Selenian Boondocks

While attending the Responsive Space Conference in Los Angeles, I had an opportunity along with many others to visit the SpaceX facility in Hawthorne on the evening of March 9th and I had a wonderful time.

We were given a brief tour of the facility by Brian Bjelde, who began by showing us a full-scale mockup of the Dragon capsule. We also saw assorted other hardware connected with Dragon.

Then we moved on to see work on a Merlin engine underway. Despite the fact it was the evening, there were quite a few people at work, building engines, writing code, running tests and so forth.

We moved on and saw a nine-engine cluster of Merlin engines, that if I’m not mistaken will be part of the second Falcon 9 launch vehicle. I’ve seen the Saturn V and Saturn 1B engine clusters up close, and I was amazed how “tight” the F9 engine cluster is. I’m a little worried about the gas generators all exhausting into the freestream rather than being ducted into the nozzles as they were on the F-1 and J-2 engines, but time will tell whether that is an issue for F9.

Also there were some very impressive friction-stir welding equipment that are used to manufacture the propellant tanks for the F9. I saw a circumferential friction-stir welder, and Brian explained that two people can make an F9 tank in 19 days. That is very impressive and part of how they keep costs down. I also saw milling machines used to mill isogrid patterns in the metal stock used for the tanks.

In the rear of the building I saw huge cube-looking structures covered by translucent deep-blue sheets of plastic. Brian explained that that was where they did welding on upper stage engines that use refractory metals (niobium) that must be welded in inert gas atmospheres. I also saw tanks of argon that I figured were used in the inert-gas welding.

SpaceX was kind enough to treat us to hors d’oeuvres afterward and we could mingle and talk about what we had seen. Next to the cafeteria area of the plant was the Falcon control room with huge screens and computer consoles. A video of Falcon launch highlights and F9 launch preparations was playing, and gave you a sense of the excitement that was building as the first Falcon 9 launch was approaching. In the cafeteria area were two statues, one of “Iron Man” and the other of a Cylon that sure gave you a sense that you were in the cool “alt.space” world rather than in a stodgy, cost-plus government contractor facility.

I looked around at the employees that would walk by. Almost all of them were younger than me (35) and I couldn’t help but contrast that with the demographics I experience at NASA, where I’m practically a baby compared to my co-workers, most of whom are in their 50s and 60s.

There was an excitement and buzz in the air at the SpaceX facility. People are designing, building, and testing rockets. They’re going to launch soon. And I think they’re going to succeed. Even if it doesn’t happen at first–I think they’re going to succeed.

guest blogger john hare

I had an interesting conversation with Jon last month about the problems with air launching rocket ships. The various flavors of air launch involve some form of altitude and velocity loss as the rocket ship drops away from the mother ship before it can light it’s engines. In most cases, it also requires wings and other aero surfaces to correct the flight path to the desired vertical. These aero surfaces are not only dead weight from Jon’s point of view, they also induce airframe stresses on the rocket ship that it really doesn’t need.

The most important things for air launch are altitude, attitude, and airspeed, in about that order of importance. A conventional air launch seems to compromise somewhat on all three. Another point Jon didn’t care for is that the rocket cannot light it’s engines until well clear of the mother ship. Ignition or other engine related failure could easily result in loss of vehicle instead of an abort and return to base to examine the problem.

In my opinion, which is not shared by many that I am aware of, the White Knight series are perhaps the best high altitude airplanes in the world by the best designer in the world, but isn’t the optimum mother ship for space craft. The space craft they carry suffer from all the problems mentioned above, with only some mitigation by launching from extreme altitude.

I believe that the best mother ship is one that works for the requirements of the rocket vehicle. The rocket should be able to light the engines and confirm a healthy burn before separation. The release attitude should be such that the rocket ship is vertical or nearly so and doesn’t need any aero surfaces or the loads they impose. And it needs to release from the highest altitude possible at the highest airspeed possible.

I suggest that conventional air launches have been done backwards. The rocket should be lit before separation, and separate from the top of the vehicle at both high subsonic speed, and high altitude. Most of this can be accomplished with a change in operational technique rather than building a brand new super duper mother ship.

