have passed the 1st formula!

我的想法是能够详细而通俗的回答这个问题；这里我将突出解释飞行力学的基本理论在各种类型飞行器上的应用（飞机，悬挂滑翔机和滑翔伞），并且分析哪些对滑翔伞如何开始转弯的错误理解；不过，（在阅读本文之前）读者至少需要学习理解第一定律（译者：估计这里说得是牛顿第一定律，惯性定律）

How does the brake act on the paraglider airfoil?

刹车是如何作用于滑翔伞的翼型？

First of all lets kill some preconceived ideas on the aerodynamic effect of the brake controls by remembering the basic rules acting on airfoils, which have been experimentally determined by great people like Otto Lilienthal and theoretically proven by mathematicians such as Joukowsky. Refer to the excellent book “Theory of Wing sections” from Abott & Doenhoff, which collects together the work of NACA during the 30s and 40s.

首先我们需要抛弃我们自己所有的先前对于刹车的气动力作用的理解，仅仅记住作用于翼型上的最基本的原理――这些由伟大的先驱们如 Otto Lilienthal （奥托·李林塔尔(1848-1896) 用试验证明，理论上由Joukowsky 使用数学方法所验证的理论。

这些理论的学习可以参考一本非常优秀的书籍 “Theory of Wing sections”――由 Abott & Doenhoff撰写, 这本书积累了三四十年代NACA 所作的研究工作。

The brake, like any trailing edge flap first acts by increasing the lift coefficient of the airfoil. This is mainly why a paraglider slows down when brakes are applied symmetrically: the decrease of the speed V compensates the increase of the lift coefficient Cz in the Aerodynamic Forces Resultant (RFA in French, summary of the field force), to equal the weight in the lift equation:

方程一：

刹车，其作用如同简单襟翼一样，首先增加翼型的升力系数，这就是为何当两侧刹车对成拉下的时候滑翔伞首先减速：（这是因为）速度的减小补偿了由升力系数Cz的增加而导致的力的不平衡，参见平衡方程

（原文为Aerodynamic Forces Resultant合力，译者评：升力系数增加，维持平衡的所需下滑速度减小，瞬间升力增大，导致滑翔伞的俯仰姿态改变，从一个平衡状态进入另一个平衡状态）

注：滑翔机之父——奥托·李林塔尔(Otto Lilienthal)(1848-1896) 李林塔尔为德国工程师和滑翔飞行家，世界航空先驱者之一。他最早设计和制造出实用的滑翔机，人称“滑翔机之父”。

注：（Zhukovski，Nikolai Egorievich茹科夫斯基（1847～1921）俄国空气动力学家。航空科学的开拓者。1868年毕业于莫斯科大学物理数学系，1882年获应用数学博士学位，1886年起历任莫斯科大学和莫斯科高等技术学校力学教授。1918年任苏联中央流体动力研究院院长。他创建了实验与理论相统一的空气动力学，为航空技术的发展奠定了科学基础。1890年前后相继发表的《关于飞行器的某些理论根据》、《飞行理论》和《论鸟的飞翔》以及1897年发表的《论飞机最佳倾角》等著作，发展了飞行动力学，为飞机气动力计算奠定了基础。1902年在莫斯科大学领导建造了世界上较早的风洞。1907年运用环流的概念阐明了升力产生的原理及计算公式。还最先运用数学方法画出一系列机翼翼型。1912～1918年提出一系列关于螺旋桨涡流理论的论文。为设计螺旋桨提供了理论根据。）

Indeed the camber the to trailing edge of airfoil is more or less equivalent to the swing of a flap and induces the following effects, every other parameters being equals (see figure 1).

实际上滑翔伞的刹车同襟翼下放一样产生如下效果，各个参数（刹车同襟翼）都是一样的

2. A very important lift increase (typically 50% for a 20° swing of a flap
measuring 20% of the chord) by translation of the curve Cz=f(a).
改变了升力曲线的位置，显著的升力增加（20％弦长的襟翼下放20°，升力增加50％）

3. An increase in the drag of 10 to a 100 times smaller than lift increase has you can see on the polar curve with and without flap.

