Reusable Rockets to Orbit

Rune · 2011-12-15 18:46:48

GW Johnson wrote:

I cleaned up my reusability study and illustrated it, and posted it over at http://exrocketman.blogspot.com a few minutes ago. It was based on parachute-slowed ocean impact recovery.

I think I have it on favorites, in case I had to dig up the stuff you put there about ramjets. I recall your fuel experiments with the beetle were also worth looking... Will keep it there!

GW Johnson wrote:

I, too, saw some stuff on Spacex's website about landing the first stage of Falcon-9 on its tail. It was a bit unclear to me exactly how they propose to do this, but I had the impression of parachute-slowed fall to a last-second rocket-braked landing on landing legs. The landing legs and the extra propellant would have the same effect as increased inert weights for ocean impact. Both scenarios have some sort of chute system.

I actually don't have a reference for chutes or the absence of them... they are not in the video and Dragon is going to retain them as backup, that's all I know for sure. If you have heard something about that somewhere I can look at it, point the way!

GW Johnson wrote:

Falcon-Heavy is supposed to fly for the first time out of their new pad at Vandenburg AFB next year, last I heard. It will use the Merlin 1-D, which then retrofits onto Falcon-9 and Falcon-1 later. It's the 1-D that got them to 53 metric tons to LEO, instead of 34 tons.

I'm sure crossfeeding their way into a three stage booster also had something to do with that, but yeah, it's amazing what they have done with the engines. And good to know hey will have to show those numbers are real soon.. as in next year the hardware must be delivered, right? Big stuff happening... kind of makes you wonder if the haste with which the Falcon Heavy is going to be fielded has something to do with the lack of flights this year. They must be really pushing their factory output, in terms of finished cores, methinks.

Adaptation wrote:

The delta wing is interesting addition on the air drop version, I am curious if perhaps they could use it for a horizontal landing on a dry lake bead or very long runway landing at a high speed and using drag chutes to slow it down.

A couple of things. First, it's more accurate to call the booster a resurrected Falcon V. It's going to have nowhere the "uumph" of its bigger brother, no matter what the advantages of air launch are. It's quite smaller, about 55% less than the F9, going by the number of engines, or a bit more if the air launch lets you go with lower T/W.

And the little delta wing in there, I am guessing, is there to perform the pitch-up maneuver any air-launched rocket requires. Taurus has a similar wing, and even though it could in principle be used to fly the booster back, I doubt it's even used for that purpose. No, I expect the booster to be expendable, at least until SpaceX proves reusability on the big boys, F9 and F9H, and then to be modified using their technology. Just an informed opinion, BTW. I have no inside info, just my personal "prophecies". And I would have never seen a vertical landing first stage coming, so I fully expect to be proven wrong again.

Rune. Ok, it's official. I'm re-hooked to this forum.

GW Johnson · 2011-12-16 11:16:02

JoshNH4H, you and Hop and Louis, don't desert us. This discussion is getting very interesting. Air drop launch has entered the fray, perhaps commercially.

I will keep my posts short here. Any long and technical stuff, I will post over at my "exrocketman" site. Y'all know where that is.

GW

JoshNH4H · 2011-12-16 15:14:08

GW- I certainly don't plan to leave this thread anytime soon! I agree that there's a lot of good stuff going on here. I can't speak for hop.

Anyway, GW, you're plenty welcome to post your analyses here. They're quite interesting. Though if you would prefer to post a link to your blog, that is of course perfectly fine too.

Anyway, as I recall I was reconsidering my choice of rocket propellant based on the fact that High Density Acid is quite expensive due to the costs associated with the handling of toxic materials. According to Astronautix, it's $6.00/kg. To give you an idea, the gasoline you buy at the pump is approximately $1/kg, though this will of course vary a good deal based on location (This is equivalent to a cost of about $3.07/gallon.) I would imagine that RP-1 would be similar to this (It is, I believe, exempt from gas taxes and the like).

