HPR Research - Static Port Holes from Nescience to Science

Transcription

1 HPR Research - Static Port Hoes from Nescience to Science The characteristic of scientific progress is our knowing that we did not know. Gaston Bacheard Purpose In 1997 I was inspired by a teevision program showing individuas aunching arge rockets in western US deserts. At the end of the program Tripoi was isted in the credits, I found the web site on the internet, and joined the nationa organization as we as my oca prefecture. I as many of you did this hoping to recapture the excitement of my youth the space race aong with a ove of technoogy, engineering, and science. Athough I ve been abe to rekinde much of this excitement over the years and recognize that this is a eisure pursuit, I have been somewhat frustrated and disappointed with the ack of engineering discipine and scientific methods exhibited in our hobby. This extends not ony to the various officia and unofficia forums but aso to commercia materias. Undeniaby, a few individuas have produced very informative web sites, some of which incude experimenta data aong with resuts and concusions. The intention of this and subsequent artices is to dispe some of the misinformation propagated in our hobby through the use of scientificay derived materia. The iusion of science as currenty propagated is dangerous as it gives those using it a fase sense of safety and security when appying such methods. It aso steers these individuas down fase paths when attempting to ascertain the root cause of faiures (by steering them away from possibe sources of the faiure). This inevitaby eads to an inabiity to identify or the misidentification of the root cause thereby eiciting future faiures and safety issues. I repeatedy witness such churning when mentoring high schoo and coegiate rocket teams for the NASA Student Launch Program as we as the Experimenta Sounding Rocket Association programs and as Technica Advisor for the Midwest High- Power Rocket Competition. Additionay, I see this with experienced rocketeers since they aso assume that the prevaiing materia has been derived and tested using scientific methods. Finay, I beieve that three of Tripoi s organizationa goas are to eiminate injuries and property damage, preserve and enhance our reationships with government agencies, and to curb insurance rates. By improving the information avaiabe to the membership we can reduce our faiure rates and thereby improve safety which wi hep us accompish a of these goas. Prevaiing Static Port Computations The proper sizing of static port hoes is critica to the correct operation of atimeters and thereby eectronics based recovery processes. As many of you may know recovery system faiures account for roughy 73% 1 of a fight faiures and of these roughy 31.5% 1 Launching Safey in the 21 st Century Fina Report of the Specia Committee on Range Operation and Procedure to the Nationa Association of Rocketry (October 29, 2005). Retrieved from Admittedy the data in this report is 1

2 are due to motor or eectronic ejection system faiures ( 23% of tota fight faiures). Athough a number of different computationa methods are pubished to size static ports they a share one or more of the foowing deficiencies: 1. Unknown derivation of equation (vaidity cannot be assessed) 2. Unjustified assumptions 3. Limited in scope (restricted set of voumes or number of static ports) 4. Equations contain undefined numerica factors Some of this materia takes the form of equations whie other information is provided in tabuar form. Let s examine some of prevaiing materia propagated over the internet as we as those avaiabe through commercia sources. In the discussion beow the foowing symbos wi be used: d s Diameter of the Static Port Hoe(s) Length of Avionics (AV) Bay n Number of Ports (restricted to positive integers) r Interna Radius of AV Bay Equation 1 d s = πr2 400 where n = 1 and πr2 100 in 3 d s = 2πr2 400n where n > 1 and πr2 100 in 3 This particuar equation suffers from deficiencies 1, 2, 3, and 4. Equation 2 d s = 2r a ref v ref n for n 1 where a ref Static port hoe area of reference (recommends a ¼ hoe in 2 ) v ref AV Bay voume of reference (recommends 100 in 3 ) When substituting the recommended vaues one arrives at the foowing forms aso found in the iterature: d s.04431r n 2 ( πr2 ) 2 ( πr2 100πn n ) This equation s derivation is demonstrated but suffers from deficiency 2 by using a widey popuar rue of thumb that one shoud use a ¼ hoe for every 100 in 3. skewed toward ow and mid power rocketry; never the ess it demonstrates that recovery is a significant cause of faiure. 2

