Archive for the ‘Models’ Category

Or The Space Game, by ESA.

The Space Game Screenshot

Minimize delta vee by moving the planets around (this changes the probe's arrival time at the planet). This shows my best solution so far, with some playing one evening, about 13 km/s

This is a nice javascript webpage where a probe is shot from Earth to Jupiter with gravity assists at Venus (twice), Earth and Mars. You try to achieve the lowest propulsive delta vee. You decide when the spacecraft arrives at each encounter and the program basically calculates the rest. It’s quite a nifty little piece of Javascript, the future of web applications is like this. It works fine with Chrome on Linux at least. Probably IE will have problems but who uses that anyway?

I’m ranked at #39 at 12.74 km/s… Far behind the gurus who get below 10 km/s readings! There are apparently some prizes for the top three, but I think people are in it for the fun of it.

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Rand Simberg talks about impedance matching. So I’d like to make a post of my comment there (I’ve always wondered why this obvious alternative gets mentioned so little…)

What to do when you arrive at Mars or Earth with your solar electric propelled vessel?

So, the problem with most low fuel demand velocity change schemes is that they only give slow accelerations. Low fuel high velocity change means solar or nuclear electric propulsion and aerocapture mainly.

High delta vee aerobraking is hard to do in one pass – it gets dangerous because of atmospheric variability and potentially other reasons.

Simple: detach a small capsule with the humans that goes directly to the surface (with only days of life support) and leave the untended craft to do multi-pass aerobraking. Hitting van Allen belts a few more times or taking a long time doesn’t matter that much with no humans onboard.

You could also potentially ultimately leave the long distance craft at some Lagrange point instead of LEO. (Cue some clever and complex maneuvers to save fuel – maneuvers that take long.)

Something similar could also be done when a long distance stack is assembled in LEO: send the humans there only after it’s through the belts. They can go with a smallish capsule again. Potentially at some Lagrange point, or in space without any fixed reference, just along the way. It could be dangerous though if the capsule doesn’t have much life support.

Many of these things have potential delta vee penalties as well as timing inflexibilities, but they could have enough other benefits that they should be considered.

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RD-180 rocket engine flow diagram

RD-180 flow diagram

This is a bit different from the NK-33 done previously, but it’s still a full flow oxidizer rich staged combustion lox-kerosene engine.

It has no gears and no flexible shaft coupling between the pumps like the NK-33, making it a real one axis engine – except that it has separate booster pumps at the engine inlet. The fuel booster pump is powered by the fuel tapoff after one main pump stage and the oxidizer booster pump by the turbine exhaust. The starting is also different, but I omitted the starter hardware from the already complicated diagram, as it’s connected to many places – the main chamber, the gas generator and the first main fuel pump inlet. Also various valves, controllers and the tank heat exchanger are left out. And naturally I left out the other chamber and nozzle as well.

Both the RD-180 and the NK-33 have the same amount of pump stages – 3 for fuel entering the gas generator and 2 for fuel entering the main chamber and 2 for the oxidizer (all enters the gas generator).

Perhaps it can be thought, simplified, that the boost pumps are only hydraulically and not axis coupled to the main shaft system, and hence both can be better optimized to their environment (like lower rpm for the boost pumps) and hence the system can reach higher pressures than the NK-33, where the two oxidizer pump stages are on the same shaft. Or then it’s the later materials or more advanced pump design, after all the engines have some ten to twenty years between them.

Source for the drawing and explanation is this patent no. 6226980. Also, lpre.de has awesome pictures of the hardware, including the shaft with all the pump stages included. I assume it’s machined from one solid piece. Also pictures of the pipe stack injector / mixer and more diagrams of the engine operations. I don’t know much Russian (having finished half a course back somewhen), but if you know most of the cyrillic alphabet (helps if you know math as it’s very close to Greek), it’s practically quite easy to read as there are so many loan words – gasogenerator should not be a mystery to anyone. 🙂

The workhorse Soyuz RD-107 and RD-108 engines are completely different as they use a hydrogen peroxide gas generator design – very old-fashioned – but the RD-0124 used on the more modern Russian upper stages is the third interesting kerosene staged combustion engine that might become even more actual if Orbital are going to use it as a second stage engine on their Taurus II (currently they are moving on with solids). The fourth staged combustion engine is the RD-120 that’s bigger than RD-0124 and is used on the Zenit second stage. And then there’s the often overlooked forefather of staged combustion, Proton’s RD-253 / RD-275, that uses hypergolic propellants. The RD-0120 hydrogen engine of Buran / Energia is interesting as a comparison to the similar SSME. So there’s still plenty of study subjects in the Russian engine families.

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But is not a real RLV program. It’s just a narrow test for one technology. Hence I think naming it Reusable Booster System Pathfinder is misleading.