My information is the same as that in my original post on fuels, which was here. Based on taking another look at the propellants on this list, I am of the opinion that pure Methlox is the best way to go, just about the equal of Kero/HDA/H2/LOX. It'll have a reasonably high engine T/W (average molecular mass of propellant 26.7, not awful, and quite a good mass ratio as well), as well as allowing some simplification of design due to the relatively similar temperatures of liquid methane and LOX. I estimated a trajectory averaged Isp of 345 s, but that could actually be an underestimate, I'm not sure. I intend for the program that I write to take all of this into account.

GW Johnson · 2011-12-16 17:26:12

JoshNH4H:

I'm fast becoming a methane convert myself. Easier to make, handle, and store than hydrogen, no matter where in the solar system you are. Also usable in ramjets instead of kerosene (common fuel rocket and ramjet). I know XCOR is getting excited about methane fuel, too. Cleaner by far than any kerosene available. Far fewer injector orifice clogging problems. I kinda like all of that.

GW

JoshNH4H · 2011-12-16 18:22:40

Yeah, it seems like it's a really good fuel to do research on. I've heard of it being fired in kerolox engines, too, so it wouldn't require too much additional development expense in order to get it working on a full-scale engine. Given the very nice possibilities for Isp with a Methlox engine, I really do believe that it is the best choice for a rocket fuel in many, many applications, most especially a Single-Stage to Orbit vehicle.

I'm writing that program now. I'm going to write it in the MATLAB programming language. I would hazard a guess that most on this forum do not have the Matlab program installed on their computers seeing as it is quite expensive. However, there is a free software designed to run matlab code. This is called FreeMat, which can be downloaded here for those who are interested. Its developers estimate 95% compatibility with Matlab, and I can guarantee 100% that my program will work with it because I will be writing it in Freemat.

JoshNH4H · 2011-12-16 18:30:09

Oh, also, GW, when you get the chance do you think that you could give a quick intro to how I should treat the impulse lost due to drag?

GW Johnson · 2011-12-17 11:35:10

I assume you are writing a finite-difference solution to the equations of motion, presumably in 2-D. It won't matter much if you do it 2-D Cartesian or round-Earth. The easiest version is a 2 degree-of-freedom flying particle in 2-D Cartesian, I'd start there.

If at any given time step, you compute all the force vectors (magnitude and direction) acting on the vehicle (thrust, weight, air drag), their sum and the current particle mass gives you the acceleration vector direction and magnitude. This force sum includes the weight force, which then automatically accounts for the "gravity loss" as you "integrate" the trajectory. Acceleration times time step is the delta-vee vector increment to the next step. This delta-vee times time step is the displacement to the next step. The velocity change and position change take place in the direction of the acceleration vector, so you do components to figure the new 2-D vector position. It is easier and more useful to keep track of velocity magnitude tangent to the current path, as that is how drag is figured. This gives you the position and velocity at the next time step, where you do it all over again.

You will need to build a "model" of your vehicle with many facets. First is a good thrust model. That can be a large topic, even for a rocket, as delivered thrust and impulse are functions of backpressure and exit area, even at constant propellant flow rate. Second is a good weight statement, such as I had been calculating for Falcon-9 and the reusability trades I just did. Third is a good drag model, which requires coefficient vs at least Mach, and a suitable reference area, for each shape the vehicle takes on as it stages. The coefficients are most definitely not constants. You can pretty well zero the drag forces above around 200,000 feet, no matter how fast you are flying, as the density is becoming too low. But, you will need a model atmosphere, so you can figure speed of sound from ambient temperature, to calculate Mach for looking up the drag.

You have to keep the time step very small. Make no more than a 10% change in any physical condition such as velocity, weight, or thrust, in any given step. 1% would be more accurate. It is possible to use this to program an adaptive time step that is very fine near launch, but "steps out" bigger as the vehicle flies fast. You can do this in the very simple forward-stepping procedure I described above quite accurately. You don't need Runge-Kutta integration, that was for the ancient computers with kilohertz or slower processing speeds.

The hardest part is initial conditions. If you are doing an adaptive time step, it may get hung up at launch. Sometimes you have to give the vehicle a trivial upward velocity to succeed with the calculation. Maybe 30 cm/sec.

