Reference / Paper · 2014
Peak of Flight #376: Deciding Which Nose Cone Shape To Use for a High Altitude Rocket
Apogee Components' Peak of Flight newsletter, issue 376 (2014-10-21).
- peak-of-flight
- apogee-components
- model-rocketry
Reference / Paper · 2014
Apogee Components' Peak of Flight newsletter, issue 376 (2014-10-21).
Apogee Components' Peak of Flight newsletter, issue 376 (2014-10-21).
In This Issue Deciding Which Nose Cone Shape To Use for a High-Altitude Roket Shrox Plan: “Bisix” Cover Photo: DFR Technology’s Atlas V LRO/LCROSS kit takes to the sky. Get your own at: www.ApogeeRockets.com/Rocket_Kits/Rocket_Kits/Skill_Level_3_Kits/ Atlas_V_LRO_LCROSS 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] Phone: 719-535-9335 Fax: 719-534-9050 ISSUE 376 OCTOBER 21, 2014 Deciding Which Nose Cone Shape To Use For A High-Altitude Rocket By Vicente Alvero and Hans Olaf Toft Background The Sugar Shot to Space (SStS) rocket has a design goal of reaching at least 100km in altitude, using a low performance sugar-nitrate propellant in a single stage rocket. In order to achieve this goal, it will be important to keep the drag loss at a minimum. Two strategies are being applied in this respect: 1. Dual phase rocket motor 2. Minimum drag airframe The dual phase motor splits the burn into two parts, divided by a coasting phase. This allows the rocket to save half of its propellant until it has passed through the denser part of the atmosphere. The minimum drag airframe will improve the rockets altitude performance by keeping the energy loss in form of aerodynamic drag at a minimum. The overall shape of the rocket consists of a nose cone and a cylindrical rocket body and one set of fins. The dimensions of the cylindrical body are determined primarily by motor design restrictions and are as such outside the scope of this report. The dimensions of the fins are to be determined according to stability requirements, and are also outside the scope of this report. The purpose of this report is to investigate the impact of shape and fineness ratio of the nose cone on the performance of the rocket, when it follows a trajectory profile that is reasonably realistic. Image 1A: Performance predictions of the DPH47 rocket. About this Newsletter You can subscribe to receive this e-zine FREE at the Apogee Components web site (www.ApogeeRockets.com), or by sending an e-mail to: [email protected] with “SUBSCRIBE” as the subject line of the message. Page 2 ISSUE 376 Image 1B: Additional specification of the DPH47. Conditions This investigation is based on Richard Nakka’s DPH47 configuration as detailed in Image 1A and 1B. Design Tools This investigation is based on the “Aerolab” drag and stability software and the “Launch” trajectory simulation software, both by Hans Olaf Toft. “Aerolab” is used to calculate the coefficient of drag in the entire Mach range of relevance for the SStS for the configuration candidates of the airframe. The calculated drag coefficients are fed into the trajectory calculator, and the output is collected into a spread sheet for comparison. The trajectory simulator is being tricked to handle the dual phase configuration by adding a zero weight first stage and a dummy stage separation. Although the overall purpose of this study is to set up a realistic scenario, some things are not known at this early stage. This affects the drag model in two ways: 1. Base drag reduction during powered flight is ignored as there is (yet) little knowledge of the nozzle dimensions. 2. The dimensions and number of fins are not yet Continued on page 3 Newsletter Staff Writer: Tim Van Milligan Layout / Cover Artist: Tim Van Milligan Proofreader: Erin Card OCTOBER 21, 2014 Continued from page 2 Nose Shapes for a High-Altitude Rocket known. Furthermore, fin canting has been suggested but not (yet) specified, so the drag contribution from the fins has to be guesstimated. All the candidate configurations are being analysed with the same set of dummy fins that are assumed to provide a reasonable first order approximation of the fins impact on the trajectory profile. The base configuration, featuring a 3:1 conical nose cone is shown below in Image 2A. Candidate configurations are being generated using all the nose shapes currently implemented in Aerolab: Image 2B: Fin planform l Conical l Tangent Ogive l Parabolic l Elliptical l ½ Power l ¾ Power (also known as “hypersonic optimum”) Configurations are being generated with nose fineness ratios of 2:1, 3:1…,7:1 for all shapes. A trajectory simulation of the DPH47 configuration is being run for all combinations of shape and fineness ratio. The trajectory simulator calculates – among other things – the altitude and drag loss (in Newton seconds) versus time. Image 2A: Configuration of the DPH47. Continued on page 4 • Holds Aerotech’s Reload Propellant • Sizes: 24mm To 98mm Diameter • Power Range: E Through N • Cases For Any Project • Rouse-Tech Quality • Affordable! ISSUE 376 OCTOBER 21, 2014 www.ApogeeRockets.com • Reusable Rocket Motors Save Money Your Source For Everything Rocketry High-Power Reload Casings Page 3 Continued from page 3 Nose Shapes for a High-Altitude Rocket the same rate as the rocket speed decreases. This is however a curiosity, as the air drag is neglible at that altitude. Trajectory profile Different nose shapes are known to be optimal at different Mach ranges, so in order to select the best nose shape, it would be advisable to look at the velocity distribution as