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Regarding your test conditions, there is one irrelevant factor there, and that is ‘sink rate’. … . with a tunnel fin there is no such thing as the fin is not free to sink, it is restrained by the bottom of the surfboard . … . in the bathtub ‘whizz test’ ( apologies for not being clearer about how it should be conducted) the hand is supposed to hold the tunnel, moving it through the water while changing the angle of attack and feeling the effects of flow through the tunnel and stall directly through the fingertips. ……
That condition was added since I assumed that the trajectory of the tunnel in free fall would be used to estimate the lift coefficient (instead of the “feel” method).
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PS In my reply to you a made a calculation which included the horizontal lift cabability of the half tunnel, not sure if the tunnel produces exactly half as much horizontal lift as it does vertical lift ( it could be more,but is unlikely to be less) the main point is that it does produce significant horizontal lift, and so for a fair comparison of surface area vs lift, this has to be taken into account (in othere words the tunnel must be compared with an equivalent planar fin combination which provides horizontal and vertical lift.
The point I was making was that the foil generates NO NET horizontal lift force unless it is aligned at an angle of attack about the yaw axis relative to the free stream flow. If it is aligned with the free stream flow in yaw, but there is an angle of attack about the pitch axis it only generates a net lift. Otherwise, by symmetry, how would “it” know whether to direct this force to its left or to its right (say, when looking upstream) ??? . The addition of a rotation about the yaw axis to generate a net horizontal force generates a new source of additional drag which must be added to the drag associated with generating a vertical lift.
Getting back to “handling” angles-of-attack for low vs high aspect ratios annular wings/foils…
I went back through the history of posts that the two of us have made in this thread and I think perhaps I have identified the source of our differences.
A wing (annular, or planar) generates lift by imparting momentum to the water approaching the foil. In the case of generating vertical (upward) lift (chosen for the following discussion for simplicity), the deflection of the oncoming water is directed downward by the action of the wing. An ideal wing would deflect all the water lying within the wing’s area of influence. In reality, a portion of this oncoming water will instead deflect to both sides of the wing instead of being deflected downward–and hence it will not contribute to the lift. The result is that if the same lift is to be generated, the angle-of-attack must be increased so that the water that is deflected undergoes additional deflection. The consequence of that is that the induced drag of the wing is increased. If the fraction of water passing around the wing, instead of under and over it, is a small fraction of the total flow, there is not much loss of lift (compared with an “ideal” wing with no deflection). This situation occurs when the path length under or over the wing is substantially shorter than if the water were to divert to the sides and pass around the wing.
An indicator of the relative “lengths” of these two “paths” is the aspect ratio, which, in its simplest form (appropriate to a rectangular wing) is simply the ratio of the span of the foil to its chord length. For other wing planforms it is the ratio between the maximum span of the foil to the average chord length. A convenient way to express this is that it is the square of the maximum span divided by the effective planform area.
The other extreme is when the aspect ratio is small (e.g. the maximum span is short compared with the chord length of the wing). In this case, a large fraction of the oncoming flow diverts around the wing rather than passing over or under it. Since the diverted fraction is large, the vertical lift generated is sensitive to any changes in the fraction of total flow that passes over or under the wing, and the vertical lift generated becomes approximately proportional to the aspect ratio, rather than only weakly dependent on it (as is the case at high aspect ratios). At intermediate aspect ratios, there is a transition from the characteristics of low aspect ratio foils to high aspect ratio foils as the aspect ratio increases.
The attached graphic (approximately) illustrates this type of dependence for an annular wing (the similar graphic in my previous post was for a planar wing).
[Edit: seems I can’t put the graphic inline, so I’ll attach it to the end] [Edit: here it is. (JM 5/21/07)]
Although there are no distinct breakpoints on the curve, it can be seen that there are regions that approximately exhibit the behavior described above. More specifically, it can be seen that low aspect ratio wings roughly emcompass aspect ratios between 0 and 2-3, high aspect ratio wings are characterized by aspect ratios roughly in excess of 7, and intermediate aspect ratio wings fall in between these two regions.
Annular wings with aspect ratios that are sufficiently large to fall in the “high aspect ratio” range have lift characteristics that are similar in dependence on aspect ratio and angle of attack as planar wings with aspect ratios that are high engough to be their “high aspect ratio group”. Wings with aspect ratios sufficiently low to fall into the “low aspect ratio group” have a different set of characteristics. In particular, the high aspect ratio group is characterized by lift coefficients that increase approximately linearly (more accurately: like the sine of twice the angle-of-attack) until reaching the vicinity of the stall angle. What happens after that depends to a considerable degree on more specific charactersitics of the wing, such as the leading edge radius, foil thickness, foil shape, camber, and wing planform).