And all of that is what it takes for non-lifting gravity turn flight. Winged lifting vehicles require at least a 3-degree of freedom model that includes moment sums and pitch inertia, for just a 2-D Cartesian model. They also require pitch control as a user input, and a description of lift curve slope vs Mach, plus drag-due-to-lift vs Mach. Not for the amateur.

Hope that guidance helps.

GW

JoshNH4H · 2011-12-17 16:03:29

GW- It certainly does help. Actually writing the program is going to be quite the test of my ability. I do intend to write it only for single-stage rockets, because the simplification obtained from doing so is IMO worth the reduction in extra effort. Once I've written it for single stage I may choose to go back to it and modify it for multiple stages, but that is certainly not something which I intend to do in the first pass; getting the program to work at all will be work enough for now. Thanks a lot.

GW Johnson · 2011-12-17 16:17:40

Josh:

That's exactly what I did writing codes like that long ago. It'll work. Going to multiple stages is not very hard, once you get the basic algorithm working. You just shift weight statement and drag, plus any thrust controls, at staging. It'll take some idiotic fractional time step to exactly hit the stagepoint. That's the hardest part, and it's not that bad.

GW

GW Johnson · 2011-12-18 10:15:34

Josh:

Use the simple jiggered rocket equation analysis technique to help you pick the problems to run with your trajectory code. dVo = Vex ln(MR), where Vex = Isp*gc is a useful approximation, and fprop = (MR-1)/MR, for which 1 = frop + fpay + finert. Actual dV = dVo/factor, to model gravity and drag losses. For lower stages flying in air and nearly vertically, I use factor = 1.10. For upper stages flying in vacuum and more horizontally, factor = 1.05. This kind of thing will get you started by landing you in the right ballpark.

Trajectory analysis takes more effort, but is more reliable. Usually, weight statements are no problem. Real thrust vs flowrate and real backpressure effects require some real knowledge of rocket engines and nozzles. The toughest nut to crack is realistic air drag. The best source of actual drag data that I know is Sighard F. Hoerner's "Fluid Dynamic Drag", which his widow published from her home until she died. I doubt it's available anymore, except in a library. Hoerner was one of the aerodynamics guys on the ME-109 before WW2. He had all kinds of stuff in his book, including hypersonics.

GW

Adaptation · 2011-12-18 12:54:58

I think I may actually have a copy in my pile of books but I cant find it right now. In any event It's available on amazon.

http://www.amazon.com/gp/offer-listing/ … er=&colid=

GW Johnson · 2011-12-24 12:35:59

Merry Christmas and Happy New Year, guys.

Hoerner also had a lift book, in addition to his drag book. Same self-published thing. Probably obtainable from Amazon, although I have never looked for them there. I have both in my library.

There's way more in them than most of y'all would ever need. It's arranged a little backwards, as Hoerner was a German. Sort of reverse, like the grammar. Fun to look at, though.

Look in the supersonic section for projectile drag. pretty close to just about any launch rocket drag. His plots go up as far as M6. Most rockets leave the sensible air at about M2 to 3. Good enough.

The real trick is getting the "transonic drag rise" modeled - that's part of the max Q worry we've heard about for decades. Biggest CD at near-M1 just before the density starts tailing off fast as you rise up past 30-40,000 feet. Biggest forces on the structures.

GW

JoshNH4H · 2011-12-26 23:45:43

GW- I'll take a look at those in my school's library after break. Wouldn't surprise me if they were there, and they should definitely be available through some kind of interlibrary loan.

Not to get too sidetracked, though, I'm going to take a look at re-entry characteristics of my proposed reusable rocket. Re-entering and landing is usually a pretty significant challenge facing designs for an SSTO vehicle because there isn't much room in the mass budget for heat shielding and that kind of thing (in the future, perhaps imports of lunar, NEO, or phobosian material will be used to coat the ships to provide a simple heat shield for re-entry, if such are cheap enough. That's out kind of out of the scope of this thread, though).

