Friday, 8 July 2016

A Constellation of Warships

So, you've designed a spaceship to fight your wars in space. It can travel between planets, perform multiple missions and is based on NASA reports and real, hard science. You've estimated your nation's military budget, and come out with a fleet capacity and a number of spaceships.
But then... your glorious collection of spaceships fly out in Napoleonic square formation. Or was it pre-WWI lines of battle? Maybe it's Star-Wars-esque clumps of capital ships with space fighters swarming around them. No, you need the ToughSF approach.

Wall of spaceships from Legend of Galactic Heroes 
Space is a strange place. You don't travel across a landscape, you throw yourself along trajectories. There are no pit-stops, no sinking, no up, down, left or right. In other words, this means that space warfare is fundamentally different from anything we've tried so far, be it underwater, surface, ground or aerial combat.

There are similarities to build upon, but the differences should not be ignored in favor of familiarity. 
From Leviathan
In this post, we'll look at how the peculiarities of space travel and the technological assumptions you've made will affect the designs of your warships and the formations they form in space.


A fleet can refer to any large collection of vehicles. Aircraft, ships, drones, even trucks...

However, each of those vehicles and their services have specific names that are much more interesting to use. Aircraft can form Wings, artillery becomes Batteries, tanks have clatters and gunships have hailstorms...

The RapidEye satellite constellation
Spacecraft have constellations. 

Mission and Enemies

Before a constellation is launched, before it is even put together, there must be a clear idea of the opponents it will face and the mission it will undertake.

Mission configuration can be a simple as hooking more boosters together
A constellation sent to deal with a suspicious spacecraft in Lunar orbit will be very different from one sent to intercept an enemy invasion en-route from another planet.

Missions affect a constellation's design and composition mainly through deltaV and acceleration requirements. Travelling to a destination in space requires a minimum deltaV equal to the Hohmann trajectory. For a time-sensitive task, a minimum acceleration might be required. 

This is important, as all spaceships in a constellation must have the same initial acceleration, so as to depart together.

The deltaV 'budget' each spaceship has is spent in three stages: departure, maneuvers and return.

The departure stage is the most restrictive, as it requires all spaceships in a constellation to have similar and acceleration in addition to expending similar amounts of deltaV. This leads to a certain uniformity in engine type and reactor output per ton.

The maneuvers stage is the complete opposite. Depending on the weapons system and the tactics employed, this can comprise the majority of the deltaV budget or only an afterthought for transitioning from a 'Go' to an 'Abort'. 
An abort here would be skipping the Mars Injection burn and heading for a fly-by.
The return stage is conditional. In some situations, it only takes a small maneuver to make a fly-by at interplanetary speeds across your target, swinging around for a return. Others require that you perform a capture burn into orbit around your target, requiring a deltaV similar to that of the departure stage to return after the mission is completed. If your fleet has been defeated but not destroyed, there is no reason to stick around...

A space station built into an asteroid. In space, it can be considered immobile.
The targets you expect to face can change the priorities of the constellation and the equipment or loadout required to handle them. A relatively immobile, long-ranged defense station can be taken out by a massed missile attack from outside its reach. A swarm of autonomous drones will instead require direct-energy weaponry such as lasers or particle beams. This matter is a complex one, with historical, economic and technological factors in play.

Specialization and classification

Regardless of the mission or the enemies, spaceships will be more effective when specialized for their role. 

An extremely large X-ray laser weapon that is the pinnacle of laser warfare
This reality is due to the tyranny of the rocket equation. A tank on the ground, if overloaded with equipment to face a variety of opponents, will move slower. A battleship, equipped with guns, torpedoes, AA defenses and a flight deck, will have a deeper draft. A spaceship, equipped with too many weapon types, will simply not reach its target.

In other words, the spaceship's equipment have to have maximal effectiveness per kilogram. Multiple weapons systems on the same spaceship trying to handle different situations and targets will always be less mass effective than a single system designed for one, specific role. This is almost always tied to range - being able to attack earlier and from further away gives you 'first strike capability' and/or the ability to attack without return fire. In space, this is complicated slightly by the fact that kinetic rounds and missiles can drift forever.

An example of this is tank designs after WWII. 