They overspecify the problem by requiring a glide landing. Why is it superior to powered landing? At the moment, there’s no clear reason to believe it is! Both need to be developed further to understand their advantages and drawbacks. To my knowledge, there have been only six liquid rocket VTVL prototype manufacturers so far: McDonnell Douglas, JAXA (who was the contractor?), Armadillo Aerospace, Blue Origin, Masten Space Systems and Unreasonable Rocket. Only a few of those have flown to higher than a few hundred meters. The design and operations space is mostly totally unexplored.

Nevermind the large number of other alternatives to boostback. Jon Goff had a recent “lecture series” about these.

I understand that this is just one program, but this should not gain the status of the reusables approach of the air force – stuff like that easily happens.

Master Design Fallacy

They also discard evolution and competition – instead just requiring a single masterfully designed prototype before something operational. Sure, this is much better than starting a multi-billion dollar program without a first lower cost prototype, but nevertheless, it sucks. Somebody brief them on newspace! Rand Simberg, Monte Davis, Jonathan Goff, Clark Lindsey, or one of the numerous people who get it. Or one of the prominent company leaders: John Carmack, Jeff Greason, David Masten.

An Ideal Program

Just specify some boost delta vee points and let companies demonstrate progress towards that. A popup tailflame lander would perhaps give more vertical velocity while some good glider or even a booster that has engines for cruising back could boost far down range to give lots of horizontal velocity. There ain’t a clear winner – there might not even be and multiple approaches would have their uses.


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Karoliina has some thoughts on plane design, looking at High Altitude Long Endurance (HALE) UAV:s as inspiration for high L/D craft, to ultimately cruise at fast speed with little power. I disagree somewhat, and I’m sketching out why, below.
Probably the drones, like sailplanes, want low sinkrate and high L/D is secondary, because they need to just stay aloft and not go anywhere.
Power needed is P = v*D (we assume). Since D = CD*v*v, P = v^3*CD.
Lift is L = CL*v*v so v = (L/CL)^(1/2). (Note this CL is different from the L = 0.5*rho*A*cl*v^2, so CL = 0.5*rho*A*cl. It’s more practical here.)
Power thus is P = v^3 * CD = L^3/2 * CD * CL^-3/2.
The lift equals mass, so the power needed is
  1. proportional to mass^1.5,
  2. proportional to the drag coefficient and
  3. inversely proportional to the lift coefficient^1.5.
This means the lift coefficient CL needs to be large for the craft to be able to loiter for a long time. So long wings and somewhat cambered profiles. A little drag doesn’t hurt as much as low lift so struts are a possibility.
Instead, for a piston cruiser, the L/D needs to be maximized for a certain minimum trip fuel consumption, not per time. Basically, you want to minimize delta_E = P*delta_t = P * delta_x/v so the cost function J = v^2 * CD = L * CD / CL which minimizes at maximum L/D. The CL term is less important compared to the loiterer. As a first guess this should optimize to a less cambered airfoil and smaller or shorter wings. And no struts.

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Altitude was 2222 m. Apparently the backup timer shot the drag chute out while the rocket was still ascending. The team said they have video and will upload it later, if asked nicely enough. 🙂
Meanwhile, some launch photos.
You can see the small roll control vanes in the forward fuselage.

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Robert Grumbine examines them in many of his recent posts. This might be good for engineers and physicists from other fields trying to get the basics.

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I just updated the blog title and again just watched the page and the blurb.

It’s when we start working together that the real healing takes place, … It’s when we start spilling our sweat, and not our blood.

It’s a quote of David Hume, my favorite philosopher. I haven’t read his books though. I was reading a Finnish translation of one but it seemed so tedious with the language that I couldn’t bother. So me favouring him is based on the works of others about him.

The quote reminded me of the conflicts that I’m witnessing. The subject line matter needs to be done. At the moment many parts of climate software seem to be science software – written by people in a hurry with little planning, and code that has seen different people adding bits and pieces here and there, making it a big mess. Fortran and supercomputers and all that. Well, most software is a mess. Twenty man years, said MT. That’s a small amount of money considering how much is at stake and even compared to the amount of huffing and puffing efforts around the subject. I am available.

What else needs healing and sweat spilling? Well, quite many things. Including stuff in my personal life.

There are lots of old (sometimes Fortran) code packages hanging around. Nuclear stuff, rocket trajectory calculations, rocket engine chemical/thermodynamics performance… You name it, anything a young man is interested in seems to depend on these archaic pieces of software. So there’s a lot of potential work here but it seems so big for just a lone person to do much on their own free time.

The blog title picture is just some hinge flapped NACA foils simulated with the vortex lattice method in QFLR5. That actually IS a free software project, mostly by Andre Deperrois and uses Mark Drela’s XFOIL for 2D calcs. In the picture, the front wing has NACA 4415 with 6 m span, 1 m chord, 25% chord 15 degree full span flap, and the tail is a NACA 0012 with 2 m span 0.5 m chord, 40% flap or elevator at -15 degrees. Flying at 5 degrees AoA (plus 4 deg to the front wing) and 18.9 m/s, lifting about 2000 N. Absolutely no guarantees about the results.

