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Post by PhantomWolf on Oct 3, 2005 1:34:43 GMT -4
Bob, I'm surprised you didn't pick up the mistake in my calculations, at least I believe it's a mistake. I forgot to factor into it the Earth's tangential velocity, so of course the X-15's inital velocity is not 500mph, but around 1540 mph (assuming a best case senario of the plane being over the equator.)
That means that the equation should have be:
a = (7,184,000 m/s - 2,622,968 m/s) / 240s
a = 4,561,032 m/s / 240s
a = 19,004.3 m/s²
g is 9.8 m/s²
so a = 1,939g
Of course the result is basically the same as far as the pilot and plane are concerned.
These sort of g-forces are the reason that the Space Shuttle and Manned Rockets have a time to reach orbit which is measured in hours, not minutes.
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Post by Count Zero on Oct 3, 2005 2:42:41 GMT -4
You've got a bigger problem than that: Among other things, you did the conversion from miles to meters, but not from hours to seconds. convertit.com is your friend. Speed of launching aircraft: 500mph = 223.52 m/sec Speed of Earth's rotation at 33 degrees latitude =388.27m/sec Initial speed =611.8 m/sec Orbital speed = 4.488 miles/sec = 7,383.67 m/sec (I think the figure is closer to 5 miles/sec, isn't it?) Required velocity change (not including drag & altitude change) = 6772 m/sec 6772 m/sec / 240 sec = 28.217m/sec^2 or 2.88 G. That sounds a little low. Have I missed something? The Shuttle boosts for ~9minutes at max 3g.
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Post by PhantomWolf on Oct 3, 2005 2:50:23 GMT -4
heh, okay, that'll teach me for trying to do math at 4am and then try nd fix it without bthering to check what else I screwed up.
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Post by Count Zero on Oct 3, 2005 5:00:38 GMT -4
OK, the 90-mile orbits of the later Apollo missions were at ~4.84 miles/sec, or 7,793 meters/sec. So plugging that in...
Speed of launching aircraft: 500mph = 223.52 m/sec Speed of Earth's rotation at 33 degrees latitude =388.27m/sec
Initial speed =611.8 m/sec
Orbital speed = 4.84 miles/sec = 7,793m/sec
Required velocity change (not including drag & altitude change) = 7181 m/sec
7181 m/sec / 240 sec = 29.9 m/sec^2
or 3.05 Gs.
Of course, that's an average. It would start out less than that, and climb higher as the fuel was depleted (constant thrust and decreasing mass makes for higher acceleration). Again, this does not include compensating for drag or gaining 80 miles altitude.
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Post by Count Zero on Oct 3, 2005 5:24:15 GMT -4
I've said this elsewhere, but I'll repeat it here, for the benefit of LOTR and any lurkers:
You've just witnessed things that conspiracy theorists and moon hoax believers almost never do:
We checked our own and each others' work. We examined each others' assumptions. We did research to improve the accuracy of our assumptions. We pointed out the limits of our model. We corrected our own and each others' work. We were gracious about accepting correction from each other.
Notice that last part. Neither of us worry about losing face by being proven "wrong". Getting the most accurate answer is the important thing. Also, our work builds on itself. I would not have looked these figures up if PW hadn't taken the time to do the initial calculations. We all gained knowledge along the way.
That's what real science & engineering is about: The joy of learning, figuring out how the universe works, gaining new skills and insights, and doing things that have never been done before.
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Post by sts60 on Oct 3, 2005 9:24:31 GMT -4
These sort of g-forces are the reason that the Space Shuttle and Manned Rockets have a time to reach orbit which is measured in hours, not minutes.Your "sanity check" on this one would have been recalling how long the Shuttle engines burn for (as Count Zero pointed out), and how often Houston calls up "No OMS-1 burn required". It means that basically all the work of getting to orbit is done after just a few minutes. In fact, until we get antigravity, or E.E. "Doc" Smith's inertia cancelling, we must get to orbit fast. With rockets, the faster you do it the better. There is an alternative "hours" approach, however. To the best of my knowledge, the only country that has pulled it off was Grand Fenwick, back in 1963. It was outlined in this documentary film.
