We’re over 40% of the way to our goal! Thanks to everyone who has supported us — special thanks to Josh Triplett, who really kickstarted our campaign into high gear!
We have 60% of the way still to go – please tell your friends and family about us! Especially let your local space geeks know that we’re trying to start a local space program, and let them know they should help out either by coming and working with us, or helping support us.
What Your Money Funds #1: “RCS: small rockets for big rockets”
So, how do you make sure your rocket flies straight? You put fins on it. But fins have problems.
Fin Problem #1: “Weather cocking”. Fins make rockets passively stable by creating corrective moments whenever the rocket fins have non-zero angles of attack. This is great because these moments automatically point the rocket in the “right direction”. You can go to space today! The problem is that the fluid velocity vector is not always strictly vertical with respect to the ground because of wind. Thus rockets with fins steer into the wind, and waste precious, precious propellant flying sideways instead of up.
Fin Problem #2: You can’t get to orbit going straight up. One does not simply “go up” to get into orbit: you have to get going really fast sideways. That’s what orbit is: a neat trick where you go so fast you fall without ever hitting the ground. And going sideways turns out to be the hard part: going up is only 10% of your energy! 90% of your energy is used to get going 7.6 km/s (17,000 mph) sideways. And not just sideways, but following a particularly weird path to minimize your aerodynamic losses. So we have to be able to point the rocket along this path (“optimal orbital injection trajectory”), and we can’t do it with just fins because…
Fin Problem #3: Fins don’t work in space! They only work when a fluid, such as air, is rushing past them. And it turns out there’s not much air above about 30 km (100,000ft) which is only about 1/3 of the way into space. So fins are great, but they’re not going to work where we’re going.
Solution: Use rockets to steer your rocket! We are building a Reaction Control System (RCS) module. A ring of six radially mounted ‘vernier rockets’ positioned near the top of the rocket (as far from the rocket’s center of mass as possible) can produce steering moments in the pitch, yaw and roll axes on command. The six vernier rockets, as part of a so called ‘cold-gas’ system, produce thrust by expanding high pressure nitrogen gas through a supersonic nozzle. A state space controller takes acceleration and attitude data inputs from an onboard accelerometer and Inertial Measurement Unit and then commands thrusters to fire by energizing their respective solenoid valves. Using this approach in lieu of passively stabilizing fins is not dissimilar from balancing a pencil upon the tip of one’s finger. But RCS can be used for more than simply stabilizing the rocket, it can be used for maneuvering and attitude control even in the rarified upper reaches of the atmosphere where fins cease to function.
Where we’re are now: We’ve just begun our work on the RCS. We’re starting with a small single thruster proof of concept, and then moving onto the larger system after we’ve characterized the small thruster. We’ve also made some computer models that have produced interesting results: The plots below, (fig. 1) are sample outputs of a numerical simulation of a single thruster with a 100% duty cycle emptying isentropically out of a 1L (paintball) tank. The model suggests the rocket thrust increases with time. This somewhat paradoxical result is interesting because thrust is a function of both mass flow rate (itself a function of density) and exhaust velocity (itself a function of temperature, among other things). During the flight temperatures in the propellant tank drop rapidly, for the same reason a spray can (or an air horn) gets very cold in your hands the longer you use it: rapid adiabatic pressure drops cause the temperature to drop as well. This in turn causes the exhaust velocity to drop (normalized as ‘isp’ in the plot). But the decrease in temperature also makes the nitrogen propellant more dense which in turn increases the mass flow rate, which more than makes up for the decrease in exhaust velocity! Another interesting result of the model is that temperatures in the tank will drop to the boiling point of nitrogen after only 13 seconds of flight time! In reality the process is not isentropic, and the solenoid valves will not be operated at anywhere close to a 100% duty cycle, but it still means that thermodynamic concerns are an interesting issue in the design process!
Fig 1. Sample output of a propellant tank thermodynamics numerical simulation
Designing a rocket nozzle is another interesting challenge at this stage of our project. Rocket nozzles (excluding exotic designs such as aerospikes) are designed optimally to operate at only one altitude. This is problematic because the altitude of a rocket is constantly changing throughout its flight. To get the most bang for your buck you have to optimize one particular factor above all others: area ratio. Below (fig. 2) is a sketch of a nozzle optimized for sea-level operation with a very low chamber pressure. It has an area ratio of 1.12:1. If you compare this, for instance, to the area ratio of the Space Shuttle Main Engines 69:1, this earns our design the nickname “cutest supersonic rocket nozzle ever”.
Fig 2. RCS rocket nozzle diagram
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