Surface proximity flapped 3d lifting foil analysis

[DrawnOnward]

I have designed the S410 foil in XFLR5 with the intention of using it as a lifting T foil in the Re 2m to 5m range on the 16.8m proa I'm building. The modelling suggests that this foil exhibits properties that might make it a good choice at Re as low as 0.5m. Of course this is only a computer model. The grey areas surrounding the real world application of ncrit values notwithstanding, I hope to establish, as at best a lay hydrodynamicist, that the design path I have followed has merit. That said, I'll run with the data. Critiques appreciated.

The computer likes the aft loading but the real world may not. I can run an FEA on the foil to determine that a particular layup will work for a given aspect ratio, but haven't the tools or expertise to run CFD. Of course, some other more conservative foil shape may not perform as well in 2d, but be stiffer and consequently more suited to higher aspect ratio loading and thus more efficient.

Figure 1. 3 foils.

Alpha plots require a little too much effort to compare positive lift angles, explaining why this Cp min analysis was conducted for positive values of Cl, rather than a fixed alpha range. It'd be nice to be able to plot foil polars relative their zero lift angle. From it we get an idea of the range of angles of attack the foils can sustain at a given Cp (and thus a given speed). From the second graph, the lift coefficient range at various Cp levels can be found. The S410 was designed to provide the widest possible angle and lift range in the -1 < Cpmin < -0.6 range. This is sufficient for my proa to hit speeds of 25 to 35 knots, explaining why I haven't targeted a lower Cp. I have no desire for more and, and with hindsight, most likely a desire for less speed.

Figure 2. Cpmin values plotted against alpha and Cl.

Cp min graphs seem pretty much universal across various Re and ncrit. One variation found is in the form of a blip in the Cp curve appearing on the plot (between 0 and -1 degrees) due to the laminar flow transition. This feature is evident on the Eppler and the S410, but not the H105. I think I can attribute this to a larger separation bubble. Tom Speer has observed in the excellent 'Foiler Design' thread (http://www.boatdesign.net/forums/sailboats/foiler-design-2447.html) that one of the goals for foil design in the laminar flow Re range was a more uniform rate of transition of the bubble across the surface of the foil, as the flatter transition (refer to the xtr1 graph in Fig. 3) seen in the Eppler and S410 will result in a longer separation bubble and increased turbulence - a problem at low Re.

Figure 3 compares the 3 foils at Re of 3m. This isn't the ideal comparison point for the H105, but I'm interested in thoughts regarding sacrificing L/D for slower bubble transition and at what Re the benefit diminishes. I presume that the Cl/Cd graph for the relevant Re contains that information. Refer to figure 5 which compares the S410 and H105 at lower Re. The H105 looks superior through the majority of the useful lift range from something like 0.5m Re down. I'm not concerned, given that 0.5m Re is roughly 3 knots for my craft and that foiling won't have higher L/D than displacement for a 16.8m craft until something like 15 knots of boat speed (the windward foil may be deployed sooner as this hull is only 11.2m long). This is however relevant for craft with smaller chorded foils and lower takeoff speeds - and perhaps unless the foil is also retractable, which is something I'm considering.

Figure 3. 3 foils at Re 3m

Figure 4 compares the L/D of the S410 with the Eppler 817. A small uniform advantage at 2m Re is lost at higher Re in the lift range targeted at higher speeds. This a direct tradeoff on my part for a wider Cp min bucket.

Figure 4. Eppler 817 and S410. Re 2 to 5m.

Figure 5. H105 and S410. Re 0.4m to 1.2m.

The configuration I'm considering is rotating T foils close to each leeward bow and a single surface piercing foil to windward. As speed increases (along with the wind speed increasing) the apparent wind moves forward and the heeling force increases. This increased heeling force: increases the load on the leeward T foils, thereby reducing the required Cl reduction; and decreases the load on the windward foil, making it relatively more suited to a tapered surface piercing foil. The loads upon these T foils and the supporting structure will not be trivial. So all this is still subject to an engineering analysis. I'm mentioning this as the reader might be curious concerning the details of the application, but it is presently only a subject for speculation. Once I've selected a suitable foil section and span, I'll run an FEA on the foil and supporting structure.

Whereas the surface piercer would not require a flap (but perhaps benefit from some pitch adjustment), the T foils will.

Figure 6. The range of flap angles under consideration. Flap hinge at 80%.

This is a small flap. I trialled larger flaps up to 33% of chord in size. They tended to be more draggy and have higher Cp peaks for positive angle. This reduced the benefit of somewhat less negative angle required for a given lift reduction.

