HW 3: Improved Aerodynamic Analysis
Now that we can evaluate the aerodynamic performance of airfoils we can improve our drag estimation. For this analysis we will use the wing from the Douglas DC-3, a very successful plane that helped make air travel popular in the U.S. Some key specs, dimensions, and airfoil schedule are below (the below picture is simplified for the purposes of this homework both in number of airfoils and chord distribution).
| takeoff mass | 11,000 kg |
| cruise speed | 93 m/s |
| cruise altitude | 10,000 ft |
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Start with a basic drag estimation. Reuse the same parasitic drag methods from the last homework. To keep it simple, use a sweep of zero (the Mach number is low enough that the sweep angle wouldn’t make much difference in these calculations), and use an average airfoil thickness. Assume fully turbulent for simplicity, though that’s too conservative for a transport aircraft so your answer won’t be very accurate. Next, compute induced drag. At early design we’d have to assume an inviscid span efficiency (assume einv = 0.98, which is a typical value corresponding to a near-elliptic lift distribution). While we now have viscous drag (with no lift), and lift-dependent drag (with no viscosity), we have to consider the interaction: viscous-lift-dependent drag. In class, we talked about a rough early-design method: \({C_D}_{lift, viscous} = K {C_D}_p C_L^2\), where \({C_D}_p\) is the parasitic drag coefficient, and a typical value for \(K\) is 0.38. Add this to the parasitic drag, resulting in total viscous drag (we could add it to either term, or really just add all three together for total drag, but adding it this way will facilitate later comparison with XFLR5).
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Let’s now compute drag using XFLR5. XFLR5 integrates the viscous drag using airfoil data, and computes an actual lift distribution to compute einv instead of assuming an elliptic distribution. The most helpful overview videos from the official set are 2, 6–8. We don’t need to do any of the inertial properties as shown in video 7 (but will in a future homework). Instead, for the analysis we are doing in this homework we can just enter the mass as a lump sum later in ``define an analysis’’.
Airfoils: you need to do the airfoil batch analysis before you can do the wing analysis. Type 1. Make sure to run a wide range of angles of attack and Reynolds numbers.
Wing: For Polar Type I prefer type 2 in this case, but you could do type 1. Either way you’ll have to iterate on angle of attack. Either to find the right speed for a fixed lift (when running type 2), or to find the right lift for a fixed speed (when running type 1). Select VLM1 as the Analysis type. Make sure to choose a viscous option. Enter the mass under inertia, and set your atmospheric properties. When iterating on angle of attack it’ll be helpful to run coarse at first (say every degree or two), then narrow it down and run a finer resolution (like every 0.1 degrees).
Report the inviscid induced drag (ICD in XFLR5, you’ll need to unnormalize), and viscous drag (VCD, this also includes viscous lift-dependent drag). Compare to your estimates across all three parts.