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RCS and Maneuvering CubeSat Details

Even tiny commercial pneumatic valves provide TOO MUCH gas flow to work well for attitude control in a CubeSat, or our similar sized “Very Low Mass” lunar landers. A typical, 40 gram air valve from Clippard or similar supplier, is rated to produce a gas flow of 0.6 to 1.0 SCFM (Standard Cubic Foot per Minute) with a pressure drop of 100 to 200 psi. A “Standard” cubic foot of gas is one expanded to standard atmospheric pressure and temperature. One Standard cubic foot of air will mass 42 grams and the 1 SCFM gas flow is a 0.71 gram per second mass flow. (Please excuse the mixed units – the valve ratings are often in the “English” units given). Incidentally, this valve would have a 0.01 CV rating (Coefficient of Velocity (or flow)) and a 0.6mm (0.024 inch) orifice. The 0.71 grams per second mass flow, with the typical 60 seconds ISP obtainable in a “cold gas” reaction motor using Nitrogen, would give a 42 gram weight thrust, or 0.415 Newtons force. For linear propulsion, this would accelerate a 1 Kg spacecraft at 42 “milli-g”, or 415 cm/sec^2. In 2.8 seconds it would have achieved a “Delta V” of 1.16 meters per second and consumed 1.99 grams of Nitrogen. This is enough Delta V to produce about 0.01 degree Plane Change, generating a 1 Km lateral position adjustment for rendezvous (+/- 1 Km cyclic), or a 4 Km Altitude, eccentric cycle. A second similar pulse could stabilize a CubeSat with +/- 4km Altitude change. The later, using 4 or 5 total grams of CO2 from the 12 grams in a small cartridge, could accomplish orbital rendezvous starting with an old launch vehicle like the Dnepr (+/- 4 km altitude, 0.04 degree inclination error spec). Phasing, following the first pulse, would adjust orbital spacing by 6 km per orbit or 100 km per day, with the second pulse stopping this motion prior to docking. Since these are not small distances, a CO2 cartridge which will fit in a CubeSat can produce many Km of orbital offset, followed by by docking demonstrations. Back to the attitude question, with jets positioned on the sides of a cube sat, the 0.415 Nt force will produce 0.021 Nt*m Torque. But the Moment of Inertia of a CubeSat will be near 0.001 Kg*m^2, and this torque will produce an excessive rotational acceleration of 21 radians/sec^2. After one second, the satellite will be spinning at 3.3 revolutions/sec = 200 rpm! It will have already completed 1.6 rotations in that one second. Admittedly, a 10 millisecond (1/100 sec) pulse will produce only 2 rpm rotation, but it is unlikely that the breaking pulses can be timed accurately enough to get the rotation below 0.1 rotation (36 degrees) per minute, and frequent pulses (with a lot of propellant use) would be necessary to keep the pointing error less than 10 degrees. The practical use of gas jets of this type will be to “Desaturate” momentum wheels, with the later being used to make precise attitude adjustments. With momentum wheels not much smaller than the 10 cm satellite cube, mass 1% of the satellite total, and 10,000 rpm max speed, a set of three wheels could “absorb” up to 100 rpm of satellite rotation. The jets would be used to unload accumulated angular momentum, if that should occur, and 0.36 grams of gas would be used to offset that maximum in a ½ second burst. Since this is too much thrust for direct attitude control of a CubeSat, how big a craft could it handle? Our 20 kg initial mass, “Above LEO” launch vehicle has an initial roll moment of inertia of 0.012 km*m^2. The assumed jets would produce a snappy, 1.7 radians/sec^2 rotational acceleration on this vehicle, with the minimum pulse producing a practical 0.017 radians/sec = 0.97 degrees/sec roll. This is certainly attractive! But in deep space, even that rotational acceleration is excessive. The Aviation Standard “Two Minute Rate Turn” is only 3 degrees per second. This may seem very slow, but it requires a considerable 27 degree bank angle to accomplish in a coordinated aircraft turn at 219 mph, and this goes up to a 45 degree bank “Steep Turn” at 438 mph! At this rate the image in a “Standard” 35 mm camera “Pans” across the film, from edge to center in 7.5 second and back out of view after 15 seconds – and about the same for a “Good View” through an aircraft window. This is about the largest “Pan” rate which will let an observer really inspect the view. It is also a turn rate which avoids disorientation and vertigo in pilots and passengers. Using these leisurely rates saves a lot of fuel, but still completes a “Turn Over” in 60 seconds. A 12 second thruster burst at 0.004 radian/sec^2, followed by a 54 second delay and a 12 second breaking deceleration would accomplish the flip at reasonable speed, with low mass jets and little fuel use. With the attitude jets mounted 1 meter from the craft cg, the 0.415 Newton thrust would produce 0.415 Nt*m torque, and accomplish this acceleration with a spacecraft moment of inertia just over 100 Kg*m^2 . This value (100 Kg*m^2) equals the calculated moment of inertia for our Human Transport System, with full fuel, prepared to land a human astronaut on the Moon! The 80 gram projected mass for our 6 DOF Reaction Control System could thus serve for fully redundant attitude control of our Human Lunar Lander. (The “Flip” described would use no more than 17 grams of propellant gas.) This example is typical of our operational developments, with small spacecraft systems proving adequate for optimized human spaceflight, and the “Virtuous Cycle” of subsystem mass reductions leading to other subsystem mass reductions making our projections more and more conservative! Now we only need to find customers who need these capabilities, sponsors who want their names associated with advanced spaceflight technology, or Adventurers who want to GO THEMSELVES!
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