It is interesting to note (Fig 7) that positive flap angles feature a very low minimum drag. The sharpening drag increase with progressively more positive flap I imagine is attributable to the rapid transit of the correspondingly larger separation bubble (refer to xtr1 in Fig 7). The biggest problem with positive flap however is the significant increase in Cp min (Fig 7). Consequently, I consider it undesirable to use flap angles greater than +4° with this foil. I can't comment on whether a bow down induced high flap angle on a moth at high speed will cause cavitation without analysing some other foil shapes, but the sharp junction at +8° doesn't look good.

In contrast, the negative flap angles are progressively more draggy, but maintain low Cp min and feature a more benign separation bubble. What is particularly of interest is the Cp min bucket shifting with the zero lift angle - effectively widening the Cp min bucket by an amount equivalent to almost a 6° pitch adjustment.

Figure 7. 2d analysis of flapped foil.

The next step in this process involved 3d foil analysis. From Fig. 12 in the NACA theoretical and experimental analysis of lift and drag http://naca.central.cranfield.ac.uk/reports/1955/naca-report-1232.pdf, which Tom Speer has referred to, it can be taken that a biplane modelled in XFLR5 can account for the free surface effects experienced by a submerged hydrofoil - where the biplane foil separation is twice that of the foil and surface separation. At least the lift can. The NACA report develops a specific set of formulae to account for drag.

First, lift. In figure 8, I have modelled 5 different chord depths below the free surface. The smallest (0.0283c) is the smallest separation that produced useful results. The single foiler is the base line, i.e. infinite depth of immersion. In the Cl vs alpha graph the foil closest to the surface generates a tad more than half the lift of the single foil - excepting the cross over at low positive values of Cl! I'm curious as to why this is happening. Perhaps the result would be more consistent with the theory if the foil was more symmetrical? Perhaps if the foil wasn't tapered? Note that the chord depth is measured relative to the chord at the centre of the foil, which tapers from 420 to 280 mm. I'm aware that the NACA report 'neglects' geometric camber in its calculation of the position of the image foil and an "infinite array of images is, of course, required to give an exact value". Does XFLR5 handle biplane theory in the same way?

Drag. I can't really be sure that the drag results accord with the empirical data from the NACA report, although they have similarites in magnitude (allowing for large Re differences). The comparison with the NACA study could obviously be made clearer by using the same foil sections and chords at the same Re as found in the study. If necessary, I can do this but I'd rather not bother if I'm on the right track. If the Cl vs Cd graph in Fig 8 is a reasonable representation of the effect that proximity of a free surface has upon the foil then none of these questions are crucial. My goal is merely to design a foil that will operate successfully at the targeted Re allowing for free surface effects. If the free surface adjustments merely entail lift and drag penalties of the order of 10 to 20% below 0.5 chords depth, then this adjustment is probably less sensitive than the selection of ncrit and accuracy of manufacture.

Figure 8. Hydrofoil depth analysis

The Cl/Cd graph is barely influence by changes in speed in the target velocity range - the only change is due to changes in viscous drag.

Fig 8a. Viscous drag at 8 and 18 m/sec and various depths

The final figure displays the results of a fixed lift analysis of the 3d aspect ratio 9 flapped biplane foil, without strut, at a depth of 1 metre (2.38 x max chord).

I'll just make a couple of points at this stage. Along with Cp min from the 2d analysis, the Cl/Cd max for various flap angles tends to track with angle of attack. That is, for a given angle of attack, the flap angle required to generate the fixed quantity of lift, will be operating close to its Cl/Cd max and Cp min. The polars in the Vx vs alpha plot track for a given flap angle, the speed required to generate a fixed amount of lift, across the range of angles of attack. Points in the graph that lie on the concave side a polar, will generate lift in excess of that required for that flap angle in static equilibrium.

Figure 9 3d flapped foil analysis at a depth below the free surface of 2.38 x max chord

 

[Erwan]

Nice Thesis, thank you for sharing.

Unfortunatly, I have not the skill to provide any constructives critics, so please accept my congratulations.

A little remark regarding XFLR5, I never could plot the H parameter and other boundary layer features. So to address separation????

As a result, I am going back to XFOIL, even if less user friendly, seems much better.

Congratulations again

Best regards

EK

 

[DCockey]

Very interesting. Thanks for the report.

Have you thought about the sensitivity of your design to:

- Build variation? How close to the design shape can you build the foil? What is the sensitivity of the shape to variations, particularly near the leading edge?

