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[15 Mar 02] I am studying in Naval Architecture Department, Ocean Engineering Faculty, Sepuluh Nopember Institut Of Technology, Surabaya Indonesia. Before I complete my studies, I must do experiments as requirement from my college. I want to experiment with about lift and drag for a foil of a Hydrofoil Craft. This experiment is using Computational Fluid Dynamic (CFD) with ANSYS 5.6. But I am confusing about what NACA Foil Series is suitable for Hydrofoil Craft, and what the principal reason for choice this NACA Series. -- Hot Pungka Purba (firstname.lastname@example.org)
[15 Mar 02]You haven't said what the requirements are for your section. Since you mention NACA foils, I assume that you are interested in the subcavitating speed range. You need to have some idea of the range of lift coefficients are required of your foil - this is driven by the load the foil has to carry and the variation in angle of attack the foil will experience as it goes through waves. Something like Cl = 0 to 0.6 with a design Cl = 0.3 would be typical. The intended speed range for the vessel is critical - what are the takeoff, cruise, and dash speeds? And you need to know how the craft will be controlled - will the foils be surface piercing or fully submerged, and will they change incidence or have flaps?
I believe there are four key problems in subcavitating hydrofoil section design. First, you want to avoid separation because this invites ventilation as well as causing drag. Second you want to avoid cavitation. Of course, you also want low drag, and fortunately the things you do to get a high cavitation speed and avoid separation are also good ways to minimize the drag. Finally, the section may be operating close to a free surface, and this modifies the velocity distribution about the foil.
Since cavitation begins when the lowest pressure anywhere on the foil drops below the local vapor pressure of water, you want to minimize the maximum velocity. That means no sharp pressure peaks allowed! At the same time, you want the average velocity over the top surface to be as high as possible so as to produce the most lift. This drives the design to shapes which have long, flat pressure distributions - shaped like building with a flat roof.
The NACA sections which have this type of rooftop velocity distribution are the 6-series laminar flow sections and the earlier 1-series (i.e., 16-012, etc). The 1-series sections have a shallow favorable pressure gradient back to 60% chord, but they have a highly convex pressure recovery that is not necessarily a good characteristic if one wants to avoid separation at the trailing edge. So a comparable 6-series section (say, 66-XXX) would probably be a better bet than the corresponding 16-XXX section.
There are other more modern hydrofoil sections, such as the Eppler designs. Try to get his book, "Airfoil Design and Data". It is out of print, but your engineering library should be able to find it. He talks about the philosophy of hydrofoil design and has several sections specifically designed to be hydrofoils.
You can also design your own hydrofoils using XFOIL, which you can download for free. XFOIL is more modern code than the Eppler code, but you can still design sections like Eppler's using XFOIL. This would be a good start to analyzing with ANSYS because ANSYS doesn't have the inverse design capability of XFOIL but it does have a more powerful analysis capability. So you would be able to compare the experimental results, the inviscid+integral boundary layer results, and the Navier-Stokes CFD results, at least for subcavitating flows.
Simulating the two-phase flow that results from cavitation would be a difficult challenge! But it has been done, and this makes a Navier-Stokes method worthwhile. Unfortunately, much of the research has been done using NACA 4-digit sections (like 0012, 0015), and I suspect this is either out of ignorance as to what makes a good hydrofoil, or perhaps because these are bad hydrofoils and cavitate more easily!
Say you are concerned with a fully submerged hydrofoil with flaps to control the height of the vessel. As the boat flies through waves, the orbital velocity of the waves will change the angle of attack on the foil and thus the lift. The control system will try to compensate for this by moving the flap. If the boat is flying along perfectly level, a good approximation of a perfect control system would be one that maintained a constant lift coefficient on the foil as the angle of attack changed. Thus you need to consider three cases: zero angle of attack with the flap at neutral, positive angle of attack with the flap deflected up, and negative angle of attack with the flap deflected down. The larger the flap deflection, the greater the angle of attack change that can be tolerated while still maintaining the same lift coefficient, and the higher the sea-state in which the ship can operate. For each of these three cases, the peak velocity will occur on a different part of the foil. You would want to design the foil so that the value of the peak velocity is the same in each case. This will give you the highest speed without cavitating. But larger flap deflections and a greater angle of attack range means higher maximum velocities and thus a lower operating speed without cavitating, so there's a tradeoff between the ability to operate in rough seas and the vessel's maximum speed. It's an interesting design problem! But one that comes back to knowing the original requirements in order to design (or select) the appropriate section.
