## Thursday, March 26, 2015

### Partial vs full reusability

This is a topic suggested by Doug Plata. What impact will partial reusability have on efforts to settle and exploit space?

Reusable Booster stages.

SpaceX is working on a reusable booster stage. This has potentially enormous savings.

Why is reusing a booster such a big deal? Some might think getting above the atmosphere is a minor challenge compared to achieving orbital velocity. Lets take a look at hows and whys of vertical ascent.

The flight path angle is the angle between horizontal and the velocity vector.

If earth were an airless world, horizontal launches would be optimal. In other words the flight path angle would be zero.

But earth has an atmosphere. To avoid a long trip through the atmosphere a flight angle closer to vertical is called for.

Taking off from the earth at 8 km/s, a nearly vertical flight path angle vs horizontal take off.

Low earth orbit velocity is about 8 km/s. If a spacecraft achieved this velocity at earth's surface with a zero flight path angle, nearly a quarter of it's orbit (about 10,000 kilometers) would be through earth's atmosphere.

Most meteorites burn up in the mesosphere about 70 km up. Air density at this altitude is less than a thousandth of sea level. Orbital velocity at sea level would subject the rocket to extreme temperatures.

Dynamic pressure is another quantity to consider. Dynamic pressure is often denoted with the letter q. The maximum dynamic pressure a spacecraft endure is referred to as max-Q. The max-Q of the space shuttle was about 33 kilo-pascals. A severe hurricane has a dynamic pressure of 3 kilo-pascals.

8 km/s at sea level would give a dynamic pressure of about 40,000 kilo-pascals.

Before making the major horizontal burn to achieve orbital velocity, we must get above the dense lower atmosphere. The shortest path through the atmosphere is a vertical ascent.

But a vertical ascent incurs gravity loss.

Earth's surface gravity is 9.8 meters/sec^2. Each 102 seconds spent in vertical ascent costs 1 km/s delta V. Gravity loss is a major expense associated with ascent.

To minimize ascent time, a high thrust to weight ratio (T/W) ratio is desirable. The more oomph a booster stage has, the less time gravity loss is incurred.

A booster stage with more rocket engines will have a higher thrust to weight ratio. The Falcon 9 booster has 9 Merlin engines as compared to the second stage which has only 1.

Since a booster has 9 engines and the upper stage 1, would reuse mean 90% savings?

The upper stage also needs avionics, a power source, propellent tanks etc.. So I'd be surprised if the upper state is 10% of the expense. My guess would be more like 1/6. Still a 5/6 savings would be substantial.

But even a 5/6 savings wouldn't be realized by re-use. Still unknown are refurbishment costs. Also unknown is how many times a booster can be re-used.

I give better than even odds SpaceX's reusable booster will cut launch costs by 50%.

Reusable Upper Stage

After the booster stage has lifted the spacecraft above the atmosphere, the upper stage provides the horizontal burn to achieve orbital velocity. This take about 8 km/s.

Tsiolkovsky's rocket equation and an 8 km/s delta V budget mandate the upper stage is about 90% propellent and 10% dry mass. The smaller dry mass fraction means more tenuous structure and less thermal protection. It is hard to see how an upper stage could endure the extreme conditions of an 8 km/s re-entry into earth's atmosphere.

I would bet against SpaceX achieving a reusable upper stage.

Reusable Capsule

A capsule doesn't need a huge delta V budget. Just enough to lower it's perigee so it passes through the upper atmosphere. With a delta V budget less than 1 km/s, a capsule can have robust structure as well as a substantial heat shield.

I give SpaceX better than even odds at achieving a reusable Dragon capsule.

What does re-use do to economies of scale?

An item can be much cheaper if many units are mass produced on an assembly line. With mass production, design and development is amortized to a marginal expense.

If the average rocket engine is re-used 10 times, we would need at least a ten fold market increase to maintain economies of scale.

Could re-use lower prices enough to boost the market ten fold or more? I am not sure this would happen. What's the market for launch vehicles? Communication sats, surveillance and weather sats, occasionally ferrying passengers to the I.S.S. It's not clear cutting launch costs by half or even two-thirds would explode this market.

Economies of Scale with Re-use

The are possible new markets such as space tourism or mining. I don't expect those markets to take off so as a launch costs millions.

