The latest meeting of the Reaction Research Society took place this past Friday, March 12th and had 20 attendees (who came & went at different times) – including a guest presenter. Society president Osvaldo began discussion by informing the group that USC has requested a launch of their 6″ booster rocket in April, before leaving the meeting to go on a Home Depot supply run.
GUEST PRESENTATION – GEORGIA TECH YELLOW JACKET SPACE PROGRAM
Sam Kim from the Georgia Tech Yellow Jacket Space Program made a presentation on their mission to be the first collegiate team to send a liquid rocket to Karman Line. The team conducted the first hot fire of an 800 pound-force LOX-kerosene engine in November 2019 (pictured below). This engine will support a sub-scale rocket which will be used to prove and test methods on this student-designed, -machined, and -assembled project.
The team has planned a launch for the sub-scale rocket in October to an apogee of 5,000 ft. An 11-second burn static fire of this engine is expected in April. The team conducts testing out of the DeKalb-Peachtree Airport, and plans to make launches from the Spaceport Camden in southeast Georgia.
BILL CLAYBAUGH’S 6″ ROCKET
Bill Claybaugh presented a number of hardware pieces related to a 6″ rocket which he hopes to launch this year. The rocket will fly on a 6″-diameter, 60″-long motor producing 1,350 lbf of thrust with an 8.3-second burn time. This design is optimized to be used as the second stage in a rocket boosted by a 9″-diameter motor, but the impending flight is only the 6″ second stage. Bill mentioned that he has a test flight planed for the 9″ first stage some time within the next year. The combined 2-stage rocket will have to fly out of a national range because of the expected altitude of 120 statute miles.
The hardware that Bill C. presented from his rocket included the tapered fins, bulkhead assemblies, and a section of the 40″ avionics payload which will be mostly contained within the nosecone. In addition, Bill provided insight on the FAA paperwork that he is currently completing for the flight of the 6″ rocket. The FAA form 7711-2 he has been working on is the same one used for airshows, and requires a supplemental that covers both class 2 & 3 amateur rockets. The final hurdle is the “splash pattern” Monte Carlo analysis of over 1,000 launches with varying launch angles, wind, and other launch parameters to determine the probability of landing in a populated area. He expects the launch will be deemed safe, and plans to submit the paperwork soon.
PLANS FOR THE UPCOMING MTA EVENT – SAT. MAR 20
Several members stated their intentions to join the launch & work event at the MTA site next Saturday, March 20th. Work on welding the new plate on the vertical test stand, clearing brush in the launch/firing areas, and other site maintenance may take place if time and equipment availability allow. There has also been discussion of taking an inventory of the working order of some Society equipment (such as the PA system) stored at the site.
Bill Inman plans to once again bring out his solar-powered steam rocket, Solar Cat, which uses mirrors to heat water with sunlight. Bill has been a fixture at MTA events the past several months, perfecting the design and procedures so that he won’t be caught unable to launch because of a minor oversight like untested equipment or cables that are too short. Although all of his equipment is flight-ready, MTA launches are always at the mercy of the Mojave desert weather. Wind, rain, and sunlight permitting – we hope to see the Solar Cat take to the skies next weekend!
Wolfram Blume is vaccinated (an impediment to his attendance at last month’s event) and ready for another launch attempt of the booster stage on his rocket, Gas Guzzler. In the final version the upper stage will include a gas-powered ramjet, but this flight will be flown with water instead. The goal of this test is to measure drag & acceleration, particularly during separation of the booster stage, which will help inform the final design parameters. We’re excited to see this launch, and expect it will be a fun one to watch!
Keith Yoerg will bring his model rockets and multi-pad wire rail launcher to test out deployment boxes and high-power solid rockets to test LoRa GPS trackers as a cheap rocket tracker. Dimitri is finishing work on a his hybrid & water rocket launch controllers (pictured above), both of which should be ready for testing on Saturday as well. It was once again agreed that a grill-out should take place, which is quickly becoming an MTA event tradition.
