Mission Configuration – 100g Payload – Lunar Descent
Section A-5.4.4
A-5.4.4 – Attitude Control
Misalignment between the Lunar Lander’s center of mass and the descent-engine thrust
direction cause a thrust-offset torque on the Lander. The magnitude of the thrust-offset
torque is the key driver in the amount of attitude control propellant and the number of
attitude control thrusters required. The magnitude of the thrust-offset torque depends on
the design of the vehicle and manufacturing limitations. The magnitude of the torque
must be estimated for our analysis. We estimate the magnitude of the torque to be the
thrust of the descent engine times one percent of the Lunar Lander’s radius as shown
here:
M offset  0.01 * Rlander * Tdescent _ engine
Equation A-5.4.4-1
The torque generated by the attitude control thrusters around each axes must be greater
than the thrust-offset torque. The thrust required from the attitude control thrusters is
calculated by dividing the thrust-offset torque by the distance between the attitude control
thrusters and the Lander’s center of mass. The 13.3 N hydrogen peroxide thrusters we
use on the Lunar Lander generate sufficient thrust to counteract the thrust-offset torque.
Rauschenbakh, Ovchinnikov, and McKenna-Lawlor (2003) describe a method for
estimating the propellant consumption of the attitude control system. They consider two
cases. In the first case, the spacecraft experiences no external perturbing torques. Here,
the vehicle oscillates back and forth between the allowable limits of its attitude control
system. The second case considers the spacecraft is acted on by a constant perturbing
torque. We make the simplifying assumption that the perturbing torque is large enough
that the spacecraft never reaches one of the limits of the attitude control system. Instead,
the spacecraft experiences one sided oscillations. Figure A-5.4.4-1 shows the phaseplane diagrams of each of the two cases considered.
Our Lunar Lander experiences the large thrust-offset torque. We use the second case
setup to analyze the propellant consumption of our attitude control system.
Author: Christine Troy
Mission Configuration – 100g Payload – Lunar Descent
.
Section A-5.4.4
.
θ
θ
+θ1
+θ1
θ
θ
-θ1
-θ1
No External Torque
“Large” External Torque
Figure A-5.4.4-1: Attitude control phase-plane schematics. On the left, the oscillations of the
spacecraft between the allowable limits of the attitude control system when no external torque is
present. On the right, the one sided oscillations of the spacecraft when acted on by an external
perturbing force large enough to prevent it from oscillating between the allowable limits of the
attitude control system. In both cases, vertical lines represent a pulse from the attitude control
thrusters. All other lines represent the coasting movement of the spacecraft.
(based on Rauschenbakh, Ovchinnikov, and McKenna-Lawlor)
(Christine Troy)
Using Euler’s equations of motion, Rauschenbakh, Ovchinnikov, and McKenna-Lawlor
derive an expression for the propellant consumed by the attitude control system for each
oscillation cycle. The propellant consumption is divided by the time for a complete
oscillation cycle to find a time averaged value for propellant consumption. The following
shows the final result of their derivation:
m attitude 
M offset
g * Isp * L
Equation A-5.4.4-2
where Moffset is the thrust-offset torque, g is the gravitational constant, Isp is the specific
impulse of the attitude thrusters, and L is the distance from the attitude thrusters to the
Lander center of mass.
Author: Christine Troy
Mission Configuration – 100g Payload – Lunar Descent
Section A-5.4.4
The methods we describe above to determine the required attitude control thrust about
each axis and the amount of propellant needed for attitude control are implemented in the
function AttitudeThrusterSizing_100g.m. The lunar descent propulsion code calls this
function as part of the Lunar Lander sizing process.
We design the attitude thruster configuration using twelve 13.3 N thrusters. The thrusters
provide force couples on the Lander in the positive and negative direction around each of
the three spacecraft axes. Figure A-5.4.4-2 shows the configuration of the thrusters
around the Lander.
Lander Top View
Lander Side view
Figure A-5.4.4-2: Lander thruster configuration. Twelve 13.3 N thrusters are required.
(Christine Troy)
Author: Christine Troy