3 Equation 3 d s = 0.2r 19.68n for n 1 This equation aso suffers from deficiencies 1, 2, and 4. Equation 4 <a> d s =.0016(4r 2 ) where n = 1 d s =.0008(4r 2 ) where n = 4 <b> d s =.006(2r) where n = 1 d s =.006r where n = 4 Both of these equations suffer from deficiencies 1, 2, 3, and 4. Athough other equations may exist these are sufficient to iustrate the prevaiing propagation of miseading information. In order to assess these equations we need to recognize that the voume of a cyinder is simpy the area of its circuar base times its ength (Figure 1): area of a circe A = πr 2 voume of a cyinder: V = πr 2 r Figure 1 AV Bay Pressure Equaization Now et s examine the above equations. It shoud be obvious that the size of the static ports must be proportiona with the voume of the AV Bay and that any reasonabe equation woud refect this reationship. A of the equations above do this with the exception of 4b. It shoud aso be apparent that any equation computing the static port size shoud resut in a singe vaue for a specific voume. If we use the foowing vaues: 3

4 r 1 = 2, 1 = 4 then V = in 3, d s1 =.096 in and d s4 =.048 in r 2 = 4, 2 = 2 then V = in 3, d s1 =.096 in and d s4 =.048 in r 3 = 1, 3 = 8 then V = in 3, d s1 =.096 in and d s4 =.048 in This exampe shows that when doubing or having the voume of the AV Bay the size of the static port hoe(s) remains the same in both the singe and the four port cases: ceary demonstrating that Equation 4b does not adequatey account for variations in AV Bay voume. Consequenty, Equation 4b shoud never be used. Now et s ook at the resuts generated by the remaining equations for the singe port case (Figure 2) and the four port case (Figure 3). Figure 2 Singe Static Port Sizing 4

5 Figure 3 4 Port Static Port Sizing Upon examination of these charts one can see that Equation 1 is an agorithmic expression for the rue of thumb of using a ¼ port for every 100 in 3. Furthermore, we aso note that Equation 1 wi aways produce the same static port hoe size for one or two ports which is ceary unrepresentative mode of depressurization. Aso notice that Equation 4a produces a port size that increases ineary with a inear increase in voume abeit at a reduced rate reative to Equation 1. As the voume of an AV Bay increases it is evident that the area of the static port hoe(s) must aso increase ineary in order to evacuate the air at the same rate. Considering that port area is proportiona to the square of the hoe diameter it is cear that Equations 1 and 4a do not accuratey predict the static port hoe sizes over a range of vaues in either singe or mutipe port scenarios. It is specified that Equation 1 is imited in range, but to meet our safety and faiure reduction goas we need a way of accuratey computing the proper static port hoe sizes over a broad range of AV Bay voumes. Athough, we have not assessed whether the vaues produced in its imited range accuratey predict the needed static port size these reasons are sufficient to discard Equation 1. One aso observes that Equations 2 and 3 are identica (accounting for a minor constant adjustment). Interestingy, the resutant port size does not expand ineary with a inear 5

6 increase in voume. Upon examination of Figure 4 we can see that port areas generated from Equations 2 and 3 do expand ineary with voume so these equations behave as expected (-x indicates the number of ports in the figure) However, we sti need to assess whether these equations produce the vaues that wi propery evacuate our AV Bays. Figure 4 Port Area vs AV Bay Voume Athough the derivation of Equations 1, 3, 4a, and 4b is unknown in some cases they may sti be reated to one another. Equation 3 appears to be in a simiar form and produces simiar resuts to Equation 2. By substituting the vaues recommended for Equation 2 we get the foowing: 2 d s = 2r a ref v ref n = 2r π ( ) 100n =.2r π(. 125)2 n =.2r 20.37n Considering that Equation 3 originates from an area that uses the metric system the cosest dri bits size that does not undersize the static port to.25 is 6.5mm. Substituting this vaue into the equation and converting 100 in 3 to mm 3 we get: 6