The rocket ship is mounted centerline bottom of an aircraft. At 25,000 feet or so, the mother ship has reached maximum altitude at the loaded condition of full tanks and rocket ship payload. The rockets ignite and feed from tanks on board the mother ship as the two vehicles accelerate and begin to climb. By 30,000 to 40,000 feet, the vehicles begin to roll inverted as you would see in a Shuttle launch. At 50,000 feet, the pair is climbing at 70 degrees and high subsonic airspeed. Then the mother ship lights some RATO type rocket engines and the rocket ship throttles back so that they are accelerating at the same rate as they separate. The switch to internal fuel supply for the rocket ship is confirmed stable at separation. With both vehicles accelerating at the same rate, they fly apart in parallel formation so that neither exhaust impinges the other. The rocket ship rolls from a 70 degree climb to vertical while the mother ship rolls from a 70 degree climb to the horizontal.

When sufficiently clear, the rocket ship  throttles back up for the climb with full tanks and 250+ meters per second velocity at extreme (for aircraft) altitudes. The mother ship reaches horizontal at nearly ‘coffin corner’ altitude for a clean ship with low fuel and no load. Coffin corner is the term I believe applies to an altitude where the  aircraft can’t go faster for engine or airframe reasons, and can’t go slower without stalling and falling out of control with a strong possibility of no recovery.

I believe this method would impart considerably improved performance to a rocket ship compared to the conventional approach. It would not require the rocket ship to have aero surfaces.(VTVL friendly) It would allow abort to base in case of rocket engine problems. It would not require developing the best high altitude aircraft in the world.

“Program manager John Shannon said Tuesday it costs $200 million a month to keep the fleet flying.”

This is why President Bush and Sean O’Keefe knew that we would have to bring the shuttle program to an end in order to have any hope of going forward with NASA’s use of space. Michael Griffin knew it. President Obama and General Bolden know this too.

Source: Money key to more space shuttle flights

Continuing on this vein, an article today in The Space Review: “Costs of US piloted programs”

“each day spent onboard by an ISS crewmember costs about $7.5 million (compared to $5.5 million for Skylab.)”

From NASA administrator Charlie Bolden:

“I find great comfort in knowing that President Obama has seen fit to put his faith in us to develop a game-changing strategy in our four mission areas, and that he has given us a $6 billion plus up on our FY10 budget as a show of support and trust. I fully believe in the plan that this budget has allowed us to set out for NASA’s road ahead, and unlike many of our detractors, I do believe it will very likely allow us to reach exploration destinations sooner and more efficiently than we would have been able to while we were struggling to develop the Constellation Program.”

I completely agree with this statement.

I predict that regardless of the outcome of SpaceX’s inaugural Falcon 9 launch, nobody is going to change their opinion. If it’s successful, Ares-huggers will suddenly begin to understand the concept that a single successful flight doesn’t prove anything about a vehicle’s overall reliability (while most on the pro-commercial space guys will start sounding like NASA guys post Ares-IX).

If it fails, commercial space people will switch back to “it was only a test” mode while to Ares-huggers, it will prove, prove, prove that all commercial vehicles (including those with existing proven track records) are all death traps. After all, imagine the national security risk of flying our astronauts on private launch vehicles! I mean, if we’re going to turn LEO crew transportation over to the private sector, we might as well all start learning Chinese and reading the little Red Book, cause them Commies are going to come and sap and impurify our precious bodily fluids.

This is my last update to the payload fraction calculation, I promise.

When I was learning how to use mass-estimating relationships (MERs) at Georgia Tech, our focus was on reusable launch vehicles, and most of our MERs came from NASA Langley, where my professor had once worked. When it came to much of the reusability aspects of the spacecraft, the MER tended to depend on the entry or landing mass of the spacecraft rather than the gross mass or the propellant mass, as I have previously defined.