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Bob B.
Bob the Excel Guru?
Posts: 3,072
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Post by Bob B. on Oct 3, 2005 10:39:39 GMT -4
OK, the 90-mile orbits of the later Apollo missions were at ~4.84 miles/sec, or 7,793 meters/sec. For those of you following along at home, that is 90 nautical miles. Furthermore, at 90 nm I get an orbital velocity of 7,804 m/s. The 7,793 m/s figure I obtain for an orbital altitude of 100 nm, which was used by the earlier Apollo missions. NOTE: The early Apollo flights were launched into a low Earth parking orbit of 100 nm where the spacecraft stayed for 1.5 orbits before restarting the Saturn S-IVB engine to inject the spacecraft into a trajectory bound for the Moon. Beginning with Apollo 15, the parking orbit was lowered to 90 nm. This was one of the changes made to accommodate the heavier payload of the ‘J-missions’. The J-missions were those including the lunar rover and longer stays on the lunar surface. Required velocity change (not including drag & altitude change) = 7181 m/sec 7181 m/sec / 240 sec = 29.9 m/sec^2 or 3.05 Gs. It should be possible for a well-conditioned astronaut to tolerate these g-forces, though it certainly wouldn’t be pleasant. Gemini astronauts experienced an average of about 2.65 g for around three minutes during the second stage burn of their Titan II launch vehicle. The acceleration maxed out at about 7 g. The bottom line is the X-15 simply wasn’t capable of the required accelerations and velocities. If we go back to the astronautix.com page for the X-15 we see the following specifications: Mass: 30,121 kg Main Engine Thrust: 26,762 kgf Main Engine Propellants: 20,551 kg Main Engine Isp: 239 sec The acceleration at ignition would be, 26,762 / 30,121 = 0.89 g And the acceleration at burnout would be (assume all propellant is consumed), 26,762 / (30,121 – 20,551) = 2.80 g We can also use Tsiolkovsky's rocket equation to calculate the spacecraft delta v. delta v = Ve*LN(Mo/Mf) where, Ve = exhaust gas velocity = Isp*g = 239*9.807 = 2,340 m/s Mo = initial mass = 30,121 kg Mf = final mass = 30,121 – 20,551 = 9,570 kg delta v = 2,340*LN(30,121/9,570) = 2,680 m/s This is a bit more than the 2,100 m/s published on astronautix.com. Perhaps there is a typo in the given figures, or maybe not all the propellant is usable, or maybe the delta v figure has been reduced to account for drag. I really can’t explain the difference; nonetheless, it is clear the X-15 falls well short of the delta v required to attain orbit. We can also calculate the propellant flow rate and maximum burn time from the thrust and specific impulse. Isp = F/q where, Isp = specific impulse = 239 s F = thrust = 26,762 kgf q = propellant mass flow rate q = F/Isp = 26,762/239 = 112 kg/s Burn time = 20,551 kg / 112 kg/s = 184 s Thus the claim the engine was burned at maximum thrust for four minutes is also not possible. edit spelling
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Post by colinr on Oct 3, 2005 10:55:07 GMT -4
I love it here ... so much info prompted by such silly claims ...
Keep it up guys .....
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Post by Kiwi on Oct 3, 2005 11:31:51 GMT -4
I love it here... so much info prompted by such silly claims... Keep it up guys ..... That's the beauty of this board and the few others like it. Those of us who want to learn can do so -- and enjoy ourselves. I have probably learned more new and useful things in the few years I've been here than I did in the previous few decades. It was only here and at the old BABB that I learnt about critical thinking and logic. I was never taught anything about them at school in the 60s. Fancy going for 50-odd years without that stuff! Some posters don't care about pig-headed hoax-believers -- they are instead posting for the other members and lurkers who are genuinely interested in learning. Naturally, they are delighted to get feedback like yours.
