Airship Sails Addendum

A recent comment gave me reason to read back over my post on using sails on an airship and realize I didn't include any pictures of how the vectors I was talking about were oriented.  In that post I was so much more concerned with finishing and organizing my own thoughts I didn't do a very good job of expressing what I was talking about at all.

This picture shows the two most important vectors when talking about either a triangular sail or a wing.  Blue here represents the prevailing wind, or possibly the current direction of motion for the vehicle.  Green represents the lift, or the direction that the sail causes the vehicle to move in.  Wings convert forward motion into an upward force, while sails convert wind into a forward force.
On a ship the collected forces cause a net motion as shown below:

Here the wind exerts a net pressure (in orange) on the hull which pushes the vehicle in that direction.  This force should be fairly weak, but on an airship can't be compensated for by the keel as on a waterborne sailing ship.  Between the lift and pressure forces a net force creates some velocity (in yellow) which in turn creates a drag force (in red) on the ship.  This is what I calculated in the previous post, merely to demonstrate that such a vehicle could indeed generate a meaningful velocity.

There is a concern in this image that I didn't raise in the previous post.  What happens when the breeze is coming from the fore, rather than the aft, of the ship?  So long as the sail can be angled properly and the wind is coming from at least a little behind, or even directly to the side, of the desired direction then this image is roughly accurate.  When it comes from ahead, though, that pressure force that normally would be compensated for by the keel becomes a serious problem:

Here the pressure and lift create a net velocity not ahead, but to the side.  Obviously a sufficiently well sized sail and a properly sleek ship can somewhat mitigate this issue, but never eliminate it.  By beating to windward, however, this problem is significantly reduced.  Doing so causes the pressure and drag forces to be almost in line, meaning velocity is reduced but the direction is controlled:

This is a pretty complex maneuver used in real sailing, one that I can't possibly do justice to here. In short, it involved keeping the desired momentum more or less opposite the direction of the prevailing wind.  The ship constantly moves back and forth about that vector, so the wind is always coming slightly to either side.  In this case so long as the forward component of Lift is greater than the backwards components of Drag and Pressure then the ship will continue moving forwards.  Since the sideways components of the two orientations are opposite each other they cancel out over time and the drift is minimal.  Unfortunately the effect of pressure here will make this a much less effective maneuver than it is for a ship at sea, but it ensures the ship can maintain forward velocity regardless of the direction of wind.

I haven't bothered here with the particulars of design or calculation, the majority of which was done in the first post.  While the new issues raised here would impact any real attempt to construct such a vehicle we've also seen that such issues could be overcome by a sufficiently dedicated designer.  There is a combination of hull and sail design that would make this work.  That is enough for now, unless we want to start really building one.

Kerbal Space Program

 Kerbal Space Program moved into full release early this year.  Although the makers, Squad, will continue with patching and minor improvements, they say the game includes all the features they hoped to include.  Which I think makes this a good time to finally give my opinion on the game.  If you haven't heard of it, Kerbal Space Program is an excellent game available at a quite reasonable price for download on their site or on Steam.  Some friends of mine downloaded the game a while back for free, I was busy at the time and didn't get it.  I feel very foolish for that now, and gladly spent the $20 to download it last year.
 The game is available for Windows, Linux, and Mac, which I am grateful for since it means I don't have to reboot into Windows and can just use my regular Linux partition to play the game when I have time, something in depressingly short supply.  However, the other week I had my wisdom teeth removed, which meant a few days with nothing to do but launch little green men into space.
 Of course I'm not a game reviewer, I'm a starship engineer.  And that's how I want to look at this game.  So first let's go over the basics of the game.  In Kerbal Space Program, or KSP for short, you take control of  the space program for a group of people called Kerbals.  Hence the title.   Kerbals are small green creatures with large heads, tremendous enthusiasm, and no sense of self-preservation.  They will happily fly whatever insane creations you design in your efforts to explore the solar system.

How Does Starfleet Track Personnel?