Systems like thermal protection, wings, aerosurfaces, and landing gear all tended to scale with entry or landing mass. So to capture these effects in order to help calculate performance of reusable vehicles, I introduce another non-dimensional term. I use the letter epsilon to describe the entry-mass-sensitive mass items divided by the entry mass. The difference between the entry mass and the dry mass depends mostly on whether or not the payload is intended to return with the spacecraft, so I include a jettison factor (f_jett) whose value is one if all the payload is jettisoned and zero if none of the payload is jettisoned before entry.

I employ the now-familiar substitution for propellant mass:

And simplify:

Which as you can see is the same as the previous expressions if epsilon is zero.

A simple way to understand this expression is to think about it in terms of one. One is the most payload fraction you could have–if all of your spacecraft is payload. But some fraction has to be propellant, according to the rocket equation. So you start out with your final mass fraction (FMF). From that point, which will always be less than one, you subtract lambda times the propellant mass fraction. Then you subtract your phi term, which depends mostly on your engines. Finally you subtract epsilon times your final mass fraction. If you have anything left over, you have a payload fraction. If you were going to jettison your payload before reentry, then the denominator gets a little smaller than one and your payload fraction improves a bit. But it can never improve a payload fraction that is less than zero.

If your payload fraction is less than zero, then you had better go change something to clean things up. You better use a better Isp to improve final mass fraction, or better tankage or propellants to improve lambda, or better engines to improve phi, or better TPS or wings or landing gear to improve epsilon. Because if the numerator of the payload fraction is less than zero, you’ve got no reason to build your rocket.

Continuing with our story from last time…

The next day, your boss pokes his head in your office and asks:

“How’s those forty trans-Mars injection stages going?”

He notices that you’re checking out scuba-dive sites in the Caribbean for your upcoming vacation with your feet up on the desk, and comes into the room with the blood rising to your face. In your defense, you blurt out that you’ve already done the analysis!

He, somewhat increduously, demands to see the results, so you show him the spreadsheet. He’s less than impressed.

“I thought you were going to design each stage! I need pictures and layouts of these things, with lists of mass and volumes and so forth…you’re showing me a little number. Furthermore, I’ve got the Ohio and Nevada congressional delegations breathing down my neck to send billions of dollars to Stan Borowski to develop an NTR that he promises will get us to Mars faster. You’ve got to show me more detail for this. And how do you even know that your equations are correct?”

Now on the defensive, you offer to try to quickly verify two of the comparison cases for your boss. He looks through your results and decides to pick a comparison point in the middle of the trade space: 4000 m/s delta-V and 0.5 initial thrust-to-weight. Your spreadsheet quickly predicts that the NTR stage will have a payload fraction of 0.3828 and that the chemical stage will have a payload fraction of 0.3955, with a ratio of the two of 1.033, but your boss wants to see proof that your equations are correct.

So how do you go about turning these expressions into masses and volume and graphics?

This time, it took considerably longer than ten minutes, but you showed that your equations match up with reality (at least to the resolution of your initial assumptions). You can see, physically, that the NTR stage is much larger than the chemical stage, even though both carry roughly the same payload. The NTR stage needs almost 6 engines to meet the T/W requirements, while the chemical stage only needs 4. The real difference between the two stages, from a mass perspective, is in the engine weight. You can see that the total engine weight on the chem stage is 1480 lb, while on the NTR stage it is 29,333 lb. This is a staggering difference, due almost entirely to the wretched thrust-to-weight ratio of the NTR engines. This could also lead to another problem. There will be every incentive to try to remove weight from the NTR engines, and with six engines in close proximity, it is almost certain that there will be a lot of neutronic leakage from one engine to another. This means that the engines won’t be able to be controlled individually, but will have to be controlled as a group. It may not be possible to shut one of them down in flight. It also means that they might have to be tested as a group which will drive costs up like crazy.

From the propellant side of the house, the NTR LH2 tank is much larger than the chem tanks, and the mass devoted to tankage on the chem side is 1554 kg, whereas the NTR tank is 4426 kg. Those big NTR LH2 tanks might cause you to hit the volume constraint on your launch vehicle before the mass constraint is reached.