7 2 π (6.5 d s = 2r 2 ) n =.2r π(3.25) n =.2r n Noting in the Entacore documentation that they recommend 500mm (not ) presumaby since this is more convenient to compute and then performing the metric to imperia conversion we get: d s =.2r n.2r 500n =.2r 19.68n.2r 20.37n Equations 1 and 4a aso appear to be reated: d s = πr2 400 = 4πr2 4(400) = ( π 1600 ) 4r2 = (4r 2 ).0016(4r 2 ) Since the four hoe case of Equation 4a is simpy the singe hoe vaue divided by two it aso corresponds to the four hoe version of Equation 1. It appears that a of these equations are using a rue of thumb of ¼ per 100 in 3 as their basis (athough you can vary this with Equation 2 but it is not specified under what circumstance you shoud do so nor is any guidance given on how to make such variations). Where did this rue of thumb come from and does it have any scientific basis? I do not know and wi eave that to a High Power Rocketry (HPR) historian or archeoogist to uncover. Improved Static Port Sizing Consider that an avionics bay is simpy a container traveing through space where the atmospheric pressure steadiy decreases or increases based on the direction of trave. Aso note that the externa atmospheric pressure rate of change is dependent upon the vertica veocity of the rocket. Finay, note that the rate of pressure equaization between the avionics bay and the atmosphere is dependent upon the pressure differentia between them. Aternativey, this can be modeed as a static pressure vesse where the externa atmospheric pressure is reduced or increased. For the foowing discussion I wi be empoying the foowing assumptions: 1) Incompressibe air fow 2) Bernoui effects are negigibe 3) Atmospheric pressure and temperature changes during fight are disregarded Unike the earier equations our mode shoud account for interna/externa pressure differentia, gas density, among other factors. Discharging of a gas through an orifice is a speciaty in fuid dynamics and as depicted beow has been modeed as part of this discipine. 234 When a gas is discharged through an opening into the atmosphere the gas 2 "Perry's Chemica Engineers' Handbook, Seventh Edition, McGraw-Hi Co., Retrieved from 7

8 veocity through that opening (static port) may be choked (the gas has reached the maximum veocity imit) or non-choked. Choked veocity (aka sonic veocity) is reached when the ratio of the absoute source pressure to the absoute ambient pressure is greater than or equa to: ( k ) k k 1 where k is the specific heat ratio of the discharge gas In our case the specific heat ratio of air is (may vary with temperature and pressure by ±.001) and the choked threshod from the above equation is This impies that the choked veocity occurs when the source pressure (AV Bay) is times greater than the externa atmospheric pressure. Assuming one is aunching from sea eve under standard atmospheric conditions this impies that if an AV Bay were perfecty seaed one woud not need to be concerned with choked veocity unti attaining an atitude equa to or exceeding 16,636.4 feet. It shoud be noted that by starting at sea eve we have generated the most conservative atitude difference. Starting at higher atitudes woud resut in sighty arger atitude separations prior to attaining a pressure difference for choked fow. Ceary, since AV Bays are open to the atmosphere and high power rockets are not traveing at veocities which woud prevent pressure equaization in the aotted trave time (more on this momentariy) we need not concern ourseves with choked air fow. The equation for the initia instantaneous mass fow rate of non-choked (i.e. sub-sonic) gas veocity with the source gas at a specific temperature and pressure is: Q = ca s 2ρP ( k 2 k+1 k 1 ) [(P A P ) k P A ( P ) k ] Eq 5 Q - mass fow rate (kg/s or bm/s) c - discharge coefficient (dimensioness, 0.62 for sharp edged orifices in thin pates) a s discharge (static port) hoe area (m 2 or ft 2 ) gas density at temperature and pressure (kg/m 3 or bm/ft 3 ) P source absoute pressure (Pascas or bm/ft-s 2 ) P A ambient absoute pressure (Pascas or bm/ft-s 2 ) k c p /c v of the gas (dimensioness, isentropic expansion coefficient) which is equivaent to (specific heat at constant pressure) / (specific heat at constant voume). For air at the typica temperatures and pressures we operate at the vaue is 1.401±.001 (increases with temperature decreases and/or pressure 3 "Risk Management Program Guidance For Offsite Consequence Anaysis", U.S. EPA pubication EPA- 550-B , Apri [ Equation (D-1), Section D.2.3, and Equation (D-7), Section D.6, Appendix D. Retrieved from 4 "Methods For The Cacuation Of Physica Effects Due To Reeases Of Hazardous Substances (Liquids and Gases)", CPR 14E, Third Edition Second Revised Print, The Netherands Organization Of Appied Scientific Research, The Hague, 2005 [Equations (2.22), (2.25), and (2.28a) on pages ]. Retrieved from 8

