Szerszen, Alex

NASA Technical Reports Server

Thermal Environment 
Modeling Practices for 
the Descent Trajectory of 
Lunar Landers
Alex Szerszen, Jacobs MSFC ES22
08-26-2019
https://ntrs.nasa.gov/search.jsp?R=20190030704 2019-09-26T19:01:48+00:00Z
Introduction 
• This presentation will discuss only one method of 
modeling the thermal environment for descent 
trajectories in Thermal Desktop. 
• The descent in arguably the most critical point in 
any lander mission
• The descent phase presents a unique thermal 
environment compared to the rest of the mission 
(launch, earth orbit, transit, moon orbit, descent, 
surface operation)
• View factor to space decreases
• Main thruster firing and plume add additional heat
• All electrical components operating at max power level. 
• Heat loads must be modeled properly to ensure 
that the lander doesn’t fail catastrophically 
Defining Thermal Environment 
• There are several parameters that control and 
set the spatial time and location of the moon.
• Right Ascension of the Sun
• Right Ascension of the Prime Meridian
• Earth's Moon’s planetary data
• Radius, gravitational mass, inclination, sidereal period, 
and mean solar day
• Ground IR (seen to right)
• Moon-centered J2000 reference frame
Building Thermal Desktop Model
• Terrestrial heating rate case used
• Right Ascension of sun and right ascension of prime 
meridian are the first inputs needed
• Determined using moon-centered coordinates of sun in 
Cartesian 
• Latitude, longitude and altitude versus time control the 
location of the lander for each time step 
Building Thermal Desktop Model
• Rotate along Z-axis by longitude plus value 
of R.A. of the prime meridian
• Result: X-axis of lander points through Z-axis 
of moon
• Rotate along Y-axis by value of latitude 
• Result: X-axis of lander points through center 
of moon
• Rotate along X-axis by the inverse tangent 
of change in latitude over change in 
longitude.
• Result: Z-axis of lander points along velocity 
vector
Additional Rotations Required
�𝑅𝑅(𝑖𝑖) = 𝐼𝐼3 ∗ 𝑅𝑅𝑧𝑧 )𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝑖𝑖𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿(𝑖𝑖 ∗ 𝑅𝑅𝑦𝑦 )𝐿𝐿𝐿𝐿𝐿𝐿𝑖𝑖𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿(𝑖𝑖 ∗ 𝑅𝑅𝑥𝑥 �𝜃𝜃𝑥𝑥𝑟𝑟𝑟𝑟𝑟𝑟(𝑖𝑖 ∗ 𝑅𝑅𝑦𝑦(135°
𝑅𝑅 = 𝑅𝑅𝑧𝑧 𝜙𝜙 ∗ 𝑅𝑅𝑦𝑦 𝜃𝜃 ∗ 𝑅𝑅𝑥𝑥 𝜓𝜓= 𝑐𝑐𝐿𝐿𝑐𝑐𝜃𝜃 𝑐𝑐𝐿𝐿𝑐𝑐𝜙𝜙 𝑐𝑐𝑖𝑖𝐿𝐿𝜓𝜓 𝑐𝑐𝑖𝑖𝐿𝐿𝜃𝜃 𝑐𝑐𝐿𝐿𝑐𝑐𝜙𝜙 − 𝑐𝑐𝐿𝐿𝑐𝑐𝜓𝜓 𝑐𝑐𝑖𝑖𝐿𝐿𝜙𝜙 𝑐𝑐𝐿𝐿𝑐𝑐𝜓𝜓 𝑐𝑐𝑖𝑖𝐿𝐿𝜃𝜃 𝑐𝑐𝐿𝐿𝑐𝑐𝜙𝜙 + 𝑐𝑐𝑖𝑖𝐿𝐿𝜓𝜓 𝑐𝑐𝑖𝑖𝐿𝐿𝜙𝜙𝑐𝑐𝐿𝐿𝑐𝑐𝜃𝜃 𝑐𝑐𝑖𝑖𝐿𝐿𝜙𝜙 𝑐𝑐𝑖𝑖𝐿𝐿𝜓𝜓 𝑐𝑐𝑖𝑖𝐿𝐿𝜃𝜃 𝑐𝑐𝑖𝑖𝐿𝐿𝜙𝜙 + 𝑐𝑐𝐿𝐿𝑐𝑐𝜓𝜓 𝑐𝑐𝐿𝐿𝑐𝑐𝜙𝜙 𝑐𝑐𝐿𝐿𝑐𝑐𝜓𝜓 𝑐𝑐𝑖𝑖𝐿𝐿𝜃𝜃 𝑐𝑐𝑖𝑖𝐿𝐿𝜙𝜙 − 𝑐𝑐𝑖𝑖𝐿𝐿𝜓𝜓 𝑐𝑐𝐿𝐿𝑐𝑐𝜙𝜙