WIRELESS LAUNCH CONTROLLERS
The last topic stimulated a great discussion on the use of wireless launch controllers, with many members providing thoughts and opinions. Richard Dierking presented the commercially available Wilson F/X wireless control box, which consists of the firing box shown in the photo below and 2 wireless modules which run on 12V gel cell batteries. This entire system cost him around $900, and larger versions of this system have been used by the Rocketry Organization of California (ROC) and Friends of Amateur Rocketry (FAR) for launches of high-power solid rockets.
Dimitri expressed his comfort and trust in the Cobra wireless firing system, which he has used many times as the Pyro Op for million-dollar shots in movies and television. The Cobra system uses 64-bit encryption (it was suggested that the Wilson F/X system uses 32-bit) and the only issues Dimitri reported was when attempting to fire directly near an ultra high-speed camera. Richard stated that he would look into getting someone from the Wilson F/X company to attend a future RRS meeting to describe that system in further detail.
Most members expressed cautious optimism about the potential of using wireless launch controllers at RRS events, though it was re-iterated that the Pyro Op in charge has the final say in what firing systems may be used at any event. The consensus best path forward was progressing slowly by starting with LED lights & low energy firings like model rockets. The aim is to build experience with and knowledge of these systems to determine if they can be safely used for more energetic firings. Richard & Dimitri plan to bring the Cobra and Wilson F/X systems up to the MTA event next weekend, where (with the permission of the Pyro Op in charge) they will be tested safely on a small scale.
NEXT MONTHLY MEETING
The next RRS monthly meeting will be held virtually on Friday, April 9th at 7:30 pm pacific time. Current members will receive an invite via e-mail the week of the meeting. Non-members can request an invitation by sending an email to:
The Executive Council has committed to an additional monthly meeting moving forward to address administrative matters. Members who would like to discuss an admin topic in detail can request attendance at a Council meeting by sending an email to the Secretary at the address above.
by Prof. Dean R. Wheeler, Brigham Young University
This posting is reprinted from the original article written March 13, 2019 with permission from the author. This article was intended for chemical engineering students to size relief valves for pressure vessels, but it applies well to amateur liquid rocketry as many use a pressure fed system to deliver propellants to the engine.
The RRS has several members engaged with liquid rocket projects. An important part of analyzing the performance of those systems is the pressurization system that drives the propellant into the engine. The tank blowdown problem is useful to designing the system and estimating performance. This derivation goes through the thermodynamics of the general tank blowdown problem and should be a useful starting point for a pressure-fed liquid rocket project.
This document provides a mathematical model for computing the rate of expelling gas through a small orifice or nozzle attached to a tank. Furthermore, two models are described for how fast the tank will depressurize. Related material on compressible flow can be found in fluid mechanics and thermodynamics textbooks and web pages.
Figure 1 shows the tank and associated nozzle. The narrowest diameter of the flow path in the orifice or nozzle is known as the throat region. The tank and throat regions are described with their own sets of equations.
Provided the tank is large and the throat is small, it will take many seconds to empty the tank and gas velocities in the main part of the tank will be much smaller than the speed of sound. This means that gas pressure, temperature, and density in the tank will be spatially uniform, though they will be changing in time. Thus, we describe the tank using a transient mass balance. One can compare this to a model in heat transfer known as lumped capacitance.
In the nozzle region however, gas velocity is large and there are large spatial variations in the gas properties. In addition, there is relatively little gas contained in the nozzle region. Thus, flowrate in the nozzle adjusts rapidly to match current conditions in the tank, making it seem as if the nozzle is operating at steady state. This approximation for the nozzle is known as quasi-steady state.
EQUATIONS OF STATE
The P, T, and rho variables in Figure 1 denote absolute pressure, absolute temperature, and density in the tank or the narrowest part of the nozzle or throat (denoted by an asterisk,*, subscript), respectively. Note that if tank pressure is given experimentally as a gauge quantity, it must be converted to absolute to be used in the equations below.