9 increases and conversey decreases with temperature increases and/or pressure decreases). We wi use the mass fow rate equation to sove for the static port hoe area and then derive the hoe diameter using the area of a circe equation for n hoes. a s = nπd s 2 4 where n is a positive integer Eq 6 We wi estimate the mass fow rate by cacuating the air mass within the AV Bay and then appying a discrete pressure differentia based on atitude and time. In order to cacuate the mass fow rate we wi use the foowing equation: Q E = πr2 ρ ( P P A P ) t Eq 7 During the foowing discussions I wi use Standard Atmospheric 5 vaues at sea eve. In Equation 7 πr 2 is simpy the voume of the AV Bay. However, in order to compute the mass fow rate we need to know the mass of the fuid (gas) so we wi mutipy the voume of the gas by its density where = kg m -3. Next we need to understand the difference in pressure between the AV Bay and the ambient environment. To do this et s make a simpifying assumption that the pressure changes discretey every meter of atitude (obviousy the change is continuous). Given that the percentage change varies with atitude and temperature we wi choose a conservative vaue of.0126% (sea eve is.0113%). Finay, we need to seect a time period over which the chamber is evacuated. This woud be done by assessing the veocity at which the rocket is changing atitude. Let s assume we are traveing verticay at 400 m/s ( Mach 1.2). In this case we woud then want to evacuate the AV Bay every.0025 sec (the time it takes to trave a meter). What happens if we don t empty the AV Bay fast enough? The reative differentia pressure wi surge and the rocket wi experience a ag in its barometric sensor readings (and derivative computations) unti it sows down enough for the AV Bay pressure to equaize with the atmosphere. By combining Equations 5, 6, and 7 to sove for d s and substituting Q E for Q we get: 4Q E d s = Eq 8 πnc 2ρP ( k 2 k+1 k 1 ) [(P A k P P ) ( AP k ) ] Upon examination of Figure 5 we see that the Equation 8 resuts in static port sizing that foows the appropriate curve (the area not the diameter changes ineary with voume) 5 The Engineering TooBox, Retrieved from 9

10 and generates a static port diameter that is smaer in size than the other equations. After a cursory assessment one may determine that the differences are immateria. However, after examining Figure 6 and Figure 7 it must be concuded that such an assessment woud be shortsighted. Specificay, 1) Optima static port sizes vary based on the absoute pressure differentia between the AV Bay and atmosphere. This differentia is dependent upon the veocity since it dictates the rate of evacuation. 2) Optima static port sizes aso vary sighty based on atitude and temperature Figure 5 Equation Mach 1.2 Figure 6 Equation Mach 3 10

