1. TMT Telescope Structure thermal model
Konstantinos Vogiatzis, Amir Sadjadpour, Scott Roberts
TMT Observatory Corporation, Pasadena, CA 91105, USA
ABSTRACT
The thermal behavior of the Thirty Meter Telescope (TMT) Telescope Structure (STR) and the STR mounted sub-
systems depends on the heat load of the System, the thermal properties of component materials and the environment as
well as their interactions through convection, conduction and radiation.
In this paper the thermal environment is described and the latest three-dimensional Computational Solid Dynamics
(CSD) model is presented. The model tracks the diurnal temperature variation of the STR and the corresponding
deformations. The resulting displacements are fed into the TMT Merit Function Routine (MFR), which converts them
into translations and rotations of the optical surfaces. They, in turn, are multiplied by the TMT optical sensitivity matrix
that delivers the corresponding pointing error. Thus the thermal performance of the structure can be assessed for
requirement compliance, thermal drift correction strategies and look-up tables can be developed and design guidance can
be provided.
Results for a representative diurnal cycle based on measured temperature data from the TMT site on Mauna Kea and
CFD simulations are presented and conclusions are drawn.
Keywords: Computational Solid Dynamics, Telescope Thermal Deformation, Ground Based Telescopes
1. INTRODUCTION
The thermal behavior of the Thirty Meter Telescope (TMT) Telescope Structure (STR) and the STR mounted sub-
systems depends on the thermal properties of the STR and its sub-systems as well as the thermal properties of the
environment and the thermal interactions between the STR, its sub-systems and the environment through convection,
conduction and radiation.
A previous study was presented in 2010 [1]. The new study was dictated by changes in the STR design and the thermal
environment (thermal load, simulation matrix). The current model also differs from the previous model in several ways.
First, it is truly three-dimensional, resolving the thickness of the structural members. It accommodates diurnal
simulations and variable elevation angles. It also incorporates all subsystems and components that are thermally coupled
to the structure and calculates their temperature as well. Finally, it introduces a "sky" body the size of the aperture, that
enables correct calculation of radiation coupling to the STR.
In this paper Section 2 describes the modeling effort, thermal environment of the telescope structure and introduces the
analyses cases studied. Section 3 describes the results. Section 4 provides a summary and conclusion.
2. MODELING THE THERMAL ENVIRONMENT
2.1 Overall description
The model presented herein is a thermal model so the simulations do not consider the effects of gravity on the structure.
Previous studies [1] suggested that the elevation structure deformation is dominant. Due to the amount of time required
to render the CAD model suitable for gridding and the associated number of elements required, the current study does
not include the azimuth structure. It is still under development and will be presented in the future. Thermal coupling
between the elevation and azimuth structures is not significant (consisting primarily of radiation between surfaces of
similar temperature). For the current modeling phase the boundary condition on the forcers and hydrostatic pads will be
fixed temperature for both models because of active cooling.
The stress solver is activated only for the telescope elevation structure. The output of the model is displacements at the
points used by the Merit Function Routine (MFR) [2]. No deformations of the Segment Support, M2 or M3 assemblies
are considered.
2.2 Model geometry
The CAD model used can be seen in Figure 1. The coordinate system used has the Elevation Axis as X and the Optical
axis as Z. It consists of the M1 cell, the M3 tower and the lower tube as a single body, the elevation journals, the upper