The first relationship between gas variables is given by an equation of state. The ideal gas law is a fairly accurate representation for air when pressure is less than around 10 atmospheres or 150 psia. It states that:
where “V” is the volume of the gas, “n” is the number of moles, and “R” is the universal gas constant (8.31446 J/mol/K). With the introduction of the molecular weight, M (effectively 0.028964 kg/mol/K for air), and the substitution that density is mass over volume, rho = n M / V, the ideal gas law is changed to
This equation could be applied separately to the tank variables or to the thrust variables.
TEMPERATURE AND PRESSURE DURING EXPANSION
The second important relationship comes from figuring out what happens when gas in the tank or nozzle expands. When a gas expands, its internal energy is used to perform work on the surroundings, and the gas therefore tends to cool off. If the gas expands slowly, there is time for itmto absorb hest from its warmer surroundings and the expansion is essentially isothermal, meaning the temperature stays at its initial value or that of the surroundings.
On the other hand, if a gas expands quickly its temperature will drop dramatically. This is called adiabatic expansion, where adiabatic means no noticeable heat transfer from the surroundings (i.e. the walls of the tank). In adiabatic expansion, the pressure drops more rapidly than it would for an isothermal (slow) expansion. Adiabatic expansion could haolen inside the tank if it is emptying rapidly, but this depends on the relative sizes of thr tank and nozzle. On the other hand, adiabatic expansion certainly occurs when a gas moves from the tank through the nozzle region. In other words, here the gas is moving quickly and therefore expanding quickly.
The thermodynamic relationships for pressure and temperature for reversible adiabatic expansion of a constant heat capacity ideal gas are:
where the subscript, “o” indicates the initial state of the gas before the expansion started. This means if we know how the density is changing from an initial state to some later state, we can compute P and T as well. In the case of the nozzle, we apply the above equations as the gas travels between the tank and the throat. In the case, they become
The parameter, “gamma” , is the dimensionless ratio of specific heats ( gamma =. Cp / Cv ), and by statistical theory of gases, gamma = 7/5 = 1.4, for low temperature diatomic molecules, nitrogen (N2) and oxygen (O2) and so that value is used here.
Next, we need to determine the gas density in the nozzle when the tank is at a specified conditions. Recall that that the nozzle is treated as if it instantaneously responds to whatever state the tank is in. A fuller discussion of the nozzle flow equations can be found in other sources like textbooks that cover ideal compressible flow in nozzles.
Choked flow means that the flow is exactly at the speed of sound in the throat region. A higher speed cannot be achieved in the throat, regardless of upstream or downstream conditions. Thus, choked flow acts to limit how much gas flow can pass through a given size orifice, This is the reason why pressure relief valves on tanks must be properly sized to accommodate sufficient flow.
Choked flow happens for a large pressure drop across the nozzle or orifice, specifically if the upstream tank pressure meets the following condition relative to atmospheric pressure downstream from the nozzle:
Equation 5 is the origin of the rule of thumb or approximation that choked flow occurs for upstream pressure that is more than twice the value of downstream pressure (absolute). If the tank pressure drops below this limit, the speed of gas in the throat is subsonic, and less gas will flow than in the choked flow regime. The solution to subsonic flow in the nozzle is complicated and is less important to know because it is at the end of the tank’s discharge when pressure is low, and so will be neglected here.
The solution to choked flow in the throat region follows a simple relationship, derived from energy and mass balances:
This can be substituted from Equation 3B and 4B to determine pressure and temperature in the throat in terms of tank conditions.
For choked flow the throat velocity is exactly the speed of sound, which is what makes it easier to analyze. For ideal gases, speed of sound, c, is determined solely by temperature. Thus, we can relate throat velocity to throat temperature, and in turn to tank temperature:
For example, if T_tank = 294 Kelvins, then c_o = 314 m/sec for air.
MASS FLOW RATE
Now we can determine the mass flow rate, “m_dot”, through the nozzle or orifice. This comes from the following standard relationship, applied at the throat, because that is where conditions are known:
where “A_*” is the throat cross-sectional area given by
and where “d_*” is throat diameter.
