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For a Grid Fin, what would be the most optimal way of finding the lift to drag ratio?

I am thinking about comparing lift to drag ratios of square lattice Grid Fins but with different geometrical parameters (such as thickness of the grid fin, the number of cells inside the fin).

I know that the lift to drag ratio depends on the aspect ratio, but I couldn't find anything about Grid Fins for this.

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    $\begingroup$ I may be wrong, but aren't lift to drag ratios only relevant in wings? I don't think the Grid Fins provide any lift at all. I suppose that would make the ratio 0, technically. $\endgroup$ – Kamil Drakari May 24 '18 at 15:36
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    $\begingroup$ @KamilDrakari lift is lift - it's just the force transverse to the airflow no matter the cause of the force. Hand out the window of a fast car, tilted, feels a perpendicular force, and the name of that force is "lift" no matter if it's up or down, as long as its transverse. See the material in Is aerodynamic lift ever useful in rocket flight? for example. Then again, grid fins are also called "lattice wings"! $\endgroup$ – uhoh May 24 '18 at 16:41
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    $\begingroup$ @uhoh so for the grid fins on the F9, "lift" would be related to their ability to steer? I suppose that makes sense from a strict aerodynamics perspective. It still doesn't seem relevant since the F9 wants both drag and lift, while planes care about the ratio because they want high lift but low drag. $\endgroup$ – Kamil Drakari May 24 '18 at 17:23
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    $\begingroup$ @KamilDrakari: It's relevant, because despite maximizing drag (while retaining lift, unlike more common airbrakes) instead of minimizing it, as common with more traditional control surfaces, actually knowing the values is important. $\endgroup$ – SF. May 24 '18 at 17:44
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    $\begingroup$ @FoxIa I believe it is just the opposite. The primary function of the grid fins is to "steer" or at least tilt the rocket using lift. Remember that it has to land within a few meters of target, while coming in fast from a great distance, and the cold gas thrusters are not so effective once the strong aerodynamic forces in the higher density atmosphere are experienced, so the grid fins take over for attitude control and use the aerodynamic forces to do the work. By tilting the rocket (note that they are at one end) they can then leverage the body-lift of the entire rocket to alter trajectory. $\endgroup$ – uhoh May 25 '18 at 1:13
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For a Grid Fin, what would be the most optimal way of finding the lift to drag ratio?

Because Navier-Stokes computations are involved you'll probably want to use a computer with computation fluid dynamics (CFD) software.

I am thinking about comparing lift to drag ratios of square lattice Grid Fins but with different geometrical parameters (such as thickness of the grid fin, the number of cells inside the fin).

This article: "Navier-Stokes Computation of Grid Fin Missile Using Hybrid Structured-Unstructured Grids" (Nov 2006), by You-qi DENG, Ming-sheng MA, Ming ZHENG and Nai-chun ZHOU explains that many factors must be considered:

  • Size

  • Thickness

  • Effects of internal grid framework

  • Mach number

  • Angle of attack

  • Fin deflection angle

The airflow is very complex.

I know that the lift to drag ratio depends on the aspect ratio, but I couldn't find anything about Grid Fins for this.

There are many designs, and adjustments to formulas that must be verified by wind tunnel testing.

For example: "Swept-back grid fins for reduced drag" National University of Singapore:

Figure 1: Conventional grid fin (left) and swept-back grid fin (right).

Figure 1: Conventional grid fin (left) and swept-back grid fin (right).

CFD Results

Figure 2: Mach number contours across grid fins for freestream Mach number 1.045: conventional grid fin (left) and swept-back grid fin (right).

Difference of calculations vs. actual results

Figure 3: Drag coefficient of grid fins from experiments and from numerical simulations. Swept-back grid fins have 30% less drag in the velocity range explored.

See how when you do the calculations the results you actually obtain in wind tunnel testing are markedly different.

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