ARES I - NOT to be re-usable?

[mrmorris]

<font color="yellow">"Adding segments doesn't make the SRB burn longer, it just adds more thrust. "</font><br /><br />Yep -- I screwed up. No matter how many times I tell myself to avoid making assumptions... they always creep in and bite me in the posterior. No matter -- we'll rerun the calculations with additional thruat rather than time. From a NASA article here I have updated thrust and burn time figures. The mass from the article matches my SRB4 mass X 1.2 estimate <b>to the kilogram</b> which is sort of fishy... but OK.<br /><br /><b>SRB4:</b><br />Gross Mass: 589,670 kg <br />Empty Mass: 86,183 kg <br />Thrust: 14,679 kN <br />Burn time: 123 sec <br />Total Thrust: 1,805,517 kN s <br /><br /><b>SRB5:</b><br />Gross Mass: 707,604 kg <br />Thrust: 16,013 kN <br />Burn time: 128 sec <br />Total Thrust: 2,049,664 kN s <br /><br />The second stage and Orion capsule mass estimates remain the same:<br /><br />Orion capsule: 25,000 kg<br />Second Stage: 141,521 kg<br /><br />The dv calcs then would be:<br /><br />Total Mass SRB4 stack: 756,191 kg <br />dv SRB4 - 2,387 m/s <br /><br />Total Mass SRB5 stack: 874,125 kg <br />dv SRB5 - <font color="red">2,345 m/s </font><br /><br />OK -- we have a problem here -- dv from the SRB5 is <b>less</b> than that of the SRB4. It's almost assuredly <b>my</b> problem... but I can't find it. Relevant quotes from the article:<br /><br /><i>"The five-segment test motor, which ran for 128 seconds and generated more than 3.6 million pounds of thrust..."</i><br /><br /><i>"This test motor ... ran five seconds longer than the motors fire when launching the Space Shuttle, produced 300,000 pounds of thrust over the motor's maximum limit of 3.3 million pounds, and included an additional fifth motor segment adding 25 percent more propellant. Of the test motor's total weight of 1.56 million pounds..."</i><br /><br />So this indicates the following:<br />

 

[mrmorris]

I'm still trying to find an error in the calculations. I decided to remove some of the estimates and calculate dv *just* for the mass of the boosters themselves. That would be:<br /><br />SRB4: <br />Gross Mass: 589,670 kg <br />Thrust: 14,679 kN <br />Burn time: 123 sec <br />Total Thrust: 1,805,517 kN s <br />dv (589,670 kg): 3062 s<br /><br />SRB5: <br />Gross Mass: 707,604 kg <br />Thrust: 16,013 kN <br />Burn time: 128 sec <br />Total Thrust: 2,049,664 kN s <br />dv (707,604 kg): 2897 s<br /><br />Nope -- the SRB5 still has less total dv than the SRB4. All of these figures came from the NASA article *except* the mass of the SRB4, which came from Astronautix. Let's work it in reverse -- what mass would the SRB4 need to have in order for 1,805,517 kN s of thrust to produce a dv of 2897.<br /><br />dv: 2897 s<br />Total Thrust: 1,805,517 kN s <br />Mass: 623,237 kg<br /><br />The mass difference from SRB5 then would be 84,367kg or 13.5%. Somehow I doubt that adding a fifth segment will increase the mass of the total system by less than this. SG... propforce... anyone? What am I missing?

 

[mrmorris]