Swiss Pz87 with a 140mm gun
In tank versus tank combat, the necessity to completely penetrate an opponent's armor at maximal range reduced the number of main guns to one. Even today, tanks do not mount more than one single weapon system, unless defensive or after special accommodations. Naval warships, despite the massive amounts of weapons systems that can be supported, focus nearly exclusively on launching large numbers of missiles and assisting them on their way. 

The result of all this optimization is that future space warships will mount a single weapon occupying the entirety of their combat payload. 

Normally, over-specification is fatal in a dynamic combat environment. The difficulty lies in the fact that facing different situations requires different weapons. To solve this, we use the combined arms concept.

In space, this would translate to multiple spaceships, each optimized for a different weapons system, configured to cover each others' weaknesses so that they may exploit their specialization fully. 

A classification system is simple to derive from the roles each spaceship and the constraints of effectiveness per kilogram optimization.

A useful classification, but only if defense, weapons and propulsion can be traded off equally 
Offensive/defensive is the simplest division of roles. Offensive craft will likely be classified depending on the type of weapon they use and their preferred tactic. Missile launchers will therefore be sub-divided into arsenal ships (very long range launch of massed missiles, with zero to negative relative velocity), lancers (short range launch of missiles at extreme relative velocities), bombers (focus on stationary or ground targets) and so on. 

Defensive craft can be classified using the type of threat they neutralize, such as shield carriers (launch drones to intercept high velocity projectiles), laser interceptors (use lasers to shoot down missiles), sensor hunters (use large cryogenically-cooled sensors to find and destroy sensor platforms) and so on. 

A second line of classification is the mission, and by extension, deltaV budget. An Earth-Jupiter warship will be much more massive than an Earth-Moon warship, even if they are identical aside from the propellant tanks. A 7-day Mars Response Craft will have quite a different propulsion module and propellant loadout than a yearly Mars Patrol Cycler. 

Further lines of classification will use characteristics such as acceleration, crew endurance or level of AI autonomy.

In all cases, classification by mass and velocity are useless at best, misleading at worst. This is because a 100 ton long-range laser can be deadlier than a 1000 ton arsenal ship loaded with ammunition, and a warship travelling at 50km/s towards the Outer Planets is tactically slower than a warship changing orbits at 1km/s.   

Fleet arrangement

Battle of Eylau, 1807
Pike squares and trenches sound outdated today, but they were tactical responses to the state of warfare and weaponry at their time. They became ubiquitous due to their effectiveness, and it took major revolutions on the way wars were fought to force their abandon.

Similarly, fleets, or constellations, in space will have tactically advantageous formations that are created in response to the threats, known and unknown, that are to be face.

The first factor to affect a fleet formation is the environment. In space, the environment of a spaceship is not material, but is a landscape of vectors and trajectories. 

A depiction of space-time curvature
During a transit between planets, the influence of gravity is negligible. It can be abstracted away into assuming that maneuvers will result in straight line trajectories for days ahead. This can be called 'flat' or 'deep space'. On short timescales, the ability to maneuver along all three axis is required. However, this is not the case on longer timescales. 

In a setting where spaceships are deltaV limited, travel is likely to be done along Hohmann trajectories. Depending on how restrictive the deltaV budget is, the approach will have to be performed along narrower and narrower corridors. Movement outside of the corridor has to compensated by acceleration in the opposite direction that becomes more and more expensive as you approach your destination. 

Accelerating along the path of travel has the least effect on your trajectory. Normal acceleration has a greater effect, and radial acceleration has the most influence on where and when you'll encounter your destination and potential targets. 

The result is that fleets will form walls, with main engines pointed in the direction of travel, and weaker thrusters pointed perpendicular directions. Weapons will face forward, competing with the thickest armor. It is pointless to have side armor, as long-range attacks will not have significant lateral velocity without incredible deltaV and propellant mass penalties. High velocity lateral attacks will therefore occur at short range, when an enemy and shoot at a significant angle without much deviation from the Hohmann corridor required to do so. 

On the contrary, settings will very lenient deltaV budgets can take perpendicular or even retrograde paths to their targets. Enemies can conversely attack from any angle. This means that fleet formations will ideally be spherical, but in practice teardrop-shaped, as attacks from the 'rear' take longer to approach combat ranges than attacks from the 'front'. 

