Positional shielding, eh? That’s what I guessed, but I didn’t want to assume. Thank you both for the clarification.
Not really the case, there, regarding altitude first, orbital speed later.
Only about 20% of launch energy is expended for orbital height; the rest of it goes toward orbital speed. If you watch a Shuttle launch, or any launch really, they tend to tilt over downrange pretty quickly. For example, a shuttle launch I just watched here http://video.google.com/videoplay?docid=4921840681729273736&hl=en has the Orbiter 10 miles downrange and altitude 8 miles, speed @1700 mph a little over a minute into the flight.
That puts even the initial climb angle at under 45 degrees, net. At 8 miles altitude air density is, ballpark, 20% of that at sea-level and as you gain altitude, with decreasing drag, you can devote even more of the launch energy to orbital speed. The point being that, even with a not-terribly-aerodynamic package like the shuttle launch package, the way to get to orbit is to point it downrange relatively quickly.
I thought we did this before. Oh, we did: [thread=402535]Why don’t rockets burn up on the way out?[/thread].
The amount of fuel needed to carry the fuel to slow down and land would be beyond prohibitive. For instance, the Saturn V rocket hat a payload to LEO capability of 118 tonnes. The dry mass of the vehicle was 178 tonnes, and the overall vehicle mass was 3,038.5 tonnes. This gives a mass ratio of m[sub]f[/sub]/m[sub]0[/sub]=0.04 and an overall vehicle mass fraction of 90.3%. So you can swag that for every kilogram of payload on orbit you need ten kg of propellant, and if you were going to stage down like you staged up you’d end up with about 20 kg of propellant to take to orbit 1 kg of propellant on the way down (assuming you aren’t taking advantage of any drag or gliding effects to land).
You can actually do a soft landing (see the 1971 Chrysler SERV concept for the STS proposal) but you still end up using aerobraking to get rid of orbital speed. It’s just a lot easier and cheaper to transfer momentum to the Earth rather than trying to use a rocket and all the propellant you have to carry around to slow down.
Stranger
One thing no one has mentioned yet is our old friend, F=m*a. Rearranged, that’s a=F/m.
For a rocket, mass is not constant. It’s basically a long, skinny tank. As the tank gets empty, the vehicle weighs a whole lot less. davekhps’s quote touched on this. A rocket may look sluggish when it’s just leaving the pad, but if the thrust stays the same there’ll be more acceleration than you can handle as it gets lighter.
I wish I had a copy of a book I remember from one of my thermodynamics classes. There was a graph of the performance of a Saturn V. Time from liftoff was along the x-axis, and there were graph lines for mass, speed, altitude, and at least one other. The numbers were jaw-dropping. From a million pounds at liftoff, it was under 300,000 within a few minutes. The rate at which it burned fuel and oxidizer was incredible.
So, rocket scientists choose launch trajectories to get out of the atmosphere quickly, and in terms of contributing to the total velocity, the rockets do their best work near the end of the burn.
This isn’t quite right, or at least, it is grossly oversimiplified. It is true that thrust is a function of mass and acceleration, and so if you keep the latter constant as the thrust constant and the mass decreases acceleration will increase, but efficiency of a rocket is typically measured in terms of specific impulse (I[sub]sp[/sub]) of the vehicle or propellant and the characteristic velocity (c[sup][/sup]) of the propellant. Some people also use the discharge coefficient (C[sub]D[/sub]) which is just the reciprocal of c[sup][/sup]. These should be mostly constant during the flight except for ignition and shutoff/burndown transients.
Because payloads (human and spacecraft) have acceleration limits thrust is controlled by throttling back the engine (for a liquid rocket) or configuring the grain geometry to decrease chamber pressure and combustion burning area (solid rocket motors). (The latter is called a “regressive burn profile” meaning that it produces less chamber pressure (and thus, for the same nozzle throat area, less thrust) over time. In general, you want the level of acceleration to be mostly constant once you’ve achieved liftoff. The reason rockets fly straight up first in the thickest part of the atmosphere is to limit the effects of unbalanced aerodynamic forces (due to a non-zero angle of attack and wind shear) on the booster body, which can tear the vehicle apart.
Stranger
I think all that was implied by my post.
I’m going with the latter.
Thanks for the post.
