Calculating Aerodynamic Shape ```Name: Angeline Status: Student Grade: 9-12 Location: MA Country: United States Date: March 2009 ``` Question: I am designing an experiment using a wind tunnel that my school owns. I've made four small towers out of wood that have the same height and base width - a cylinder, a rectangular prism, a triangular prism, and a pyramid. I want to figure out which shape is the most aerodynamic. I will put the towers one at a time into the wind tunnel, perpendicular to the ground, and exert the same amount of horizontal wind force on each of them. I need to know how I can calculate which shape is the most aerodynamic. How can I measure each tower's air resistance against the wind? Replies: That will be a good experiment. What you need to determine is the area that the wind is blowing perpendicular to on the tower and where the centroid of that area is. From the shapes you have chosen I think you are making the area of the tower you see (from the direction of the wind) equal and the centroid of that area would be at mid-height. This keeps the comparisons more simple. When the wind blows it tries to topple the tower and if the tower is fixed at the bottom it creates what is called a 'moment' in the column, which is the twisting the column experiences from the force of the wind. This wind force also deflects the tower. So if you can either measure the deflection at the top of the tower or measure the 'strain' at the tower base you can relate that to the wind force. The 'strain' is a lengthening of the windward side of the tower as it bends backward in the wind. It is measured with a stain gage you cement onto the tower. When you know the strain you can determine the stress in the tower from the equation E = stress / strain with E being the modulus of elasticity for the material your tower is made from. Probably, having a deflection gage and measuring the deflection at the top of the tower would be the easier measurement. Assuming you have chosen to measure deflection for each tower you now have data to make a comparison of how the shape affects the wind load. You have to use a formula for deflection of a cantilever (your tower is a cantilever fixed at the ground) and from that determine the wind loading. That formula for deflection = w x L**4 / 8 E I. It would be best to check a civil engineering text to get all the terms correct. w is the wind load and is the unknown you are determining. With the same wind test speed it will vary from tower to tower because of the different tower shapes and will give you the information you want. L is the height of the tower; E is the modulus of elasticity and is dependent on what you build the tower from; I is the moment of inertia of the tower and is determined from the cross-section area of the tower about an axis perpendicular to the wind. Based on the tower shapes you have chosen the I's will be different and have to be taken into account because they will affect the strength of the tower. You have to be consistent in your use of units throughout the calculations This all sounds pretty complicated but you will learn a lot doing the experiment and calculations. There are factors or coefficients that have been determined from tests like you are doing that compare how these shapes react to the wind; after you have made you own determinations you might want to see how they compare to available data. Carlton Schroeder I am not an aerodynamic engineer, and I know you have to keep things simple. So here are some "simple minded" suggestions. 1. Set up the experiment as you describe, and start the wind tunnel at a very slow RPM which I assume you can control. Be careful because the objects have different symmetry with respect to the direction of air flow. That is, the rectangular prism and triangular prism are going to behave differently depending upon their orientation. Record the RPM that is air speed at which each tower falls. You can alter different air flows by putting weights in the tops of the block you are measuring. Admittedly, this is pretty crude. 2. The following setup should give you better results. Attach the base of each object to a loosely coiled spring (You will have to find one, maybe from a lab supply vendor). I also assume you have a viewing port in the wind tunnel. Behind each object, mount a piece of graph paper glued to a board, or alternatively have some way to mark off etch marks of the background. In front of the viewing port mount a digital camera -- this does not have to be fancy. Then start the air flow and photograph the assembly as a function of wind speed. The object will tilt a certain angle (x) as a function of wind speed. If I have done my trig correctly tan(x) will measure the deflection of the blocks. The smaller the value of tan(x) , or "x" the more aerodynamically "smooth" the object. You could also check the effect of the axial symmetry. You could also do a relative comparison vs. the cylinder since that should not show any axial differences like the other shapes. Also note that you can reverse the configuration and use a hanging spring, but you may have to put a ballast on the blocks to prevent them from "waving in the breeze". Vince Calder Hi Angeline, Interesting experiment. It is not possible to calculate which of your shapes has the least air resistance, without getting into fiendishly difficult and involved equations that are likely beyond high school level math, and even then the results will not be particularly accurate. Nowadays, this type of a problem is solved using Finite Element Analysis (FEA) software and even then it will take several hours of time on a fast computer to come up with an accurate answer. Millions of calculations are needed! Of course I suspect, you already know the answer... the cylinder will have the least air resistance. You can make measurements, however. You will need to measure the force on the object as the air blast tries to push it "downwind". One method might be to mount the object under test so it is restrained from moving backwards (as a result of airflow impinging on it) with springs holding it at the top and bottom. Thus, the drag caused when the air flows, causes the springs to stretch a little. The amount that the springs stretch, indicates how much drag is occurring. The test object that stretches the springs the least, has the least air resistance. Regards, Bob Wilson Hi Angeline, this sounds like a great experiment! Your teachers might have told you that the first step in science is defining the problem, and I think that is the first step that is needed here. I suggest you start by defining what variables you can control, measure, or calculate. For example, you can control the wind speed of the wind tunnel and the design of the towers. You may be able to measure forces that the towers exert on whatever surface they are resting on, but you cannot control it directly. The force on the tower is a dependent variable, while the wind speed is an independent variable (if you have not heard these terms, you can look them up on-line). The force exerted on the tower by the wind would have to be calculated from some other measurements, as it cannot be directly measured. My point here is that you have to be careful in thinking about what you can actually control or measure and what you cannot. A term like "most aerodynamic" is vague, and vague terms are things we want to avoid in science. So with this in mind, what would you like to test? You mentioned forces, so I am assuming you have the ability to measure forces. Perhaps you could put your pressure sensors under the posts of the towers and measure the values compared with different wind speeds. You did not mention sizes of your equipment, but the type of measuring apparatus definitely depends on the sizes involved. Alternatively, if the towers are very flexible, you might be able to use a camera to capture them bending in the wind. In both cases, you could then estimate/calculate how much force is applied by the wind. You might also compare the cross-sectional area of each tower to the force applied and draw some conclusions there. Hope this helps, Burr Zimmerman Click here to return to the Engineering Archives

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