In orbit around a planet, space is 'curved' or 'shallow'. There is a minimal altitude, under which spaceships will be burned by the atmosphere or collide will surface elevations. There is a maximal orbit velocity, beyond which a spacecraft must quickly burn in a retrograde position lest it fly out into interplanetary space. Moons, orbital installations, captured asteroids and even the planet itself form a physical landscape to hide behind. These restrictions are of little importance to spacecraft that accelerate at milli- or centi-gee rates, but a Heinlein-esque torchship with mulit-gee acceleration will feel trapped and claustrophobic. 

In low orbit, small differences in orbital altitude equal large relative velocities. Fleets will have to stay very close to each other and perform constant station-keeping if they wish to form a cohesive group. Alternatively, if the planetary body is small enough for the number of ships in the fleet, a constellation can be formed with the planetary body in the center, with spaceships supported by the preceding and following units along the orbit. 

In high orbits, space is much flatter, and warships start resembling their deep space brethren more closely. 

Despite other inaccuracies, at least they are pointing away from the planet being defended.
Combat between spaceships in low and high orbits is quite asymmetrical. Lower orbits have much shorter orbital periods, meaning they spend the majority of their time outside the reach of their opponents and behind the planet. Higher orbits are on the other hand exposed constantly. This is important for laser-dominant warfare.

However, lower orbit spaceships must fight gravity to shoot projectiles into higher orbits. Due to the distances involved, higher orbit spaceships will have a long time to evade or intercept incoming threats too. This means that they are better protected in missile-dominant warfare.

There are also some slight advantages to each position that influence tactics but do not have influence over the fleet's formation. For example, high orbit spaceships' positions change slowly, and they cannot exploit aerobraking for sudden changes in trajectory. This means that their position is predictable enough for low orbit spaceships to fire from behind the planet and 'bend' their shots onto their target's position, without ever being seen firing. Another example is laser traverse rate. High orbit spaceships only have to fire at targets within a narrow cone, meaning that their optics don't have to move as much and become more accurate...

The second, much more important factor to influence fleet arrangement is the technologies being used as a result of the author's assumptions. We will discuss this vast subject in the next part of this post. 


  1. There are a number of errors in this post.
    First, you apear to treat a fleet as an equivalent of a wing, battery, etc. This is not the case, and not just because you are dealing with different sized components. most importantly, the components of fleets very seldom travel in formation. A fleet is nothing more than a body of assets that are assigned to the same regional command, and include not only the naval vessels, but also any craft, vehicles, and personnel. Fleets tend to be semi-permanent allocations, with major components very rarely being swapped out. Even personnel are very rarely exchanged during the term of their tour.

    This brings us to the next major error. Formations such as batteries, wings, tank battalions, infantry battalions, and naval battlegroups and task forces are quite fluid entities. The expectation that all the units within will depart together, or even depart from the same location, is not valid. For example, a carrier battle group is defined by the requirements to protect its carrier(s). There might be one, two, or even three carriers assigned to the battle group, depending upon the existing strategic mission of that group. Other vessels and assets routinely come and go, being detached or attached to and from other formations, again depending upon current strategic or tactical requirements. Task forces are even more ethereal. These tend to respond to the tactical situation, rather than the strategic environment. Often, such task forces qre comprised of vessels and assets detached from a number of other formations.
    It is not the departure that counts, but the rendezvous. There is no requirement for vessels to travel together, unless they are part of a convoy. The requirement is that the different elements can rendezvous when and where required. Even this is not necessarily going to be at the same place. Many elements of task forces and battlegroups are spread fairly widely apart, never actually being able to see one another. The factor that denotes they are part of the same formatiƓ is not so mich proximity as the fact that they operate in unison with each other, tightly coordinating their actions.
    Even those elements travelling in convoy are not constrained to matched velocities. Naval vessels, and other formations, frequently have very different capabilities. Proximaty is only as close as necessary for the elements to be able to respond to each others' needs, within their function. Tactically, it is the responsibility of the elements with superior capabilities in a given dimension to restrict themselves to function in coordination with less capable elements. Faster vessels will reduce acceleration to match the slower vessels. Heavily armed vessels will create a wall shielding the lesser armed vessels. Vessels with greater fuel capacity and range will often transfer fuel/propellant to other vessels that have lesser capacities.