Take a look at ...
-- Tom Speer (email@example.com) website: www.tspeer.com
Just after I pushed the "Send" button for the preceding email, I found a good link about using Fluent to calculate cavitating flows, but I didn't save the link. I can probably find it again if anyone is interested. I've also thought some about why the 16-XXX sections are so popular for hydrofoils over the 6-series, and I think it must be because they have a much thicker and stronger trailing edge. So perhaps I was too hasty in recommending the 6-series because they may not be practical for the very high loadings of hydrofoils. Flexing of the trailing edge can lead to singing, too. By the way, there are some interesting papers at U. Mich. on their large-scale hydrofoil (8' chord!) test. -- Tom Speer (firstname.lastname@example.org) website: www.tspeer.com
[22 Oct 01] I am presently dealing with the design of a hydrofoil boat with fully submerged hydrofoils. The foil section design as well as the strut design are already well established but the hull design is still under development. Since the craft will be powered by a water jet system very similar to the Jetfoil propulsion system, the hull resistance near take-off speed seems to be critical for the overall power requirements according to my calculations (hump speed power). I have not found any reliable literature information regarding the hull resistance characteristics from standing to take-off speed. Of special interest is the hull resistance decrease when lifting the hull off the water near take-off speed. An article from Charles G. Pieroth/Grumman Aerospace Corporation dealing with 'hydrofoil hullform selection' published in Hovering Craft & Hydrofoil in 1977 does just give general recommendations. Also on the IHS-homepage I could not find further useful information. Can anyone provide me with more detailed information? -- Sebastian Muschelknautz (Sebastian.Muschelknautz@Linde-VA.de)
[22 Oct 01] I don't know if the following will be of assistance, but you may like to look at these papers:
Sakic, Prof Dr Vinko (Maritime Institute, Split); 'Approximate determination of the propulsive power of small hydrofoil craft', High-Speed Surface Craft, March 1982. (This discusses resistance in hullborne mode and transfer into foilborne mode but only over about two pages).
Latorre, Dr Robert; 'Hydrofoil Craft Performance Calculation', Naval Engineers Journal, March 1990. (again, this addresses performance on take off).
Finally, the Maritime Research Institute Netherlands (MARIN) once offered for sale a program for the hydrodynamic design and analysis of hydrofoil craft in calm water called 'HYDRES'. This included "the calculation of the resistance for hullborne, take-off and foilborne speeds". It was apparently based on the use of Series 65 hard chine planing hullforms. Further details may be available via the MARIN website but I have not checked that. -- Martin Grimm (email@example.com)
[3 Apr 01] I'm assessing high-speed sailboat designs, using the expression for maximum wind-factor asymptote, 1/( (1/Ga) + (1/Gh) ). This requires reasonable values for aerodynamic and hydrodynamic glide ratios, Ga & Gh. I have no trouble finding glide ratios for airfoils, subcavitating foils, and planing steps, but where do I find data relating aspect ratio and angle of attack to glide ratio for supercavitating foils? I need reasonable, but not exact values, within 20% or so. Some suggest using one-third the glide ratio of a subcavitating foil, but... is the planing step glide ratio a better approximation? -- Phil Morris (firstname.lastname@example.org)
[4 Apr 01] The reference to 'glide ratio' is unusual but it actually corresponds to the overall lift-to-drag ratio of the airfoil / hydrofoil (or aircraft / boat) in question. For instance, a high performance glider has a glide ratio of 1:40, i.e. in still air, it will drop 1 metre in altitude for every 40 metres in horizontal travel. To achieve such a good glide ratio, the drag of the whole glider has to be no greater than 1/40 of its lift (which is equal to its weight). A lot of work was done on supercavitating hydrofoil sections for US Navy hydrofoil projects in the 60s and 70s timeframe. You would find some of it published in the Society of Naval Architects and Marine Engineers (SNAME) journals such as Journal of Ship Research. One main researcher in the field was Marshall P. Tulin. You are right that the glide ratio (lift to drag ratio) of supercavitating foils is not generally as good as fully wetted foils so your use of 1/3 of the glide ratio is at least tending in the right direction. The glide ratio will vary considerably as a function of the angle of attack of the foil. The greatest glide ratio is achieved for relatively small angles of attack on typical airfoils such as on gliders. -- Martin Grimm (email@example.com)
[3 Apr 01] I believe by glide ratio you means the lift/drag ratio. A sailplane's glide ratio is the same as its L/D. The equation you listed is the correct performance relationship for a sailing vehicle, but you have to ensure that the lift and drag you plug in is the lift to the side (in the horizontal plane and perpendicular to the oncoming flow direction) and the total drag. The vertical L/D is irrelevant except that it dictates the drag that will be added into the total. With hydrofoils it's easy to get confused, because the L/D one has to use in the performance equation is really the lift of the strut divided by the total drag. Since you didn't ask about the strut, I will not get into a long discussion on the topic. I also don't have the parametric design information for which you're asking! Here's what I have been able to put together on the feasibility of high speed supercavitating sailing hydrofoils.