Anyway, the general rule for re-entering the atmosphere is that the larger the surface area, the smaller the heat flux, because the craft will slow down more in the less dense upper atmosphere. The shuttle has a pretty tough re-entry trajectory, which is what necessitates its fragile reinforced Carbon-Carbon tiles and its other thermal protective materials, and which ultimately made the Columbia tragedy possible. Though this is not strictly speaking correct given new technological developments in the 30 years since the Space Shuttle was developed, I don't think that we're going to want to go beyond that, given that we have a minimal thermal protection mass budget.

It is my understanding that a decent figure of merit for this is kg per m^2. This doesn't take into account the coefficient of drag, which if our rocket is cylindrical will be lower than, for example, the flat delta-wing shape of the Space Shuttle (And of course, it will vary with velocity. Nevertheless, we need to compare something to something else, so on to it.

The Space Shuttle has a mass, at re-entry, between 78,018 kg (no cargo) to 104,000 kg (maximum landing cargo). I found an image in this wikipedia article, probably from this NASA report, which is unfortunately mostly unreadable. The image:

This indicates that the area of the heat shield is approximately 479.7 m^2, giving a mass to area ratio of 162.6-216.8 kg/m^2 (depending on how much cargo the orbiter is carrying down).

Now, let's take a look at our proposed launcher. We're giving an approximation for the Isp of 345 s (though this is very possibly an underestimation, seeing as 375 s vacuum has been done, and Methane hasn't seen much development). This gives a mass ratio of 16.1. This means that the dry mass will be 6.21% as much as the wet mass at launch. When one includes the payload mass, this will be even lower. Seeing as I haven't done calculations yet, I don't know how much will be payload. For the sake of approximation and the sake of margin, I will ignore the payload fraction. Remember this when looking at my numbers, because no matter how many significant figures I give, they are only an approximation.

Anyway: The ratio of re-entering mass to heat shield cross-sectional area is not constant with rocket size. As GW has mentioned, volume (E.g., total mass) scales with dimension cubed, while the cross-sectional area scales based on dimension squared. I'm going to make another technically false simplifying assumption, and assume that the entire re-entry mass is in the shape of a cylinder where its length is four times its width, and therefore 8 times its radius. Volume will be pi*r^2*h, or 8*pi*r^3. Cross-sectional area will be 8*r^2.

For an initial mass of 1,000,000 kg (Not having done any calculations whatsoever, think 5-25 tonne payload, yes I know that's exceptionally broad), the radius would be 6.5 m. The mass at re-entry would be (less than) 62,112 kg, and the surface area would be 338 m^2. This gives 183.8 kg/m^2. This is unfortunately right around what the shuttle is. Odd thing is, I don't understand why. It should be a lot lower since we're basically talking about an empty tank.

GW Johnson · 2011-12-27 14:55:00

Josh:

The idea of using what aircraft designers call low wing loading, and ballistics guys call low ballistic coefficient, is a good one for reducing peak skin temperatures during re-entry. It actually increases the total amount of heat that must be absorbed (a heat sink design issue), but skin temperatures are really the more critical issue, because that sets what materials can be used.

I’m not sure of the actual numbers, yours are probably better, but shuttle looked like a combat jet fighter, as I recall. That would be in the neighborhood of 100-200 pounds per square foot of wing planform (488-976 kg/sq.meter). (That’s converted at 4.88157 kg/sq.m per lb/sq.ft.; I’m used to working in US customary, because all those around me worked in it, although I speak metric, too.) The old one-man Mercury space capsule was near the 200 lb/sq.ft (976 kg/sq.m) figure, too.

What you want in order to achieve lower skin temperatures is a wing loading closer to that of a Piper Cub or Cessna 150: around 6-12 lb/sq.ft (29.3-58.6 kg/sq.m). That would be very difficult to achieve indeed in a practical design, but if you could, skin temperatures under 2000 F (1367 K, 1094 C) are possible . In principle, that makes a fabric-covered steel truss structure just like the old Piper Cub possible as a re-entry vehicle, as long as you use ceramic fiber fire curtain cloth for the skin covering.