seen in Image 4. The main highlights of the trajectory when using the standard drag model from Launch is: 1st phase burnout 2nd phase ignition 2nd phase burnout Apogee 8.70s 16.50s 25.20s 164.75s 2232m 5882m 13664m 107689m 558m/s 401m/s 1638m/s 257m/s The drag varies mostly with the Mach number, so one wants to check out the variation in Mach number as seen in Image 3. One notable feature of this chart is that the Mach number stays constant between approximately 60 and 70km. This is not because the rocket travels at constant speed, but rather that the Mach velocity decreases Image 3: Speed of the rocket versus with altitude at altitude Image 4: The amount of time the rocket spends at different flight speeds. Again, the Mach 3 peak is clearly visible. Even ignoring this, the rocket will spend approximately 50% of the travelling time at Mach 1.5+, where the hypersonic optimum Continued on page 5 Roam In Our Forest of Over 190 Different Types • Unique and exotic kits from over 20 different manufacturers • Skill Levels range from “easy” to “fiendish” • Sizes from 1/4A motor to level-2-high-power • We build & fly them to find out what they’re like, saving you grief • More new ones arriving all the time • Educational bulk packs available too Continued on page 10 www.ApogeeRockets.com/Rockets_By_Manufacturers Page 4 ISSUE 376 OCTOBER 21, 2014 www.ApogeeRockets.com Looking For A Fun Rocket Kit? Continued from page 4 Nose Shapes for a High-Altitude Rocket The main conclusions are shape has minimum wave drag for any given fineness ratio. For comparison, the same rocket spends approximately 35% of the travelling time at transsonic speeds, where the hypersonic optimum shape is not the optimal choice. Simulation results The simulation results are listed below. l For any given fineness ratio, the hypersonic optimum shape has the least drag loss. The difference in drag loss between conical and hypersonic optimum shapes decreases however for increasing fineness ratio, and at 7:1 it has nearly vanished. l For any given shape, altitude increases with increasing fineness ratio. However, the benefits of increasing fineness ratio beyond 5:1 are small. l For fineness ratios up to 6:1, the hypersonic optimum shape yields the highest apogee - but for increasing fineness ratios, the conical shape gets increasingly closer in performance, and at 7:1 fineness ratio, the conical shape yields the highest apogee, although only by a very small margin. The wave drag contribution decreases at higher fineness ratios, so skin friction becomes more important, and it becomes less important what shape has the least high Mach number wave drag. Image 5: The performance predictions of different nose cone shapes at different length-to-diameter ratios. Not surprisingly, the elliptical shape has poorer performance than the other shapes, but except from that, and perhaps the parabolic shape, the difference in apogee between the other shapes is so small for the higher fineness ratios, that other criteria may be taken into account when selecting the shape. A 5:1 fineness ratio may be chosen over 7:1 for practical reasons. The hypersonic optimum shape may be chosen for performance, but the penalty for choosing a conical shape is neglible, and it would have the advantage of simplicity. Also there are the thermal considerations. In general, the aerodynamic heating increases with the equivalent nose vertex angle, so a conical nose would be expected to have higher temperature at the base than the hypersonic optimum but lower temperture at the tip. However, the temperature rise also depends on the loContinued on page 6 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 376 OCTOBER 21, 2014 Page 5 Continued from page 5 Nose Shapes for a High-Altitude Rocket cal heat capacity, and the tip of a hypersonic optimum nose can have a larger heat capacity so it may still have the lowest skin temperature overall. A blunted cone could be a reasonable way of approximating the hypersonic optimum shape while keeping the simplicity of a cone. The estimated wave drag coefficient of the different nose shapes can be seen in Image 7 for comparison. Fineness ratio is 5:1. Image 7: Wave drag coefficient for different nose cone shapes (fineness ratio is 5:1). About the Author: Image 6: Shapes of the nose cones simulated. Vicente Alvero Zambrano is a Student of physical science and lives in Santa Marta de los Barros ( Badajoz- Spain). His goal in model rocketry is to make space more accessible. He also enjoys cycling, robotics, electronics, chemistry, physics, and geology. • Big Kits with Classic Styling and Bold Graphics • All Rockets Feature Laser-Cut Plywood Fins and Rings • Easy-to-Build. Durable. Exciting, and a Real Joy to Fly! Page 6 ISSUE 376 OCTOBER 21, 2014 www.ApogeeRockets.com Mid & High Power Rocket Kits! Everything Rocketry North Coast Rocketry Shrox Plan: The “Bisix” By Shrox Download the RockSim file (which includes the parts list) and the decal file at: www.ApogeeRockets.com/ Downloads/Bisix.zip Join The NAR.org Mention Apogee Components Think of the convenience of getting everything to professionally install your dual-deployment or other electronic payload into a e-bay of your rocket! Includes: nylon standoffs, screws & nuts, wire, push-switch, drill & tap, ejection charge cannisters, barrier strips, wire ties, and step-bystep DVD instructions. www.apogeerockets.com ISSUE 376 OCTOBER 21, 2014 www.ApogeeRockets.com Electronics Hardware Installation Kit Page 7