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How to Determine the Drag Coefficient of Your Rockets

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How to Determine the Drag Coefficient of Your Rockets In This Issue How To Determine The Drag Coefficient of Your Rockets Cover Photo: Apogee’s NEMSAR Rocket Kit Get one now at: www.ApogeeRockets.com/nemsar.asp Apogee Components, Inc. — Your Source For Rocket Supplies That Will Take You To The “Peak-of-Flight” 3355 Fillmore Ridge Heights Colorado Springs, Colorado 80907-9024 USA www.ApogeeRockets.com e-mail: [email protected] ISSUE 303 JANUARY 3, 2012 How To Determine The Drag Coefficient of Your Rockets By Tim Van Milligan As the members of the TARC teams become more titude from the altimeter, and lower if it didn’t simulate high knowledgable about rocketry, the event is becoming more enough). Run a new simulation. and more competitive. Everyone is looking for that extra 5. Go back to step 3. Repeat this process until the edge that will get them to the finals in Virginia. altitudes match. The one question I get every year is how to determine The final C entered into RockSim that was used to the Drag Coefficient (C )of the rocket more accurately. The d d match the actual altitude from the Altimeter is now your reason this is a big question is because with an accurate “back-tracked” C value. value for the Drag Coefficient, teams can reduce the num- d ber of test flights they need to make. That really helps lower This process does involve a little bit of effort. But you can usually zero-in the C value within 5 or 6 iterations of the cost to the students. d the process. Making RockSim Better We used to sell a program called SMARTSim that sped Because it accounts for so many of the variables up the process. But unfortunately, the programmer got tired associated with flight, people really have a pretty good of repairing it every time Microsoft created a Windows OS understanding of just how accurate RockSim can be. The update. Our long-term goal is to get that program back, and one Achilles heel is determining the Drag Coefficient of the maybe even incorporated directly into RockSim. We have rocket. lots of ideas on how to make it better… This is a problem that even plagues NASA. While How Good Is Altitude Back-Tracking? software has gotten better, and it will continue to get better, there is still an uncertainty of just what is the actual Drag That is the million-dollar question, isn’t it? Coefficient of the flying object. It should be pretty good. And many successful TARC But still, people want to know how RockSim can be teams have proved that it does work well. made more accurate at predicting the Drag Coefficient. But, the big assumption is that the rocket flew the That will be the topic of this article. same trajectory as predicted by RockSim. In RockSim, you probably set the conditions to try to match the actual Altitude Back-Tracking flight conditions, but it may not be “perfect.” And, as a lot of The method that most people use to get a better value TARC teams know, there is some variability between rocket on the Drag Coefficient is called back-tracking. It is pretty motors. So while RockSim assumes the motor may have easy to do, and here is the procedure: put out exactly 80 N-s of total power, in real life, you might 1. Put an altimeter in the rocket. Measure the actual have gotten to the altitude with just 75 N-s of power. height of the rocket. For example, in your test flight, the So on your next real-life flight, if you have a motor altimeter says the rocket went to a height of 1000 feet. with 79 N-s of power, it is going to go a bit higher, and now you’re thinking that your back-tracked C is too low. 2. Input the design into RockSim. Run a simple simula- d tion, using a fixed Cd value. A good starting point is to set The solution to this, of course, is to fly a high number the Cd at 0.75. of test flights and back-track the dC value for each of them 3. Compare the altitude that RockSim predicts against so that you average out the variability of the motors. Then the altitude measured by the altimeter. you’d average them so that you’d get a better approxima- tion of the actual Cd value for the rocket. 