Nextel 312, and whatever 400-series Nextel product has replaced it in recent decades, is alumino-silicate fiber, good to 2300 F (1533 K, 1260 C) without solid phase change cracking. Meltpoint is actually 3200 F (2033K, 1760 C), but you’ve lost structural integrity once the solid phase change occurs.

For a stage tank coming back, consider turning the thing sideways (broadside) to the oncoming stream. That gets you max stream blockage area for the weight. Especially for voluminous hydrogen tanks, your mass / blockage area might get down into that range without any aerosurfaces at all.

One would have to seriously question whether it could take the pressure loads, though. Especially as it decelerates through Mach 1 just about 20,000 feet altitude, while still hot, and weakened from that heat. That’s where Skylab and Shuttle Columbia’s cabin both broke up. Tough design problem.

Upper stages will likely require some sort of fixed or deployable aerosurface to hit ballistic coefficients (wing loadings) that low. That is substantial added inert weight, which is why I keep saying upper stage inert fractions under 10-15% are total nonsense in reusable designs. No one is yet really listening.

First stages are far easier, as Mach 10-or-less entry speeds are far less challenging, both heat- and force-wise. Under about Mach 3, you can even heat-sink your way through it with plastics, if the deceleration is about 4 gees or more. Steady state would require steel or titanium, but re-entry is not steady state.

On another note, I’m not at all sure the achievable Isp with liquid methane is very much higher than kerosenes. Both are hydrocarbons at crudely 2:1 hydrogen:carbon. It’s just that methane is inherently far cleaner of contaminants than kerosene, for far fewer practical injector-plugging troubles, and it doesn’t coke-up flow passages so easily upon overheating. The cryogenic nature of it can be used to absorb and dispose of (re-use, actually) waste heat, too.

There is very little difference among RP-1, Jet-A or A1 (same as JP-5), JP-10, JP-8, and K-1 camp fuel / lantern / heater kerosenes, except the filtering for cleanliness. Of those, the two commercial aircraft jet fuels are the cleanest, and they’re still noticeably dirty. Because of that, I am fast becoming a liquid methane fan. But be careful, the mods to a rocket engine to burn liquid methane instead of kerosene are not trivial; just ask XCOR, they’re the experts in LM-LOX.

BTW, Jet B (same as JP-4) is just kerosene cut with essentially a gasoline, to thin it down and lower its freezepoint.

GW

Terraformer · 2011-12-27 15:50:38

Surely somekind of deployable, inflatable wing system can be used to lower the wing loading sufficiently to make a reusable SSTO easier? I'm thinking of a telescopic system which rolls out a suitable fabric.

GW Johnson · 2011-12-28 10:57:14

Oddball ideas for reusable / recoverable upper stages, or pieces of them

None of this is developed: we are merely at the idea generation stage. All concepts needs evaluation before any selection takes place. Classic “brainstorm” process.
Fact: lower wing loading / ballistic coefficient reduces skin temperatures during re-entry to about 2000 F (1094 C) if refractory protection is used. This makes wider choices of materials survivable.

Idea: inflatable extended aerosurface. Possibilities: reusable or sacrificial. Might not take the form of wings per se, but just a shield between the stage and the oncoming re-entry air stream, most likely deployed from the front end, so that bags plus stage protects the engines at the rear. Would require active attitude control throughout re-entry. Any such system is an inert weight penalty against payload.

Sacrificial inflatable: multilayered polymer bags, with outer layers the sacrificial ablative that is eroded away during re-entry. Not at all sure how to thermally isolate the layers from each other. Typical polymeric material ablation decomposition (pyrolysis) is around 600 F (316 C) material internal temperature. All polymeric materials are thermally destroyed as structural materials at 200-300 F (94-149 C) internal material temperatures. It is rather likely the typical Mach 1 / 20,000 foot airloads peak would rip these structures away if not jettisoned by then. In any event, ocean splashdown forces probably would rip them away. But, it would be nice to retain the inflated bags as floats on the sea surface, or as impact attenuators for landing on the land.

