Tuesday, June 24, 2008

What is wrong with sailplane airfoils for powered planes

Everything might look very obvious at first, but after digging more and more, it becomes clearer and clearer what kind of compromises all aircraft are made of and why.

A known thing is that the more efficient the airfoil the higher L/D ratio it has and vice versa. So one could go and find that sailplane airfoils produce very high L/D ratios. There is a little but on that though: Sailplane airfoils commonly achieve the best L/D ratio at higher Cl than what is optimal for a powered aircraft with reasonable wing loading where the cruise Cl is between 0.15 and 0.20. E.g. NLF 215F seems to achieve its L/D max at around Cl 0.5 which is unusually low compared to some other airfoils that require Cl being close to 1.0. That is acceptable for a sailplane that is thermalling at close to the stall speed. However, that is not where one wants to cruise with a powered aircraft, there is usually a requirement to get somewhere in a reasonable time, thus speed has some importance.

I have previously mentioned that the wing loading and cruise Cl has direct relation. The higher the wing loading, the higher the cruise Cl vice versa. Then the speed where the best L/D ratio occurs has a relation to the previous and it also tends to have relation to the top speed.

Diamond DA40 uses Wortmann FX 63-137 airfoil. It has best L/D ratio higher than the optimal < 0.2 (for light wing loading). Therefore the best L/D speed is the same as the approach speed on the aircraft. Similarly on Diamond DA42 Twin Star the same airfoil was used but the wing loading is as high as it is on Cirrus SR20. The result is that the best L/D speed is higher than on DA40, the top speed is higher (it is not only because of the two engines, the two engines produce also more drag than one). Because of the substantially heavier wing loading, the DA42 cruises at higher Cl than the DA40 and it gets closer to the airfoil optimum resulting better aerodynamic efficiency.

Cirrus SR20 is very similar to the DA40 but it has a different airfoil and higher wing loading. That results best L/D ratio speed being 96 kts. SR22 has that value even higher, it is over 100 kts, but it can be misleading that the best glide speed mentioned in the operating handbook is lower than on SR20. That is the best glide speed, it is not the best L/D ratio speed of the airfoil, it is a compromise of the airfoil + fuselage + propeller and in the SR22 the propeller is braking a lot more than on SR20, which alone is enough to explain the lower best glide speed - because of the propeller braking, the SR22 sinks faster, but if there was no propeller, SR22 could have higher glide speed than the SR20. But what this has to do with the topic? The interesting thing is that the Cirrus has different airfoil and higher wing loading and the optimum glide speed is higher than on DA40 which results potential to faster cruise speed than DA40 (whereas it is not exactly the airfoil's best L/D speed because of the mentioned reasons). Providing that there is enough power available, the Cirrus airframe is faster although the larger fuselage cross section and wetted area most likely pretty much diminishes the benefit from the wing, that is also partly a reason why the best cruise speed performance of DA40-180/XL and SR20 is not that much different, SR20 is just slightly faster - the Diamond has better fuselage shape and it simply is a lot smaller aircraft than the Cirrus and size does not tend to come without penalty when it comes to aerodynamic drag.

However, it would be beneficial for efficiency to have an airfoil which could achieve higher L/D ratio at the cruise Cl of the DA40 already. It does not come without penalties of course, the airfoils which have high L/D ratio at low Cl don't necessarily always produce optimal Clmax (which then has also relation to the required wing area which gets back to the stall speed and wing loading).

And it is not all in that, Daniel Raymer notes in his book that usually only 90% of the theoretical Clmax of the airfoil gets realized in practice. Therefore it is a interesting compromise between the wing sizing, and the best L/D at cruise Cl. Daniel Raymer notes in high book that the Cl is one of the hardest things to estimate without experimental data from test flights, and often test flights result in the need of modifications (e.g. if the Clmax in practise is not as good as was predicted, a larger wing is required to meet the maximum stall speed criteria, which is for single engine aircraft 61 kts).

It would be really interesting if someone would have a batch processing functionality in a airfoil program that would ingest the UIUC airfoil database data and simulate through all airfoils and put them into a correct order for the given specification (cruise Cl below 0.2), as high L/D at cruise Cl for a low wing loading, and at the same time, as high Clmax as possible, and at the same time, gentle stall charasteristics at low Reynolds number. And of course, the pitching moment also has some importance, high pitching moment tends to cause more trim drag which reduces the achievable Clmax (of the total airframe) considerably - if the wing can achieve e.g. Clmax 2.2, the airframe may be left to below 1.5 in total because of the download in the tail that is negative lift.