I recently started a new job, in a new city. So those lesson plans I spent all summer putting together saw only one semester of use.  Well, I hope my replacement finds them helpful. I've moved on to a federal internship.  Not often one goes up from instructor to intern.  But, in beginning this job, I've noticed a bizarre trend.  I spent almost two weeks filling out forms, online forms.  There are several different human resources programs; different systems for pay, retirement, health insurance, life insurance, and other benefits; at least four different systems for training; and none of these software packages or databases communicates with the others, or if it does it does so poorly.
It's been just a few weeks and already I cannot remember how many different systems I've been registered or filed in.  I was struck, reading the user manual for one of at least four different document tracking and storage systems in place, how utterly nonsensical all of this is.  Why have a system that is organized like this at all?  And since we're here to discuss science fiction from a practical, engineering standpoint, let's ask the obvious question: how would a better system work?  How would a system designed to utilize a computer system correctly and efficiently work?  And ultimately the question I've been asking myself every time I learn anything about the modern US military: how would Starfleet do it?
Usually the answer is the exact opposite of what's going on here.

Death Star Incident Investigation Report

Section One: Cause
 
The Death Star was lost with all hands (save two surviving TIE pilots whose reports are attached in Appendix 3) following a catastrophic failure of its primary power core.  Simulation reveals that reactor coolant ignited, causing a sudden loss of core containment.  The core exploded, sending molten debris, hot reactor plasma, and radiation throughout the Death Star structure.  This, in turn, ignited a number of other systems resulting in secondary explosions throughout the station.  Total failure of the Death Star took less than a second after the initial core breach.

Reactor coolant was ignited by a proton torpedo fired from a Rebel controlled X-wing class starfighter (see Appendix 4 for details on known Rebel vehicles, including the X-wing).  Rebel propaganda suggests the fighter was flown by Rebel pilot Cmdr. Luke Skywalker, though this cannot at this time be confirmed (see Appendix 5: Intercepted Rebel Reports).  The torpedo entered an auxiliary thermal exhaust port on the external structure.  When it exploded it ignited reactor coolant, causing a chain reaction that resulted in core failure and ultimate loss of the station.

Rebel fighters were able to penetrate the Death Star defenses due to an oversight in shield design.  The Death Star's defenses were designed to defend against large scale cruiser attacks, but were easily penetrated by small fighters.  Its point defense teams were unable to target the maneuverable fighters.  Attempts to intercept them with the Death Star's own TIE squadrons failed in part due to loss of maneuverability close to the Death Star structure (see Appendix 4 for a comparison of X-wing and TIE maneuverability close to large structures).


Section Two: Origin of the Flaw

It is natural at this point to wonder how such a disastrous flaw could exist on such a massive project.  In fact that statement has its own answer.  Investigation reveals that the flaw that destroyed the Death Star was a result of a breakdown in communication.

Construction of the various elements began well before design was completed on others.  This was considered necessary by Imperial oversight to complete the massive station in a reasonable amount of time.  As a result the primary weapon, the inappropriately named "Super-Laser," was not yet completed when the power design team had completed their task.

The super laser ultimately required far more power than originally anticipated.  To compensate a larger power reactor was purchased to meet the new needs.  The power contractor's report on the change was never submitted to the thermal design team, who completed design using the heat output of the original core.

Simulations revealed a serious over-heating issue in the core during the final checkout of the thermal control system.  To compensate the thermal design team added an auxiliary thermal control duct to the core.  A flash evaporator was added to remove excess heat from the core during peak power utilization, typically firing of the primary weapon.

Addition of the core and the new thermal vent was noted by the contractor oversight panel.  It did not, however, result in any change to the existing structural blueprints, which had been finished for some years.  The addition of the new vent was noted only during installation of the thermal control system into the already finished superstructure.

A technician installing the thermal control system noted that there was no opening for the new thermal exhaust duct.  He submitted a change request to structure engineering management, who observed no structural reason why a new hole could not be added.  As the project was already behind schedule and over budget contract management approved the request with no additional analysis.  The vent was drilled into the surface of the Death Star and the auxiliary duct installed.

At no point were the point defense or shield grid contractors informed of the changes.  It is not required by Imperial guidelines for contractors to communicate with each other and contract oversight saw no reason to share the work of different contractors.  The thermal control team was never informed that they duct might come under fire.  The power design team was never informed that the reactor coolant was potentially combustible.