    1. I will discuss the advantages of travelling in very close formation in Part II and Part III.

  2. This brings us to the third error. Even for formations travelling in close proximity, there no constraint requiring the elements to have the same engine types, fuel/propellant capacities, and/or sizes. In fact, having a well balanced variety of capabilities pretty much ensures that the formations WON'T have similar drives, etc. A larger vessel will require a much more powerful drive than smaller vessels, in order to maintain the same acceleration. And such drives are likely to be 'gas guzzlers'. Medium craft might have fairly powerful engines, but these can be more efficient because they don't need anywhere the same actual thrust. Still, they are likely to carry much more propellant than they actually need, just in case they need to make an emergency burn. Small vessels and craft can be very efficient, because they have limited mass. OTOH, these will have limited propellant supply, but the medium and larg vessels will provide sufficient refueling from their reserve stores.
    Smaller vessels and craft will have a more limited range of mission responsibilities. Larger vessels will be able to support much more flexibility. More than anything else, it is the size which will determine the drive requirements, etc; as well as the performance capabilities.

    Finally, for the moment, the capabilities of specific vessels and craft will be decided long before launch... but not those of a given fleet, let alone a given formation. The constitution of a formation will be determined according to the strategic and tactical requirements, and the assets available to meet those requirements. Again, such formations tend to be 'ad hoc', depending upon what is available within a given time frame... And these resources will be drawn from wherever they currently happen to be.

    1. I'm pretty sure that engine type will be uniform across all vessels of a fleet, at least when performing a mission. Having an entirely different engine is more likely to be tied with having to complete a different mission.

      For example, an Earth-Mars fleet might all be equipped with open-cycle gas-core nuclear engines engineered for maximal performance and thrust, but a small group of stealthy spaceships loaded with kinetics for a first strike might instead use nuclear-electric engines.

      Another factor I didn't mention is busses - essentially, bare-bones propulsion stages where the 'payload' is other spaceships. They can accept huge mass-ratios and large-fragile engines to perform the departure burn, as they never see combat. They can then kill their velocity and return for refuelling on relative fumes in the tank.

    2. You appear not to be taking into consideration vessels that perform different roles within a single mission. There will likely be carrier type vessels that exist to transport and service smaller craft, which will require large, multi-unit gaseous-core nuclear thermal propulsion for high acceleration tasks (lesser powered, but more efficient, ion engines would suffice for routine manoeuvres). A number of other slightly less heavy vessels will require single-unit nuclear thermal engines that could be solid, liquid, or gaseous core, depending upon the size of the vessels and the acceleration requirements. Smaller vessels might be able to keep up with the larger just from using VASIMR or ion engines (technically, a VASIMR is NOT considered an ion engine, but an electrothermal engine), or might use chemical engines for short high acceleration burns. The smaller vessels and craft that use chemical engines will, in turn, receive resupply from the larger vessels. This mirrors current naval operations, and the existing precedence of different vessels within a group having very different engines and capabilities.

  3. You tend to undervalue the importance of velocity and mass. These are far more important in classification than you might think, and other aspects less so... although these terms are somewhat over simplified.
    Your most important factors are going to be: acceleration, determined by differential mass and drive thrust; delta-v range, determined by differential mass, propellant reserve, and specific impulse; and load, determined by maximal mass for a given minimal target acceleration. These three factors are going to determine all other possible integral capabilities, which will determine the possible mission configurations.
    Defence vs offence actually isn't very useful, as any weapons system can be employed in both capacities, depending upon the strategic and/or tactical situation. A missile frigate armed with SAMs could be employed to 'soften' aerial defenses in preparation for an assault, or it could defend a carrier or other asset from an incoming aerial strike force.
    Likewise, theatres of operation might not be useful either. The same vessel that can conduct an Earth-Jupiter mission could very easily conduct extended Earth-moon tours of duty. Similarly, a small vessel built for limited Earth-moon operations could be part of an Earth-Jupiter convey, receiving frequent replenishment from a larger vessel, either one dedicated to support functions, or one that has plenty of reserves.
    Finally, unless you are engaged in a protracted war, it is unlikely that future vessels and craft are going to be dedicated to military functions. Such vessels and craft are expensive resources. Future navies are going to employ them in a wide variety of tasks in order to justify their existence. Even today, there is a trend toward modular systems that are designed for 'plug n play' operations. VLT systems are designed to support a number of different missile systems, with the exact balance depending upon the existing strategic environment.