- The best supercavitating foil performance I've found (and admittedly I don't have much to draw from) was a T-foil and strut designed for operation at 60 kt and tank tested at the Lockheed Underwater Missile Facility. Aspect ratio was 5, taper ratio was 0.5, and the foil was swept back so that the trailing edge was straight. The section was 7% - 7.5% thick. That foil's design takeoff speed was 35 kt, where it had an L/D of 13 at a lift coefficient of 0.5 based on the wetted section. At high speed, the chord was effectively less due to the aft 20% or so on the lower surface not being wetted (the structural annex portion). It required a lift coefficient of at least 0.2 to avoid wetting of the upper surface at high speed. It achieved an L/D of 9 at a speed of 65 kt and a depth of one chord. An 18% thick parabolic strut tested for side force at 70 kt had a maximum side force coefficient of 0.1 at one chord depth and a leeway angle of 4 degrees. Strut chord is typically 50% bigger than lifting foil chord due to the taper in the latter. So adopting this same design to support a sailing hydrofoil, at high speed, the maximum sideforce is 15% of the lift. L/D for sideforce is probably around 5 at best. The total drag divided by the sideforce gives a ratio of 1.06, for a "drag angle" [arctan(D/L)] of 46 degrees. Even if the aerodynamic L/D were 10 (which is probably twice current practice), this results in an apparent wind angle of 52 degrees and a top boatspeed/windspeed ratio of 1.3, so the required wind speed would be 46 kt to achieve the 60 kt the design speed of the foils. At a depth of 3 chords and assuming the lateral L/D also went up to 9, the achievable sideforce is 90% of the weight, the transverse drag angle of the foils is 13 degrees and the apparent wind angle is 19 degrees, for a boatspeed/windspeed ratio of 3 and a true wind speed of 23 kt. This is about the same performance as a competitive land yacht in these winds, operating on a smooth flat surface. So these numbers have to be considered as highly optimistic at best and the feasibility of the supercavitating hydrofoil is a long shot.
- Here's another example of supercavitating hydrofoil design that shows how sophisticated one's design capabilities have to be. One can make a guess at possible performance, as I've done above, but to actually achieve those numbers requires the ability to accurately compute the details of the drag components. Hydronautics designed a helicopter-towed minesweeping sled that had 4 ladder foils at the corners. Each ladder had three foils - one subcavitating, one base-ventilated, and one supercavitating. The central strut was a modified parabola (parallel surfaces at the trailing edge) canted 25 deg from the vertical. The top rung and a diagonal strut were a 16(35)04 section (4% thick subcavitating NACA design), the base ventilated rung looked to be a cambered parabola with nearly a delta planform, and the bottom rung was a tapered, swept-back planform with a sizeable annex (rectangular structural addition) behind the wetted supercavitating portion. At light weight (27,000 lb), takeoff was around 22 kt and the drag was nearly constant out to 80 kt with a bit of a rise from there to 100 kt. At heavy weight (40,000 lb), takeoff was around 25 kt and the helicopter had enough thrust to pull it to 70 kt. L/D was 7.5. "The most significant problems which had to be overcome related to achievement of full ventilation of the strut, base ventilated, and supercavitating foil. Positive air channels were finally provided at the strut base in the vicinity of the upper and and middle foil-strut intersections. These changes which were necessary to insure the ventilation assumed in the basic design, improved the lift-drag ratio achieved by incomplete ventilation (for full submergence) by approximately 30 percent. The highly swept supercavitating wing was originally designed without twisting the wing to account for the induced effects of sweep. When the wing was twisted to account for sweep-induced effects, the optimum lift-drag ratio was increased by approximately 40 percent!" [quoted from: Johnson, Virgil E., and Scherer, J. Otto, "Some New Results of Research on High Speed Hydrofoils," Hydrofoil Symposium Held at the 1965 SNAME Spring Meeting, Seattle Washington.]