11 Figure 7 Singe Port Size by Mach Veocity At the beginning of this discussion we made three assumptions. Incompressibe fow is reasonabe unti your rocket begins traveing above Mach 0.3. Above these speeds we need to minimize the effects of pressure waves and turbuence. Therefore, the static ports must be positioned without obstructions in the airstream above them in order to maximize the possibiity of aminar fow. Since compressibiity may affect the air density this is an area for improvement of the provided equations. Bernoui effects caused by the fow of a gas over an opening woud typicay resut in a decrease in ambient pressure effectivey creating an increase in pressure differentia resuting in more rapid evacuation of the chamber. Again further anaysis is required but this effect may counter the compressibe fow effects to a sma or perhaps arge degree. Finay, the continuous variations in atmospheric pressure and temperature as we as AV Bay chamber pressure during the fight might be accounted for through the appication of cacuus but I have not performed such inferences. During the course of our discussion we aso disregarded choked fow. This woud be a concern under the foowing scenarios: 1) Static ports are undersized 2) High veocities 11

12 Under sizing of static port hoes is not recommended as this woud resut in a reporting ag by the barometric sensors in the AV Bay which may negativey impact atimeter operations. Excessivey high veocities (in excess of Mach 15) may resut in choked fow situations. I am unaware of any amateur rocket fying at these veocities so I have not incuded those equations in this document. Equations 7 and 8 have been used successfuy for the past four years to design and impement static ports with the coegiate teams as we as others I ve advised. No depoyment faiures have been traced back to inadequate static port sizing. Admittedy the equations are not as simpe to use as earier abeit inaccurate ones. Therefore, I have provided a spreadsheet accessibe to any who desire it in the Resources section of my web site: Recommendations The reasoning depicted in this paper has not ony demonstrated that the sizing of static port hoes is critica to the evacuation of AV Bays but that the soutions derived from existing modes are inadequate for a broad range of scenarios. Therefore, the foowing recommendations are made: 1. Use Equations 7 and 8 as described in this paper to determine the minimum static port hoe size required based on your AV Bay size and maximum expected veocity. Discontinue the use of Equations 1, 4a and 4b under a circumstances and Equations 2 and 3 particuary when conducting supersonic fights. This paper has not addressed the gas fow within AV Bays resuting from the use of static ports. This is eft for another and may require the use of Computationa Fuid Dynamics to assess whether oversizing static ports truy resuts in increased turbuent fow within AV Bays. Unti that time it is recommended to size the static ports as cosey to the size needed as specified by the suppied equations. It is not recommended to undersize the static ports due to the inevitabe ag in sensor readings. 2. Ensure that a static port hoes are dried ceany with square edges. If they are not the vaue of the discharge coefficient wi change and/or the static port hoe area is reduced (consider fiber strands bocking the airstream). 3. At a minimum use three static ports eveny spaced around the circumference of the AV Bay. As stated in recommendation 1 this paper has not addressed the gas fow within AV Bays resuting from the use of static ports. Again this requires further anaysis; however, a my tests have been conducted with three or more static ports. Conventiona wisdom is that mutipe eveny spaced static port hoes wi reduce the amount of turbuence experienced inside of an AV Bay. Concusion It has been shown that the prevaiing computations for static port sizing do not mode the AV Bay evacuation process accuratey and at worst wi provide fyers with a fase sense of security that may resut in repeated fight faiures. Consequenty, their propagation does not support Tripoi s safety goas. Finay, it has been shown that Equations 7 and 8 can be used to more accuratey predict static port sizes particuary 12

13 those with arge AV Bays and/or traveing at high veocities thereby eading to improved safety. Acknowedgements The author wishes to thank Dae Hagert (#11958) for his review of this artice and insightfu comments. Gary Stroick (#5440) has been a member of Tripoi since 1997 and is L3 certified. He has been on the Tripoi Minnesota Board of Directors since 2006 (VP: , President: ), Technica Advisor for the NASA s Space Grant Midwest High Power Rocket Competition ( ), and is owner of Off We Go Rocketry. He hods a MS in Computer Sciences as we as an MBA. He can be contacted at or president@offwegorocketry.com. 13