    1. I agree with most of what you say, but I tend to see spaceships as composed of hardware and wetware.

      Hardware is engines, armor, weapons, crew cabins, ect... equipment that is hard to remove and replace even in a modular design.

      Wetware is mission-flexible equipment that is very easily to add or remove in blocks. It mainly includes unarmored propellant tanks.

      They way I see it, 'mass' should refer to dry mass, or the mass of hardware, of the spaceship. If we go by absolute mass and add wetware into the classification, then the same spaceship will slide up and down categories over the course of the same flight.

      This is further complicated by the fact that velocity, even if it refers to the average transit velocity, is very misleading. A warship must maintain deltaV reserves for combat, and can choose to make a transit between planets at wildly different velocities depending on the amount of wetware it has chosen to take along, and other factors.

      For these reasons, I believe it is best to leave mass and velocity at the door when classifying spaceships, and concentrate instead of hardware-related performance, such as acceleration and Isp.

      As for defense vs offense, I believe the distinction exists. A weapon designed to shoot down incoming projectiles is very different from that designed to hit spaceships, and the overlap in capabilities is a desperate, inefficient margin that should be ignored.

      Theatre of operation is not a very good class, which is why I didn't mention it. I said mission, which indicates a deltaV requirement. There is a strict minimum, that is the Hohmann trajectory, that is required of a spaceship to accomplish an interplanetary mission. This is because what matters is mass-ratio, and not size. A 'small spaceship' could make an Earth-Jupiter trip more easily than a huge one by virtue of having a larger proportion of its mass dedicated to propellant. The propellant choice (liquid hydrogen, ice, molten sodium...) and the density it has also skews spaceship size in a way to make it a non-factor.

    2. I agree with with your hardware and wetware designations, although the wetware will actually tend more toward sensor packages, weapons packages (missile loads, projectile loads, laser platforms, etc).
      You are correct that current mass is essentially meaningless. For some considerations, delta-mass (total wet mass minus structural mass) will be the important feature; but this will be mission-balanced into consumables mass (total wet mass minus combined payload mass and dry mass) vs payload mass (total wet mass minus combined consumables mass and dry mass).

      Rated delta-v is more important than actual velocity. Range, manoeuverability, and speed are pretty meaningless, but the delta-v capability of a specific mission will be very important. This will determine how far out a vessel will be able to operate, how many orbital transfers can be performed for a given distance, and/or how long the vessel will be able to operate in a given theatre.

      Acceleration will be rather important... or, rather, thrust performance, which will determine the available range of acceleration for a given total or current mass. Isp effects efficiency of an engine, but that has relatively little relevance on mission performance, per se. Instead, it just determines how often replenishment will be required.

      As for defence vs offence, take a look at existing designations. It is rare that you find a "defence" designation anywhere in the military. Instead, virtually all assets are designated as either a kind of offence or support role.

      We might be considering size from different points of view. A small ship has a very limited range of mass ratio, because a certain fixed mass must be set aside for essential components (such as the reactor and crew). Large vessels have much more flexibility as to how much of the non-structural mass can be set aside for propellantm and how much can be set aside for load.

  4. Regarding high and low orbits: it is not quite so easy to simply dip into the atmosphere to change your velocity. It actually takes considerably more delta-v to change orbit at lower altitudes than it does to change orbit at higher altitudes. To get an idea, it takes 9 km/s to attain LEO at 250 km altitude; only 2.5 km/s to cover the next 35 OOO km from there to geosynchronous orbit; and then only 680 m/s to cover the next 200 000+ km to get to the moon. Altitude is a significant advantage. You can't just fire blind from lower altitudes, as you suggest.

    1. Hi, sorry for being off-topic, do you plan to post something on Google group? I would be really happy if there is somebody to discuss some stuff there...

    2. I strongly suggest playing Kerbal Space Program with the Real Solar System mod to get a feel for how spaceships handle in various orbits. An insignificant 100m/s retroburn in low orbit will plunge the periapsis deep into the atmosphere, where a winged spacecraft can change inclination with little expenditure of propellant.

      We have been sending satellites into higher altitudes 'blind', from the other side of the planet, for decades now. It is not hard.

    3. The issue with the blind firing is not that the weapon can not get there, but that your assumption that the target will still be there is invalid. Vessels in higher orbit can actually make much larger orbital changes for a given delta v.