Reusable inflatable: multilayer bag, inner layer polymer inflatable, outer layer refractory ceramic fiber cloth. Not at all sure how to thermally isolate the layers, since the refractory is so much hotter than the polymer can withstand, and the refractory is not a gas-tight structure so it cannot be inflated. How to deflate and stow for re-use is also a big unknown and a huge technical risk, as compared to the sacrificial inflatable. This re-stow would most likely have to be done during descent before the (somewhat ill-defined) max airload point at Mach 1 / 20,000 feet.

Idea: refractory or ablative material applied to tankage lateral surface, stage re-enters broadside to oncoming stream, to reduce ballistic coefficient to inert weight divided by lateral flow blockage area. Might require active attitude control throughout re-entry, and would definitely require engines to be protected by retaining an interstage skirt ring as a shield (a weight penalty against payload). Simple spin stabilization is a possibility for attitude control.

Broadside with ablative: could be layer of cork, could be layer of a hard char-forming rubber, such as DC-93-104. Might even be “intumescent paint”. The rubber would require retention ribbons to retain the char layer once charred through. Probably not suitable for aluminum tanks, well-demonstrated heat protection scheme for steel ramjet combustor cases. Not sure about the paint, the cork would have to be thick enough not to char through. For any of these, a serious inert weight penalty against payload is incurred, because this is installing a re-entry heat shield all over the lateral surface of the stage. Plus, an interstage skirt ring must also be retained as a shield to protect the engines. Rolling the stage rapidly for stabilization might also help distribute the heat loads onto all the lateral surface, lowering the effecting char rates.

Broadside with refractory: could be tiles or blankets of low-density ceramic. If tiles, suggest ceramic fiber-reinforced composite to avoid the fragility experienced with shuttle tiles. Either way, a serious inert weight penalty against payload is incurred, because this is installing a re-entry heat shield all over the lateral surface of the stage. Plus, an interstage skirt ring must also be retained as a shield to protect the engines. The thickness and weight of the required shield might be somewhat reduced by spinning the stage for stabilization during re-entry, thus spreading the heat load evenly all around the stage. These kinds of materials will be very susceptible to impact force damage at sea or on land, and to internal porosity contamination by sea water or dirt.

Other ideas??? Such as recovering just the engines, not the tankage? Or recovering engines (dense and heavy) separately from the tankage (low density, lightweight, usually rather fragile)? Fragile tankage can be made stronger structurally by internal pressurization (such as early Atlas)!

The trade matrix for evaluation is going to be rather large and complicated, if the “brainstorm” process model is followed properly. We need a lot more ideas to evaluate, for one thing. It would probably take to real engineering analysis or test to fill some of the cells out in the trade matrix. Once filled out, some weighting factors get assigned to the various evaluation categories, and the trades can be evaluated. Assigning weight factors is not simple, either. But properly done, this process usually gives a good answer that can really be built.

Somebody take this on and run with it. I have to go back to work, and I have a book to write on the art and science of ramjets, before shuffling-off this mortal coil.

GW

Rune · 2011-12-28 17:53:26

Two (actually just one) quick cents on the subject:

As a useful comparison to trade against, take the classic full ablative heatshield on top of the stage. It may be much heavier for the same area, but the area is much, much smaller. An smallish additional inflatable skirt could put the rest of the rocket in it's aerodynamic shade and "keep it cool". IIRC, those are already tested at small scale, sub-orbital reentry speeds.

Actually, now that I write about it, make the full heatshield inflatable. No interface between solid and inflatable that way, so in accordance with the KISS principle. These may actually be up to three different options to include in the trade analysis (solid heatshield alone and some thermal protection on the rest of the rocket, solid heatshield + inflatable "skirt", full inflatable).

Rune. Awesome idea, I'm already waiting for that book. Go write it!

JoshNH4H · 2011-12-29 16:48:20

Sorry for the delay, I was up skiing in the mountains and had no internet connection. Without further ado:

GW- When you talk about wing loading, what exactly do you mean? Is that the force on the surface from the airstream on the wing, or the mass of craft per area of wing? I was calculating the latter, though the former sounds more useful if you can get it.