- Surface roughness?

- Turbulence in the "free stream"?

 

[DrawnOnward]

Thanks Erwan. I’m not the best person to ask to compare XFLR5 and XFOIL. I haven’t worked with XFOIL. If the analysis would benefit I’d look at using it and possibly AVL. All I’m going with is observing the transit of the pressure peak caused by the separation bubble in the Cp profile. Notice the pressure drop immediately behind the transiting peak due to turbulence (Fig 10 and 11) (alpha = 01 & 0.5). At least this is my understanding.

Fig 10.

Fig 11.

Thanks David. Dealing with build variation is a manufacturing quality control exercise, constrained by budget. CNC machined moulds would be nice. A split mould for a flapless foil would entail both concave and convex surfaces for the underside. I haven’t costed this or looked into alternatives at this stage. I’m relatively new to composites, having had more experience designing and building machinery.
Leading edges are generally very sensitive, so accuracy is important. Imperfections would typically narrow the Cp min bucket. I'd consider getting some leading edge profiles cut in order to confirm shape.
I've included a comparison between 4 foils I've drawn (Fig 12). Some have higher aft loading than others. The S198 was my attempt to produce a section with a longer upper surface pressure recovery. At the crossover point of 0.5m Re where the H105 comes into its own, the S198 performs no better than the S410 (Fig 13). Consequently, I suspect that the S410's higher aft loading is doing much the same job.

The more supercritical foil shapes clearly perform worse at low Re - a product of the slope of the xtr1 curve and the resultant bubble size. At ncrit =1 (and to an extent Re = 5m at ncrit = 3) the more supercritical S701 and Eppler foils develop the longer drag buckets: this it seems is a product of very late transition at Cl = 0.2. The modelling at ncrit =1 is probably the only way I can assess the effect of surface roughness.
Figs. 14 and 15 show the effect upon the foils of switching from ncrit = 3 to ncrit = 1. The effect is more marked with respect to the drag bucket of my foils than the Eppler. This prompted me to draw the S710 using inverse methods with ncrit = 1. The foil is still pretty rough, but demonstrates what control of the trailing edge can do for the drag bucket.

Fig 12.

Fig 13.

Fig 14.

Fig 15.

With regard to your free stream turbulence inquiry, I honestly don't have an answer - other than presuming that a CFD analysis might provide answers. Do you have any suitable technical references or modelling suggestions?

Apologies for my delayed response. Drawing the S701 and other various other commitments got in the way.
Cheers,
David

 

[DrawnOnward]

One final point re leading edge sensitivity: Although I don't know of objective measures other than the behaviours exhibited in the analysis graphs, a relative comparison is worthwhile. In the image shown below of leading 2% of the foils I've considered, the Eppler is clearly the finest. The H105 is a different shape but seems to have a similar radius to my foils. The larger the radius the easier to accurately reproduce.

 

[DCockey]

Thanks David. Dealing with build variation is a manufacturing quality control exercise, constrained by budget. CNC machined moulds would be nice. A split mould for a flapless foil would entail both concave and convex surfaces for the underside. I haven’t costed this or looked into alternatives at this stage. I’m relatively new to composites, having had more experience designing and building machinery.
Leading edges are generally very sensitive, so accuracy is important. Imperfections would typically narrow the Cp min bucket. I'd consider getting some leading edge profiles cut in order to confirm shape.

A different approach is to consider deviation from the design from multiple build variation as both a manufacturing quality control exercise and a design consideration. Estimate both the type and magnitude of build deviation from the nominal design which can be expected with various constraints including cost, and then develop a design which will be satisfactory within that range of variation. The nominal performance of the design which is less sensitive to variation may be slightly less than the design which optimized without regard to variation, but in practice the less sensitive design may perform better.

 

[tspeer]

Here is a different way to present the cavitation characteristics of a section. As you've discovered, plotting Cpmin vs lift coefficient is more useful than Cpmin vs angle of attack, because different sections have different zero lift angles, making angle of attack a very arbitrary independent variable. Lift coefficient is more useful, because you can calculate the lift coefficient from the requirement that the equilibrium lift has to equal the weight.

But Cpmin is not all that useful for the designer, either. What the designer really wants to know is the speed at which cavitation will begin at that pressure coefficient. Fortunately, it's easy to convert Cpmin into the incipient cavitation speed.