But what if the entire package was re-usable? The upper stage as well as booster and capsule? Reducing the cost by another order of magnitude opens many new markets: orbital hotels, lunar and asteroid mining, bases on the moon and Mars, etc..

But for upper stage re-use we would need propellent sources other than from the bottom of earth's gravity well. We would need orbital infra-structure: ferries between the various orbits and regions in our earth moon neighborhood: LEO, GEO, EML1, EML2 and DRO.

Establishing this mining and transportation infra-structure could provide the initial market. Once infra-structure is established, development of space would proceed like a snow ball rolling down a hill.

In my opinion partial re-use isn't sufficient to get the ball rolling. But it's an important step toward achieving full re-use. What happens after full re-use? If we can cut expenses down to the point where propellent is the dominant cost, I'd expect the market to explode at an exponential rate.

Tony Mach said...

Very informative!

Just some tiny bits I wanted to add:

SpaceX's initial plans were for a reusable Falcon 9 upper stage (complete with heatshield on the top bulk head of the upper stage), but they dropped their plans last year if I am not mistaken.

I read something along the lines that a reuseable first stage adds a weight penalty only somewhat larger than the weight for landing gear, plus weight of fuel for retro burn and fuel for landing. With the upper stage we are in Rocket Equation territory as you note, so one does pay dearly for any additional landing gear, additional fuel for landing and so on.

Regarding the "capsule", the Dragon consists of the capsule itself, and a service module. The service module is expendable and burns up after each flight. Possibly some day in the more distant future the service module will be reusable (either through landing of its own, or through integration into the capsule itself), but my guess until then we will not see a fully reusable Falcon 9.

Unknown said...

Regarding ferries, a week or so ago in comments on a Selenian Boondocks post, I accidentally hijacked the thread with an idea for moving up and down a gravity well without expending propellant by having two satellites in opposite orbits (one retrograde) exchanging mass between them as they pass. If they both kick out a ball at, say, 200 m/sec rearward, then magnetically deflect the other satellite's ball back to it (at an extremely high closing velocity), they both get a kick to a higher or lower orbital velocity while retaining the mass that gave it to them. Then they meet up on the opposite side of the planet and do it again.

My original idea was to eject the ball at exactly twice their orbital velocity, so the other satellite just reaches out to pick it up, but the muzzle velocities were impractical from a kinetic energy standpoint.

If the second idea is feasible, staging to GEO and beyond wouldn't have any more mass penalty than LEO, and the same would apply to getting up and down the moon's gravity well.

In between, it would be difficult to use the technique because orbits get sketchy (Earth-moon interaction differences on two opposite traveling satellites) and the orbital periods get extremely long so the delta-V boosts become very infrequent.

And then I thought "I know who loves problems like that." ^_^

DougSpace said...

Excellent post. Thanks. There were more issues involved than I was aware of.

After achieving orbit, is there gravity loss when boosting beyond LEO? Is avoiding gravity loss the main reason for using solid strap-ons?

I imagine that there would be a modest modification of the flight path towards vertical for the F9 booster if it is going to fly back to the launch site. I have never understood why returning to the launch site is so much more cost-effective than simply not expanding the fuel to return to the launch site but rather have it land on a barge and then simply ship it back. The latter cannot be that expensive.

AlanSE said...

There's one question that I think is just begging to be a followup - if the 2nd stage reuse is so hard, why not make it a two-stage to orbit?

Of course you will lose some (in fact, a lot) of propellant budget due to the staging. Also, the idea isn't coherent unless the 2nd/final stage can be reused. So that somewhat forces us to a lifting body design. But I don't see the problem with this.

Obviously we can make something which will fit the mass ratios required. If the X-33 was remotely workable, this would be too. The form factor and other details might be a bit of an issue, that all goes into the detailed engineering. I'm just thinking in terms of the large theoretical picture. A lifting body doesn't experience reentry forces as strong as a capsule, and the heating loads would hypothetically be less, although there might still be problems with hot spots. If you can get relatively good lift (better than the Space Shuttle for sure), and if you can land horizontally, it seems like this might even work for suborbital passenger travel.

Hop David said...

Doug, it's hard to know what SpaceX has in mind, they seem to keep their cards close to their chest. That's one reason I've taken so long to write this. A lot of what I wrote is speculation.