I did realize a mistake in my calculations, in that I obtained cross sectional area by multiplying the radius by the length, instead of the diameter by the length. Therefore, there would be 91.9 kg/m^2, which is much nicer than the number I got before. The relationship between "wing loading" (if I am indeed using the term correctly) and skin temperature is obviously far from linear, but that has to make a difference. Also keep in mind that the fact that the payload would not be involved in reentry mass could make this as much as half as much, and will decrease it at least a bit.

Something I've brought up at least a few times before when talking about atmospheric aerobraking, we should really consider the use of aerogels for atmospheric entry. They would seem to have just about everything that we could possibly want for a material to be used in heat shields: it's thermal conductivity is nearly zero, or as close as you can get with available materials. It's light, having a density only slightly higher than air. Just as importantly, take a look at what it's made of: Silicon Dioxide or Carbon. These are some of the highest-temperature materials known. I don't know about it's behavior at lower pressures, but given a wikipedia-style introduction, it seems pretty good. What does everyone think?

I am personally a huge fan of inflatables for reentry. I would think that if you're going to use them, I would say put them at the end and make it as big as you want. Ideally reusable but if you can get it really cheap disposable that's just as good.

Rune · 2011-12-30 04:58:26

JoshNH4H wrote:

GW- When you talk about wing loading, what exactly do you mean? Is that the force on the surface from the airstream on the wing, or the mass of craft per area of wing? I was calculating the latter, though the former sounds more useful if you can get it.

Wing loading is aerodynamic force per unit of area, or at least that's what I've always been told. If a plane is flying level, it roughly equals the weight (roughly because of drag), but when executing maneuvers, it can go up or down, depending on whether the plane is accelerating upwards or downwards. Very important design factor, by the way.

Rune. Skiing... I miss that! Sigh, I guess when I'm a rich engineer and can't find the time, I will have the money.

GW Johnson · 2011-12-30 12:09:24

I was using weight (mass) divided by wing planform (or flow blockage for broadside entry) area, which is very similar to ballistic coefficient. Load factor in aircraft design would be lift divided by weight. Load factor times wing loading would be lift divided by wing are, same as lift coefficient times dynamic pressure. Ballistic coefficient is what I was really trying to get at. If the craft has wings, wing loading is what they usually compare. If no wings, they usually do ballistic coefficient.

Aerogels might be a tad fragile, they are typically very insubstantial structures. Would need a surface layer to stop the flow right through it. Decades ago, I built a ramjet combustor liner out of a low-density silicate hobby potting compound from Cotronics in NY, reinforced by Nextel 312 fire curtain silicate cloth. I sealed the surface with a coat of Cotronics ceramic (silicate) adhesive cement. Because of the thermal gradient through the material, there was always uncracked cooler stuff supporting the stuff that cracked that was over the solid phase change temperature. Because of that, I could use it right to its meltpoint at 3200 F surface temperature. This was tough enough to withstand very violent pressure oscillations driving the engine into rich blowout instability. The temperature and the force levels are way beyond anything the fragile unreinforced shuttle tile ever endured.

GW

Hop · 2011-12-31 15:41:13

Rune wrote:

I know how to figure out hyperbolas since I was 17. Doing that wouldn't have answered louis' question, since he gave no specific departure point or date, and a hyperbola isn't a transfer orbit.

A Hohmann path is an elliptical orbit with regards to the sun.

However departing earth to enter this solar orbit, you are in an hyperbolic orbit with regard to the earth.

On arrival at Mars, you are in a hyperbolic orbit with regard to Mars until you do a deceleration to enter mars capture orbit.

Knowledge of hyperbolic orbits is a needed if you want to be be competent in orbital mechanics.

The answer you gave Louis remains very wrong. Until you show a little time and effort, I will not bother investing time and effort explaining why.

Hop · 2011-12-31 15:56:00

JoshNH4H wrote:

The blue arrow is the length of the Green arrow minus the Red arrow. The integral of this arrow with respect to time from launch until orbit is going to be equal to 2,370 m/s for a 300 km orbit. 2,370 m/s is 2.81 MJ/kg expressed as a velocity. If you separate the two different vertical ⌂V components in this manner, the methods you would have to use to calculate both become much clearer.