Your boss is happy, for now. He’s got the numbers to show that for 4000 m/s and 0.5 T/W, the NTR stage only has a few more percent payload, and that’s not worth paying the billions to develop it.

But unfortunately for you, now he knows you can get this kind of preliminary analysis work done much faster, so he’s loaded you down with all kinds of new analyses. And that beach vacation is looking further and further away…

Now that I’ve gotten the math and derivations out of the way, let’s us the payload fraction expressions in a real-world example.


Let’s say you work for the chief technologist of NASA, and he’s thinking about sending humans to Mars. He’s considering whether or not to invest in a seemingly-promising new technology: nuclear thermal propulsion. He’s intrigued by the higher levels of specific impulse that you can achieve with nuclear thermal propulsion, nearly twice that of chemical, but he knows that it will cost billions to develop and test. He wants to know if the technology improves the payload enough to make it worth developing, so he asks you to do a study. He says:

“Assume that you have a nuclear thermal rocket engine with an Isp of 850 seconds and a chemical engine with an Isp of 460 sec. You have a heavy-lift launch vehicle that will put 80 metric tonnes into LEO. How much more payload will the nuclear thermal rocket get over the chemical rocket?”

You being a diligent engineer point out that you need a bit more data to do the analysis, so your boss tells you that you can make some more assumptions.

The NTR has a vacuum thrust of 15000 lbf and a weight of 5000 lbm with an Isp of 850 sec. It uses hydrogen with a density of 71 kg/m3 at a mixture ratio of zero. The chemical engine is based on an RL10 burning LH2 and LOX at a mixture ratio of 5.5 with an Isp of 460 sec. The RL10 has a vacuum thrust of 22,000 lbf and weighs 370 lbm. The LOX has a density of 1142 kg/m3.

For both vehicles, he tells you that you can assume that the thrust structure weighs 0.3% of the total vacuum thrust, and that the LH2 tank has a factor of 10 kg/m3 and the LOX tank is 14 kg/m3. The ullage in both tanks is 3%. You can “rubberize” the engines so that any particular thrust you need to get the stage thrust-to-weight can be calculated. Otherwise you’ll get weird effects from integer numbers of engines.

Since the delta-V to do a trans-Mars injection (TMI) burn from LEO varies from opportunity to opportunity, he wants you to run a sweep of DVs from 3800 m/s to 4400 m/s, incremented by 200 m/s. He’s also unsure of the initial thrust-to-weight that the injection stage should have in LEO, so he tells you to run a sweep from 0.2 to 1.0, incremented by 0.2. With four values of delta-V, five values of thrust-to-weight, and two different engine technologies for each case, he figures that you’re going to be pretty busy for the next few weeks designing forty different trans-Mars injection stages.

Little does he know that you’re a Selenian Boondocks reader, and that you think this would be a good chance to use the payload fraction derivation to simplify your workload substantially. So you reluctantly agree to take on this “huge” analysis effort, and with your head down trudge out of his office.

Meanwhile, you get to your office and call your wife and tell her not to worry, your beach vacation is still a go, and that you’ll be able to finish the analysis he wants by the afternoon.

Within about ten minutes, you’ve finished your analysis and have the results in front of you:

You are somewhat surprised. Although at higher levels of delta-V the NTR stage has more payload than the chemical stage, it is not nearly the improvement over chemical that you would have first expected by looking at the much higher value of Isp. And the NTR only has more payload fraction than the chemical stage at low values of initial thrust-to-weight. You know that the initial T/W can’t be too low, or else the stage will incur large gravity loss penalties in the form of higher DV. Using two separate perigee burns to do TMI might reduce this somewhat, but that will subject the crew to two extra passes through the Van Allen radiation belts, as well as bring a “hot” nuclear thermal core back within close proximity of the Earth’s atmosphere for the next perigee burn, and that might cause somebody some heartache.