For traditional planar planforms (e.g. rectangular, elliptical, etc.), the rate of increase in vertical lift with increasing AOA for a low aspect ratio wing is similar in shape, but lower in magnitude, to that of a high aspect ratio wing (e.g. approximately linear but with a small convexity). But in some ways, the characteristics of the low aspect ratio wing can be influenced by specific characteristics of the wing, such as planform. For example, the rate of increase in vertical lift of a low aspect ratio wing with a delta wing planform is also roughly linear, but now with a small concave addition rather than convex. Overall, the general trend of low aspect ratio planar wings is toward a reduced slope to the rate of increase of lift with increasing angle of attack, accompanied by lesser reduction in the maximum value for the lift coefficient at stall. The end result is that as a group low aspect ratio planar wings encompass a greater range of angles of attack between no lift generated, and the stall angle.
The characteristics of annular wings with high aspect ratios (i.e. falling within the “high aspect ratio group”) share many similarities in their characteristics to those of planar wings with high aspect ratios (i.e. that are members of their respective “high aspect groups”)–although the magnitudes of various parameters may be different (e.g. as reflected by the differences between the theoretical maximum “wing efficiency” values for an annular wing and a planar wing).
The situation becomes more complex for annular wings with small aspect ratios. But the “stall” plot at the Hummingbird site and “Tom Bloke’s” description of his observations may provide some insight and guidance.
The Hummingbird has a duct aspect ratio of about 1.9 – in the low aspect ratio group, but near the upper end for an annular wing. Their web site states that stall occurs at an angle-of-attack of 19-20 degrees, but that the wing is “still lifting powerfully” at an AOA of 24 degrees and “the inside surface stall pattern has reached forward only about as far as the aft propeller”. It’s not clear what criteria was used to identify the stalled condition, nor do they show the lift coefficient as a function of AOA, so it’s difficult to draw definitive conclusions, however it does appear that the lift coefficient is still large at 24 degrees. This is in contrast to a high aspect ratio annular wing, which would be expected to stall (in the absence of high lift devices) at an AOA less than this and accompanied by a substantial loss of lift. Therefore it seems likely that at least this low aspect ratio (1.9) annular wing has a greater range of angle of attack between the zero lift angle and the stall angle (and especially between zero lift angle and where a substantial reduction in lift occurs than an annular wing belonging to the high aspect ratio group.
Getting back to your objection:
I posted on May 18, 2007:
I’m claiming that a low aspect ratio tunnel handles higher angles of attack that an high aspect ratio tunnel (in the sense–as I said in my earlier post–that the onset of a stall occurs at a lower angle of attack for a high aspect ratio foil than for a low aspect ratio foil).
To which you responded:
No it doesn’t, a low aspect ratio ratio tunnel stalls at a lower angle of attack than a high aspect ratio tunnel
I have reviewed all your and all my posts on this thread and I think I understand why we differ. In summary, in my discussion when I refer to “high aspect ratio” foils/wings I mean foils/wings with aspect ratios that fall within the “high aspect” ratio range in my graphic of aspect ratio function vs aspect ratio. It appears from your posts (and your suggested examples) that “high” and “low” relate to a pair of foils/wings in there relationship to each other in regard to aspect ratio (i.e. “higher” or “lower”) – independent of what their actual aspect ratios are. Indeed, your recommended aspect ratios of 1 and 3 in your early post in this thread, as well as your examples for the bathtub experiment (0.25 and 1) I would classify as low aspect ratio foils. So as I see it, none of your discussion relates to a comparison between high aspect ratio foils and low aspect ratio foils, but rather to higher and lower aspect ratios within the group of low aspect ratio foils.
For an example of an intermediate aspect ratio foil (Ar ~ 5) check the “ringwing” graphic at
http://www.esotec.co.nz/hb/HTML/Aero_F.html
An example of a high aspect ratio foil would be the Mellor foil that is the focus of this thread if the chord of the hoop was constant and equal to that of the smallest section (Ar = 8)
[Aside: It appears that you made the same mistake I did in one of my earlier posts. For an annular wing, the aspect ratio is not simply the span divided by the chord, but rather the span squared divided by the effective planform area. The difference is that the effective area is the sq-rt of 2 (1.414) times the projected planform area. Hence your (and my earlier) aspect ratios must be reduced by dividing by 1.414. With this correction, your recommended aspect ratios should be changed to 0.707 to 2.12, and the bathtub experiment aspect ratios to 0.18 and 0.707. These are certainly well within the “low aspect group” range shown in the aspect ratio function graphic.]
Your bathtub observations regarding the cessation of flow through the (very) low aspect ratio wing/duct are interesting and I have a couple of comments I’d like to make. But in view of the length of this post already, I think I’d better wait for a while.
mtb