−𝑐𝑐𝑖𝑖𝐿𝐿𝜃𝜃 𝑐𝑐𝑖𝑖𝐿𝐿𝜓𝜓 𝑐𝑐𝐿𝐿𝑐𝑐𝜃𝜃 𝑐𝑐𝐿𝐿𝑐𝑐𝜓𝜓 𝑐𝑐𝐿𝐿𝑐𝑐𝜃𝜃
• If more than 3 rotations are desired, then the use of rotation 
matrices is required. 
• Rotation matrices allow the conversion of any number of 
rotations down to 3 base rotations. 
• To do this you:
• Rotate lander by any number of rotations at each time step
• Obtain a 3X3 matrix for each time step
• Equate the 3X3 matrix at each time step to the base rotation matrix 
seen below
2-Argument Arctangent
𝜃𝜃 = 𝐿𝐿𝑐𝑐𝑖𝑖𝐿𝐿(−𝑟𝑟31)
𝜓𝜓 = 𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝑎(𝑟𝑟32, 𝑟𝑟33)𝜙𝜙 = 𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝑎(𝑟𝑟21, 𝑟𝑟11)
• Equate the final matrix at each time step to the 
base rotation matrix below and solve for theta (𝜃𝜃), 
phi (𝜙𝜙), and psi (𝜓𝜓)
• 2 solutions for both phi and psi
• Must use 2-argument arctangent
𝑅𝑅 = 𝑅𝑅𝑧𝑧 𝜙𝜙 ∗ 𝑅𝑅𝑦𝑦 𝜃𝜃 ∗ 𝑅𝑅𝑥𝑥 𝜓𝜓= 𝑐𝑐𝐿𝐿𝑐𝑐𝜃𝜃 𝑐𝑐𝐿𝐿𝑐𝑐𝜙𝜙 𝑐𝑐𝑖𝑖𝐿𝐿𝜓𝜓 𝑐𝑐𝑖𝑖𝐿𝐿𝜃𝜃 𝑐𝑐𝐿𝐿𝑐𝑐𝜙𝜙 − 𝑐𝑐𝐿𝐿𝑐𝑐𝜓𝜓 𝑐𝑐𝑖𝑖𝐿𝐿𝜙𝜙 𝑐𝑐𝐿𝐿𝑐𝑐𝜓𝜓 𝑐𝑐𝑖𝑖𝐿𝐿𝜃𝜃 𝑐𝑐𝐿𝐿𝑐𝑐𝜙𝜙 + 𝑐𝑐𝑖𝑖𝐿𝐿𝜓𝜓 𝑐𝑐𝑖𝑖𝐿𝐿𝜙𝜙𝑐𝑐𝐿𝐿𝑐𝑐𝜃𝜃 𝑐𝑐𝑖𝑖𝐿𝐿𝜙𝜙 𝑐𝑐𝑖𝑖𝐿𝐿𝜓𝜓 𝑐𝑐𝑖𝑖𝐿𝐿𝜃𝜃 𝑐𝑐𝑖𝑖𝐿𝐿𝜙𝜙 + 𝑐𝑐𝐿𝐿𝑐𝑐𝜓𝜓 𝑐𝑐𝐿𝐿𝑐𝑐𝜙𝜙 𝑐𝑐𝐿𝐿𝑐𝑐𝜓𝜓 𝑐𝑐𝑖𝑖𝐿𝐿𝜃𝜃 𝑐𝑐𝑖𝑖𝐿𝐿𝜙𝜙 − 𝑐𝑐𝑖𝑖𝐿𝐿𝜓𝜓 𝑐𝑐𝐿𝐿𝑐𝑐𝜙𝜙
−𝑐𝑐𝑖𝑖𝐿𝐿𝜃𝜃 𝑐𝑐𝑖𝑖𝐿𝐿𝜓𝜓 𝑐𝑐𝐿𝐿𝑐𝑐𝜃𝜃 𝑐𝑐𝐿𝐿𝑐𝑐𝜓𝜓 𝑐𝑐𝐿𝐿𝑐𝑐𝜃𝜃
Building Thermal Desktop Model
• Add in the additional rotations on the 
orientation tab for terrestrial heating rate 
cases
• Select “align to celestial coordinate system”
• Create array symbols for theta, phi, and psi in 
the symbol manager
• Interpolate between time steps of heating 
rate case
Quality Checks
• Two methods to check that the lander is properly 
oriented at each time step 
• Display the orbit in the heating rate case manager
• View the lander from the planet
Conclusion
• Modeling the thermal environment for a lander descent correctly is 
essential for a successful mission. This can be difficult due to the 
transient nature of a descent and the addition of new thermal conditions 
such as component heat loads, changing view factors/radiative sink 
temperatures, and thruster/plume heat loads. 
• The method shown above is one way to obtain the desired results but is 
very versatile and easy to use if more detailed rotations are required. 
Questions?
• Questions?
• Comments?
• Other ways of achieving desired effects?


Thermal Environment Modeling Practices for the Descent Trajectory of Lunar Landers

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server