Section Three: Institutional and Oversight Failures

The failures of analysis and communication observed in the preceding section are not the only breakdowns the investigation has discovered in the Death Star design.  A number of potential flaws, though less severe, were neglected or dismissed by leadership.

A spirit of invulnerability pervaded the entire Death Star project, up to its demise.   The potential for disaster was ignored because all involved considered failure impossible.  The original design for the Death Star was overly optimistic and changes to the design were simply accepted with little or no question.

Partially to blame is Imperial doctrine regarding capital ships.  Imperial doctrine relies on increasingly large cruisers for massive bombardment, overwhelming enemy ships and bases, and establishing superior presence.  Contrast with the Rebel hit-and-run fighter assault doctrine, Imperial fighters and bombers are used primarily in support roles.

As a result the Death Star defense teams had a "bigger is better" approach to design.  They did not consider small ships a threat because Imperial doctrine doesn't consider them a threat.  Their design never considered the idea that the Death Star's armor might have a weak point.  Minimal defense of the exhaust port was in place only because regulations required ray-shielding of all surface openings on any Imperial station or capital ship, not because the potential for failure was noted.

Over-confidence on the part of the contractors and project leaders led to dismissal of potential design flaws.  Pressure from Imperial leadership for completion of the project, which was behind schedule and over budget, also contributed.  Again those in power did not consider project failure a possibility, so they ignored requests for additional time and funding.  As a result additional tests and simulations were cancelled.


Section Four: Conclusions and Recommendations

A full list of technical design recommendations for the "Site B" Death Star is supplied in Appendix 7.  In short modified reactor design is called for.  This change should eliminate the need for coolant, making the core inaccessible to enemy forces once the superstructure is complete.  Tighter defense screens are also required.

More important is an institutional change.  Imperial leadership must be aware of the danger posed by small craft and understand the advantages of the Rebel fighter doctrine.  The bigger is better attitude has to be overcome, since Rebel forces will consistently deny Imperial forces the sort of head-on engagement those larger vehicles are built for.

Further the spirit of invulnerability must be dealt with.  The Death Star was lost largely because none involved in its design, construction, and operation believed it could be lost.  If "Site B" is to succeed where its predecessor failed the operators must understand that it isn't invincible.  The major concerns at the end of the Death Star's construction were schedule and budget, not survivability.  If safety is not made the first priority then the project is doomed to failure.

Habitability of Binary and Trinary Star Systems

For a story he's working on my father asked me what sunrise and sunset would look like on a planet with three suns.  The question seemed to warrant investigation.

Naturally we have to start with what, exactly, multiple star systems look like.  Consider the Alpha Centauri system:

Note two stars Alpha Centauri A and B in orbit around each other with a third star, Proxima Centauri orbiting the binary system.  Normally the three body problem has no closed form solution, it cannot by analytically solved but can only be investigated by simulation.  However this system can be approximated as a collection of two body problems.  One with the primary and secondary star orbiting each other about their center of mass, and another with the ternary star and the binary pair in orbit about each other.  In this case the first problem involves solving a two body problem with A and B, and the second involves another two body problem with the combined set of A and B and Proxima.
It can also be seen from the image above that both Alpha Centauri A and B can support planetary systems.  The question here is could a multiple star system support a life bearing planet?

First consider where the planet orbits the system.  In a binary system a planet could conceivably orbit either member, provided there is adequate separation between the two that it is allowed to form at all.  The planet could also, however, orbit the center of mass of the binary system.  Rather than orbiting either star it orbits both stars, with a focus at their center of mass and with a total mass equal to the sum of their masses.  Could such a planet support life?
Neglecting more complex analysis the rule of thumb for the center of a star's habitation zone in astronomical units is based on the luminosity, L, of the sun in terms of stellar luminosities:
 