You seem to state this as a general rule. If so, a single counter example suffices.

Call the net vertical acceleration a(t). If a(t) is a constant it is quite easy to integrate. Call it a.

/
| a dt = at + c
/

Where c is constant of integration. This is typically initial velocity, Vo. At the beginning of launch, vertical velocity is zero so we can ignore the Vo

I'll set the constant a = 8 m/sec^2.

/296
| 8 m/sec^2 dt = 2.37 km/sec.
/0

Altitude reached is an integral of vertical velocity over time:
/
| a t dt = 1/2 a t^2
/

Over 296 seconds 1/2 a t^2 is 351 kilometers. Already your conjecture is proven false as a general rule.

But it gets worse. At an altitude of 351 kilometers it will have a vertical velocity of 2.37 km/s. This will take it to an altitude of about 700 kilometers.

Last edited by Hop (2011-12-31 16:04:10)

Hop · 2011-12-31 16:01:25

JoshNH4H wrote:

I don't recall even ine post of yours in this thread on reusable rockets, rather you were critiquing a model

Modeling ascent trajectories is relevant to a discussion of reusable rockets.

JoshNH4H wrote:

that was mentioned as support of a point that has since been mostly vindicated)

I was hoping someone would notice your erroneous model gives wrong results. But evidently I am the only one to plug some numbers into your integral. Please see post above. Your point hasn't been vindicated.

Last edited by Hop (2011-12-31 16:06:03)

GW Johnson · 2012-01-01 14:17:22

I personally never found in 30 years any analysis worth a plugged nickel between the extremes of the jigger-factored rocket equation, and full 2-D (or 3-D) computerized trajectory analysis.

GW

Rune · 2012-01-01 17:12:22

Hop wrote:

Until you show a little time and effort, I will not bother investing time and effort explaining why.

Which keeps on being fine by me. Extremely sterile argument.

Rune. Fighting is a collaborative effort.

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#76 2011-12-15 18:46:48

Re: Reusable Rockets to Orbit

#77 2011-12-16 11:16:02

Re: Reusable Rockets to Orbit

#78 2011-12-16 15:14:08

Re: Reusable Rockets to Orbit

#79 2011-12-16 17:26:12

Re: Reusable Rockets to Orbit

#80 2011-12-16 18:22:40

Re: Reusable Rockets to Orbit

#81 2011-12-16 18:30:09

Re: Reusable Rockets to Orbit

#82 2011-12-17 11:35:10

Re: Reusable Rockets to Orbit

#83 2011-12-17 16:03:29

Re: Reusable Rockets to Orbit

#84 2011-12-17 16:17:40

Re: Reusable Rockets to Orbit

#85 2011-12-18 10:15:34

Re: Reusable Rockets to Orbit

#86 2011-12-18 12:54:58

Re: Reusable Rockets to Orbit

#87 2011-12-24 12:35:59

Re: Reusable Rockets to Orbit

#88 2011-12-26 23:45:43

Re: Reusable Rockets to Orbit

#89 2011-12-27 14:55:00

Re: Reusable Rockets to Orbit

#90 2011-12-27 15:50:38

Re: Reusable Rockets to Orbit

#91 2011-12-28 10:57:14

Re: Reusable Rockets to Orbit

#92 2011-12-28 17:53:26

Re: Reusable Rockets to Orbit

#93 2011-12-29 16:48:20

Re: Reusable Rockets to Orbit

#94 2011-12-30 04:58:26

Re: Reusable Rockets to Orbit

#95 2011-12-30 12:09:24

Re: Reusable Rockets to Orbit

#96 2011-12-31 15:41:13

Re: Reusable Rockets to Orbit

#97 2011-12-31 15:56:00

Re: Reusable Rockets to Orbit

#98 2011-12-31 16:01:25

Re: Reusable Rockets to Orbit

#99 2012-01-01 14:17:22

Re: Reusable Rockets to Orbit

#100 2012-01-01 17:12:22

Re: Reusable Rockets to Orbit

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