4. Adjust the Cd value in the software (make it higher if the previous simulation went higher than the measured al- Continued on page 3 About this Newsletter Newsletter Staff You can subscribe to receive this e-zine FREE at the Apogee Writer: Tim Van Milligan Components web site (www.ApogeeRockets.com), or by Layout / Cover Artist: Tim Van Milligan sending an e-mail to: [email protected] with “SUB- Proofreader: Michelle Mason SCRIBE” as the subject line of the message. Page 2 ISSUE 303 JANUARY 3, 2012 Continued from page 2 Determine A Rocket’s Drag Coefficient This is where it starts getting a little expensive, be- cause you’re burning a lot of rocket motors. But it is actually the right thing to do. We Need More Data As you can tell, we need to gather a lot of flight data, so that we can dial-in on that elusive Cd value. The more data you can get, the quicker you can find that Cd value. One additional piece of data that we can get on the flight is the velocity of the rocket, either through the record- ing altimeter, or through the AltimeterTwo altimeter (www. ApogeeRockets.com/AltimeterTwo.asp). It is better to use a device that has an accelerometer on board, as you’ll get more accurate readings. A pressure-sensing altimeter can give you rougher Figure 1: Altimeter data from a recording altimeter. The speed readings on velocity, but it isn’t quite as accurate. curve is nice and smooth indicating good data. For one thing, it has a little lag in sensing the air pressure inside the rocket. To understand this, think of the electron- cur when the rocket is moving slow – such as when it nears ics bay as a balloon filled with air. There are holes in the the apogee point in the flight (see Figure 1). At this point, balloon, so air is escaping. Air continues to flow out until the there is no upward velocity, so it is a great time to make a pressure inside the balloon equals the outside air pressure. pressure reading. There is plenty of time for the air pres- It doesn’t change instantly, as you know. It takes a few mo- sure to equalize when the outside pressure is staying con- ments for the air pressure to equalize. stant. And that is exactly why pressure sensors are used to measure height. The same thing happens in a rocket. On the ground, the pressure inside the e-bay is the same as the outside. But unfortunately, when it is moving slow, even subtle As the rocket ascends, the outside air pressure decreases. changes in pressure readings can indicate fast speed So the air inside the e-bay has to flow out until they equal- changes. If you look at the speed chart from a recording ize. When it is equalized, that is the point where you want Barometric altitude sensor, they fluctuate wildly when the to take the pressure reading. The big problem comes rocket is moving at a slow speed. For example, in Figure 2, when the rocket is moving really fast, since the outside air notice how jagged the graph is when the rocket is descend- pressure is rapidly changing because the altitude changes ing under the parachute. Also note, that even before the quickly. rocket is launched, the speed is rapidly changing. And you know that can’t be right, since the rocket is actually station- The most accurate readings for a pressure sensor oc- Continued on page 4 Your Cool Rocket Designs Look So Much Better In RockSim Version 9! Design It. Launch It. v9 www.RockSim.com Space Foundation certified as an excellent teaching aid. For further information, call Apogee Components at: 719-535-9335. ISSUE 303 JANUARY 3, 2012 Page 3 Continued from page 3 Determine A Rocket’s Drag Coefficient Now you have this extra velocity data, what do you do 400 with it? Motor Burnout 350 Basically, you treat it the same way as you’d treat peak 300 altitude. You back-track out a Cd based on that velocity. 250 1. Put an accelerometer in the rocket. Measure the 200 Coast Phase Apogee maximum speed of the rocket. For example, in your test 150 flight, the accelerometer says the rocket went to a speed of 100 250 miles per hour. 50 Speed (Feet/Sec) 0 2. Input the design into RockSim. Run a simple simula- 0 2 4 6 8 10 12 14 16 18 -50 tion, using a fixed Cd value. A good starting point is to set -100 Ignition the Cd at 0.75. Descending on Parachute -150 3. Compare the maximum speed that RockSim predicts Time (seconds) against the speed measured by the accelerometer. Figure 2: Speed graph created from barometric altitude data. Notice the data is more jumpy at slow speeds. 4. Adjust the Cd value in the software (make it higher if the previous simulation went faster than the measured ary prior to launch. speed from the accelerometer, and lower if it didn’t simulate Pressure sensors are great for measuring peak alti- fast enough).
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