Man of Honour
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- Stoke on Trent
KizZ said:Yep but its a lot smaller. Its located at ST4 3NP
The balloon needs to go up about half again.
KizZ said:Yep but its a lot smaller. Its located at ST4 3NP
Eliot said:basically, if they made the blackbird ages agooo that when fomr new york to london in like 2 hours? what do they have now.
laiman said:When was the stealth fighter the (F-117) first widely known to the public? Ive got a few photos that my dads had since before I was born.
Flibster said:Aurora.
Allegedly the project name for the SR-71 replacement.
A vast amount of runours, conjecture, eye-witness sightings and other evidence point to an aircraft, funded as a Black Project, built by the Lockheed Skunk Works, operating out of the Groom Lake / Area 51 location.
Always at night, never photographed, officially denied - sound familiar?
Details are non existant - but current guesses are Mach 5+
However - Lockheed and Groom Lake have always been very good at keeping projects under wraps even when they've become service aircraft - just look at the F117.
This could be in service now and we may not find out about it for 10 years.
Simon/~Flibster
i'm by no means a physicist, but my thoughts are as follows.Overlag said:and as it said in one of those videos.... why are we exploring space (mars, venus etc) with liquid rockets that are very slow, when by all account we (well they) might have something MILES better?
The_Dark_Side said:i'm by no means a physicist, but my thoughts are as follows.
once in space there's almost no friction so your speed stays almost constant, therefore the faster you go, the more effort it'll take you to slow down at the other end of your journey.
basically more fuel to accelerate then more fuel to decellerate when you get there=much larger craft.
anyone more clued up than i please feel free to correct me.
any ideas why this is?Overlag said:i understand that, but our rocket technology doesnt really allow us to go anywhere too fast....i can understand you need to slow down as well, but we cant get fast enough anyway
The_Dark_Side said:any ideas why this is?
iirc the saturn 5 hits about 17k miles/hour (although it's late and i may be WAY off with that)
are there any technical reasons to prevent more speed though?Overlag said:that is slow though by space travel standards
the fastest (or stongest at lifting) was the russian "copy" of the shuttle booster systems. although no longer made
The_Dark_Side said:any ideas why this is?
iirc the saturn 5 hits about 17k miles/hour (although it's late and i may be WAY off with that)
What would be the final speed of a Saturn 5 rocket built fueled and fired in space after all three stages burned completely?
Answer:
This question can be answered in different ways, at different levels of precision. Even when we want an accurate answer, it is worthwhile to do rough estimates first, both as a check on later answers and because the insight gained in the estimation process is often valuable.
At the simplest level, the Saturn V was required to launch the lunar exploration spacecraft (the Command Module, CM, Service Module, SM, and Lunar Module, LM) on a trajectory to the Moon. In the approximation that the Moon is far from the Earth (compared to the size of the Earth), it must provide the payload with a mission velocity close to the earth escape velocity, 11.2 km/s, or roughly 7 miles per second. While there are corrections to this figure for several reasons (see below), they are mostly at the few percent level for a large rocket like the Saturn V, so the final answer must be not too different from 11.2 km/s, but of course somewhat larger, to take account of the various inefficiencies discussed below.
Because the question specified the velocity reached in space when beginning fully fueled (sometimes called the ideal velocity), now let us guesstimate the major corrections to the above 11.2 km/s.
These are as follows, roughly in order of magnitude.
Gravity:
While the engines must obviously do work against gravity to lift the vehicle, here this term refers to another sort of gravitational loss that may be understood by imagining the extreme case in which the rocket's thrust was exactly equal to its weight. Then the vehicle would not move at all (at least until it became lighter), yet fuel would be burned: it would simply sit on its exhaust, being supported against gravity but making no progress.
If, on the other hand, the thrust were extremely high, so the propellant were used almost instantly, the rocket would immediately reach its final velocity, and no such loss would be incurred. Because of the large heavy engines required, atmospheric drag, and stress on the vehicle and its occupants, this extreme is not a feasible choice.
The optimal compromise is somewhere in between these two extremes. Alternatively, one could avoid gravitational losses entirely by accelerating only horizontally to escape velocity. This is also not possible due to the effects of atmospheric drag. The best trajectory will thus go up to get above the effective limits of the atmosphere as fast as possible, but also bend over to do the major acceleration somewhat above about 60 km. The losses due to gravity near the optimum trajectory are typically about 10% of the mission velocity for launches from the surface of the Earth.
Earth rotation:
Because the Earth rotates, whenever possible one attempts to take advantage of this free velocity increment by launching towards the east. At the latitude of Cape Kennedy, this gave about 410 m/s, or -3.6% of the mission velocity (minus meaning reduces necessary velocity requirement from the launch vehicle).
