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What Is the Best Fin Shape for a Model Rocket?

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What Is the Best Fin Shape for a Model Rocket? ISSUE 442 May 2nd 2017 IN THIS ISSUE What is the best fin shape for a model rocket? www.ApogeeRockets.com/Rocket-Kits/Skill-Level-3-Model-Rocket-Kits/Skonk-Wulf What is the best fin shape for a model rocket By Tim Van Milligan they looked at it) which did tell them what shape Theoretically, the best fin shape for a rocket is was most likely the best. an “elliptical fin shape.” It is obvious that they must not have understood I wanted to get that conclusion stated right the technical jargon in the report. Otherwise they here at the start. wouldn’t have to ask me what the answer was Did you get that young student? I’m writing when it was already answered. So that is why I’m this for you. You came to the Apogee web site writing this article, to try to clarify what was in the looking for information on “What is the optimum Technical Publication #16 report in simpler lan- fin shape for a model rocket?”, and if you want an guage. answer, then write this statement down on your paper: “the elliptical shape is the optimum shape Why is the Elliptical Fin the Best Shape? for a model rocket (Figure 1).” Please, write that The reason the elliptical fin shape is best is that down! It is an acceptable answer to the ques- it produces the least amount of “induced drag.” tion. And now you can go play, your homework is Induced drag is a fancy aeronautical engineer- done. ing term that means that the drag force produced is actually a result of something else happening. That means that two things are going on at the same time, and that the first thing causes the sec- ond thing to happen. Elliptical Trapezoidal Square Rectangular Clipped (Theoretical Delta The two things are: Best!) 1. The Lift force on the fin is causing... Figure 1: The elliptical fin (far left) is the best from a 2. A drag force increase on the fin. theoretical point of view. The lift force is the key factor. Lift is only creat- In this article, I’ll explain why it is the right “the- ed when the symmetrical airfoil is oriented at an oretical answer.” But sometimes, theory runs into “angle-of-attack” to the wind. That means the fin is practicality, and that might not be the best answer tilted in the wind as it flies forward. if you are building a model rocket for an altitude Why would the fin be tilted? That doesn’t seem competition. right, because don’t we launch the rockets straight The reason I’m writing this article is that grade up? school students come to the Apogee web site Yes, we do launch the rockets straight up. And and download Apogee Technical Publication #16 in a perfect world, the wind created over the fin “What is the Optimum Fin Shape for Altitude?” as the rocket rises into the sky would strike the fin (https://www.apogeerockets.com/Rocket_Books_ right at the leading edge (the very front edge of Videos/Pamphlets_Reports/Tech_Pub_16), and the fin). Half of the air would flow over each side then send me an email asking that exact same as the paths of the flowing air were split by the question: “which shape is it?” I’m left shaking leading edge. No lift would be created in such a my head, wondering where the disconnect was, situation. All you would have is a small drag force because they did download the report (I assumed created from profile drag and skin friction drag. But the atmosphere that the rocket flies About this Newsletter Continued on page 3 You can subscribe to receive this e-zine FREE Newsletter Staff at the Apogee Components website Writer: Tim Van Milligan www.ApogeeComponents.com, or by clicking the link Layout/Cover Artist: Chris Duran here Newsletter Sign-Up Proofreader: Michelle Mason Page 2 Issue 442 | May 2nd, 2017 What is the best fin shape for a model rocket Continued from page 2 through is not perfect. Little gusts of wind are underside to the top side (from the high pressure always present. side to low pressure side). This is not the direc- What happens when the rocket flies through tion we want the air to flow. We just want the flow a small gust of wind is that the rocket sees a of air be parallel to the direction of the rocket. But slight wind direction change. From the rocket’s since it flows around the tip, it now has a perpen- perspective, it is tilted very slightly relative to dicular flow direction. In mixes with the parallel the wind flowing over the fin. This is called an flow closer to the rocket body tube, and causes a “angle-of-attack.” swirling motion (Figure 3). α Angle-of-Attack Figure 3: When lift occurs, air flows around the edge of the fin, from the high-pressure side on the bottom to the low pressure side on the top. This creates a tip vortex. Figure 2: When a symmetrical airfoil is tilted relative to the air flowing over it, it generates a lift force. Continued on page 4 As soon as the rocket is flying at an an- gle-of-attack (Figure 2), a lift force is created. And this is a good thing. We need this lift force You get: to pull the rocket back to a straight path rela- (4) AT 29/13 (4) AT 41/18 tive to the air flowing over it. In other words, if it (2) AT 56/18 were not for the lift force produced by the fins, (2) AT 66/18 the rocket would go unstable. Your rocket will (1) AC-56 not fly very high if it cartwheels across the sky. (1) AC-66 Having a lift force to restore the rocket to a straight path is a needed in unguided model rockets. Even though the rocket may not be pointed perfectly straight up, it will still go higher You get: (6) AT 13/18 than a rocket that doesn’t have any fins. (6) AT 18/18 Induced Drag occurs at the tips of the fins (6) AT 24/18 (6) AT 33/18 (the portion of the fin that is furthest away from the body of the rocket). What happens is that air flows around the corner of the tip edge from the www.ApogeeRockets.com/Building_Supplies/Body_Tubes Page 3 Issue 442 | May 2nd, 2017 What is the best fin shape for a model rocket Continued from page 3 Why Does An Elliptical Fin Have The Lowest Whenever you change the direction of a Induced Drag? moving object, a force is needed. Remember The reason the elliptical fin has the lowest Newton’s First Law of Motion? “An object will induced drag is that the shape of the fin orients move in a straight line unless a force acts to more of the lift force closer to the body tube of change the motion.” The object in this case is the rocket because the fin is longer near the the air molecules in the wind. Since the wind body tube. That means there is less of a lift force went from flowing parallel to the rocket to per- created near the tip of the fin because the fin is pendicular to the rocket, a force must have shorter in that section of the fin. Figure 5 shows acted on the rocket. We call this force “drag,” the span-wise distribution of the lift over the wing. because it slows down the speed of the rocket. And it has the special name of “Induced Drag” Total Lift since it occurred because a lift force was the of entire fin root cause of the air flowing from one side of Lift at each the fin to the other. Without a lift force, there section of fin would be no extra drag force, and hence no induced drag. Figure 5: Span-wise lift distribution over an elliptical shaped fin. The summation of the lift forces (dark red line) is closer to the body than it is to the tip. Because there is less lift near the tip of the fin, the difference in pressure (comparing the pres- sure on the top surface to that on the the bottom surface) is a lot lower near the tip. So less air flows around the tip. Hence, the induced drag force is lower. Lower drag means the speed of the rocket isn’t being slowed down as much, so Figure 4: This rear-view from a computer simulation it can coast higher into the sky. That is why you program shows how the air swirls behind the rocket off of can say that the elliptical fin has the most efficient the fin tips. shape. Continued on page 5 www.apogeerockets.com/Rocket-Kits/Skill-Level-2-Model-Rocket-Kits/SkyMetra Page 4 Issue 442 | May 2nd, 2017 What is the best fin shape for a model rocket Continued from page 4 the other and thereby lowering the induced drag What is the worst shape fin? produced. The worst shape fin would have the highest In contrast, in rocketry, we don’t need lift to get induced drag. In other words, more air flowing us into the sky. That is the rocket engine’s job. around the tip edge of the fin. So making fins with Moreover, we don’t even want a lift force, except an axe-head shape (shown in Figure 6) would be to keep the rocket stable.
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