



17. We could now go ahead and use the aerofoil sections we have to create our wing surfaces, but before we do that we should check how smooth the curves are. If they are not very smooth, the surfaces will be uneven too. Rhino has several tools for examining curves and surfaces and a very useful one is the Curvature Graph. This plots a graph along a selected curve, with the height of the graph indicating the degree of curvature at that point. Here is the graph in action, selected from the Analyze menu, with the upper section curve selected. Points to note include, at A the graph crosses the curve a couple of times. The graph goes on the ‘outside’ of the curve, so at the rear third of the section the curve reverses slightly as it gets closer to the trailing edge, before flipping back the other way at the last moment. That is OK, this reflex curve is typical of such high performance wing sections. 
18. At B the graph is very rough, showing that the degree of curvature is changing sharply, A surface generated from this line would appear to be a series of flats with creases in it. Not what we want at all! Finally at C we notice that the last line of the graph is angled upwards. The lines that make up the graph are perpendicular to the curve at that point. Since the leading edge of our aerofoil should wrap smoothly around with the undersurface, we would prefer the very end of our curve to be vertical, so the last line of the graph should be horizontal. Why these anomolies occur when we use good original data is due to several factors. We will have to be careful how we edit the curve so as not to loose its overall shape, but we can clean it up and get much betterlooking surfaces as a result. 

19. Rhino has a great many tools for editting curves. Check out the Rhino help files and tutorials for full details. We will look at several of the basic methods of editing curves, then go back and check our work with the Curvature Graph. The first image shows our aerofoil with ‘Display Points’ selected. These white markers indicate the vertices we imported from the raf34.dat file, and the curve we created with the InterpCrv tool will pass exactly through each point. Rhino has to make an educated guess as to where the line goes between the points, and this is where some of the roughness in our curve originates. We could select and move these points to smooth the curve, but since these are from our original source material, it is better to leave these alone at this time. 

20. Next tool to look at is Control Points. Selecting a curve this way brings up another series of points, this time linked by a dotted line. 

21. We will zoom in to the leading edge to get a clearer view of these Control Points. 

22. These Control Points ‘influence’ the way the curve changes direction as it runs through its vertices. The mathematics involved with this are fundimental to the way NURBS systems work, and I won’t attempt to explain them here. Much better to grab hold of a control point and drag it about. You will see immediately how the curve reacts as the point is moved. Here we have dragged the second control point (not the first one, which is on the end of the curve) and moved it forwards slightly so the leading edge is more rounded. The solid yellow line is our revised aerofoil curve, the black line the original one. The short black line shows the position of the control point before and after the move. It is a good idea to copy/paste the original curve, so you can see how far the edited curve has been moved, and to judge the improvement in smoothness. 

23. It is easy to move along the curve smoothing out any irregularities this way. Control points can be moved or even deleted entirely, but do not move the points at the ends of the curve. Compare against the original as you go, using the Curvature Graph as a final check. Here is the curve we edited, showing a much smoother graph. Repeat for the other curves if needed. 

24. You can move these control point around manually with a mouse, or use the nudge keys. You will probably have to adjust the nudge key settings to a very small amount, but this gives much greater control than moving the points manually. You alter the nudge values in the Rhino Opions dialogue box, shown here. Remember the values are in the same units set for the whole document. 

Now we can return to locating our aerofoil sections correctly and start work on surfacing our wings. Any comments, just drop us an email. 


