The Wheels on the Spacecraft Go Round and Round

Spinning a ten kiloton spacecraft around is no easy feat. Even more impressive if you want to be able to turn on a dime. This article covers the issues of Attitude Control of spacecrafts.

A capital ship with four main engines gimbaled off to the side to provide torque.

On land, sea, or in air, rotation is easily done by pushing off the nearest medium, with anything from a tractor tread to an impeller to a rudder. In space, no such thing is possible, which means rotation can only be accomplished in one of two ways: by expelling mass via a rocket engine, or by storing rotational momentum internally. Incidentally, the second technique is only really viable in space due to the lack of any major medium, as friction would quickly degrade stored internal momentum.

The goal of these systems is to rotate enormous spacecrafts at reasonable or high speeds in combat, while being both cheap and non-massive.

The first technique is simple. Firing a thruster off center of your spacecraft will cause it to torque. Since rotation is the goal, and rotational acceleration is not, a second thruster must be fired to decelerate it at the end. And because such a thrust would send the center of mass off center, often two thrusters on opposite sides are used to start rotating, and two different opposing thrusters are fired to stop rotating.

A capital ship fires two vernier thrusters at opposite ends and directions to rotate. The rockets are water resistojets (hence the transparent plumes) and they tap into the main NTR propellant tanks.

These are called Vernier Thrusters, and see heavy use in space travel.

There are significant disadvantages to this method, however, chiefly that additional reaction mass is needed. Not only that, such thrusters usually can’t be Nuclear Thermal Rockets (NTRs), due to radiation concerns (recall that most crew modules are placed as far away from the main engine NTRs as possible). Cold gas thrusters don’t provide near enough thrust to be useful in combat, which means combustion rockets and resistojets are in.

Combustion rockets suffer from the issue that they require propellant(s) that are almost guaranteed to be different than NTR propellants, so additional propellant tanks must be added in, which takes up space and mass. This leaves resistojets as the prime method of providing torque to your spacecraft, since they can use the same propellant as your NTR.

Alternatively, instead of a system of multiple Vernier Thrusters spread out across your hull, simply putting a gimbal on your main thruster will do the trick instead. This allows your main engine to turn, producing off center thrust on your ship, rotating it. In this way, your main engines can serve the dual purpose of getting you places as well as orienting you in combat. This is one of the cheapest forms of thrust vectoring.

A few more complex thrust vectoring designs for achieving reverse thrust.

The primary disadvantage of it is that propellant is still expended when turning, however, no additional propellant tanks are needed as your main thrusters are doing the turning. For capital ships, the amount of delta-v spent turning is negligible, though for smaller crafts like missiles, the delta-v spent can raise a few eyebrows.

A more subtle disadvantage of gimbaled thrusters is that the size of the opening that the engines need to have can balloon significantly. This can yield much larger aft sections of the ship, and increase the targetable cross section of the spacecraft heavily.

Gimbaled thrust tends to be the cheapest and simplest solution to turning in space, and many capital ships and all drones and missiles in Children of a Dead Earth use them. Some capital ships opt for resistojet Vernier Thrusters, primarily for getting a smaller targetable cross section.

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A missile’s rocket nozzle is slightly gimbaled to the side, only a few degrees off center, generating tremendous torque. Screen distortion is from the camera being inside the rocket plume.

But suppose you don’t want to spend precious propellant turning? Then you need to invest in the second technique towards turning in space: exploiting Conservation of Angular Momentum.

Given a system without little or no external medium (such as space) and assuming you don’t want to expend propellant, the only way to rotate is by using conservation of angular momentum.

A quick example. Consider a pair of identical masses loosely attached to one another, floating in space. If one of the masses begins to spin in one direction, the other mass must spin in the opposite direction at an equal speed, otherwise it would violate Newton’s Laws of Motion.

This is the basic principle of operation for a Reaction Wheel, which is a flywheel with a motor attached. A flywheel is a mass with a high Moment of Inertia, or ability to resist rotational changes, along a single axis. When you spin a reaction wheel inside your ship using the motor, your spacecraft must spin in the opposite direction. Three reaction wheels must be used to get a full range of motion (one for each axis: pitch, yaw and roll). The Kepler Spacecraft uses reaction wheels.