    4. Mr Anderson: I don't know if you actually meant to address me, but I routinely visit the rec.arts.sf. science pages you mention.

    5. Yes, at about 250 - 300 km altitude, 100 m/s will be sufficient for a craft to deorbit (a large vessel probably would not survive the entry stresses); however, the burn would be followed by a half-hour coast, and another 15 - 30 minutes of ionisation, during which it will be unable to see the heat-seeking hypervelocity missiles coming in for the kill. If the craft were to survive, it would be effectively out of the fight, not having enough energy for the 5 - 7 km/s delta-v required for even LEO recovery... the only limited hope to stay in the fight would be if it were equipped with high performance anti-sat missiles. Alternatively, the craft or vessel might achieve perhaps an extra couple hundred meters altitude. Meanwhile, a for the same 100 m/s, a vessel at geosynch will have a nice 15 - 20 km window of vertical manoeuverability.

    6. If a spacecraft only intends to dip into the upper atmosphere, it won't deal with much ionization, and since it isn't punching through the lower layers to slow down much, it doesn't have a minimum structural integrity required. It can tailor its periapsis within the atmosphere to the drag and thermal forces it can handle.

      Maybe it dips into a slightly higher altitude, to compensate for drag lowering its orbital velocity and lowering the periapsis further in a feedback loop, or it goes for the lowest it can handle, and stops itself from going further using a combination of lift and thrust.

      The timescales involved must be lengthened compared to your estimates. Relatively flat space, in 'high orbit', is an altitude of 35000km+ on Earth. A missile that cancels its orbital velocity AND burns radially inwards to a velocity of 10km/s still takes up to an hour to reach lower orbits. For a deltaV of 13km/s, a chemical-fuel missile will have a small warhead too.

      The atmosphere is also very useful, as the periapsis you choose gives you a huge variety of options. You could make an emergency radial-in burn to dive into the atmosphere, and accept a sustainable level of damage to shift your trajectory. If it is an armored warship built to withstand hypervelocity and laser damage, then the crewed core will likely survive re-entry. The critical point would be if you went too deep or stayed too long in the atmosphere, that your engines gets damaged or your propellant tanks (huge, voluminous, likely unarmored) burst. Not a problem if you're defending your home planet, but quite a risk around a gas giant.

    7. If a craft intends to make use of aerodynamic control surfaces for manoeuvering, then it will have to go sufficiently deep that friction will come into play. But, okay, we'll say this is not deep enough for ionisation... a REALLY questionable assumption, but I will look up more info for a working scenario.

      You have a point about the timescales. OTOH, I was getting a little sloppy with my language... I did not mean that the missile had to penetrate at hypervelocity, rather, I meant that the delta-v is equivalent to the launch of a hypervelocity missile, which could be E/M launched. Interestingly, it takes relatively little energy to cancel out orbital velocity at geosynch (just over 3 km/s), meaning that an object will begin to fall under normal gravitational acceleration (for the altitude, which at geosynch is around 7 to 8 m/s^2, if I remember correctly). If you also include a downward component (actual vector of acceleration will be downward aft), high altitude de-orbit can be performed in minutes. In fact, an existing DARPA coilgun test design (for a heavy shell) could launch a lightweight projectile at anywhere from 4000+ km/s (10 kg missile/projectile) to 40 000+ km/s (1 kg) without the need for any propellant (assuming vacuum launch conditions)... or just enough propellant to guide the shell... offering impact in seconds, rather than minutes.

      Heavy armour does not necessrily mean strong structure. More often than not, the armour is actually a strain on the structure. For example, the CVN ENTERPRISE was unable to support the stress of running its engines at full power (just over 40 knots), which is why modern CVNs have only 2 reactors, rather than Enterprise's 8 reactors.

    8. i think I might have made a calculation error in my last post. If I made the mistake I think I did, then the performance of the DARPA coilgun would actually allow only for the square root of my estimated delta-v performances. This means 200+ km/s for the 1 kg projectile, taking about 3 min for the inercept. OTOH, this performance can easily be improved by simply adding coils (the DARPA project used 45 coils... I will need to check the figures for the size of each coil, but if I recall correctly the combined length was the equivalent to a WWII 16" gun. Also, the DARPA project was from about 10 years ago.