So here's a format that tells the designer what one wants to know:

The black lines are curves of constant loading - the lift divided by the area. At a given loading, the lift coefficient is inversely proportional to the square of the speed. The section Cpmin has been converted to the incipient cavitation speed, so the cavitation buckets are like the Cpmin vs CL plots laid on their sides.

It's easy to see from this presentation that having the widest possible cavitation bucket is not really very useful. A high CL at high speed means very large loads, and it's likely the foil will break before getting to that loading. At a loading of 45 kPa, the E817 and H105 sections have essentially identical cavitation performance. Both have a high-speed incipient cavitation speed of 40 kt, and a low-speed incipient cavitation speed (due to the formation of a leading edge pressure peak) of 22 kt. The E817 can go to a loading of 95 kPa without cavitating, but no real hydrofoil can stand to have its takeoff speed and its maximum speed be the same. And the materials don't exist that would allow a 12% thick section to have a useful span with that kind of loading. All of this becomes a lot more evident when plotting CL vs speed with the loading lines superimposed.

I've attached plots of the pressure distribution for the E817 section at angles of attack from -3 deg to +2 deg. If you look at the pressure distribution for 0 deg, you'll see the long, flat rooftop. The minimum pressure occurs at the end of the rooftop. This gives the maximum cavitation speed for the lift coefficient, but that's not what is really needed. At a lift coefficient of 0.4, the cavitation speed doesn't need to be much more than 30 kt.

At a lift coefficient of 0.2, which is more typical of operation at 40 kt, the minimum Cp point is also at the end of the rooftop. It would be possible to shave off the top of the pressure distribution at -2 deg angle of attack in order to raise the cavitation speed. This would make the rooftop convex instead of being flat.

As the angle of attack increased, the minimum pressure point would move forward and the minimum Cp would be more negative, lowering the cavitation speed. But that's OK, because when the foil is operating at the increased angle of attack, it will be running at a lower speed where cavitation is not as much of a concern.

If you repeated this exercise for the E817 - setting the angle of attack, shaving off the top of the pressure distribution - for a range of angles of attack, you would be tailoring the cavitation bucket to the actual loading the foil would see. The result is a thicker section (for more strength) that still meets the cavitation constraint. It may also need less aft loading.

 

[tspeer]

...
With regard to your free stream turbulence inquiry, I honestly don't have an answer - other than presuming that a CFD analysis might provide answers. Do you have any suitable technical references or modelling suggestions?...

Ncrit is the parameter that accounts for freestream turbulence. The more turbulence, the lower Ncrit will be. The idea is that if transition occurs when disturbances in the boundary layer grow to a critical size, then if the disturbances start off large (due to freestream turbulence) they don't require as large an amplification factor for them to reach the critical size.

Unfortunately, the appropriate value of Ncrit to use for hydrofoils is uncertain, and it could even depend on the conditions of the day. For example, if you were operating in pure, calm water, Ncrit could be higher than if you were operating in dirty, rough water. About the only thing a designer can do is to analyze for a range of Ncrit values and also trip the flow so as to be fully turbulent. A practical design should be able to perform adequately for all these cases.

 

[DrawnOnward]

Thanks Tom for your as usual perspicuous observations.

What Tom is saying makes perfect sense when loadings and pitch are constant, or fluctuate moderately, as he does refer to equilibrium loads. Even if the pitch angle changes, loading on a single main lifting foil near the centre of mass is not going to change as much as in my proposed configuration. My application is very different and I think I need to spell out the reasoning behind it and the more general application that may arise from this.

I'm build a 16.8m proa. This proa doesn't tack, so canard steering is feasible. With a centrally mounted una rig the CE is a long way back. I recall Tom (and probably others) observing that the CLR should be even further back in a canard configuration. This suggests deploying two widely spaced rudders - a common feature on proas, notably the Harrys, which I have based my design upon (and featured on Rob's web site). When it comes to steerable lifting foils, the almost universal choice is the T foil. Not much dihedral can be tolerated as steering would change the angle of attack. The exception is of course C-Fly with super-ventilated foils designed to operate at wide attack angles. So two steerable, flapped, T foil rudders. This is a weight to windward proa with fairly modest accommodation, yet won't fly a hull easily. So a windward lifting foil is required. The L/D of the shorter windward hull (11.2m) suggests flying this hull first. Probably a surface piercer, and positioned to windward but between the windward and leeward hulls, this foil will lift approaching half the weight of the boat. This allows the lifting T foils to be sized somewhat smaller and accept increasing load due to heeling as apparent wind and speed rise. This configuration is in contrast to the J foiler situation where only one lifting foil is deployed.