A simple reaction wheel.

A Momentum Wheel is a reaction wheel which is constantly spinning at a very high speed. If a momentum wheel is spinning inside a spacecraft, simply braking it can cause a huge change in rotational momentum, causing a significant torque on your ship. Six momentum wheels are needed instead of three, two for each axis in opposite directions.

Momentum Wheels are often used for spin stabilization, as the huge amount of stored rotational energy will resist external torques. The Hubble Space Telescope uses Momentum Wheels.

Control Moment Gyroscope (CMG) is a single momentum wheel on a dual-axis gyroscope. By rotating the momentum wheel about the two gimbal axis, the angular momentum balance of the spacecraft can be altered at a whim. A single CMG can rotate a spacecraft along any axis by simply rotating the gyroscope to be in line with that axis. They are the most expensive and complex of the above systems, and are used on the ISS.

A Control Moment Gyroscope. The two axis of the gimbal allow the wheel to be oriented in any direction.

These systems promise the ability to rotate your spacecraft without expending propellant. Not only that, they require no exposed external systems, so they can’t be damaged unless the main bulkhead armor is penetrated. Sounds like a win-win, right?

Unfortunately, their effectiveness is very poor for combat operations. Modern CMGs are often used to very slowly change orientations over the course of minutes and hours. I originally had never intended to implement Vernier Thrusters or Gimbaled Thrusters in game, and was only going to use Momentum Wheels and CMGs. That rapidly fell apart when I did the math on them.

Consider the above example with the two masses on a string. Because they are identical, the spins will be equal and opposite. But if one mass has twice the moment of inertia, it will spin at half the (reverse) speed as the other. The greater the moment of inertia, the slower the spin.

If one of these masses is the spacecraft and the other is the reaction wheel, you want the spacecraft to have a lower moment of inertia. Thus, if your spacecraft has a moment of inertia 100 times that of your reaction wheel, it will spin 100 times slower than that reaction wheel.

Moment of Inertia is proportional to mass and the square of distance from the rotation axis. Roughly speaking then, very voluminous and very massive objects will have the greatest moment of inertia.

When headspinning, rotational speed can be increased by pulling ones’ legs in. This reduces the distance from the rotation axis and thus reduces the moment of inertia.

Spacecrafts by nature will have a greater volume than your reaction wheels, since they envelope these wheels. And they are guaranteed to have a greater mass than your reaction wheels, unless you are okay with an abysmal mass ratio (less than 2). Thus, you are guaranteed a moment of inertia far tinier than your spacecraft’s moment of inertia. And as I discovered, even spinning your wheels at enormous speeds yields rotations that take minutes or even hours.

In short, these techniques were not viable for combat rotations, barring some sort of future technology.

This leaves thrusters as the only viable method of spinning about in combat. How fast can they spin?

Because thrusters affect acceleration rather than velocity, the answer is that it varies. For instance, the time to spin 90 degrees is not going to be twice the time it takes to spin 45 degrees. And it varies based on which axis of rotation is used.

A simple metric is the Full Turnabout Time, which is the time it takes to spin 180 degrees about the slowest axis. This is essentially the “slowest” possible turning time for the ship, and most turns will be much faster, a fraction of this time.

When the enemy targets parts of your ship away from your center of mass, you can dodge simply by spinning along one axis. This particular ship is spinning with a single gimbaled NTR.

For medium sized capital ships with gimbaled thrusters in game, 20-30 seconds is a common value. Capital ships with vernier thrusters tend in the 10-20 second range, as do small sized capital ships. Very large capital ships can take up to a minute to do a full turnabout. Gimbaled drones and missiles tend to take 5 seconds or less for a full turnabout, with some being able to do a 180 in under a second.

Much faster turnabouts are possible by simply adding more and more vernier thrusters or gimbaled thrusters. However, this is often fast enough to deal with the rapidly changing nature of space combat. It is rare for a capital ships to ever need to flip a 180. Most of their turns are much smaller angle shifts, small dodges and broadsides.