确定一个平均弧线 [英] Determining a mean camber line

问题描述

研究员程序员，

我知道这是一个小的juridistiction外面，但我想知道也许如果你有时间，如果你能帮助我有一个过程。不考虑数学的，但什么是采​​取的最好办法。

I know this is a little outside your juridistiction, but I was wondering perhaps if you have time, if you could help me with one "procedure". Not in view of math but what would be the best way to take.

这是一种翼型/ profile文件。一般，型材有定义两组数据。一个是平均弧线线的位置，在X，Y的其中x通常在弦长的百分数给出的形式给出。第二组数据是厚度在弦长的百分比。厚度总是画垂直于​​弧线（！），并且，使该剖面点

This is an airfoil / profile. Usually, profiles are defined with two sets of data. One is the position of mean camber line, given in the form of x,y where x is usually given in percentages of chord length. Second set of data is thickness at percentages of chord length. Thickness is always drawn perpendicular to the camber line(!), and that gives the profile points.

现在，我有一个相反的问题 - 我有一个轮廓点，我需要确定弧线的位置。插值贯通点方法可以不同，但​​没关系，因为我需要我可以一直插尽可能多的积分，所以谈到到底是线性的。

Now, I have a reverse problem - I have points of a profile, and I need to determine the position of the camber line. Method of interpolation through points can vary, but it doesn't matter, since I can always interpolate as many points as I need, so it comes to linear in the end.

记住，由于thinkness绘制垂直于弧线，弧线的位置曲线的上部和下部线的点之间的不平均（称为简档的背面和面）。

Remember, since the thinkness is drawn perpendicular to the camber line, the position of camber line is not mean between the points of upper and lower line of profile (called the back and face of profile).

编辑（这是如何在纸面上完成）：的呃，痛苦和大型（我这里所说长A0纸，那是1189x5945mm在大绘图桌可以通过绘制启动通过的面的点和背部在相同的x坐标之间的中点（平均分）的第一弧线（CL）的迭代。之后绘制了大量的垂直线，垂直于该CL和找到面和背面之间的中点（在正面和背面的积分将不再有相同的X值）的连接，这是你的第二个迭代CL。之后，你只是画垂直线到了第二CL重复该过程的第二个步骤...（它通常在3或4次迭代收敛）。

Edit (how this is done on paper): Uhh, painfully and in large scale (I'm talking long A0 paper here, that is 1189x5945mm on a large drawing desk. You start by drawing a first camber line (CL) iteration through the midpoints (mean points) between the points of face and back at same x ordinates. After that you draw a lot of perpendicular lines, perpendicular to that CL, and find their midpoints between face and back (those points on face and back will no longer have same x values). Connect those, and that is your second iteration CL. After that you just repeat the second step of the procedure by drawing perpendicular lines onto that 2nd CL ... (it usually converges after 3 or 4 iterations).

2日编辑：的替换的画面，其中一个更显示了如何thinkness被拉到弧线（CL）。 $ P $的另一种方式psenting它，就如同画面二号。如果你画了很多圈，whoce中心点位于弧线，并且其半径是厚度的量，然后切线这些圈子将是线（将弥补这个曲线）的配置文件。

2nd Replaced the picture with one which better shows how the thinkness is "drawn" onto the camber line (CL). Another way of presenting it, would be like picture no.2. If you drew a lot of circles, whoce center points are at the camber line, and whose radiuses were the amounts of thickness, then tangents to those circles would be the lines (would make up the curve) of the profile.

的弧线不是平均线（脸的点和背面之间的意思）;它可以用它（因此通常是混淆）一致。这种差异是很容易看到更多的弧形轮廓（更弯曲的）。

The camber line is not the mean line (mean between the points of face and back); it can coincide with it (therefore usually the confusion). That difference is easily seen in more cambered profiles (more bent ones).

3的编辑 - 来说明差异显着（对不起，我花了这么长的时间绘制）平均线和弯度线之间，这里是如何通常是纸上谈兵的过程。这是一个相当变形轮廓，其原因，这两者之间的差，可以更容易地示出（虽然这样的配置文件也存在）。

3rd edit - to illustrate the difference dramatically (sorry it took me this long to draw it) between the mean line and camber line, here is the process of how it is usually done "on paper". This is a rather deformed profile, for the reason, that the difference between the two can be more easily shown (although profiles like this exist also).

在此图象平均线所示 - 它是由脸的平均值和背面上相同的x坐标形成的线

In this picture the mean line is shown - it is a line formed by the mean values of face and back on the same x coordinates.

在这幅画上的平均线，垂直线绘制（绿色的）。这些垂直线的中点弥补弧线（红色间断线）的第1次迭代。看到那些圈子如何适应比起第一张照片的机翼内更好。

In this picture onto the mean line, perpendicular lines were drawn (green ones). Midpoints of those perpendicular lines make up for the 1st iteration of the camber line (red intermittent line). See how those circles fit better inside the airfoil compared to the first picture.

在弧线的第二迭代下面的图片所示，沿着与来自第一图像的平均线作为说明两者之间的差异。这些圆圈装修更好，现在里面（除非它飞出了第一个，但不介意他）。

In the picture below the 2nd iteration of the camber line is shown, along with the mean line from the first picture as to illustrate the difference between the two. Those circles are fitting even better now inside (except that first one which flew out, but don't mind him).

推荐答案

据我可以从图中聚集，弧线是被它的切线平分上下的两条切线之间的角度线确定边缘。

From what I can gather from your diagram, the camber line is defined by it being the line whose tangent bisects the angle between the two tangents of the upper and lower edges.

在换句话说，你的弧线总是两个边缘之间的平均点，而是沿着一条线的顶部和底部边缘之间最短距离的

In other words, your camber line is always the mean point between the two edges, but along a line of shortest distance between the top and bottom edges.

所以，给出的y坐标 Y =顶部（X）和 Y = BOT（X），你为什么不：

So, given the y-coordinates y=top(x) and y=bot(x), why don't you:

<pseudocode>
for each x:
  find x2 where top(x)-bot(x2) is minimized
  camber( mean(x,x2) ) = mean( top(x),bot(x2) )
</pseudocode>

然后插值等。？

and then interpolate etc.?

抱歉！关于第二个想法，我认为这应该是

Sorry! On second thought I think that should be

  find x2 where ( (top(x)-bot(x2))^2 + (x-x2)^2 ) is minimised

显然，你应该尽量减少垂直线的长度。

obviously you should be minimising the length of that perpendicular line.

是吗？

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