Moments if Inertia - Making more nimble craft

[Smidge204]

Since I couldn't find any other topic on this, thought maybe I'd make my own! The goal of this tutorial is to help you improve handling of your crafts through a basic understanding of Moment of Inertia, which affects how easily your craft turns. know I'm not the only one who's build rockets that turn like sleeping elephants! Hopefully, this tutorial can help you understand why so you can fix this at the design stage. I plan to avoid any actual math here, but the math isn't terribly hard... I just think a general understanding of principle is enough to be useful in construction.

Most people are familiar with Inertia - the characteristic of an object to maintain its velocity. Inertia is closely related to, but not the same as, Momentum... an object that is not moving has no Momentum, but any object with mass always has Inertia!

Moment of Inertia is the same thing, only for rotation rather than linear velocity. While linear Inertia is basically the object's mass, the Moment of Inertia is a function of both mass and where that mass is located relative to the center of mass. Let's consider these two craft having equal number of parts and equal mass:

I think most people will intuitively understand that the second example, with the fuel tanks near the center, will spin much more easily.

The rule is this: Each individual part pas a Moment of Inertia (MoI) about its center of mass, and the assembly as a whole is the sum of each part's MoI multiplied by that part's distance from the Center of Mass (CoM) squared. Therefore, doubling the distance between a part and the CoM increases it's effective MoI by a FOUR TIMES!

So when designing your craft, doing your best to keep the mass concentrated at the CoM will help reduce the MoI, and make the whole thing easier to steer. These two rockets have exactly the same mass and the same amount of fuel, but the one on the right will be much easier to turn due to much lower MoI:

(You'll need some fuel lines to make them 100% equivalent, but that extra mass would only be less than 1% more and is really negligible!)

Of course, aerodynamics may also be a concern- "Clumping" fuel tanks increases frontal surface area and therefore drag. However once you're out of the atmosphere the short, stumpy crafts will generally have better handling.

Applying Torque

Torque is required to turn your craft. There are three mechanisms in the game to apply this torque: Reaction wheels, RCS thrusters and vectored thrust engines.

Reaction wheels apply "pure torque" - a simple twisting force wherever they happen to be. A torque will cause a rotation around an object's center of mass no matter where it's located in the craft, so you can put reaction wheels anywhere you like! Again, keeping the mass concentrated in the center is better than not, but there will be no performance penalty from putting a reaction wheel at some other convenient location.

In contrast, it matters where RCS and vectored thrust systems are located. (This is the only part where I get a little Mathy, I swear!)

Torque is a force applied at a distance. The greater the distance, the greater the torque for the same force. This is why wrenches have long handles! Since free bodies rotate around their CoM, this distance is the length of the thrust vector acting perpendicular to the line of action. This also means that thrust vectors that pass directly through the CoM contribute no torque!

The LV-T45 has a thrust vectoring angle of 1 degree. We extend a line from the engine to the CoM, and then another line that is one degree off from that.

Then we draw a line from the CoM that intersects that 1-degree line at a right angle. The length of that line, "L", is the Moment arm for that force... the length of the wrench handle. The longer this line, the more turning force the engine will be able to provide. This means that the farther away the engine is from the CoM, the better! But don't forget that placing the engine far away also increases MoI which makes it harder to turn... so it's a tradeoff.

However, generally you don't want your main thrusting engines to be providing that turning force anyway, so the difficulty in getting good turning torque with them is actually a good thing! You only want to to gentle, minor maneuvers while thrusting. For more turning trust, we use RCS:

(Forgive the lack of RCS fuel tanks... Practice Problem! Where and how would be the best place to add RCS fuel to minimize increase in MoI?)

RCS thrusters are very weak, but because they apply that force at (hopefully) the maximal distance, they can provide much more torque! Basically you're using a wrench with a HUGE handle so you don't have to work as hard. For turning, you want RCS thrusters as far from your CoM as possible. In the above example, there are thrusters at roughly equal distance to the CoM on both sides... double the turning power!

If your RCS thrusters are not balanced like this, then some of your thrust will be wasted pushing your craft sideways. For translating, you want NO torque so either the RCS needs to act through the CoM or be balanced so the net thrust vector acts through CoM, but balancing RCS is another tutorial entirely!

I'm out of time for now, but I think that just about covers the basic concepts. Questions, comments and discussion welcome!

=Smidge=

[blizzy78]

Nice writeup, just two minor points:

You'll need some fuel lines to make them 100% equivalent, but that extra mass would only be less than 1% more and is really negligible!

I believe fuel lines do not have mass in the flight scene.

Of course, aerodynamics may also be a concern- "Clumping" fuel tanks increases frontal surface area and therefore drag. However once you're out of the atmosphere the short, stumpy crafts will generally have better handling.

In the stock aerodynamic model, surface area does not influence drag. It does not matter whether you build wide or tall.

[Smidge204]

Nice writeup, just two minor points:

"Until they fix it"

I didn't want to write something that might be rendered obsolete later.

=Smidge=