You note that at initial T/Ws of around 0.6 and greater, the chemical stage actually has BETTER payload fraction than the NTR stage. There are two reasons for this–one is hydrogen and the other is engine thrust-to-weight. The hydrogen propellant of the NTR has a really low density, so you get very large tanks and a significantly greater tank penalty than the chemical case. But even worse is the wretched thrust-to-weight ratio of the NTR engine (3.0) versus the chemical engine (~60). With such a low thrust-to-weight, getting the required initial stage thrust-to-weight is very penalizing. So if the initial T/W is not kept low, then the NTR stage can’t beat the chemical stage for payload performance, and there’s really no reason to spend billions to develop it.

But all of this you keep to yourself for just now. Your boss expects you to be cranking the numbers for a few weeks, so you keep the door shut and let him keep thinking that.

(in case you’re curious, here’s the spreadsheet–took me about ten minutes to write)

In the last post, I attempted to calculate a basic expression for the propellant-mass-sensitive term (lambda) and in this one I will attempt to do the same thing for the gross-mass-sensitive term (phi). In so doing, I will hopefully be able to show how a number of key factors in the rocket design affect the payload fraction. We begin by reiterating the definition of the gross-mass-sensitive term:

Then I make the assumption that this term consists only of two things—the engines and the thrust structure. This assumption will have to be modified for different designs. For instance, if you have a vertically-launched rocket that is taking off from landing legs, like a moon lander, then those landing legs are gross-mass-dependent. Or if you have a winged horizontally-launched rocket on Earth, then the wings and landing gear are gross-mass-dependent. So alter this assumption according to your needs.

Then I commit a sin against the SI system of units by switching from a mass ratio to a weight ratio. This is done to get everything in terms of forces rather than masses. You’ll see why I did this in just a second.

Now I make the assumption that all of the engines on the stage are the same kind of engine, and assume that I can multiply the number of engines (n) by the individual weight of the engine (W_engine). I also assume that the thrust structure weight is proportional to the total thrust that the thrust structure will ever feel, which is the total vacuum thrust. This proportionality factor between the weight of the thrust structure and the vacuum thrust I call f_TSW.

Now, in an effort to get the vacuum thrust in terms of the engine weight, I’m going to replace vacuum thrust with the total number of the engines, multiplied by the individual engine weight, multiplied by the vacuum thrust-to-weight ratio of the engine. That should give me a substitute value for the total vacuum thrust.

Now I can group some terms and simplify things a bit.

I need the gross weight of the vehicle. What should that be? Well, let’s assume that the vehicle has to have some initial overall thrust-to-weight ratio. If it’s sitting on the surface of the Earth and it’s meant to launch, then that value had better be greater than one! Actually, it better be a bit more than that or the vehicle’s not going to accelerate. So I’m going to assume that the overall vehicle thrust-to-weight ratio at liftoff is something that we’re going to specify in the design, and that by knowing that value and the initial thrust (not the vacuum thrust) of all the engines, we can calculate the gross weight of the vehicle.

Now something really important happens. The number of engines (n) is sitting in both the numerator and the denominator and cancels out of the expression altogether. I can’t tell you how happy I was to find this result when I first tried this derivation! I had had this hunch that phi would depend on the number of engines, but it turns out that it didn’t. It only depended on the vehicle’s initial thrust-to-weight ratio and the initial and vacuum thrust-to-weight ratios of the engine. And the thrust structure factor of course. But that cancellation means that phi becomes something that can be calculated for each engine type rather than for the number of engines.

Three values of thrust-to-weight and the thrust structure factor give you phi. Isn’t that amazing? If you’re doing a calculation for a rocket stage that operates entirely in space, then the initial thrust-to-weight value for the engine IS the same as the vacuum value, and you only need two thrust-to-weight values.

If you assumed that your thrust structure factor was negligible, which often isn’t such a bad assumption, then the expression would just be:

This actually wouldn’t be a bad place to stop, assuming that you knew the initial and vacuum values of engine thrust-to-weight. But if you didn’t know initial engine thrust-to-weight you can calculate it, or thrust-to-weight at the desired altitude (which would determine the back pressure) by using this variation of the expression. I find this version especially useful when I’m trying to do air-launch calculations, because the ambient pressure is neither vacuum nor sea-level.