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Perhaps the biggest phenomenon from a western view has been the rise of China as a superpower.

Internet services and applications, terrorism and wars in the middle east, oil, global warming politics, are some of the big things as well.

What will 2010 see? Well, my bet is that energy will be a big part of it. Oil is limited and is getting more expensive, coal is not. But coal is bad in the global warming sense. The big coal powers USA, China, Germany, UK, Canada, Australia at least are probably just going to keep burning it and not care what it does to the rest of the world.

During the noughties, CO2 rose from about 365 to 385 ppm. If the decadal rate is constant at 20 ppm per decade, then 600 ppm, a doubling from 1950s levels will require 215 ppm more, or about 110 years. Of course, the decadal emissions rate is probably going to accelerate. Local climate change phenomena will come earlier than things like significant sea level rise but it’s harder to point out that greenhouse gases are responsible for them. A fascinating experiment, this atmosphere alteration.

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Someone was asking on ARocket about where to start with building a differentially throttled hovering vehicle. Lots of advice were given by various people. I’ll show some stuff I quickly sketched back in 2007 with Simulink. It’s such an easy to use and awesome software (especially compared to a recent short battling with LabView), that whipping up any control system or any process or system models are really quick jobs.

This is just some really trivial basics, it doesn’t take into account nearly enough things to produce a real hovering vehicle. I guess it’s just a way to show how things could be started.

So, here’s a pic of a simple one-dimensional rotational feedback system. Just tested some feedback coefficient values for the PD controller.

1) You can see the placeholder “guidance algorithm” output at the top left “scope” graph. This is the reference or target value of the angle where we want the vehicle to be. At the start it’s giving a desired angle of zero radians, then from 4 seconds onwards it suddenly wants 0.5 radians, then again zero after 6 seconds. This could be holding a tilt for a while for getting up some lateral velocity for a transverse move.

2)  Below that, you see Theta, the angle that the vehicle actually had during the simulation. It follows the desired angle quite nicely. Below Theta, there’s omega, the angular velocity.

3) The tilting is done by throttling the two thrusters. At top center and top right you can see the values of the throttles. Since this thing only concerns tilt and not stationary hovering, the throttles are at zero when the vehicle is at the right attitude (reference=Theta) and there’s no angular velocity. When the refence is moved, at 4 seconds, throttle 1 shoots up for a while and the vehicle starts tilting. At around 4.8 seconds the other thruster, throttle 2 shoots up to stop the rotation, since the vehicle is nearing the desired angle.

You can see from the block diagram how the error value, E = theta – reference is calculated. And also omega is used. From these the throttle values are calculated, simply by Throttle1 = E*Kp1 + omega*Kd1 and so on. By fiddling with the Kp and Kd values, called gains, one can tune the system. The values currently are just some I quickly tried back then.  This Simulink model actually has a bug, a sign error. The error signal’s difference calculation is backwards, hence Kp1 and Kd1 are negative. It should be the other way around.

You can tune the model. Basically, raising the proportional values makes the system faster (reach desired values quicker) but gives overshooting and can make the system oscillate unstably. Higher derivative gains remove the tendency to oscillate, but the system becomes more sensitive to noise (noise can after all have large derivatives). If the vehicle had problems of always staying some amount off from the final required attitude value, an error integrator could be added that would fine tune the vehicle a little (making it a PID controller). This is probably not needed here though – the guidance system could notice if the vehicle travels somewhere it doesn’t want it to go.

The MDL file for the above is available here.

This is just a very quick first brush analysis, there are much much more things to take into account. The other tilt axis, roll, the need  to actually stay airborne (altitude or vertical velocity feedback loop) that ties into the throttle values too. One could abstract this tilt in one axis to a single control block, and produce another similar block for altitude holding, then couple these blocks into a whole system of altitude and tilt holding (by mixing the throttle values). This should avoid clutter and enable one to isolate problems.

Also, one should add some noise to the sensed angle vs real angle as gyro noise seems to be a real issue for VTVL vehicles. One wouldn’t want to tune a PD controller’s values in a noiseless simulator and then find out it gets wildly out of control in the real world. Even when not simulating noise, one can be quite conservative with the tuning values, and that helps too. The throttles probably would be another source of errors as well, if one used ball valves like here. One could also use pulse width modulated solenoids (John Carmack is fond of those for quick work) and those should be modeled. Digital valves (for liquids) have also improved lately, and hydraulics uses are emerging.

I’ve only done real world PID stuff on lab experiments. But it’s still very cool to see it work. It can balance a ball on an unsteady position on a moving cart, which humans have trouble with using a joystick, and the math in the controller is not complex since linear approximations can be used for that problem.

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