<font color="yellow">"Are you considering the thrust profile? "</font><br /><br />I don't have a thrust profile. However -- I'm not seeing exactly what you're indicating. The two of them burn for very nearly the same length of time, so the thrust profile won't be *vastly* different. Generally delta-v is the critical factor in deciding what a booster can or cannot do. dv isn't a complex equation -- it's just total impulse divided by mass. Total impulse is average impulse time the burn time.<br /><br />I did some more searching to see what I could dig up. From: NASAexplores Article: Building A Better Booster, I found an interesting tidbit:<br /><br /><i>"Each of the rockets can generate up to 14.7 million newtons (3.3 million pounds) of thrust."</i><br /><br />They're referring to the SRB4's. This is no suprise -- it's the figure I had. But then a paragraph down, the document says:<br /><br /><i>"During the test, the rocket generated 16 million newtons (3.6 million pounds) of thrust, and burned for 128 seconds. In comparison, during a launch, each SRB generates an average of 11.6 million newtons (2.6 million pounds) of thrust, and burns for about 123 seconds."</i><br /><br />Ah!! The 14,700 kN figure for the SRB4 is a max, rather than an average. However, but the context of everything I've seen, the 16,000 kN figure for the SRB5 is a max figure as well. Unfortunately, the doc does not go on to give the average thrust of the SRB5. It does provide a bit more on the mass of the two:<br /><br /><i>"A standard SRB weighs about 590,000 kilograms [kg] (1.3 million pounds) at launch, of which about 499,000 kg (1.1 million pounds) is fuel. The modified version had a total weight of 708,000 kg (1.56 million pounds), with propellant accounting for 621,000 kg (1.37 million pounds) of the total. This represents an increase of about 25 percent in the fuel capacity over the current SRB</i>

 

[mrmorris]

OK -- I'm pretty sure I know where the extra lift capacity is supposed to come from. The SRM5 is said to have a larger percentage of the mass as propellant. From my quote above:<br /><br /><i>"A standard SRB weighs about 590,000 kilograms [kg] (1.3 million pounds) at launch, of which about 499,000 kg (1.1 million pounds) is fuel. The modified version had a total weight of 708,000 kg (1.56 million pounds), with propellant accounting for 621,000 kg (1.37 million pounds) of the total. This represents an increase of about 25 percent in the fuel capacity over the current SRB design. "</i><br /><br />I'll have to work the calculations on this. However... I have a <b>wee</b> bit of a problem swallowing those figures. Let's look at them:<br /><br />SRB4: 499,000 kg / 590,000 kg = 84.6% propellant<br />SRB5: 621,000 kg / 708,000 kg = 87.7% propellant<br /><br />That's a pretty good increase and could indeed account for the improved performance. Um... however...<br /><br />SRB4: 590,000 kg - 499,000 kg = 91,000 kg<br />SRB5: 708,000 kg - 621,000 kg = 87,000 kg<br /><br />Sooooo -- they added another segment, switched to a larger & longer nozzle and the inert mass went *down* by 4,000 kg?!? C'mon -- pull the other one. I don't doubt that adding a fifth segment would increase the propellant fraction somewhat. However -- if they dropped the inert mass in the SRB5 -- then they did so by making some structural changes that would also be applicable to the SRB4. An SRB4 with the same enhancements then would be lighter than the figure they're using for comparison.

 

[bitbanger]

In order to get the proper evaluation of dv you must include the payload mass in the equation. In this case that means the second stage and CEV. <br /><br />Also, your dv equation isn't correct. It is equal to the acceleration integrated over time, taking into account propellant mass, dry mass, and gravity losses. Gravity losses is why the thrust profile is important. You need higher thrust at liftoff in order to overcome the mass of the fuel you haven't yet burned.<br /><br /><br />[edit]<br />A better way of stating the problem is that acceleration is instantaneous thrust divided by current mass, and dv is acceleration integrated over the burn time. Instantaneous thrust comes from the thrust curve and mass is continually decreasing as the propellant is burnt off.<br /><br />

 

[mrmorris]

