Intuitively, which of these coroplast fins has less drag?

[Anachronist]

Here's a crude model rocket fin made out of a material called Coroplast (corrugated plastic):

And here's the exact same fin with the flutes cut out from all around the edges, allowing the edges to be squeezed shut and sealed with tape:

It may look like there are small openings, but they're not openings, they're covered with clear tape.

My question is, which version would have the least drag?

Intuitively, my first thought was that the version with open edges has the least drag because it presents negligible frontal area (the top edge is the leading or windward edge).

Then I had second thoughts, which prompted me to seal the edges, but I'm still unsure. On one hand, the open version also has more than twice as much surface area as the version with closed edges. So maybe it has more drag. On the other hand, the version with closed edges has an order of magnitude larger frontal area. Then again, the closed-edge version is more or less airfoil shaped with tapered edges, so maybe it has less drag.

I don't really have any way to test this. I'm curious though, what would be the dominant contributor to drag? Surface area with negligible frontal area, or large frontal area of a somewhat streamlined shape?

If it matters, the fin is roughly 5 cm tall and 6 cm long, and is expected to experience a velocity of 76 m/s (170 mph).

 

[jerromyjon]

I think the fin with the open corrugation would have less drag, I bet you could test it easily enough if you could suspend the fins from 2 threads each and use a straw to blow on the leading edge to see how far it was displaced...

 

[jack action]

My guess would be that the one with the end sealed with tape will have less drag. if turbulent flow develops (which I think it will), it can change things a lot with respect to the ratio frontal drag / skin friction.

Also, even if you seem to have less frontal area with the open design, with just a little incident angle, your effective frontal area will increase drastically (the sides of your inner edges will be added).

I'm curious what @boneh3ad has to say about this.

 

[boneh3ad]

I'd hazard a guess that the sealed end fins would have substantially less drag. The frontal area really isn't all that much larger suggested here because that corrugated structure is going to look awfully "solid" to the oncoming flow due to the fact that the air will have to slow down to move through the ducts that are formed. It will therefore still have to deflect a nonzero portion of the air around the fin that can't be forced through it.

 

[Anachronist]

I think the fin with the open corrugation would have less drag, I bet you could test it easily enough if you could suspend the fins from 2 threads each and use a straw to blow on the leading edge to see how far it was displaced...

That would test the drag at low speed, and it may indeed be the case that the open edge version has less drag at low speed. But to do a proper test I'd have to reproduce a 170mph wind. Unlikely I can do that by blowing through a straw! Even if I could, I'd surely need something more substantial than a couple of suspension threads for the test to be meaningful in a high wind like that.

I'd hazard a guess that the sealed end fins would have substantially less drag. The frontal area really isn't all that much larger suggested here because that corrugated structure is going to look awfully "solid" to the oncoming flow due to the fact that the air will have to slow down to move through the ducts that are formed. It will therefore still have to deflect a nonzero portion of the air around the fin that can't be forced through it.

Hmm. I hadn't thought of it that way. I thought the presence of the ducts would actually relieve the pressure from the leading edge. And the closed fin would be deflect all of the air around it. Then again, I can see that at high airspeeds, the duct openings might approximate a solid surface.

 

[256bits]

But to do a proper test I'd have to reproduce a 170mph wind.

Then test it in water, where the velocity would be much less than that of the air to obtain the same Reynold's number.
Dimensional Analysis.
See 5.4 as an example... a bunch of worked examples.
About 10 times reduction in velocity for the water versus the air.
http://www.sfu.ca/~mbahrami/ENSC 283/Solution manual/Chapter5_SM.pdf
Maybe you could pull it behind a boat at about 17mph , which is still pretty fast.
http://users.metu.edu.tr/csert/me305/ME 305 Part 7 Similitude and Dimensional Analysis.pdf

 

[Anachronist]

Then test it in water, where the velocity would be much less than that of the air to obtain the same Reynold's number.

Great idea. But your reply and @boneh3ad's made me think of the problem in a different way.

The drag on the open-ended fins boils down to a simpler physics problem: Given a tube of radius $r$, length $L$, and negligible wall thickness, lined up with an air stream flowing past at velocity $v$, what is the velocity of air flowing through the tube? This is reasonably straightforward to calculate. There's a shearing effect for air flowing past a surface (Law of the Wall) in which the airflow is near zero at the boundary of the tube wall. So the smaller the tube diameter, the slower the overall flow, and the greater the effective backpressure at the leading edge of the fin.

The drag on a NACA 4-digit symmetrical airfoil is fairly well understood, and by tapering the edges, I'm approximating that (it won't be as low).

Also, even if you seem to have less frontal area with the open design, with just a little incident angle, your effective frontal area will increase drastically (the sides of your inner edges will be added).

Yes, you're right. The flutes would have to be lined up perfectly with the air stream. And because it's a rocket fin, it would be toward the back of the rocket, where the air flow is more likely to be turbulent, having already flowed past the nosecone-body transition and flowed down the body, so it would be impossible to get any real alignment of the flutes to the air flow.

 

[boneh3ad]

Hmm. I hadn't thought of it that way. I thought the presence of the ducts would actually relieve the pressure from the leading edge. And the closed fin would be deflect all of the air around it. Then again, I can see that at high airspeeds, the duct openings might approximate a solid surface.