The same paper has a chart showing a supercavitating foil stalling at 80% of cruise speed when maintaining lift through incidence control, flying down to 57% of cruise speed when fixed but extended with a 60% chord trailing edge flap, and operating down to 50% of cruise speed with both the flap and incidence control. Drag at that condition was about 5X that at cruise. This might give some guidance as to what's reasonable in the way of takeoff speed with supercavitating foils and variable geometry. -- Tom Speer (firstname.lastname@example.org) website: www.tspeer.com fax: +1 206 878 5269
[21 Apr 01] My specific interest is not so much for vehicle support, but wind propulsion. So, the foils are indeed turned up spanwise vertical to generate principally lateral lift (like sails and centerboards). One of the proposals I'm trying to assess is a supercavitating paravane. It's basically a centerboard detached from the boat, and flown like a kite underwater (but sideways, like a skier outside the wake). In the abstract, it has some striking similarities to Tom's minesweeping sled. So, the datums he provides for supercavitating L/D between 5 and 9 are quite helpful. Moreover, those insights let me know that yes, it is *theoretically* possible for high-speed sailcraft to attain both high speed and high wind factor (4 to 8) with supercavitating centerboards. The lateral lift application doesn't have an actual take-off problem to deal with. But, my engineering skepticism still remains, centered around cavitation transition and ventilation issues. While I slowly admit that some of these high-speed sailing schemes are possible, their success seems to require some pretty spectacular engineering. -- Phil Morris (email@example.com)
[16 Mar 01] Concerning the practical application of using elecro-magnetics in drag reduction... How can I try this out on a home built catamaran? It seems to me that the amount of drag reduction could be extreme, and the speed increase would also be equally radical. I am in the most early stages of planning to build a multi-hull yacht and I want extreme speed with extreme luxury (don't we all?). Electromagnetic hull drag reduction might allow enough of an increase in speed to make hydrofoils a real world option. In this case I see it as transitional. A help to obtain the required speed for a cruising cat to get to hydrofoil speeds. Even if 100% lift is not induced, increased lift is a form of anti-gravity and reduced wetted area, so speed is increased. Certainly, however if this will work with only permanent magnets to some degree then so much the better. I also have other drag reducing ideas for the hull as well but obviously electromagnetics should work with any shape. So how can I practically do this? Implant wires, magnets and whatnots into the gel coat? I'd really like to know. If you have anything for me I would appreciate it and who knows maybe I will be able to make use of it. -- Steve Van Brown (firstname.lastname@example.org)
[23 Mar 01] What can you have read to lead you to think you could do this?! The concepts for electromagnetic turbulence control for drag reduction remain quite immature and still lacking any definitive demonstrations of success at meaningful Reynolds numbers. I wouldn't encourage you to continue his thinking in this direction. Let me know if you have any questions about where things stand. -- Stan Siegel (Stansiegel@aol.com)
[23 Mar 01] Electromagnetics for drag reduction falls into the same category as magneto-hydrodynamic propulsion; that is, fun but no payoff. A Japanese gambling magnate spent about $20M to produce a great looking ship that went---you ready?---5 knots. The U.S. Navy topped this by giving Textron $25M to reduce drag and make a propulsor for subs. Result: 00000000. If you want to reduce drag for about 100x the potential payoff, put the power into a two-phase (non -Newtonian) flow system like Prairie Masker. That system introduced air bubbles at the bow to ventilate the surface. It may not work well with hydrofoils but it would make an interesting experiment and a real contribution if you could pull it off. -- Nat Kobitz (KobitzN@ctc.com)
[23 Mar 01] I am very much interested in this subject also. If you haven't logged onto the German website (http://www.fz-rossendorf.de/FWS/FWSH/EBLC/separation-control/), you should because it has some interesting info. -- John Meyer (email@example.com)
[20 Feb 01] Do you know of any references or anybody who has investigated Reynolds number scaling effects of hydrofoils under the free surface. What I am primarily interested in the loss in lift of model foils due to their lower operating Reynolds numbers. So far the only info I have on the subject is Dr. Frans van Walree's Ph.D. thesis. My own calculations show this loss of lift depends on the Reynolds number as well as the submergence of the hydrofoil and can be as high as 30%. -- Günther Migeotte (firstname.lastname@example.org); Dept. of Mechanical Engineering, University of Stellenbosch; Banghoek Rd; Stellenbosch,7600