I was mostly taking issue with the statement “the rockets do their best work near the end of the burn.” Certainly the thrust to mass ratio is most favorable near the end of burn because you’ve lost a lot of propellant mass, but that doesn’t mean that the motor does “the best work” (i.e. is most thermodynamically or ballistically efficient) at the end of burn; in fact, while you get some modest improvement in nozzle performance due to P[sub]a[/sub]~0, the overall performance of the motor or engine usually drops off because of lower chamber pressure, underexpanded exhaust plume (nozzle optimized for lower altitude/higher P[sub]a[/sub]), throat erosion, et cetera.
In general, high thrust does not correlate to most efficient propulsive performance; solid rocket motors typically develop higher thrusts than liquids of the same mass (and the propellants are more dense, requiring less physical space) but have a measurably lower I[sub]sp[/sub] and poorer thermodynamic utilization. The highest propulsive efficiency motors (in terms of propellant weight, not power utilization) are low thrust ion, Hall effect, and magnetoplasmadynamic thrusters.
It’s a pedantic point, but one near and dear to my heart. Plus, I’m almost terminally bored by the meeting I’m sitting in. So…there you go.
Stranger
Not at all. It’s interesting stuff, and I think I’m still mostly following you. I remember seeing a diagram of the shuttle’s solid rocket boosters, with cut-aways showing the cross-section of the fuel at different levels. I remember thinking that was pretty clever. When we had a calorimeter lab in college, I wanted to cook up a gram or two, but my prof said it would be too corrosive.
It may have been a calculus class where I saw that graph of the Saturn V, but I remember thinking just how hairy a Physics problem it was. Speed depends on acceleration, acceleration depends on thrust and drag, drag depends on altitude; now add the fact that the mass of the vehicle changes (and not in a subtle way) based on fuel burn. I expect you also have to account for the decrease in gravity with altitude.
There’s a reason they call it “rocket science”. There’s also a reason why my posts are “grossly oversimplified”.
And drag also depends on speed.
The actual flying of a rocket does get ferociously complicated at times–in addition to the factors you mention, there are also controllability, aerothermal heating, plume recirculation, combustion instability, feed system resonance (for liquids), slag accumulation (for solids), and many others than can affect performance and reliability–but the basic theory is pretty straightforward and accessible to anyone with a basic grounding in physics and first semester calculus. Sutton’s Rocket Propulsion Elements and Humble’s pace Propulsion Analysis and Design cover the basics of liquid and solid propellant rocket propulsion without digging into the niggling technical details of specific flight hardware or esoteria. The real “rocket science” for chemical rockets is in interior ballistics and combustion kinematics (i.e. how stuff burns), high temperature materials, novel nozzle configurations, and computational aerofluid dynamics modeling (especially in low ambient pressure regimes).
Stranger
Well, speed and altitude; the point of maximum aerodynamic effect is called max Q (the greatest Mach number seen in flight) which occurs at some point in midflight. The biggest effects from aerodynamics in ascent to orbit is generally heating rather than aerodynamic loading, and is usually addressed by gluing on sheets of Thermal Protection System (read: cork) or in a few extreme cases an ablative composite compound.
One notable exception to this is the STS Shuttle; because of the large wing structures and because it pitches over relatively early in flight resulting in a large angle of attack, and, it sees considerable aerodynamic load, which is why it actually flies upside down into orbit; if it flew cabin topside the aerodynamic loading would exceed structural limits of the wing structure; this, in fact, is what ultimately caused Challenger to break apart after the External Tank ruptured and spewed flaming propellant all over the place.
The decrease in gravity actually doesn’t play much of a role in the energy required for orbital ascent; by the time gravity has substantially decreased you’ve already got a hella speed going and are close to lofting into orbital space anyway; most of the effort then is pulling the orbit into a stable ellipse rather than a terminal parabola that ends up in Central Asia or the Indian Ocean. Of course, even a few percent matter when dealing with rockets, but in the overall scheme of things it’s a smaller influence than many other factors.
Stranger
That’s still not actually a parabola. Both the stable orbit and the crash-into-Asia are ellipses; it’s just that one of them has perigee less than the radius of the Earth.
And I didn’t mention the drag dependence on altitude because Robot Arm already mentioned that part.