Musk has said RTLS incurs a 30% penalty on payload and the barge landing a 15%.

I believe one motivation for RTLS is quick turn around time.

I suspect Musk will use both barge landings and RTLS when he starts re-using boosters. He will probably want to have a variety of options.

Chris said...

Are you assuming that the second stage provides deltaV=8 km/s? This is a bit much. As a rule of thumb, the total deltaV to LEO, including gravity losses and air drag, is 10 km/s. I was running once some calculations on what would be an optimal staging (i.e. giving greatest payload) of a two-stage rocket, including tankage and engine weight. The optimal staging depends on the Isp difference between the stages. If the stages have the same Isp, then the optimal solution is when each of the stages delivers half of the deltaV, i.e. 5 km/s. If the fist stage has lower Isp, then the stageing should occur somewhat earlier. This seems to make sense with reality, because rockets usually stage at Mach 10 (~3 km/s), so plus the 2 km/s for the gravity and air drag losses, it gives roughly 5 km/s deltaV of the first stage. The fist stage is also the most challenging one to design, because it needs high chamber pressure to get a reasonable Isp at sea level, it needs high thrust and high thrust density. By comparison, the second stage is a walk in the park. Vaccum helps get high Isp, high expansion nozzles are possible, because the entire rocket diameter is available for one single engine, the thrust required is not as high because the stage is lighter.

I was actually wondering, whether the second stage could be integrated with the capsule. The large volumes of tanks would give a lower ballistic coefficient, which should reduce the reentry heating. Naturally there are significant challenges - launch escape with a stage optimized for vacuum performance? Landing? Aerodynamic forces on take off?

Hop David said...

Chris, Do you know the vertical and horizontal components of that 3 km/s?

If that 3 km/s has a large horizontal component, that would also increase the boost back burn for RTLS. Barge landing also entails a boost back.

Because of the boost back expense, I'd expect the reusable booster launch profiles to be more vertical than the usual expendable launch.

Chris said...

David, counting that 1 km/s goes to gravity loss, 1 km/s goes to air drag in the dense layers of the atmosphere, then the 3 km/s is the horizontal component left. Note, that the is all a very rough approximation.

So yes, this makes boost-back to the launch site very difficult. It however makes sense for SpaceX. Why? Because:
1) They are building a space port in Texas.
2) They are building landing pads in Florida. After lunch in Texas, booster landing in Florida makes perfect sense.

At least, this what I would do if I were to decide.

Tony Mach said...

Just stumbled across Elon Musk's comments at the "MIT AeroAstro 1914-2014 Centennial Symposium" (October 24, 2014), thought you might be interested.
(These are Elon Musk's views, not necessary mine. With a three order of magnitude decrease in cost of launching payloads from Earth to Space, we might indeed not get an cost advantage from mining fuel on the Moon or on Asteroids – however, such a decrease in cost is not yet here.)

Propulsive Landing Penality
https://youtu.be/PULkWGHeIQQ?t=6m3s
Landing gear acts as flaps, cuts terminal velocity in half.

Reusble Second Stage
https://youtu.be/PULkWGHeIQQ?t=6m59s
Specific impulse of Falcon 9 not high enough – next generation SpaceX rocket (MCT?) will improve specific impulse with cooled methane/oxygen fuel.

Two Order of Magnitude Decrease in Costs
https://youtu.be/PULkWGHeIQQ?t=13m53s
10,000 fold reduction in cost desirable.

Moon?
https://youtu.be/PULkWGHeIQQ?t=16m19s
For Mars-trips no need to go to Moon – but if people want to go, why not.

Tony said...

I wrote:
"Regarding the "capsule", the Dragon consists of the capsule itself, and a service module."

Well, I was wrong. What I called the "service module" is actually called the "trunk". It is a roughly cylindrical but mainly hollow structure. Attached to the trunk are the solar panels (with radiators on the back). Besides attachment for the solar panels it mainly serves as a space for unpressurised cargo and as a adapter to the second stage.

It might contain some equipment (maybe e.g. batteries), but I doubt it is much. Most of the equipment (e.a. dragon's equivalent to the "orbital manoeuvre engines") is located within the capsule. So the dragon spacecraft in cargo configuration returns with pretty much of the equipment it is launched with – definitely no Apollo or Soyuz style "service module" that is lost.