从极曲线可以看出，阻力的增加大约是升力增加的1％到10％，

4. A move of the centre of pressure towards the trailing edge.

压力中心向尾部移动（译者注：实际是翼型改变了，焦点力矩增大了）

5. A decrease in angle of incidence (plus something that does not make sense in French because of typo, maybe that at 0° of incidence the lift is null)

安装角增大

6. A increase of pitch down moment

低头力矩增加

The naming “brake” is therefore improper because it is firstly a control of lift increase

所以“刹车”这个名字实际上是不正确的，因为其首要的作用是增加升力；

（译者注：这个地方可以修正一下，在45度以上的偏转的时候，刹车增加的阻力还是不少）

figure 1 : brake effect on airfoil characteristics

Why does an action on the left brake starts a left turn?

为何左刹车会让滑翔伞左转？

At first sight one could think that an action on the left brake, increasing the lift on the left, would initiate a right hand turn. To answer this question, one needs to analyse the paraglider by looking at it from the back and determine what spin motion is induced by the acting on the brake. As for any lifting surface for which the camber is increased, the main effect is the strong increase in the lift of the left wing; the side effect is a small increase in the drag… Therefore the RFA moves toward the left, as you would guess however that is not all what happens. The RFA tilts more or less depending on the repartition of the lift obtain through the swing of the brake and through the shape of the arc of the canopy, c.f. fig. 2.

看了前面的论述，您可能感觉一拉左刹车，增加了左侧的升力会引起滑翔伞右转。回答这个问题我们必须从具体分析滑翔伞的受力，参见图二，从滑翔伞的后面向前面看，注意拉下刹车之后，升力增量是主要的，阻力增量是次要的。合力RFA指向左侧

figure 2 : brake effect on aerodynamic force

图二：刹车对于气动力的分布改变

对于任何类型的航空器而言，任何转动的触发都需要由对于质心的力矩引起。对于滚转力矩这里标注为Cl 从图三可以看出究竟是左滚还是右滚，还是不滚都是有伞绳的长度和翼伞的弯度来决定。（译者：大家注意一下啊，这里的质心是指整个系统的质心，不是指人的质心，不过由于伞头和伞绳的质量比较小，系统质心基本在人这一端）

For any kind of aircraft, the rotation movements occur at the centre of gravity (CG) and can be characterized with the moment of rotation at this point (the moment coefficient for the roll is called Cl). Everything is based on the shape of the arch and the length of the lines. Figure 3 explains why acting on the brake initiate a turn, or inverse roll on a canopy with an arch too “flat”(figure 3).

figure 3 : roll moment as a function of arch and lining height

Therefore, the roll momentl can either be positive, negative or null depending on the following fundamental design drivers:

因此滚转力矩Cl为正还是为负，或者为零由以下设计特点决定

1. . The shape of the arc

2. . The length of the lines that fixes the position of the centre of gravity

3. . The spread of the braking along the trailing edge

1 伞的弯曲形状

2 伞绳的长度，决定了质心位置

3 刹车在后缘的分部情况

The yaw moment is created by the increase of the drag of the left flap and the increase
of the induced drag of the left wing.

刹车产生的阻力在航向上的作用通常是有利于转弯的，但是在一些高性能伞上阻力产生很小。
It is always in the “good” direction because it is always on the side of the swung flap.
If the airfoil of the wing is too high performance and does not drag enough some
manufacturers use drag devices on the wingtip (Advance on the Sigma and Omega).

Why is a canopy spiral stable or in stable?

为何有的伞头是螺旋稳定的，有的不是？

In a stabilised turn, the paraglider is the aircraft with the record of the smallest turning circle, as shown in figure 4 comparing paraglider, hang-glider and sailplane.

figure 4 : turn radius comparison

图四：转弯半径的比较

在一个稳定的盘旋中，滑翔伞保持了航空器的最小盘旋半径的记录，图四是滑翔伞同悬挂滑翔机和固定翼滑翔机的比较

To give you a simple idea, one can say for instance that a paraglider usually turns with a radius of 2 wingspans, where a hang-glider and sailplane turn respectively with a radius of 3 and 4 wingspan The speed ratio between the left and right wingtip is from the above example; 2 for a paraglider but only 1.5 for a hang-glider and 1.3 for a sailplane. Therefore, the lift ratios, proportional to that square of speed as we know, are respectively 4 for a paraglider, 2.25 for a hang-glider and only 1.7 for a sailplane. Hence, even with symmetrical control, the lift spread along the wingspan varies greatly on a turning paraglider, as shown on figure 5.