The ducts would relieve some of the pressure but not all of it, and for ducts as small as you are using, I'd be willing to bet it's a lot less than you think.

The drag on the open-ended fins boils down to a simpler physics problem: Given a tube of radius rrr, length LLL, and negligible wall thickness, lined up with an air stream flowing past at velocity vvv, what is the velocity of air flowing through the tube? This is reasonably straightforward to calculate. There's a shearing effect for air flowing past a surface (Law of the Wall) in which the airflow is near zero at the boundary of the tube wall. So the smaller the tube diameter, the slower the overall flow, and the greater the effective backpressure at the leading edge of the fin.

Now you're cooking with gasoline. However, I wouldn't worry about something as relatively complicated as the Law of the Wall just yet. For now you can approximate everything as laminar (not necessarily a good assumption but easier to handle for now) and come up with the flow characteristics through each duct. That's already a nontrivial problem even ignoring the influence of turbulence (which is the topic of the Law of the Wall). You aren't going to be able to get an analytical solution to that, and the exact details of that inner flow cannot be decoupled from the details of the outer flow (these are still elliptic PDEs, after all).

The bottom line is that the ducts will reduce the stagnation pressure at the front of the airfoil, but they won't lower it all the way to static pressure. How far they lower that stagnation pressure depends on the size of the ducts. The benefits of this will be offset by the drastic increase in surface area you are creating. The effect you cited about velocity being zero at the wall (relative to the wall) is the result of viscosity and sets up a shear stress that opposes the motion of the plane. This is what is commonly called viscous drag or skin friction drag. The large increase in surface area means you will have a large increase in viscous drag that will likely offset any gains you make in pressure drag due to the ducts.

If you think about it, biplanes, triplanes, etc. sort of represent the logical limit of "ducts" in a wing, where they are separated to the point where they are two or more separate wings. They used to make planes that way because two wings means more lift and they just had to live with the extra drag. However, those have been almost entirely supplanted by planes with single wings because we now have the knowledge and technology to make a single wing with sufficient lift and much lower drag. I know there has been some research performed into low drag biplanes, but it's not mainstream and certainly hasn't shown up in modern aeronautical design.

 

[EspressoDan]

From an aerodynamic perspective, think about the two forms of Drag.

Parasitic Drag and Lift Dependent Drag.

Given that this is a symmetrical aerofoil, it won't be producing any lift at zero angle of attack. However, given the shape of it it might be worth considering the effect that the leading edge on the unsealed fin will have at a non-zero angle of attack relative to the free-stream flow during flight.

For your parasitic drag, consider the simple equation: D = Cd.½ρV^2S

ρ and V will be the same for both fins and so can be discarded.

First, consider the coefficient of drag for the two find:

From the above, we can see that your streamlined body will have a low Drag Coefficient. Some might argue that the holes through the first fin mean that you have a flat-plate (which will give you some big problems with non-zero angles of attack at low speeds) but actually, I would expect compression effects to mean that the boundary layer flows around the fin leading edge, with only a small amount moving through. This will simply result in turbulent flow, which will increase drag. In this case, my intuition tells me that you're dealing with a fin that has a higher Cd than a streamlined body, and probably more surface area due to the flow-through. So I would say that the second fin with the sealed leading edge had the lower drag, and as a fin which needs to keep your rocket flying straight has other advantages too.

Perhaps another litmus test. Consider the aircraft that you see today. If this approach really did decrease drag, they'd all have holes through the leading edges. None do.

One more pointer. When designing your model rocket, don't take too much of a lead from NASA, or military missiles/rockets. These rockets are designed to fly above the speed of sound (often at many times the speed of sound). Here, the main concerns are controlling shock-waves and separation points as a means to control both drag and structural integrity, and so flat-plates start to make sense. Your rocket will be subsonic, and so conventional aerodynamics apply. No need for funny stuff.

 

[Anachronist]

Thanks, great discussion. The consensus I'm seeing is that closing the edges, like in my second picture, will result in less drag.

Two things came to mind when I read this comment, though:

Perhaps another litmus test. Consider the aircraft that you see today. If this approach really did decrease drag, they'd all have holes through the leading edges. None do.

First thing that came to mind was parafoils, which have leading edge openings... but those are just to inflate the airfoil and don't flow through, and the parafoil is a very low speed airfoil where the drag from the leading edge is probably minimal compared to the drag of the entire parafoil surface.

The second thing that came to mind was my memories of being a sailplane pilot decades ago, during which I learned about high-performance sailplane airfoils with bleed holes built in, for the purpose of transferring air from a high pressure region near the front/bottom to the top/rear of the airfoil where laminar separation bubbles are likely, to preserve the laminar flow. I can imagine that we would have laminar flow inside those rocket fin flutes, but the situation is still different because that flow isn't being used for any useful purpose, and there's still turbulent flow on the outside of the fin.

One more pointer. When designing your model rocket, don't take too much of a lead from NASA, or military missiles/rockets.

NASA actually has several useful pages devoted to hobby model rocketry, although they're written with pyro rockets in mind (some of which can achieve supersonic speeds), and my application is a water rocket, which is definitely subsonic.