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.

Saturday, February 28, 2015

Clive Cussler - Two Thumbs Up

I was lamenting to a friend that science fiction is ignoring robotic advances and the near term possibilities they create. He replied "You must read Clive Cussler. I wouldn't call him a science fiction writer but he uses ROVs a lot. DARPA, the military and mining entities show up in most of his stories. I know you will like the characters from NUMA."

I took his advice and am now 3 books into the adventures of Dirk Pitt and friends. Not high literature by any means. Just entertaining, satisfying adventure yarns. And Cussler does his homework. The printed words in his books are the tip of a large iceberg. It is obvious many hours of research lie beneath the surface of each story. Cussler's interests are eclectic. He likes to study engineering and technology. Also biology, oceanography, chemistry, geology, archeology, art, history, culture, food, religion, etc., etc. Each book I've learned new stuff from many different fields.

Why am I so fired up about ROVs, AUVs, etc? It is my belief advancing robotics will be the game changer that opens the door to space, the final frontier. Cussler's stories are more relevant to space exploration than most current science fiction.

Already remotely operated robots are doing work in places too dangerous or hard to reach for human workers. This technology is being advanced by many players: DARPA, NOAA, British Petroleum, Rio Tinto, the military and others.

It is interesting that Google bought up the best performers in a recent DARPA robotics competition. Google has also invested in Planetary Resources and SpaceX as well as funded the Google Lunar X-Prize. Dot com billionaires opening the door to space could be a rich vein for story tellers.

On my wish list: Cussler taking a look at the void that lies between us and our neighbors in the solar system. Asteroids and planets are islands and continents in an ocean that extends past all horizons.

Thursday, January 29, 2015

Will I be banned from Nasa Space Flight Forum?

The largest space forum I know of is There are a lot of knowledgeable people who participate including a number of professional aerospace engineers.

I enjoy this forum but in my opinion there is a bias for NASA sponsored HLV.

For example, the forum has subsections devoted to manned missions to Mars, the Moon and Near Earth Asteroids. There are a number of ways such missions could be accomplished. But evidently Chris Bergin feels SLS is the only option:

Notice all the HSF (Human Space Flight) missions come under the HLV/SLS/Orion/Constellation heading.

I mentioned to Chris Bergin that there may be other routes. For example an architecture based on propellent depots might get us to the moon. Chris retorted that some of the ULA depot guys participate in NSF and they don't bad mouth SLS. Well, one of ULA's parent companies is Boeing. Umm, Chris, maybe there's a reason ULA employees would be hesitant to criticize SLS.

I posted a cartoon to NSF:

Chris found my use of the "pork" offensive. He also didn't like didn't like my portrayal of Senator Shelby.

There are a few things Apollo, Ares and SLS have in common:
1) They're very large rockets
2) They're completely expendable.

Since they're big, that means big expense. Since they're not reusable, that big expense will be incurred each and every trip.

If every mission is going to cost a few billion, we are not going to colonize the Moon, Near Earth Asteroids or Mars. Settlement would take a long, sustained effort and this sort of expense just isn't sustainable.

If Shelby et al are trying to sell SLS as a way to open a new frontier, they are committing fraud.

So what is the goal of NASA's human space flight program? The occasional flag & footprints publicity stunt doesn't justify the expense. If NASA's human space flight program is all about jobs in Florida, Texas and Alabama, it should be axed.

I make no apologies for my cartoon.

Thursday, July 10, 2014

Space topics from Dr. Plata

Doug Plata recently suggested some possible space exploration topics. All of them are very interesting.

Dr. Plata has good ideas and invests a great deal of time and effort looking at them. He's involved in two excellent websites: and .

July and August is a slow period for the Ajo Copper News, the weekly newspaper my sister and I publish. Most people with money and good sense leave Ajo, Arizona for the summer months. Hopefully I will have time to examine some of Plata's topics in my blog over the next few months.

Here they are:

Partial vs full reusability
Falcon 9 has nine engines on the first stage and one engine on the second stage.  So, if only the first stage is reused, it would seem to me that 9/10 engines would be recovered.  That's got to be a huge reduction in launch cost right there, yes?  Just how much?  Certainly achieving even partial reusability would make SpaceX even more competitive that it already is.  If the Falcon Heavy were to be partially reusable, reusing the lateral boosters would mean only 18 out of 28 engines would be recovered unless the central core could be reused as well.

Propulsion service options
For a cis-lunar transportation system we most often think of fuel depots in LEO.  One problem with this is the need for fuel depots in multiple LEO planes with those depots being used only occasionally.  However, if propellant were coming from ice harvesting operations at the lunar poles, then conceivably an OTV could bring propellant into any LEO inclination just prior to a launch into that orbit from Earth.  However, in this scenario, do we even need LEO depots?  Why couldn't the OTV dock with the launched satellite and then use its own engines to boost the satellite to GTO or even GEO?  Do we need fuel depots or could propulsion service be enough?