Dimensionless parameter, Cd, in Equation 8 is the discharge coefficient, accounting for friction between fluid and walls and a phenomenon known as vena contracta. In essence, Cd, is needed in Equation 8 because the effective area for fluid at speed, v_o, is somewhat smaller than actual throat area. Cd would be equal to 1.0 for a perfect (frictionless or thermodynamically reversible) nozzle: in practice for a smoothly tapering nozzle it might be as high as 0.98, while for a sharp-edged orifice it might be as low as 0.60. Anything that causes separation of flow from the nozzle wall or increases frictional contact will decrease Cd.
Making the appropriate substitutions into Equation 8 leads to an equation for mass flow in terms of readily determined quantities:
Frequently in industrial situations, mass flow rates are expressed instead as volumetric flow rates corresponding to a gas at a standard temperature and pressure (even though the gas is not actually at that temperature and pressure). For instance, a mass flow meter used for gases may express mass flow as standard liters per minute (SLPM) or standard cubic feet per minute (SCFM). In other words, even though m_dot (mass flow) is the key value being measured, it is expressed as
which requires knowing what rho_std value is programmed by the manufacturer into the flow meter. This can be determined from the ideal gas law, given specified P_std and T_std values. As an example, the American manufacturer, Omega, assumes a standard temperature “T_std” of 70 degrees Fahrenheit (294.26 Kelvins) and a standard pressure “P_std” of 1 atmosphere which equals 14.696 psia (101,325 Pscals) thus by the ideal gas law, the standard density “rho_std” would equal 1.2 kg/m3 for air (molecular weight 28.97 g/mole).
Combining Equations 10 and 11 and the ideal gas law leads to
where “c_std” is the speed of sound at the standard temperature:
Makers of valves and orifices may provide an experimentally determined size parameter known as flow coefficient, Cv. For gases this dimensionless parameter can be converted to Cd*A_* by
The key design principles resulting from the above analysis are, provided tank pressure is large enough to generate choked flow, that (1) mass flow rate of a gas through an orifice is proportional to throat area and tank pressure and (2) flow rate does not depend on downstream pressure.
TWO MODELS OF TANK BLOWDOWN
Equation 10 gives the rate of mass loss from a tank at a given gas density and temperature. To determine how long it will take to depressurize the tank, we must do a transient mass balance on the tank. The ordinary differential equation for this is:
where “m_dot” comes from Equation 10 and “m” is the mass of gas in the tank. This in turn is:
where V_tank is the fixed tank volume. With these substitutions we get for the governing equation
To make things more manageable, let us create a discharge time constant called “tau”
where “c_o” is the speed of sound at the initial temperature “T_o” (i.e. at the beginning of blowdown)
With this new time constant, Equation 17 becomes:
The last thing to do before solving this equation is figure out what to do with T_tank. We have two options:
ISOTHERMAL TANK ASSUMPTIONS
Assume gas temperature in the tank does not change in time, based on blowdown taking a long time so that heat can be readily absorbed from the walls. Thus, T_tank = T_o. This leads to Equation 20 becoming
which can be separated and integrated to give the solution
where “rho_o” is initial density in the tank. We then convert densities to pressure using the ideal gas equation.
The equation tells us how tank pressure varies with time, for an isothermal tank and choked exit flow.
ADIABATIC TANK ASSUMPTIONS
Assume the gas cools as it expands in the tank, due to no heat transfer from the walls, based on the blowdown taking a short time to complete. Thus, T_tank is given by Equation 4A. This leads to Equation 20 becoming
which can be separated and integrated to give a solution.
We then convert densities to pressures using Equation 3A for adiabatic expansion.
This equation tells us how tank pressure varies with time, for an adiabatic tank and choked exit flow. The tank temperature can likewise be predicted from Equation 4A.
COMPARISON OF THE TWO MODEL ASSUMPTIONS
The isothermal and adiabatic models of tank blowdown can be considered two extremes, with the correct answer (i.e., with the true amount of heat transfer) lying somewhere in between them. Figure 2 shows an example of the respective blowdown curves (Equation 23 and 26). As noted previously, adiabatic tank conditions lead to more rapid pressure loss than do isothermal conditions.
