Digitizer Results

(Note, “-PT" (Princeton Tests) is appended to the airfoil name to distinguish the digitized coordinates from the nominal coordinates.)

In Chapters 10 and 11, each of the actual sections is plotted against the nominal coordinates at half scale (6 vs 12 in). The legend inside the airfoils shows what is being compared; the solid line is always the first airfoil, normally the prototype, and the broken line the second, normally the test section. In a few cases different prototypes are compared. Before they are plotted, the two airfoils are fitted in a least squares sense. The fitting uses two variables—relative vertical location of the entire section and relative rotation of the entire section— to produce the lowest possible RMS difference without distorting the airfoil. This difference is shown under the trailing edge of the upper plot.

The lower plot shows the difference, or error between the two airfoils on a much expanded scale. The upper surface difference is the solid line and the lower surface the broken one. If the two sections were perfectly matched, the plot would be two straight lines lying on the horizontal axis. A displacement above or below the axis means the test section surface lies above or below the nominal, respectively. If the solid line is above (or below) the broken one, regardless of its position with respect to the axis, the section is too thick (or thin) at that point. If both lines sweep up or down together then the camber is in error. Camber error as well as thickening is frequently seen at the trailing edge.

The short, inward-facing tics show the positions of the leading and trailing edges. The most difficult point to measure is the vertical position of the leading edge. (It is quite possible for a model to have more than one leading edge.) This is because the slope becomes infinite and a very small change in the chordwise position of the probe produces inordinately large changes in the measured thick­ness. Consequently, the vertical locations of the exact edges, as shown by the position of the tics, have somewhat reduced accuracy. However, because many points were digitized near the leading and trailing edges and because the contri­bution of each point to the overall accuracy number was weighted in proportion to the distance between it and the adjacent points, the effect of the end points on the overall error is very small. In addition, the most forward and most rearward points themselves were not included in the error calculation.

As a check on the digitizing procedure, two of the models were digitized more than once: the SD7080-PT and the SD7003-PT. The SD7080 pair was done early in the profiling as a general check for repeatability, but the spanwise stations were not the same. Even so, the agreement was within 0.003 in. The SD7003-PT was digitized six times; once at the beginning of the profiling, five times at the end (a time span of about 75 days). Two profiles, the SD7003-PT and SD7003-PT (R) were taken at the same station and are a good indication of the overall repeatability of the measurement setup—about 0.0007 in, 0.006% of chord. The remaining four profiles were taken at 3 in intervals centered on the span and were intended to discover how much spanwise variation a good airfoil model might show. As can be seen in Figs. 10.46-10.49, it is very small indeed.

Several observations can be made about methods of construction based upon the models digitized in this study. Built-up, sheeted models tended to have a problem with the blend between. the leading edge and the beginning of the sheeting. The trailing edge also tended to be thick. Foam core sections usually had sharper trailing edges, but any errors in contour were more prolonged; with built-up sections the errors were more local. One model had excellent contours for the separately molded upper and lower surfaces, except the joint at the leading edge was too wide. Because of the type of construction, the increased thickness at the leading edge carried back through a large part of the airfoil. This was a problem that was not present in models that used a single piece—usually wood—leading edge. The open-bay models have no single profile—over the ribs it can be accurate, but inevitably there is sag between the ribs.

Neither the cost nor the type of construction was a good indicator of the accuracy. For example, a balsa-sheeted, rib and spar section built over a weekend for under $10 had one of the most accurate profiles measured. On the other hand, the accuracy of some models costing many times this amount was only average.

Trailing edges are a problem for all types of construction. As can be seen from the plots, the most common error is a poorly contoured trailing edge; it is warped either up or down, with the preponderance being up. Since the

sensitivity of performance to trailing edge location is high, clearly there is a general problem here. One model, the S4180-PT, had a very thin trailing edge which was so warped that it was meaningless to measure it at all; there simply was no representative section. (This was the only model with such a major contour discrepancy.)

Some of the nominal airfoils differ less between themselves than the models do with the ideal coordinates. The HQ2/9, RG15, and S2048 are an example of this, and several plots compare these prototype sections. This has significance when comparing polars, because small differences in performance on similar sections could be a result of the inaccuracy of the model or random variations in the test results rather than an indication of the superiority of one prototype section over another. One model, the E193-PT, was actually a better fit to the E205 than to its true nominal coordinates (see Figs. 10.5 and 11.12). These airfoils are, of course, quite similar, but the point is that one must be careful in claiming performance for the prototype based on the model’s performance. In cases where the model is inaccurate, the performance applies to the model airfoil and not necessarily to the nominal airfoil.

One section, a SD7032, was first tested in the tunnel with no covering over the sanded balsa sheeting (version A: SD7032A-PT), then with Monokote covering (SD7032B-PT), and finally with a flap (SD7032C-PT). Only the flapped version was digitized.

The DF102-PT and DF103-PT are compared to the DF101-PT, not to a nominal airfoil. (The DF101-PT is compared to the nominal.) Since the point of these variants was to explore the effects of changes on the forward upper surface, the relevant prototype is the DF101-PT. The plots show what and how much was added or removed in that, area. The minor differences along the rest of the airfoil are due to the fact that the sample chords were not all at the same spanwise stations, and because the fitting routine tends to distribute the deliberate “error” over the entire airfoil so as to keep the RMS error down.

For a few airfoils (SPICA, WB135/35, and WB140/35/FB) the coordinates were supplied by the builders. In these cases small errors in fit are not meaningful because hand-generated coordinates are not smooth in the mathematical sense, and therefore the spline routine that compares the airfoils can have residuals of the order of the errors. This is particularly noticeable on the upper surface of the WB135/35 between 1% and 3% chord, where the model is smoother than the nominal.