# Airfoil and Wing Analysis for Transonic Speed (M = 0.85 and Re = 42 million)

I am working on a project where I have to design a plane which has to cruise at 0.85 Mach at 35,000 ft. While working on the wing design, I quickly discovered that 6 series airfoils, with a good amount of thickness ratio, have a low Critical Mach Number. So, I started exploring Supercritical Airfoils (SC Airfoils). F or doing analysis of SC airfoils can XFLR5 be used?

Moreover, Aspect Ratio and Sweep also influence Critical Mach Number.

Is there are a relationship that connects these three entities?

Lastly: is there a credible source that compiles the analysis of Transonic Airfoils (Supercritical Airfoil)? (Similar to Theory of Wing Sections by Abbott and Doenhoff, which contains data for conventional airfoils)

• Can I suggest you take the site tour? You have a bunch of questions posted as one, which runs counter to the format. Could you edit this down to a single question? – AEhere supports Monica Feb 9 '20 at 13:44
• @AEheresupportsMonica Thanks for providing guidelines for improving the question ! – Pavan Feb 9 '20 at 18:29
• @KorvinStarmast Thanks for further more reframing the question ! – Pavan Feb 9 '20 at 18:30

I am working on a project where I have to design a plane which has to cruise at 0.85 Mach at 35,000 ft. While working on the wing design, I quickly discovered that 6 series airfoils, with a good amount of thickness ratio, have a low Critical Mach Number. So, I started exploring Supercritical Airfoils (SC Airfoils). For doing analysis of SC airfoils can XFLR5 be used?

This is a direct copy-paste from XFOIL manual which is the underlying library for 2D analysis in XFLR5

One should always be wary of trusting solutions which show regions of supersonic flow. Such flows can be reliably predicted only with a truly nonlinear field method (such as the MSES code). As a rule of thumb, if the maximum Mach number doesn't exceed 1.05 anywhere, shock losses will be very small, the Cp distributions will be reasonably accurate, and the drag predicted by XFOIL is likely to be accurate.

Moreover, Aspect Ratio and Sweep also influence Critical Mach Number. Is there are a relationship that connects these three entities?

AR does not influence the Critical Mach Number. However, sweep does A direct copy-paste from old USENET message archive.

The airfoils on a swept wing behave as though they were flying at a reduced speed, reduced Mach number, and reduced dynamic pressure.

• effective speed = V cos(L)
• effective Mach = M cos(L)
• effective q = 0.5 rho V^2 [cos(L)]^2

where L is the sweep angle, and V and M are the airplane's speed and Mach.

Lastly: is there a credible source that compiles the analysis of Transonic Airfoils (Supercritical Airfoil)? (Similar to Theory of Wing Sections by Abbott and Doenhoff, which contains data for conventional airfoils)

NASA supercritical airfoils: A matrix of family-related airfoils

I tried using XFLR5 for the analysis at Re = 42 million and 0.85 Mach Number. But, solution diverges

There was 2 issues I could see in the given dat file.

1. finite TE gap and coarse coordinates. I fixed this in XFOIL by going to GDES menu and setting the TGAP to 0 with the blending distance 1. And then used MDES to filter out glitches in the UE distribution.

2. Mach effects.
Say your plane is flying at CL=0.6 but what happens when the MACH increases with constant alpha is, it improves CL. So the non-converging solution actually refers to a very high CL in the ranges of 3-4 which is not realistic and cp is high above the critical CP. Please refer to the images attached. when you directly use cl or reduce alpha accordingly you can get this sorted as shown on the last pic.

• Thanks for the source! I tried using XFLR5 for the analysis at Re = 42 million and 0.85 Mach Number. But, solution diverging. Can you please tell me what should I keep the values of Re and M on XFLR5 while doing analyses? – Pavan Feb 10 '20 at 7:03
• @Pavan XFLR5 exhibits numeric solution instability if you do not keep the aspect ratio of the wing surface panels low. Given that the default settings of its mesher tend to produce such "streched" panels, it is a common issue for people starting out with the software. Have a look at that and at your airfoil analysis data, which is fed to the wing analysis. – AEhere supports Monica Feb 10 '20 at 19:32
• Here is the link for .dat and .xfl file related to the analysis: drive.google.com/open?id=173AR9RFrAKpuWFsEtIAuPIMxG6R-TJ-x. Please do have a look at it. – Pavan Feb 11 '20 at 2:28
• @m2as3registeredservicesohmone XFLR5 has a 3D panel method for single wings (in the past it was enabled for entire plane assemblies, but the author disabled it due to the lack of a proper algorithm to intersect all the surfaces). The issue I describe was notable enough to make it some handbooks. – AEhere supports Monica Feb 11 '20 at 10:22
• @m2as3registeredservicesohmone Thanks for the help! – Pavan Feb 11 '20 at 14:31