Yep -- I realized in my last post that I had to use the rocket equation rather than a straight dv calculation. However, I didn't have time right then to do so. Those calcs are below. The SRB5 wins... but I have doubts about how level the playing field is. I suspect some fudging of the numbers in favor of the SRB5 as my previous post indicates.<br /><br />dv = isp * g * ln((m1 + x) / m1) <br /><br /><b>SRB5</b><br />dv = 266.2 s * 9.8 m/s2 * ln (708,000 kg / 87,000 kg )<br />dv = 2608.76 m/s * ln (8.137931)<br />dv = 2608.76 m/s * 2.1<br />dv = 5478 m/s<br /><br /><b>SRB4:</b><br />dv = 266.2 s * 9.8 m/s2 * ln (590,000 kg / 91,000 kg )<br />dv = 2608.76 m/s * ln (6.4835165)<br />dv = 2608.76 m/s * 1.87<br />dv = 4878 m/s<br /><br />So -- for the SRB4 to have the same performance as the SRB5 -- Mf/Me would have to be ~8.14. Assuming the propellant mass stayed constant at 499,000 kg, this would mean an inert mass of 61,302 kg. Mind you this assumes that the current dry mass figures are correct. As I indicated in my previous post -- something is fishy about the dry mass of either the SRB5 or the SRB4. I don't know if the SRB5 has been understated or the SRB4 overstated or what.<br /><br />If we work with the assumptions from my first post on the subject, where dropping the recoverability and going with the filament-wound composite would save at least 15,185 kg -- we'd have the following dv:<br /><br /><b>SRB4 -- NR/FWC:</b><br />dv = 266.2 s * 9.8 m/s2 * ln (590,000 kg / 75,815 kg )<br />dv = 2608.76 m/s * ln (7.7821)<br />dv = 2608.76 m/s * 2.05<br />dv = 5348 m/s<br /><br />At that point we're getting pretty close to the performance of the SRB5. Considering the 'fishyness' of the SRB5 massing 4000kg less than the SRB4 -- I would imagine that the end result of the non-recoverable composite SRB4 would be even closer than that.

 

[trailrider]

I'll leave the math to you...it's been a looong, looong time... As was pointed out, adding the 5th segment increases the thrust of the SRM5 over the SRM4. The total impulse or the thrust profile would be tailored to the trajectory and the payload mass (in this case the second stage and the Orion payload).<br /><br />The delta-v isn't the most important factor here. The capability to lift the payload is. Don't forget, the first stage has to lift from a standing start, and get the vehicle through max-Q without overloading the vehicle and contents. With liquid rocket engines, you can throttle back going through max-Q, then throttle up again. With a solid rocket, you have to tailor the grain by shaping the internal burning area and/or varying the propellant mixture when the grain is cast.<br /><br />You make up for delta-V with the second stage, which, in this case is almost completely for acceleration to orbital velocity, not so much for lift. The enlargement of the tank not only compensates for the reduced thrust of the J2X versus a Space Shuttle Main Engine derrivative (the original idea), but for any loss of delta-V you may have in the first stage.<br /><br />Oh, and for us dino-soars, can you run those calculations in English units. I CAN convert, but I don't THINK in metric. <img src="/images/icons/wink.gif" /><br /><br />Ad Luna! Ad Ares! Ad Astra!

 

[j05h]

<i>> The delta-v isn't the most important factor here. The capability to lift the payload is. ... the vehicle and contents. With liquid rocket engines,....<br />You make up for delta-V with the second stage, which, in this case is almost c... any loss of delta-V you may have in the first stage. </i><br /><br />Every bit of news shows this ARES I as having more than just growing pains. The CEV should be designed such that it can fly on any of several rockets. Lockheed is already talking "commercial capsule" with Bigelow. As the CEV prime, they should have a strong interest in maximizing return, as there is an obvious market emerging. If NASA absolutely requires HLVs, they would be advised to just develop one with Big Aero now, instead of half-hiding behind ARES I development. <br /><br />There are a lot of 5-25 ton launchers available right now. In fact, there is a glut in this market, both here and internationally. Bulk orders and many fuelling flights to a Lockheed (or other) propellant depot will drive down per-flight costs further. Jon Goff has been writing about this at Selenian Boondocks, highly recommended reading. <br /><br /><i>> Oh, and for us dino-soars, can you run those calculations in English units. I CAN convert, but I don't THINK in metric.</i><br /><br />I half-think in metric, but not as well as standard. I was in grade school when they actively taught both. One cubic meter of water = 1 metric ton. In orbit. <img src="/images/icons/wink.gif" /><br /><br />Josh <div class="Discussion_UserSignature"> <div align="center"><em>We need a first generation of pioneers.</em><br /></div> </div>