When you use the expression this way, you can “hit” the engine for pressure losses in the atmosphere. If you know the vacuum thrust, and the exit area, and assuming you can calculate the ambient pressure by knowing what altitude you are at, you can figure out the initial thrust-to-weight ratio and use the expression effectively.

Now as I mentioned earlier, if you’re designing a vehicle that has other gross-mass-sensitive terms, like landing gear or wings or landing struts or whatever, don’t forget to tack them onto the end of this expression so that their effect makes its way back into the payload fraction calculation.

Like with lambda, here’s some examples to get you started:

The upper group of engines are assumed to start at sea level, and the lower group of engines are assumed to operate entirely in vacuum.

In my last two posts I’ve been talking about calculating payload fraction of a rocket using the mass ratio from the rocket equation and some vehicle parameters that have been sensitive to propellant mass and gross mass. To use these parameters successfully, it would be helpful to have some idea what they should be for different designs. For instance, we all know that hydrocarbon fuels are more dense than hydrogen fuel, so how would that affect that parameter? To try to answer these questions better, I’ve taken the previously-defined lambda term and created a derivation of what its value ought to be in different circumstances.

Let’s assume that the propellant-sensitive mass consists of only two things—the fuel tank and the oxidizer tank. In the expressions I abbreviate fuel tank as FT and oxidizer tank as OT.

When I was at Georgia Tech, my professor gave us some mass-estimating relationships (MERs) for propellant tanks, but they were all based on volume. For instance, they would tell you to estimate the mass of a hydrogen tank as some number of kilograms per cubic meter of tank volume. So to use these mass-estimating relationships, I rewrite the expression in terms of a factor (f) for the fuel and oxidizer tanks and their volumes.

The volume of the fuel and oxidizer tanks will simply be the mass of the fuel or oxidizer they contain divided by the density of the fuel or oxidizer. To account for the role of ullage (extra volume) in the tank, we throw an ullage factor in the denominator, to make the tank have a little more volume than it would otherwise have if it was 100% full of fuel or oxidizer.

With expressions for fuel and oxidizer volume computed, we substitute these expressions back into the overall expression for lambda. The ullage term is collected and moved to the denominator.

Now the expression has fuel mass, oxidizer mass, and overall propellant mass terms in it. But we know that these terms aren’t actually independent. The fuel mass plus the oxidizer mass equals the propellant mass. And the oxidizer mass divided by the fuel mass gives us the mixture ratio (MXR). I use MXR in the expression because I already used MR for the mass ratio, and I want to limit confusion as much as possible.

Thanks to mixture ratio and the propellant summation, we can calculate fuel and oxidizer mass entirely in terms of propellant mass and mixture ratio.

Substituting these definitions for fuel mass and oxidizer mass back into the lambda expression, we get something that looks complicated but is on its way to being simplified.

With propellant mass showing up in the numerator and in the denominator, it cancels out nicely. The mixture ratio terms moves to the denominator, and we get a nice compact expression.

There’s some really nice aspects to this simple expression for lambda. Propellant mass has been completely removed from the equation, which means you don’t need to know how big or small your rocket is to calculate lambda. You need to know the mixture ratio (MXR), which is determined by whatever rocket engine you choose. Choosing the rocket engine also chooses the fuel and oxidizer, which lets you plug in their densities. Assuming you have an idea what ullage would be and what the factors for the fuel tank (f_FT) and oxidizer tank (f_OT) would be, you can calculate lambda pretty quickly.

To help get things started, here’s a table of tank factors based on both real and conceptual tank designs, from Langley Research Center. Remember to make sure that you’re using the same units for tank factor and propellant density (kg/m3 or lbm/ft3).

And here’s some different calculations I did based on a couple of different engines (including a nuclear thermal engine, which has no oxidizer at all and a mixture ratio of zero) showing the effects of propellant selection and mixture ratio on lambda.