Development of a Cold Gas Propulsion System for the ... - SSL - MIT
Development of a Cold Gas Propulsion System for the ... - SSL - MIT
Development of a Cold Gas Propulsion System for the ... - SSL - MIT
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(1) Lifting <strong>the</strong> hopper’s lunar weight<br />
At <strong>the</strong> conclusion <strong>of</strong> <strong>the</strong> spring 2009 16.83/89 class and <strong>the</strong> start <strong>of</strong> this requirements definition process,<br />
<strong>the</strong> target mass <strong>of</strong> <strong>the</strong> TALARIS hopper was 45 kg, giving it an Earth weight <strong>of</strong> 441.45 N, or 99 lbs [38].<br />
The EDFs are designed to lift 5/6 <strong>of</strong> this weight. However, <strong>the</strong> CGSE must be able to provide a vertical<br />
<strong>for</strong>ce greater than 1/6 <strong>of</strong> <strong>the</strong> hopper’s Earth weight in order to accelerate it upward at lift<strong>of</strong>f. It was<br />
decided that <strong>the</strong> TALARIS hopper should be capable <strong>of</strong> rising to its operational altitude <strong>of</strong> 2 m in less<br />
than 3 s. (This time was originally chosen arbitrarily; later, results <strong>of</strong> <strong>the</strong> computer model discussed in<br />
section 4.1 showed that 3 s was approximately 25% <strong>of</strong> <strong>the</strong> shortest expected total flight time, which was<br />
deemed to be a good fraction since it left <strong>the</strong> majority <strong>of</strong> <strong>the</strong> flight time <strong>for</strong> <strong>the</strong> horizontal transit while<br />
still being long enough to observe and control <strong>the</strong> hopper’s behavior during ascent.) This ascent can be<br />
accomplished with a net upward acceleration <strong>of</strong> 1 m/s 2 , or equivalently a total thrust-to-weight ratio<br />
(T/W) <strong>of</strong> about 1.1, at <strong>the</strong> moment <strong>of</strong> take<strong>of</strong>f. 3<br />
If <strong>the</strong> EDFs provide a constant T/W <strong>of</strong> 5/6 or 0.83, this<br />
means that <strong>the</strong> CGSE must provide vertical thrust equivalent to 0.27 times <strong>the</strong> Earth weight <strong>of</strong> <strong>the</strong><br />
TALARIS hopper. For a 45-kg hopper, this is approximately 120 N.<br />
(2) Propelling <strong>the</strong> hopper horizontally<br />
The horizontal thrust requirements <strong>of</strong> <strong>the</strong> TALARIS hopper are not defined as sharply as <strong>the</strong> vertical<br />
thrust requirements. The distance <strong>of</strong> <strong>the</strong> hop is <strong>the</strong> critical parameter; <strong>the</strong> speed at which <strong>the</strong> hopper<br />
travels is not important, except in that <strong>the</strong> hopper must be moving fast enough to cover <strong>the</strong> required<br />
distance be<strong>for</strong>e it runs out <strong>of</strong> propellant to hold itself up. (The velocities indicated in Figure 3-1 are<br />
estimates <strong>of</strong> capabilities, not necessarily design goals.) Fur<strong>the</strong>rmore, thrust affects acceleration as<br />
opposed to velocity; effectively, any velocity could be provided by any thrust level by simply firing <strong>the</strong><br />
thrusters <strong>for</strong> <strong>the</strong> appropriate amount <strong>of</strong> time given <strong>the</strong> acceleration <strong>the</strong>y provided to <strong>the</strong> vehicle.<br />
There<strong>for</strong>e, it was decided that <strong>the</strong> horizontal and vertical thrusters would be made identical. This would<br />
allow <strong>for</strong> greater simplicity, as <strong>the</strong> interfaces, pressure requirements, etc. would <strong>the</strong>n be <strong>the</strong> same <strong>for</strong> all<br />
thrusters. Fur<strong>the</strong>rmore, fewer different types <strong>of</strong> spare parts would have to be kept on hand, and<br />
replacements and o<strong>the</strong>r types <strong>of</strong> repairs would be easier if necessary.<br />
3 In order to have zero vertical velocity when <strong>the</strong> hopper reaches its target altitude, it must have a net upward<br />
acceleration <strong>for</strong> <strong>the</strong> first half <strong>of</strong> <strong>the</strong> ascent and a net downward acceleration during <strong>the</strong> second half <strong>of</strong> <strong>the</strong> ascent.<br />
If <strong>the</strong> hopper accelerates upward <strong>of</strong>f <strong>the</strong> ground at 1 m/s 2 , it will reach an altitude <strong>of</strong> 1 m in √2 s, or approximately<br />
1.4 s, with an upward velocity <strong>of</strong> √2 m/s. It can <strong>the</strong>n immediately begin to decelerate its rise at a rate <strong>of</strong> 1 m/s 2 ;<br />
<strong>the</strong> second half <strong>of</strong> <strong>the</strong> ascent will <strong>the</strong>n be <strong>the</strong> mirror image <strong>of</strong> <strong>the</strong> first half, and <strong>the</strong> hopper will achieve its target<br />
altitude <strong>of</strong> 2 m with zero vertical velocity at a time approximately 2.8 s after lift<strong>of</strong>f.<br />
42