Power options for lunar mining
Say you are wanting to do ice harvesting operations in a lunar polar permanently shadowed crater with the rim of such having a peak of eternal light (PEL).  Great, but there's still potentially kilometers of distance between the source of power and the ice harvesting operations site.  How to deal with that gap?  RTGs?  Laser beaming of power?  Drive a rover laying a cable down the side of the crater?  Hop the lander from the rim to the floor while draping a (superconducting) wire?  Or forget a solar panel farm at the PEL and crack the water at a fuel depot in orbit?  An interesting trade analysis.

OTVs tend to be painted as broad, turtle-shaped craft.  But how do you launch and assemble such a thing?  Can aerobraking be done about as easily with a cylindrical-shaped OTV?  How about heat flaps popping out giving more surface area and control?  Necessary?  If one skims high enough in the atmosphere does one even need a heatshield?  What about using a lifting body form?

Travel times further out into the solar system
So if we develop the ability to safely send humans to Deimos, how much longer would it take to send them to Vesta, Ceres, and a Moon of Jupiter?
Heavy Lift vs Single Stage vs Reusable vs Gun
Air launch
Partial vs Full reusability
Chemical versus liquid rockets

Propulsion service options
Power options for lunar mining

The orbital dynamics of a Phobos vs Deimos vs surface mission

Mass calculations of open-loop, vs closed chemical, vs ECLSS
How could an RP5 be provided?
How do the space radiation numbers compare between locations (i.e. LEO, free-space, lunar surface, Phobos, Mars?)
Animal studies
Partial gravity options

O'Neillian vs lunar colony - Where first?
Travel times further out into the solar system

Wednesday, July 2, 2014

Kerbal Space Program

Lately this blog has been getting some hits from the Kerbal Space Program forum.

This looks like a good game. It seems based on the patched conics approach to orbital mechanics. It's good to see a popular game teaching users concepts like Hohmann or bi-elliptic transfers, sphere of influence, etc.

The art is appealing. Descriptions are entertaining. I purchased a copy for $27.00. It might be a way to become acquainted with some folks who share my orbital mechanics hobby. Hope it's a good investment!

Using the Kerbal Wiki I whomped up a HohmannKSP Spreadsheet. A few people like my spreadsheets for our solar system. Hopefully I'll be making some useful spreadsheets for this game.

Usual disclaimers apply:

My spreadsheets assume circular, coplanar orbits. Some of the game orbits are inclined and eccentric.

I occasionally make mistakes -- data entry as well as arithmetic errors. I'd be grateful if users check my efforts.

Wednesday, June 25, 2014

Travel on Airless Worlds Part II

This is a continuation of Travel on Airless Worlds where I looked at suborbital hops.

The surface of airless worlds will be exposed to radiation so it's likely the inhabitants would live underground.

Moreover, it is not as hard to burrow. The deepest gold mine on earth goes down about 4 kilometers. The heat and immense pressure make it hard to dig deeper. In contrast, the entire volume of a small body can be reached.

Courtney Seligman shows how to compute the pressure of a body with uniform density. The bodies we look at don't have uniform density but we'll use his method as a first order approximation.

Central pressure of a spherical body with uniform density is 3 g2/(8 π G)

Where G is universal gravitation constant, g is body's surface gravity and R is body's radius.

At distance r from center, pressure is (1 - (r/R)^2) * central pressure.

What is the pressure 4 kilometers below earth's surface?
Earths's radius R is 6378000 meters. r is that number minus 4000 meters. g is about 9.8 meters/sec^2.
Plugging those numbers into
(1 - (r/R)^2) * 3 g2/(8 π G)
gives 2120 atmospheres.

Besides pressure, heat also discourages us from burrowing deeper. So it might be possible to dig deeper on cooler worlds but for now we'll use 2120 atmospheres as the limit beyond which we can't dig.

3/(8 π G) * g * R2 gives different central pressures for various worlds:

Ceres center is 1430 atmospheres, well below our 2120 atmosphere limit. And Ceres is a cooler world than earth. We would be able to tunnel clear through the largest asteroid in the main belt. Since smaller asteroids would have smaller central pressure, we would be able to tunnel through the centers of every asteroid in the main belt.

Imagine a mohole going from a body's north pole to south pole:

The diagram above breaks the acceleration vector into vertical and horizontal components. The mohole payload has the same vertical acceleration components as an object in a circular orbit with orbital radius R, R being body radius.

Somone jumping into this mohole could travel to the opposite pole for zero energy. Trip time would be the orbital period: 2 π sqrt(R3/μ).

Other chords besides a diameter could be burrowed. I like to imagine 12 subway stations corresponding to the vertices of an icosahedron:

The red subway lines to nearest neighbors would correspond to the 30 edges of an icosahedron .

Green subway lines to the next nearest neighbors would correspond to the 30 edges of a small stellated dodecahedron.

And there could be 6 diameter subway lines linking a station to stations to their antipodes.

The energy free travel time of all these lines would be the same as the diameter trip time:
2 π sqrt(R3/μ).

It would be possible have a faster trip time than 2 π sqrt(R3/μ). A train could be accelerated during the first half of the trip and decelerated the second half. During the second half, energy could be recovered using regenerative braking.