Atmospheric drag:
The trajectory is designed to get above the denser atmosphere as quickly as possible, then bend over to the east to avoid unnecessary gravitational losses. Here the large size of the Saturn V is a big help; let us guess +5% of the mission velocity.
Finite distance to the Moon:
Since the Moon is about 60 Earth radii away, the potential energy (proportional to 1/R) is about 1/60th that at the Earth's surface. Thus the energy to reach the Moon is (59/60)*(escape to infinity energy) and the lunar mission velocity is about -1% (less) than escape velocity, or 11.1 km/s.
Collinearity:
Ideally the rocket would accelerate in a straight line. The same effect may be largely achieved by keeping the thrust direction parallel to the velocity vector, but some steering accuracy errors must be expected. They should be quite small, let us guess 1%.
Contingency reserve.
This is a matter of policy as much as physics, although the uncertainties in the above factors from one flight to the next play a role. In any case, it will not do to come out 0.5% short, and some margin must be allowed. For the space shuttle I believe I recall 3%, so I adopt that here.
Adding everything together, we get 14.4%, (1.00+0.10-0.036+0.05-0.01+0.01+0.03 = 1.144), which then gives about 12.8 km/s as the necessary vehicle velocity capability. While the approximations and guesses above are rough at best, they give us a tighter bound on the answer to expect. I will be surprised if the answer computed in part 3 below comes out above 14.4 km/s or less than 12.0 km/s, in particular.
At the next level of precision, we can compute the ideal answer based on the various masses and the performance of the engines.
The essential fact one needs in computing the velocity is the rocket equation, which gives the ideal velocity v of a single-stage rocket in terms of the exhaust velocity c and the masses via
v = c*ln(M1/M0).
Here M1 is the initial mass of the rocket, M0 is the final mass (empty tanks, engines, payload, any residual propellants, etc) at engine cutoff, and ln is the natural logarithm. ( The natural logarithm is the inverse of the exponential function. That is, if y=ln(x), then x=e^y = exp(x), and vice versa, where the number e=2.71828... is a universal irrational mathematical constant, rather like pi. ) The equation is valid for a rocket accelerating in a straight line, in empty space, in the absence of any complications due to gravity, atmospheric drag, or other factors.
The quantity M1/M0 = R is known as the mass ratio of the rocket. Hence, if R = e, v = c, and the rocket reaches a speed just equal to its own exhaust velocity; if R = e^2 (= 7.389... approx), v = 2c, and if R = e^3 (= 20.086... approx), v = 3c, etc. In practice engineering factors limit R to fairly small values, generally less than 10 for vehicles taking off from the Earth and carrying any significant payload.
For a multi-stage rocket like Saturn V, we apply the formula to each stage in turn, adding up the velocities as we go. Thus we need, for each of the three stages,
the total mass, M1, at ignition
the remaining mass, M0 at engine cut-off
the exhaust velocity, c.
The Saturn V used five large Rocketdyne F1 engines, powered by liquid oxygen (LOX) and RP-1 (roughly kerosine) for the first stage, five Rocketdyne J2 liquid hydrogen (LH2) and LOX engines for the second stage, and a single J2 for the third stage.
Sutton & Ross (1975 Rocket Propulsion Elements, Wiley) quote a specific impulse Isp of 304.8 s for the F1 and 426 s for the J2, both in vacuum. Isp is defined as the number of pound-s of impulse (thrust times duration) given by 1 pound (mass) of propellant. It is related to the exhaust velocity c [m/s] by c = g*Isp, where g = 9.80665 m/s^2 is the standard acceleration of gravity.
The most comprehensive information on the masses that I have been able to find is in The Saturn V Launch Vehicle Home Page:
Code:# Stage m0 mp m1 1. S1C 300.0 4492.0 4792.0 2. S2 95.0 942.0 1037.0 3. SIVB 34.0 228.0 262.0 4. IU 4.5 0.0 4.5 5. payload - - 109.6
where the payload is for Apollo 11, IU is the Instrument Unit (logically, part of the dry mass of stage 3), and SIC, SII, and SIVB are the three rocket stages.
Here m0 is the stage empty weight, mp is the propellant, and m1 is the stage total, in thousands of pounds. Note that M0 differs from m0 (and M1 from m1) in that the lower case letters denote the masses just for each stage alone, without regard to the mass of any stages higher up, where the upper case letters, which we need to apply the rocket equation, are cumulative, so that, eg, for the Saturn V, M0 for the second stage includes the loaded mass m1 of the SIVB, and the masses of the IU and the payload.