Being a long vessel, the intended fully foiling operating speed range of the T foils is 16 to 35 knots. Approaching 30 knots might be more realistic, but we live in hope (and fear). The higher speed equates to an increase in lift by a factor of 4.8, for a given Cl. This factor could effectively be reduced to something like 2.4 (whilst mindful that it's still an increase in lift of 4.8 with a doubling of load) in full flight due to heeling and the load coming off the windward surface piercer. Of course, the dynamics of sailing at speed mean the craft could operate anywhere in that range at top speed.

With increasing speed, the T foil Cl/Cd will decrease (refer to Fig 9 in my first post) and hull windage will increase, increasing the pitching moment experienced by the craft: increasing drag at a distance below the C of E. So, increasing speed further increases the load on the leading foil (7 'de/in-creasings' in two consecutive sentences - clarity or clumsiness?).

Note that it is the pitching moment (and ride height controlled flaps) that should yield the required pitch and heave stability. With equal sized foils near each end of the craft, the trailing foil must be more lightly loaded (hats off to Tom again). When it comes to greater heave stiffness for the leading foil, I haven't fully analysed the dynamics of this configuration but have the following observations. Referring to Figs 8 and 9 in my first post (and necessarily in the absence of flap angle change - an instantaneous measurement): because the Cl/alpha curves are near linear (and parallel for various flap angles), the more lightly loaded foil will experience a proportionally greater increase in Cl, for a given increase in alpha, than its counterpart. This effect will be weakest when Cl is high at low speed and strongest when Cl is low at high speed - amplified by the increase in pitch moment. What remains to be done is analysing the effect that flap response has upon relative heave stiffness. I am not going to put any thought into this problem today - other than observing that flap response could, if required, be altered to modify stiffness.

The final reason I have leant toward a wider Cp min bucket relates to pitching. I am interested in foiling offshore. This entails considering the effect of pitching in a dynamic context. 15m of foil separation and a pitch of +- 1m over this distance is +- 3.8 degrees. The relative motion of water in swell faces may also change the angle of attack. Consideration of the sea state may influence whether the craft profiles or pierces waves. The dynamics of foiling in a seaway will at times ideally entail having foils accelerate the craft upward (and possibly downward). These changes in loading can be very large. I've read of bow accelerations of 2g or more. Of course it is likely that full foiling mode is abandoned long before the sea state generates these sorts of forces. If the craft pitches up, then the leading edge of the foil will determine whether the foil cavitates. If the foil is pitch adjusted in response, then the leading edge is tamed. With fixed pitch (or insufficient pitch response) flapped T foils, I'd like to have that Cp min bucket wide enough to avoid cavitation. Negative flap angle can reduce the Cl, and shift the Cp min bucket (fig 7 first post), but will flap angle track as well with alpha as this graph suggests? I'd say not. If flap angle tracks with foiling height, then heave stiffness is achieved (subject to the type of motion sought through waves). In much the same way, setting flap angle relative to alpha (for a particular speed only) would decouple the heave stability. Of course, one way to get the craft to pitch down again is to let the leading edge of the forward foil cavitate - but the trailing foil may well be facing the same problem, which won't help with pitch and heave stability.

All these factors can increase the load on the T foils / forward foil: first, load shifting onto lee foils and coming off the windward foil due to heeling; secondly, load increasing on the forward foil due to increasing pitching moment; and finally, sea state induced load fluctuations. Which suggests to me that the wide Cp min buck has merit. If the design loading on the T foils at take off can be lowered sufficiently through shared loading with the surface piercer, then this will allow dynamic increases in loading due to sea state and heeling forces at speed. This naturally means a larger foil than required for a more static condition, but the foil was smaller to begin with due to the shared loading.

Of course there is also my argument that it's better to design in aft loading with a flapped foil and shift the flap angles to predominantly negative in order to preserve Cp min that is lost at higher positive flap angles. I guess it depends upon the dynamics and speed range of the craft as to how much positive flap can be tolerated.

Some of these considerations I believe to be applicable to the more conventional offshore foiler, even if not to the same degree as in my application.

All this is tempered by my conjecture that none of this modelling is useful unless the FEA analysis stacks up, but more particularly Tom's precise observation that: "The E817 can go to a loading of 95 kPa without cavitating, but no real hydrofoil can stand to have its takeoff speed and its maximum speed be the same. And the materials don't exist that would allow a 12% thick section to have a useful span with that kind of loading."