Most of small bodies in our solar system have internal pressures that don't prohibit access. But in some cases central pressure exceeds 2120 atmospheres. We'd be able to burrow only so deep. Here's my guesstimate of the maximum depth for various bodies:

Luna 40 kilometers
Mars 15 kilometers
Ganymede 77 kilometers
Callisto 97 kilometers
Europa 55 kilometers
Titania 318 kilometers
Oberon 61 kilometers
Pluto 200 kilometers
Haumea 82 kilometers
Eris 108 kilometers

Here is the spreadsheet I used to look at internal pressures.

The top four kilometers of earth's surface is only a tiny fraction of the accessible mass in our solar system.

Tuesday, June 17, 2014

Travel on airless worlds

When we get to other worlds how will we get from point A to B? There are no roads on Ceres. No rivers or oceans on the moon. No airports on Enceladus or even air for an airplane to glide on.

Until transportation infrastructure is built, suborbital hops seem the way to go. A suborbital hop is an ellipse with a focus at the body center. But with much of the ellipse below surface.

For a suborbital hop from A to B, how much velocity is needed? At what angle should we leave the body's surface? At what angle and velocity do we return?

Points A and B are two points in a Lambert Space Triangle. The triangle's third point C is the body's center.

Two of the sides are radii of a spherical body so the triangle is isosceles.

A point's distance from one focus plus distance to second focus is a constant, 2a. 2a is the ellipse's major axis. Since A and B are equidistant to the first focus, they're also equidistant to the second focus. Points A & B, the planet and ellipse are all symmetric about the ellipse's axis.

The payload returns to the body at the same angle and velocity it left.

There are a multitude of ellipses whose focus lies at the center and pass through points A and B. How do we find the ellipse that requires the least delta V?

Specific orbital energy is denoted ε.

ε = 1/2 v2μ/r. 

1/2 v2 is the specific kinetic energy from the body's motion. μ/r is the  specific potential energy that comes from  the object's distance from C, the body's center. For an elliptic orbit, | μ/r | is greater than 1/2 v2, that is the potential energy overwhelms the kinetic energy. If potential and kinetic energy exactly cancel, the orbit is parabolic and the payload's moving escape velocity.

So to minimize 1/2 v2 we'd want to maximize | ε |.

It so happens that

ε = - μ/(2 a).

To grow |μ/(2 a)| we shrink 2a. So we're going for the ellipse with the shortest possible major axis.

The foci of all these ellipses lie on the same line. Moving the focus up and down this line, it can be seen the ellipse having the shortest major axis has a focus lying at the center of the chord connecting A and B. That would be the red ellipse pictured above. 

The angle separating A and B is labeled θ. Recall the black length and red length sum to 2a

2a = r + r sin(θ/2).

a = r(1 + sin(θ/2))/2.

Now that we know a, we can find velocity with the vis-viva equation:

V = sqrt(μ(2/a - 1/r)).

At what angle should we fire the payload?

It's known a light beam sent from one focus would be reflected to the second focus with the angle of incidence equal to the angle of reflection:

Angle between position vector and velocity vector is (3π - θ)/4. A horizontal velocity vector has angle π/2 from the position vector. 
 (3π - θ)/4 -  π/2 = (3π - θ)/4 -  2π/4 =
 (π - θ)/4

 (π - θ)/4 is the flight path angle departing from point A. If A and B are separated by 180º (i.e. travel from north pole to south pole), flight path angle is 0º and the payload is fired horizontally. If A and B are separated by 90º (i. e. travel from the north pole to a location on the equator), flight path angle is (180º - 90º)/4 which is 22.5º

When A and B are very close, θ is close to 0. (180-0)/4 is 45º. When A and B are close the the payload would be fire at nearly 45º. With one focus near to the surface and the other at the body center, the ellipse would have an eccentricity of almost 1. The trajectory would look parabolic.

Here's a few possible suborbital hops on our moon:

Minimum energy ellipse from pole to pole is a circle. Launch velocity is about 1.7 km/s. It'd take the same amount of delta V for a soft landing at the destination. Trip time would be about 54 minutes

From the north pole to the equator would take a 1.53 km/s launch. Trip time would be about 27 minutes.

Period of a circular orbit (T) is 2 π * sqrt(r3/(Gm)) where m is mass of planet.

Mass can be expressed as ρ * volume where ρ is density.

π * sqrt(r3/Gm) = 2 π * sqrt(r3/(G * 4/3 *π * r3 * ρ).

The r3 cancels out and we're left with T = sqrt(π/(G * 4/3 * ρ).

Thus trip times for a given separation rely solely on density. Period scales with inverse square root of density.

I did a spreadsheet where the user can enter angular separation on various airless bodies in our solar system. Delta Vs vary widely depending on size of the bodies. But trip times between comparable angular separations are roughly the same. This is because most the bodies have roughly the same density. Denser bodies like Mercury will have shorter trip times while icey, low density bodies will have longer trip times.

I got some help on this from a Nasa Spaceflight thread. My thanks to AlanSE and Proponent.

After time we would establish infrastructure on bodies and burrow into their volume. With tunnels we could reach various destinations with very little energy. I look at this in Travel On Airless World Part II.