It is important to realize that the above figures are not absolute; the launcher improved steadily even during the few years it was in use. For example, Von Braun (1975, NASA SP-340) quotes the payload mass above the IU as rising from less than 80,000 lb on Apollo 8 (which carried a structural test article instead of a live LM) to 116,000 lb on Apollo 17 -- a 45% improvement.
Then converting Isp to c, m's to cumulative M's and expressing everything in metric units, we obtain for the exhaust velocities & cumulative masses, [kgm]:
Code:Stage c [m/s] M0 M1 1 2989.1 777065.8 2814637.0 2 4177.6 213694.6 640985.8 3 4177.6 67181.8 170602.6
With these numbers in hand, it is easy to compute the mass ratios and the natural logarithms ln(R) of each stage, the stage velocities and finally the total velocity:
Code:Mass Ratio (R) and Velocities [m/s] Stage mass ratio R ln(R) Stage v Total v 1 3.622 1.287 3847.1 3847.1 2 3.000 1.098 4589.0 8436.1 3 2.539 0.932 3893.3 12329.4
The answer to the problem is thus 12.33 km/s.
Looking back at our guesstimates in Section 2 above, we see that the value we obtain is close to, but a little less than, our best guess. Considering that the guesses were really just off the top of my head, this seems okay. Taking 10.7 km/s as the absolute minimum (considering the rotation of the Earth and the finite distance of the Moon), the ratio 12.3/10.7 is 1.1495, so the ideal vehicle capability exceeds the bare minimum mission velocity by about 15%.
Afterword:
After submission of the above I realized that in Part 2 I had neglected to include the effect of reduced engine efficiency at sea-level pressure. This does not affect the final answer of 12.33 km/s, but does come into the efficiency estimates. Sutton & Ross (1975) give the sea-level Isp of the F1 engine as only about 265 s, 15% less than the vacuum value. The J2 engines all operate at high altitude and should be unaffectd. The effect for the F1 engines on the SIC 1st stage can be roughly estimated as a 15% loss during the time it takes to traverse the first scale height of the atmosphere (about 1 min), and 0 thereafter. Given the first-stage burn duration of 170 s, this means the loss is about 5% of the SIC ideal velocity of 3847 m/s, which is 193 m/s, or about 1.7% overall. In particular, if considered above it would have raised my lower "surprise threshold" from 12.0 km/s to 12.2 km/s, nearly the 12.3 obtained. While the discrepancy can hardly be called serious, the obvious places to look for its origin would be my guesses of the gravitational effect and atmospheric drag, as these are both relatively large and uncertain. If they were reduced from 10% and 5% to 9% and 4.5%, respectively, good agreement would be restored. At the least, this suggests that the losses due to the factors in Section 2 may be somewhat less than my guesses.
Third Stage (S-IVB): The third stage contains one J-2 engine.
This engine burns for 2.75 minutes boosting the spacecraft to orbital velocity of about 17,500 mph. The third stage is shut down with fuel remaining and remains attached the spacecraft in Earth orbit.
The J-2 engine is reignited to propel the spacecraft into translunar trajectory (speed of 24,500 mph) before finally being discarded.
i knew the 17k figure was in my head for some reason. orbital velocity.Flibster said:Although:
Getting the fuel to power the rocket up out of the atmosphere. You can gain speed by diving into a gravity well. The Helios probes reached speeds of approx 150,000 mph at closest approach.The_Dark_Side said:i knew the 17k figure was in my head for some reason. orbital velocity.
but to ask again once free of the atmosphere, what limits higher velocity?
and the more fuel you're carrying, the more fuel you'll expend carrying the extra weight right?Sleepy said:Getting the fuel to power the rocket up out of the atmosphere.
Yep.The_Dark_Side said:and the more fuel you're carrying, the more fuel you'll expend carrying the extra weight right?
so what we need is some type of solar system forecourt
The_Dark_Side said:and the more fuel you're carrying, the more fuel you'll expend carrying the extra weight right?
so what we need is some type of solar system forecourt
Flibster said:Aurora.
Allegedly the project name for the SR-71 replacement.
A vast amount of runours, conjecture, eye-witness sightings and other evidence point to an aircraft, funded as a Black Project, built by the Lockheed Skunk Works, operating out of the Groom Lake / Area 51 location.
Always at night, never photographed, officially denied - sound familiar?
Details are non existant - but current guesses are Mach 5+
However - Lockheed and Groom Lake have always been very good at keeping projects under wraps even when they've become service aircraft - just look at the F117.
This could be in service now and we may not find out about it for 10 years.
Simon/~Flibster