Zach Milbradt    Physics 211    Fall 2014

Gyros and Angular Motion

In Kerbal

Among the community, there is still experimentation to understand what calculations are used in the calculation of angular momentum. In a rocket, most methods of angular control are accounted for: SAS modules (also referred to as inline reaction wheels), thrusters that are not in line with the center of mass of a rocket, gimbals in engines redirecting thrust slightly, atmospheric drag and control surfaces such as aileron flaps. Ultimately calculation comes out to

I*αz=Στ=ΣτSAS+Σ(T×r)+Σ(FD×r)I*α_z=Στ=Στ_{SAS}+Σ(T×r)+Σ(F_D×r)
Drag force calculation is covered under Atmosphere and Aerodynamics. By experimentation players have found that the reaction wheel's location in regards to the center of mass does not appear to matter.


No torque applied


Torque applied at edge


Torque applied at center of mass
Kashua. KSP Torque Experiment. Digital image.
KerbalSpaceProgram.com. Imgur.com, 9 Apr. 2014. Web. 24 Nov. 2014.


Reality

This however runs contrary to basic physics. Using the formula for moments of inertia, making the simplification of a thin rod of length L and mass M, the moment of inertia can be calculated for the two instances.

τ1/α1=τ2/α2=Iτ_1/α_1=τ_2/α_2=Because Because the torques are both stopped at the same angle, torque is the same.
In addition, acceleration was reported to have been the same.
Moment of inertia remains the same because it is the same body.

1/12*M*L2=1/3*M*L21/12*M*L^2=1/3*M*L^2

1/4=


1
1/4=1

However, following the calculation through gives two different values of I.

Other experiments by the community supported Kashua's findings, such as that regardless of reaction wheel location, the location about which the body rotated was the center of mass.

The game seems to calculate torque about certain vehicle parts, very differently from how torque works in reality. This only applies to reaction wheels, not to other sources of torque, such as rockets, whose location is accounted for.

There is also the fact that this is still an approximation, assuming a thin line of uniform mass.