Oh, and Tom: am I right to assume by omission (of critique on your part) that I was on the right track with the surface effects analysis? With an academic background in other disciplines, I am acutely aware that the equivalent of a couple of months of self directed research and a year or two of musings must inevitably leave significant gaps in completeness of comprehension of a highly technical field - which is why I am testing my ideas for their robustness - and expecting to find some of them quite brittle at times.

 

[tspeer]

A flap on a foil is very useful for shifting the operating range, as you've shown. It really complicates the analysis, though, because you have to run through several flap deflections.

While a foil producing a vertical load has to lift the weight of the boat, a foil producing a horizontal foil also has a load that is approximately constant. The foil has to oppose the side load from the rig. The force on the rig is limited by the righting moment from the hull. Once you start flying the ama on your proa, from that point on, the load on the board won't vary very much.

There are times when the lift coefficient on the foil can be quite high, however, like when accelerating out of a shunt. The flap might be very useful then.

As for the surface analysis, I'm not familiar enough with XFLR5 to know if it can represent the surface effects or not. I doubt it, though, because it is based on XFOIL and XFOIL can't be used that way. XFLR5 might be able to have two lifting lines that are in close proximity and capture the increase in induced drag from operating close to the surface. But I don't think it will represent the surface effect on the section characteristics. One way you might try to validate it would be to simulate the data in these papers:
NACA RM L52D23a
Kuhn, John C. and Scragg, Carl A., "Analysis of Lift and Drag on a Surface Piercing Foil", Eleventh Chesapeake Sailing Yacht Symposium, January 1993.

 

[DrawnOnward]

Tom, returning to the problem of 95 kPa being too much structurally for a 12% foil: I’ll explore this in more detail when time permits. I’ll note that my foil can be thicker (13.5%), although the various flaps are thin and the cross-sectional area fairly low, the moment of inertia may help. FEA will help. I understand the points you made re foil shape and the shape of the Cp min bucket – I had gained quite a degree of understanding of this whilst drawing these shapes. As I observed in the previous post, I am mainly interested in the suitability of the these foil shapes for flapped foils. But there’s no point in designing a foil where the flap can kick to an angle that results in a load that could break the foil.

 

[DrawnOnward]

Tom, in light of our discussions, I went back to the drawing board and applied the principles we had discussed - up to a point. I took the S410 (13%) and ran through 10 full inverse iterations, seeking a more uniformly sloped xtr1 curve. The result was the S820 (14.55%) (Figure 17). The result of scaling the S820 to 12.55% can be seen in Figure 18. Allowing for the aft loading, the similarity to the H105 is rather striking. The lift to drag of the S820 (figure 19) can't be as good as the roof top S410 (analysed at the same 14.55% chord). In light of our discussions, it's apparent that chasing this drag bucket in an over assiduous fashion can be counterproductive. I then exported the Cp min vs Cl data and converted this to a Vcrit vs Cl plot with an overlay of constant load lines in Excel. This was a little clunky but sufficient for the task. By the way, does Xfoil have this plot capacity. If not, what software do you recommend?

Figure 17.

Figure 18.

Figure 19.

These two 14.55% foils still load significantly higher than the H105. I was looking for precisely this result because: given that stiffness increases to the fourth power of a given section thickness multiplier for a given foil. Increasing a foil thickness from 12% to 14.55% will increase stiffness by a factor of 2.1. Now, I'm aware that comparing an aft loaded foil to a more symmetric one is not comparing like for like: the cross sectional area moment of inertia will be lower for the same percentage chord thickness aft loaded foil.

The principle that arises from this is that making a foil thicker for a given application allows more aft loading and consequently allows it to operate at higher Cl. This can be observed in Figure 20. The highest possible speed for the S410 and S820 coincides with a 45 KPa loading. If the load cycle is sufficiently benign, occasional excursions to higher loading can presumably fit to the fatigue cycle. In fact, for my application, the foils could still be a little thicker.

Figure 20.

The argument then goes: well we now can get away with a smaller foil! Well it's not quite as simple as this because the smaller foil will have smaller chord and thickness for the same aspect ratio and loading, so the gains are not that great. I'm not going to crunch any more numbers on this - the FEA, when I get a chance, to run it, can resolve it. Tom has observed much the same before when asked if the H105 was the best section. As I recall, the reply was: it's a good one but the best one for a given task will be tailored to the operating conditions.

The Cl operating range of these foils would be sufficient for my entire speed range without flaps - but this would entail pitch adjustment - potentially a bit tricky with a steerable foil.