[21 Feb 01] I've not been able to find any information on Reynolds number effects on hydrofoils, either. It's not clear to me just what the mechanism would be for Reynolds number-dependent free surface effects on a fully submerged foil, except indirectly through modification of the pressure distribution and thereby the boundary layer. For surface piercing foils and struts, I could see how viscous effects would affect the spray drag etc. All the investigators I know have assumed that the foils would be operating at fairly hi Re and would be pretty much fully turbulent. For what it's worth, I've designed some hydrofoil sections which should tolerate a much wider Reynolds number range, suitable for models operating down to 300,000 - 400,000. Possibly less with BL trip. Xfoil results are at http://www.nasg.com/afdb/show-airfoil-e.phtml?id=1187. I'd like to know more about what you've found and how you do your calculations. I don't have any free-surface capability other than the infinite-Froude number linear approximation. Two big issues I wonder about are spray drag of struts and surface piercing hydrofoils producing lift, and prediction of ventilation. -- Tom Speer (email@example.com) www.tspeer.com fax: +1 206 878 5269
[21 Feb 01] One good reference for these effects is the Ph.D. thesis of Dr. Frans van Walree at MARIN. If you check out the IHS website, somewhere you will find a link on how to obtain a copy of his thesis. He found that there is a viscous reduction in lift curve slope for all Reynolds numbers, but for Rn>1e6 the effect is small. If one is using thin wing theory, the extra lift caused by the thickness of the foil is cancelled by the viscous effect giving a lift curve slope close to 2pi. As the Reynolds number gets lower one is forced to introduce viscous corrections and account for the thickness of the foil. I have followed a similar line to van Walree in trying to calculate viscous effects. I have compared experimental results for hydrofoils with numerical results of the vortex lattice method of AUTOWING ( http://www.cl.spb.ru/taranov/Index.htm ). Autowing has been well validated for hydrofoils. Comparing the exp. and calc. lift curve slope, I found that for the 3D hydrofoils I examined, the viscous effect on lift disappears as the foil approaches the free surface. For h/c<0.25 it is practically negligible. After thinking about this, I think it makes good sense. Viscosity affects mainly the suction side of a foil, as it has adverse pressure gradients. Using Xfoil one can clearly see that the boundary layer reduces the suction pressure (compared with potential flow) and hardly affects the pressure side as it has favorable pressure gradients. I have not heard of anybody else mention this. Close to the free surface the suction side of the foil contributes very little lift, so the effect of the boundary layer is small. Xfoil predicts the viscous loss in lift quite well if Rn>5e5 with leading edge turbulence stimulation for deep submergences. For free transition, Xfoil under predicts the viscous loss in lift. If you come up with any other info please let me know. What is needed now is a version of Xfoil with a free surface model to investigate this further.... -- Günther Migeotte (firstname.lastname@example.org)
[21 Feb 01] I can suggest one fairly old reference on model testing of hydrofoils compiled for the International Towing Tank Conference (ITTC) which may be of help: DTNSRDC-81/26 (or 81/026 ??) 'Status of Hydrodynamic Technology as Related to Model Tests of High-Speed Marine Vehicles', July 1981. Unclassified, Approved for Public Release, Distribution Unlimited. David W. Taylor Naval Ship Research and Development Center. Author of Hydrofoil section: B. Müller-Graf (who is still an IHS member) Abstract reads: The High Speed Marine Vehicle Panel of the 16th International Towing Tank Conference prepared hydrodynamic technology status reports related to model tank tests of SWATH, semidisplacement round bilge hulls, planing hulls, semisubmerged hydrofoils, surface effect ships, and air cushion vehicles. Each status report, plus the results of an initial survey of worldwide towing tanks conducting model experiments of high speed vessels, are contained herein. Hydrodynamic problems related to model testing and the full-scale extrapolation of the data for these vehicle types are also presented. -- Martin Grimm (email@example.com)