The curves predict that the tank will have lost 80% of its original pressure at a time in the range of 1.3*tau < t < 1.6*tau. This shows the value of evaluating the variable, tau, to get an approximation of the time it takes to depressurize the tank.
The Reaction Research Society held another launch event at the Mojave Test Area (MTA) on February 20, 2021. The weather was not cooperative for much of this day with wind gusts well beyond acceptable limits for launch (> 25 MPH). Our neighbor, Dave Crisalli and his Polaris Propulsion team, were using the Dosa Building as he had construction activities planned but were cancelled for that day. The RRS and Polaris Propulsion were glad to share the Dosa Building as we both made good use of the day.
The three planned objectives (weather permitting) for this MTA launch event were:
Build a new pit toilet restroom just north of the original site.
Conduct Solar Cat operations at the MTA
Conduct model rocket launches from Keith Yoerg’s new wire launcher array
THE ALL-SOLAR POWERED SOLAR CAT PROJECT
Bill Inman and his colleague, John Wells, made the long journey to the MTA from Nevada. Bill had made further improvements to the launching system and solar collector powering the Solar Cat steam rocket. He was able to and a remote tracking motor and drive system to further automate his solar concentrator, but several minor problems in setup prevented a launch that day.
Bill is striving to use an entirely solar powered system including a photovoltaic power system for his auxiliary functions. Because of the east to west passage of the sun through the sky, the steam rocket must be launched in a northerly direction. This is possible if done from the northern or western edges of our launch site.
Although the winds were excessive throughout most of the day, Bill could still conduct some assembly testing and even conduct steam rocket heating operations while keeping the rocket secure on the ground. Launch would only be attempted if the winds lowered in that time. Sadly, much of the day passed in correcting minor problems and system tests. The system proved ready but insufficient sunlight remained that day and launch would have to be conducted from the MTA at the next opportunity.
BUILDINGA NEW PIT TOILET AT THE MTA
The society has been examining many improvements to our Mojave Test Area which has stood for over 65 years. The site has been improved over the many years but time has taken its toll and renovations are needed.
The top priority selected by our membership and visitors was the restroom facilities. Our short term plan was to build a second pit toilet while we work on plans for a more luxurious option in the longer term. This effort is viewed as a stopgap solution which will serve our society for at least a few years. Dmitri Timohovich and Wilbur Owens contributed greatly to this effort. With the many people we had at the site, we were able to start and complete the project with time to spare that day.
The pit toilet project was a success thanks to both our members providing their physical and material labor and the careful planning and coordination that took place starting in this new year. This improvement project will be only one of several to come. We hope to make our remote testing site both more functional but also a bit more comfortable to all who visit us after many hours drive from the city.
LAUNCHING ROCKETS FROM A NEW MULTI-WIRE RAIL STRUCTURE
With the last hours of the day upon us, the winds had subsided to a more reasonable speed. Keith Yoerg had a few model rockets prepared for launch with commercial motors. He had also built a multi-wire launcher which is a convenient way to display and launch several small vehicles successively.
Second thing introduced at this MTA launch event was a four channel launch box built by Dmitri Timohovich. With a clean wood finish and a rugged latched case, this box proved its function well with the launch of three model rockets that day.
After some glitches with the electric matches, Keith was able to launch and recover the Baby Bertha (A8-3) and the Big Bertha (A8-3) rockets. We got excellent footage of these classic model rocket types. The last of the three launches was the slightly larger Star Orbiter (E16-6) which left the rails cleanly and the recovery system deployed without issue. Although the winds had subsided sufficiently at ground level, the higher level winds carried the Star Orbiter for a long horizontal trek west well beyond the property line, After some searching, the Star Orbiter was lost to the desert hoping to be recovered
The team cleaned up the area and put away the gear at sunset. We talked about setting the next launch date in March 2021. We hope to have a new date set soon, likely after March 12th.