Note that Earth is actually inside the center of the sun's habitability zone by 0.34AU.  The zone is large enough to also encompass Mars, which is too small to maintain a dense atmosphere and has no appreciable magnetic field to protect it from solar radiation.  It is thought that only stars of stellar class F, G, K, and M can support life.  Larger stars are too short-lived to allow life bearing planets to evolve.
For a planet orbiting both members of a binary system we would use their combined luminosity.  If the two stars are extremely close together then this is the only way they can support planets at all, tidal forces between them would destroy a body in orbit about one or the other.  In such a tightly orbiting system one or both stars may be larger than their Roche lobe.  This typically invisible line determines the range of dominance by one body in a two-body system.  Material inside a star's Roche lobe is bound to that star.  If the star's radius is larger than its Roche lobe then some stellar material is actually bound to its partner, forming an accretion disk abound the heavier body.  If both stars are larger than their Roche lobes then they begin to merge, stellar material moving freely from one body to the other.  Such a condition can lead to the two stars fully merging into one.  The boundary of the Roche lobe for one member, where a is the semimajor axis of the system and q is the ratio of their masses m1/m2:

What do we get from this?  For a planet to orbit two suns, and those two suns to visibly be such, they must orbit with a semimajor axis (a=a1+a2, the system semimajor axis equals the sum of the individual semimajor axes) greater than some value based on their masses and radii.  In turn the planet must be some distance from the pair, this distance substantially larger than the distance between the two stars.  Dividing the habitability distance by the separation of the two stars:

The constant portion and that depending on q, the mass ratio, approaches 87.5 as the ratio nears 0 and 233 as it nears infinity (for a mass ratio of one it gives 108).  We can simplify our criterion to one based only on the sum of luminosities and the radius of the larger star, in terms of solar luminosity and radius (the selection of 1 is arbitrary, it simply places the above criterion at somewhere between 87.5 and 233):

This isn't a difficult criterion to use nor is it that strict.  However these conditions, extremely tight stellar orbits, are less common than more distantly orbiting stars.
For a planet to orbit only one star it must be inside that star's Roche lobe, which must in turn extend beyond the star's own habitability zone.  Not only must the planet be within the habitability zone of its parent (the star which it orbits) but it must also not be exposed to unnecessarily harsh conditions from the partner star, nor should it suffer too severe changes during its revolution.  Excepting, again, the second Lagrange point, the orbit of the planet will put it between the two stars at one point in its orbit and facing them both at the opposite point.
Consider first the requirement, that of the orbit.  We'll take another look at the Roche lobe, last time we found the minimum separation based on stellar radius.  This time we'll find the limit of the star's reach from the separation.  Require that the Roche lobe extend beyond the habitation zone.  Using the same limits found above we have an equation dependent only on the binary system's semimajor axis and the parent star's luminosity.  The limit as q approaches zero is 0.3 and as it approaches infinity is 0.82.  For a mass ratio of 1 this term is 0.38.

This requirement is even easier than the above one to meet.  The left hand size is unlikely to exceed about 3 for a large F type star.  This requires at most a stellar separation of only 10 AU's.
Although this ensures the planet is bound to its parent star and at an appropriate range from it, it does not address the added problem of light from the companion star.  In this case the concern is the intensity of stellar radiation from the stars.  Intensity is simply the luminosity of the star divided by the surface area of a sphere at the radius we are considering from the center.  So the total intensity reaching the planet is the contribution from both stars.  When one side is facing both stars the intensity is:

(Note that when using astronomical units we can ignore the 4-pi terms, doing so will give us the intensity in terms of the average intensity of sunlight reaching earth)
At the opposite end of its orbit one side of the planet is facing either sun.  So there is a different, but not negligible, intensity hitting both the day and night sides of the planet

For life to evolve and prosper on this planet the intensity must be in a tolerable range during both seasons, without a severe shift between them.  This can easily happen for a very low L2 or high a.
If we treat the planet as a black body then we can still add the intensities, even when facing different sides of the planet.  Planets are not, of course, generally black bodies.  Earth's greenhouse layer prevents it from radiating heat at that rate.  However any system with heat input and output, even Venus which has an extremely thick greenhouse layer, achieves an equilibrium temperature.  Heat in should equal heat out for any system.  So the temperature in terms of intensity, emissivity (for earth about 0.64) and albedo (earth's 0.3):

The rate of heat input is, naturally, proportional to the intensity of incident light.  Simply multiply the value of I by heat reaching earth from the sun (S=1367 W/m2).  If the difference in intensity is small then the difference in temperature will be too.  We've already seen what the minimum possible allowable spacing is, it's the case where rough a=3r.  Using that and solving, with representative values for earth, for distance is astronomical units and luminosity in stellar luminosities provided the change in T is significantly smaller than T:

Of course it isn't necessarily that simple.  Not only have we neglected axial tilt, we've also forgotten that the greenhouse layer can suffocate a planet.  Using the example of Venus again, if surface temperature gets too high the greenhouse layer thickens due to evaporation, increasing heat retention and further increasing surface temperature.  For high surface temperatures the emissivity is a function of temperature.  If, however, these two temperatures are kept within an acceptable range then this won't become a problem.  And so another criteria, for any habitable planet really, becomes its emissivity, or the thickness of its greenhouse layer.
So now we have a planet in the appropriate butter zone.  It's just far enough away from the suns not to fry or be torn apart by tidal forces, close enough to get enough light and heat for life to form.  It doesn't experience too extreme a temperature difference between seasons or between night and day.  These are, naturally, not the only requirements, but other constraints are similar to those on planets orbiting a single star system.

A third star in the system can be approximated like the Alpha Centauri system shown above.  Primary and secondary companions orbit each other and this binary system is itself in orbit with a ternary companion.  This makes an ordinarily unsolvable three body problem into a solvable two body problem.  Doing so also greatly simplifies our question of the habitability of this system.  If the planet orbits the ternary member then we can simply reuse our previous analysis exactly, save that now the second star becomes the sum of the binary pair.  The solution for intensity, surface temperature, and temperature difference is unchanged.  Distances involved will be much greater, so much so that we can simplify somewhat:

But chances are that the separation, a, between the ternary and binary pair will be so great that the second term will be negligible.
This holds exactly if the planet orbits the binary pair, the only difference is which term is divided by r and which by a:

If the planet orbits one member of the binary pair the influence of the ternary is the same.  Distance between planet and ternary is great enough that the planet's location in its orbit does not seriously impact the intensity of light it receives.  So the temperature increases slightly, but the difference in temperature between seasons remains the same.

Finally we have one last concern.  So far we've assumed circular orbits for simplicity.  But binary orbits are not generally circular.  For a planet orbiting a safe distance away from a binary pair this makes no difference.  However if the planet is orbiting one star in a binary or trinary system then the difference in temperature due to eccentricity is likely to be much higher than the difference from facing.

The eccentricity dependent part of this equation is nearly linear in the 0 - 1 range.  eccentricity cannot actually equal 1 for a stable orbit, e=1 gives an escape trajectory.  At the largest value, e=1, this term is about 0.3.  Combine that with reasonable terrestrial albedo and emissivity values.  Given the luminosity of the the range of stars we're considering the fourth root of luminosity is in a range of about 0.5 to 1.5, most being very close to 1.  So the temperature difference is about:

Which gives us a range of allowable eccentricities and semi-major axes for the binary pair.


What we've found here is that life can indeed develop in a multiple star system provided the basic requirements are met.  For a planet revolving about a binary pair it requires only that the pair be closely orbiting and that the planet be an adequate distance from the pair.  If the planet orbits one member of a pair we add the requirement that the difference in temperature caused by presence or absence of the companion star not be extreme.  For a trinary system we can use the same kind of method, simply treating the binary as one body when it interacts with its ternary member.  Indeed one could have two binary systems interacting in this method the create a 4 star system, and so on to model even larger systems.

Steampunk Airship Alternate Propulsion - Sails

In a previous post I looked at, and rejected, the idea of steam powered airships.  Simply put steam engines are too heavy to practically lift, which is why the airplane and airship had to wait for more weight efficient diesel engines.  But why stop looking at the idea there?  After all steam power isn't the only means of locomotion used by 19th century sea going vessels, why should it be the only method used by airships of a society with similar technology?  Ships of that time, and today, used the wind to move, by sail.

Steampunk Airship Design

Given the time I've spent on a modern airship design it seems an appropriate moment to look at the commonly seen airships of steampunk.  Since the genre is largely governed by a what-might-have-been look at industrial revolution technology, particularly steam power, airships are a large factor.  The "Golden Age" of airships began in 1900 with the launch of Count von Zeppelin's LZ-1 and the beginning of the Zeppelin Airship Company.  His designs used diesel engines and aluminum for dope and structure, and neither was available in the mid 19th century.  It is reasonable to ask if 19th century practical airships would even be possible.  If so what would they look like?