Friday, June 13, 2008

Wing structural considerations

Martin Hollman's book seems to describe structural calculations of wing in a pretty understandable way. Even I can follow how the resulting equation comes from the integration. I may write some software for spar sizing and layup schedule later after I get the aerodynamics part good enough to be useful. Martin Hollman's book includes Basic language programs for spar sizing etc., but they are not that easy to convert into modern programming languages because they are full of gotos and gosubs and global variables used in a crazy manner (the traditional Basic-spaghetti way). So it seems to be easier to understand the equations first and create the calculation algorithm from scratch by myself.

However, it would be interesting to know how much weight penalty comes from high aspect ratio. I am particularly interested in AR higher than 10 where around 14 would be great, because I am interested in high flight efficiency. However, my structural needs would be for a lot higher speeds than used on gliders, so it would be interesting to know how feasible it is to achieve a structure for AR=14 that can have Va >= 200 mph without adverse effects e.g. like aileron reversal and flutter.

I wrote a review in Finnish about Diamond DA40D handling qualities

I got type check out for Diamond DA40D yesterday and I wrote an article about it. I was very pleased with the handling qualities of the aircraft, it has the most well defined control feel than any other plane I have ever flown to the date. If you understand Finnish, you can read the full article from here http://lentokone.blogspot.com/2008/06/kokeiltua-diamond-da40d.html.

Thursday, June 12, 2008

What Reynolds number fits into my car

I was thinking which is the highest Reynolds number I can fit into our car for transportation. And it seems like it goes as low as 136000, which makes 40 km/h stall speed (~10 m/s) in wing chord being 0.2 m and length 2 meters where aspect ratio becomes 10. This would already require two separate wings, joint left and right wing are not feasible to transport. So the airfoil selection gets a new twist, I can not reach 500000 in any meaningful way with high aspect ratio wings on a model that fits into a car. Also the achievable Cl is quite limited on the low Reynolds number and Cd is not as nice as could be achieved with higher Reynolds numbers. Even this is quite overkill as 40 km/h is very fast for a small model aircraft.

Wednesday, June 11, 2008

Comparing different configurations and plotting fuselage cross sections

Each configuration is a different compromise. I have been thinking hard which would work out the best. This may need to be proven to do a design for all the different alternatives as follows:

1. Laminar body fuselage with prop in rear. Boom tail. Front free of protruding elements until the laminar-turbulent transition point. Rotax 914 might fit into the rear of a rotated NACA 66-030 with no (or at least not long) extension shaft needed.
2. Laminar body fuselage shape with prop in the front, potential for laminar flow lost because of the prop disturbing air in the front. Like Stemme S6.
3. Laminar body fuselage with prop in the rear of the tail. Requires extension shaft which is structurally challenging.

Each design would need to be identical (fuselage pod length in Reynolds number should be equal) and the objective would be to investigate which one produces best compromise for low drag and is structurally the best solution (without unacceptable risk of in-flight failing parts (extension shaft in any circumstances must not fail)).

Measuring the difference actually is quite difficult because of the difference in the Reynolds number of a model aircraft and a full size aircraft because it affects quite heavily the laminar low drag area and where the transition to turbulent flow occurs. Also airfoil which is proper for full size aircraft would not work on a model. The NLF414F I discovered earlier does not work with low Reynolds number, it has nasty stall characteristics with low Reynolds number.

What interests me most in this is that how much drag the two tail booms would add. Would the penalty be more than the benefit of achieving laminar flow in the forward fuselage? Is the extension shaft the only way to achieve laminar flow without sacrificing the benefit?

I have been thinking possible concept for a model: try out the boom tail configuration as specified above. Fuselage would be rotated NACA 66-030 with propeller in the rear. Wortmann FX38-153 profile might work with the target Reynolds number range (the wing span and fuselage length would be determined by the interior size of our car, must be able to be disassembled to a size that fits inside for transportation, using a trailer for moving a model aircraft would be overkill). Target aspect ratio could be around 12-14 for main wing. I haven't done any calculations yet though.

I want to also create a plotting program for the fuselage. Martin Hollman's book has a Basic language program listing for a such thing. I am not sure if it is useful actually, I have been thinking how to parametrize a fuselage cross section (often it is not circular but rather boxy with rounded corners or it might have entirely different airfoil shape in horizontal and vertical axis), how to modify the shape of the centerline where the fuselage cross sections are referenced to and how to make the cross section follow a airfoil coordinates, possibly using the same data files that work with X-foil. Making circular or elliptical (LH-10 cross section for example seems to be elliptical) cross section plots from nose to tail for a rotated airfoil wouldn't be that impossible task to do and visualization could be even quite reasonable to do with OpenGL. Before doing the visualization, I however, need to determine how to parametrize it, in other words, how to make it easy to produce differently shaped fuselages. Rhino3D does all this, but I don't have Rhino3D, and this task is not that complicated, it should be doable with some little C++ work.

Any advise on the math and how to make the fuselage design easy would be great, feel free to add comments if you invent something or know something already.