为了比较简单的说明，这里以实例进行说明：滑翔伞以2倍翼展的半径稳定盘旋，而悬挂滑翔机和固定翼滑翔机以3，4倍翼展进行稳定盘旋。在如上的例子中，左右翼尖的的速度差别对于滑翔伞是2，对悬挂滑翔机是1.5，对于固定翼是1.3。由于升力于速度的平方成正比，因此在对称操作的情况下，小半径稳定盘旋的滑翔伞展向升力分布变化是非常大的，参见图五：

figure 5 : lift variation along span, in turn

图五：小半径盘旋的滑翔伞升力的展向变化

滑翔伞的螺旋稳定性由如下设计参数决定

Modifying the symmetry, according to the same “design drivers”, of the lift spread can cause either a stability or instability in spiral:

1. Shape of the arc (more or less flat)

2. Length of the lines

3. Spread of the braking along the trailing edge

1 伞的弯曲形状

2 伞绳的长度

3 刹车在后缘的分部

图六显示了三种可能

Figure 6 shows the different cases that can occur:

1. First case: with a flat arch and/or short lines, a paraglider is subjected to an inside induced roll and tends to engage in the turn (spiral instability)

第一种情况弧度很平的伞或者伞绳比较短的伞，其升力分部是趋向于减小盘旋半径，螺旋不稳定 2. Second case: with curved arch and/or long lines, a paraglider is subjected to an inverse induced roll and tends to exit the turn (spiral stability)

弯度比较大的伞或者伞绳比较长的伞，升力分部趋向于向外转动，增加半径，螺旋稳定

3. Third case: if arch and line length are combined to obtain a null moment, the paraglider stays at constant bank angle(neutral in spiral).

第三中情况，中性稳定，转动力矩为零

figure 6 : spiral stability

Obviously the results obtained for a canopy for a given bank angle have no reason to be the same for a different angle, this explains the strange or even dangerous behaviour of some models.

显然同一顶伞在不同半径盘旋的时候，所产生的表现是不相同的，这就解释了某些设计在某些状况下是非常危险的。

As a rule of thumb, the certified canopies on the market (not all of them…) are usually rather spiral stable or spiral neutral for “normal” bank angle. This explain, still as a rule of thumb, that constant bank angle needs for this canopy continues application of the inside brake to compensate the speeds spread and cancel the inverse induced moment roll, as shown in figure 7.

所以，上市的伞（当然也并非所有上市的伞）通常在常见的倾角下都是螺旋稳定的，至少是中立稳定的，这也就解释了为何要保证稳定的螺旋（而不改出），需要保持内侧的刹车，以平衡由内外速度差异导致的改出力矩，如图七：

figure 7 : stabilized turn

Are this thoughts of any use?

这些道理有啥用呢？

They are probably essential for a paraglider designer since they allowed for a new project with the right computational tool to determine the curve of the canopy, the length of the lines and the spread of the braking. Admittedly, you still have to do many long and meticulous tests and tunings to refine the turning behaviour. This is where with a lot of means, pilots and prototypes professional manufacturers make the difference with small amateurs. However, nowadays, a designer can almost guaranty that a paraglider will fly “properly” straight out of the computer.

对于设计者而言，明白这些理论结合现代计算工具可以方便的确定伞的形状和伞绳的长度，可以减少为了取得优异的转弯性能而做的很多费时费钱费料的原型号伞飞行试验和调试工作，而这些飞行试验和调整工作正是职业的厂家和飞行员比业余设计者所不同的地方。所以，现代设计师几乎能够完全保证一个能够正常表现的滑翔伞从计算机中“飞”出来！

For the average pilot, they will help him/her to know better his/her or other canopies, to understand them and appreciate piloting them avec the feeling the one knows a bit more of these wonderful flying machine.

对于普通的爱好者而言，可以更加深入的了解他们的滑翔伞从而更好的飞行。

Finally, I would very satisfy if my modest contribution could prevent what you can hear a the “terrasse du Planfait” or somewhere, even read in some “specialized” media: the never-ending speech on the completely mysterious and extraordinary complex nature of paraglider turns, so complicated that even the major aero-spatial companies would not have cracked it!