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Post by RAF on Oct 3, 2005 11:35:58 GMT -4
NOTE: The early Apollo flights were launched into a low Earth parking orbit of 100 nm where the spacecraft stayed for 1.5 orbits before restarting the Saturn S-IVB engine to inject the spacecraft into a trajectory bound of the Moon. Beginning with Apollo 15, the parking orbit was lowered to 90 nm. This was one of the changes made to accommodate the heavier payload of the ‘J-missions’. Why do I come here? For "stuff" like this. It's something I should have known (being the Apollo phile that I am) yet did not know... Thanks!
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Bob B.
Bob the Excel Guru?
Posts: 3,072
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Post by Bob B. on Oct 3, 2005 11:39:31 GMT -4
I love it here... so much info prompted by such silly claims... Keep it up guys ..... That's the beauty of this board and the few others like it. Those of us who want to learn can do so -- and enjoy ourselves. Agreed. I wouldn't be here if all I did was talk to a bunch of close-minded knuckleheads who refuse to learn anything. Naturally, they are delighted to get feedback like yours. Absolutely! Thanks, colinr. I glad you're finding this forum informative.
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Bob B.
Bob the Excel Guru?
Posts: 3,072
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Post by Bob B. on Oct 3, 2005 11:43:21 GMT -4
You're welcomed.
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Post by JayUtah on Oct 3, 2005 12:18:40 GMT -4
Often I feel that the only reason I post here is for the benefit of spectators. I don't fear opposition or challenge. Disagreement prompts research and deeper understanding. I've had people who worked on Apollo say to me, "You know, I always wonder why such-and-such was done that way, and I didn't know until I read your site."
Now disagreements that arise as part of the learning process are one thing. Disagreements that persist simply because people are predisposed to disagree have a limited value in enriching the intellectual process.
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Post by PhantomWolf on Oct 3, 2005 20:52:56 GMT -4
[We were gracious about accepting correction from each other.Gracious, yeap, embarassed, very. But yes, unlike most CT's I'm willing to admit my monumental stuff-ups, and this was probably my worst for a while. Still if I had a dollar for ever mistake I've made, I'd be rather rich. I d learn though, as opposed to some, and it's a mistake I won't repeat. Not, just have to write "Check the clock and not the calculator" on the board 100 times. Thanks for the clean up guy, I still feel embrassed about making such an obvious muck up, but hey, I'll live.
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Post by Kiwi on Oct 3, 2005 23:00:34 GMT -4
I've said this elsewhere, but I'll repeat it here, for the benefit of LOTR and any lurkers: You've just witnessed things that conspiracy theorists and moon hoax believers almost never do: We checked our own and each others' work. We examined each others' assumptions. We did research to improve the accuracy of our assumptions. We pointed out the limits of our model. We corrected our own and each others' work. We were gracious about accepting correction from each other.Notice that last part. Neither of us worry about losing face by being proven "wrong". Getting the most accurate answer is the important thing. Also, our work builds on itself. I would not have looked these figures up if PW hadn't taken the time to do the initial calculations. We all gained knowledge along the way. That's what real science & engineering is about: The joy of learning, figuring out how the universe works, gaining new skills and insights, and doing things that have never been done before. An excellent post, CountZero, one I've saved to my HD for future reference. It would be excellent if more hoax-believers behaved the same way. I often wonder why they don't. Lacking basic intelligence? No real common sense? Ego far to big to engage in an intellectual pursuit? Narrow minded? It's hard to tell with some of them. Proper debate is one area where a "defeat" can mean a big step forward for the "loser", so it's neither a defeat nor a loss, it's a gain. I delight in being proved wrong because it means I've learnt something. Speaking of calculations, I've been looking at many of the official NASA Apollo films recently and it's lovely to see so many scenes of engineers using pencil and paper or blackboard and chalk to figure out how to get Apollo 13 home. Not a calculator or even a slide rule in sight. Even I can still add pounds, shillings and pence on paper and do small sums in my head, but my late Dad would be horrified at how slow I am.
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