Characterizing the Lift, Drag, and Stall Properties of Airfoils

I have recently been collecting aerodynamic data on the three different airfoils (flat-bottom, semi-symmetric, and symmetric) in Juno: New Origins. My experimental setup was relatively crude and due to the heavy use of curve fitting, high accuracy predictions should not be expected. For now, these C _ L and C _ D curves will only be a rough approximation until I can apply a more consistent way to gather data.

The problem I ran into was that there is no Vizzy block for aerodynamic lift and only drag (in m/s^2). There is no problem with the drag as you simply multiply the drag acceleration by the vehicle mass to find the drag force. This is via Newton's second law.

Of course, there are ways to find aerodynamic lift from drag, but they require unrealistic assumptions, even for a video game. One way is to apply the thin-airfoil theory, but it generally is only reasonable for small angles of attack and does not capture stall characteristics. We will not be applying thin-airfoil theory for this study and I do not really recommend it, but this is the solution methodology anyways.

So,

Or more simply,

Make sure that alpha is in radians for this calculation.

The main reason why thin airfoil theory is not a reasonable approximation for this purpose is that it assumes a maximum lift curve slope (2*pi = 6.28 per radian). This expectation is also unreasonable because hence the name, it assumes an infinitely thin airfoil, which is obviously not possible in reality. In reality, most airfoils can have a lift curve slope anywhere between 4.00 per radian to 6.20 per radian.

For Juno: New Origins, I found a lift curve slope of 5.22, 4.21, and 5.07 per radian for the flat-bottom, semi-symmetric, and symmetric airfoils, respectively. I would not expect these to be the true values though due to the curve fitting I did on the somewhat erratic data.

If you have read this far, thank you in advance, but here are the lift and drag curves of each airfoil along with their respective equations. For these curves, the angle-of-attack must be in degrees. Each equation predicts the lift and drag coefficients from angles-of-attack from -45 to 45 degrees. They also predict the stall characteristics, but if you would rather like to find stall speed, I would use the following equation:

The equation requires the 1g stall speed of the aircraft, stall speed under 1 g of gravitational acceleration (9.81 m/s^2), and in sea level air density (1.225 kg/m^3), so make sure to calibrate it accurately to your particular vehicle. You can find this value experimentally. Once you do that, it is extremely accurate on any planet.

Now for the results:

Flat-bottom:

Symmetric:

Semi-Symmetric:

This post is already long enough, so I will try my best to leave my conclusion brief. I would rather leave further analysis for comments anyways, so feel free to discuss these results. If they make sense, suggestions, questions, etc. Each airfoil has approximately the same stall angle-of-attack (30 deg), but different zero-lift angles-of-attack. The symmetric is obviously 0 deg, and the semi-symmetric and flat-bottom share about the same zero-lift angle-of-attack at -3 and -4 deg. However, two distinctions that must be made are that the flat-bottom airfoil exhibits better stall characteristics than semi-symmetric. It generates more lift at high angles-of-attack and does so more efficiently. A C _ L of 2.47 vs. 1.71. Although the second distinction is the offset drag curve of the flat-bottom. It is offset towards negative angles-of-attack. This simply means that the flat-bottom generates slightly more drag per deg at positive angles-of-attack than the semi-symmetric.

Aircraft configuration is a complex topic, but in general, I would say that the flat-bottom airfoil is superior for use in wings, due to its excellent stall characteristics and overall higher lift-curve. I would say with a good degree of certainty that symmetric is ideal for control surfaces or at least vertical stabilizers. However, for some configurations, you may want your horizontal stabilizer to generate a natural pitch-down moment. For this, the flat-bottom would be ideal. Overall, I do not see a use for the semi-symmetric airfoil in most applications due to its less ideal stall characteristics and lower aerodynamic efficiency (C _ L / C _ D). Discuss in the comments below, thanks for reading.