[29 Aug 00] I wish to construct a few recreational dynamically supported pleasure craft. I have been conversing with Mr. Larsen (an IHS member) and Mr. Mateev (Cal Tech and IHS Member). They have been most helpful in helping me to assess the basic design constraints required. Based on their correspondence, I would first like to pursue the construction of a hydraulically retractable surface piercing (shallow draft) hydrofoil. The prototype craft is to be in the 20 foot (6 meter) range with a displacement of 2500 to 3000 lbs. (1150 kilograms to 1350 kilograms). I believe this to be the standard displacement for this size of craft. Target speed to be 50 knots. Power to come from an I/O arrangement with a standard V-8 gasoline motor generating approximately 300 hp (223.8 kW). Engine may be further modified to increase output. Leg to be a modified unit with a "Vari-Prop" pitch adjustable prop. Ride height is as of yet undetermined. I have not purchased the boat yet. I am hoping to construct a two piece interlocking foil arrangement that could hydraulically split for the purpose of retraction. Time line is (10) months to construction. Among these design criterion is foil selection. I was referred to you by Professor Kinnas (University of Texas at Austin, Department of Civil Engineering, Ocean Engineering Studies). I presently have little knowledge of the physics involved in foil selection. Any assistance would be gratefully accepted. -- Wayne Gillespie (firstname.lastname@example.org)
[29 Aug 00] Regarding hydrofoil sections, I like the NACA 16-series hydrofoils because they provide good cavitation resistance, which you will need at 50 knots. As design speed increases, the hydrofoil thickness/chord ratio and lift coefficient must reduce to prevent cavitation. I used a NACA 16-510 hydrofoil section for surface piercing hydrofoils developed in the 1950's, which had a max speed of 46 mph with the 65 hp outboard I was using at the time. You might want to read my article on hydrofoil boats in the pioneer section of the International Hydrofoil Society Web Pages. An excellent source for other hydrofoil cross sections is in the book "Airfoil Design and Data" by Richard Eppler, published by Springer-Verlag, 1990. -- Tom Lang (email@example.com)
[8 Sep 00] Thank you very much for the input. I suppose that I will have to find a supplier / method of production for the foil(s). How are the actual; dimensions obtained? Are there on line resources available to this end? Distance between supports will have to be determined as well. I have visited the University of Texas at Austin pages and found an interactive applet design page that models relative lift and drag ratios of given foil dimensions. Most interesting. I however presently lack the understanding of the data to interpolate. Do you know the approximate cost of dies for aluminium extrusion? Are there any points of interest in the production end of foil extrusion that you have learned through your experience? I will endeavour to obtain the referenced book. You mentioned that a 1.5 deg twist in the foil of your kit allowed the craft to lean into the turn by allowing the inner foil (on the turn) to ventilate first. Can you elaborate on the process involved that cause this to happen? Conversely, it there is information within existing reference texts, I would be most grateful if you might simply direct me in the appropriate direction. -- Wayne Gillespie (firstname.lastname@example.org)
[8 Sep 00] You might want to consider making composite hydrofoils; however, extrusions are easier to work with. The foil cross sectional dimensions are available from the Eppler book, or in the case of NACA sections from the Dover book by Abbott et al, "Theory of Wing Sections". The Marks Handbook on Mechanical Engineering is one of many references on beams and structural strength. You might re-contact IHS to see if he has a list of references on hydrofoil design, and if they know of any sources of extrusions. Also, you could contact Alcoa for their list of existing dies and the cost of new dies. I think that there are many hydrofoil enthusiasts who would like to buy extrusions. You might ask IHS about references concerning ventilation. Also, it would be helpful to join the IHS; the special student cost is very low. My experience showed that ventilation occurred when angle of attack increased around two-to-three degrees above the design angle at a 30 deg dihedral, more with a higher dihedral, and less with a lower dihedral. Much depends on the accuracy of the hydrofoil nose region. Ventilation occurs when the hydrofoil boundary layer separates near the nose on the upper side, and air fills the separated region, generally superventilating the entire foil section downward for several inches; the result is the sudden loss of all lift in the supervented region. Sharp nose sections ventilate sooner than airfoil noses. Fences can be used to stop ventilation at intervals, but add some drag. -- Tom Lang (email@example.com)
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