2. tube and the spider as a single body (see Figures 1 to 5). Contact interfaces between the distinct bodies are equivalent to
welded surfaces. The segment handling and cleaning systems have been omitted, as well as the M1 cell and LGSF
platforms. Additional components, that are only radiatively coupled to the structure, are also included: the M1 control
system node boxes, the SSA as a single block of equivalent volume, the M1 as a single body (no segment gaps), the M3
and M2 assemblies, the LGSF, M3 and top end electronics cabinets, the Beam Transfer Optics duct section above the
spider and the Laser Launch Telescope. The appropriate/desired level of contact thermal resistance between these
components and the structure is under assessment.
Figures 2 and 3 respectively show details of the grid for the primary mirror top chord and the spider. The average grid
resolution is 0.05 m, resulting in 4.3 million elements.
Figure 1 – Telescope elevation structure CAD model
2.3 Environment
The model uses environmental inputs as formulated in the TMT Monte Carlo framework [3], along with results
generated by the TMT Aero-thermal Modeling Framework [4]. However, the current study incorporates information that
has been updated since previous studies were reported. There is an updated heat dissipation budget, more complete CFD
case matrix and updated SSA simulations that have not been incorporated in [4]. Updated aero-thermal seeing and
diffraction limited image quality estimates also exist, that have not been incorporated in [3].
After studying the latest expected inputs and estimated environment we made the following selections for the
environmental conditions.
Input ambient temperature TA (t, Y) (t in h, 0-24, Y in m):
Night: 277.6 - t*(e-t
+0.3) K (resulting mean: 275.5 K) (Eq. 1)
Day (enclosure interior): [274.7+0.8*(1-e-(t-12)/1.5)
] +0.06*Y K (Eq. 2)
This is an approximate curve-fit to the average diurnal behavior of the telescope environment [5]. The daytime
temperature vertical gradient is conservative (by about a factor of 1.5) and it is also assumed to be attained immediately
after sunrise (also conservative). Note also that the telescope is pointing at horizon after sunrise (hence the Y in the
vertical profile).

3. Figure 2 – Mirror cell top chord grid detail
Figure 3 – Top end grid detail
Effective temperature for radiation:
Night Day
sky through aperture: 250 K, enclosure surfaces: TA-1 K TA
The effective sky temperature can vary by a few degrees following zenith angle variability but it is assumed that the
structure senses an average value due to its thermal inertia.
Convective heat transfer coefficient:
Night Day
4 W/m2
/K 2 W/m2
/K
The night time heat transfer coefficient can vary both in time and in space following telescope orientation variability and
vent operation, but it is assumed that the structure senses an average value due to its thermal inertia. Values of up to 10
W/m2
/K have been estimated by CFD on certain parts of the structure, making the selected value a conservative one.

4. 2.4 Material properties
Material properties, telescope structure (steel):
 = 7860 kg/m3
k = 15 W/m/K
Cp = 480 J/kg/K
 = 0.3, CTE = 1.2x10-5
K-1
, E = 206 GPa
The thickness of the M1 cell middle and bottom pipes could not be resolved with a reasonable amount of elements, so
they were gridded as filled solids instead. To properly capture their thermal response their density and Young's modulus
were reduced by the appropriate factor, 6 for the middle and 10 for the bottom pipes.
Material properties, mirrors (glass):
 = 2500 kg/m3
k = 1.52 W/m/K
Cp = 773 J/kg/K
For the remaining components/heat sources the temperature is calculated by heat flux continuity on the surface (the flux
reaching the surface from the interior equals the net removal due to radiation and convection).
2.5 Thermal boundary conditions
The model is initialized at T = 275.5 K.
Table 1 summarizes the thermal boundary conditions used in the model with no diurnal variability (these conditions are
conservative).
Table 1 – Thermal boundary conditions (see Figures 4 and 5)
Component/surface Emissivity
Convective coef.
(W/m2
/K)
Power dissipation (W)
or Temperature (K)
M1 cell 0.8 1 -
M1 mirror surface 0.02 4 -
M1 rest 0.8 1 -
SSA (each) 0.8 1 Dissipation: 12 (W)
Node box (each) 0.8 1 Dissipation: 20 (W)
M3 mirror surface 0.02 4 -
M3 rest 0.8 4 -
M3 electronics 0.8 1 Dissipation: 200 (W)
LGSF cabinet (each) 0.8 1 Dissipation: 40 (W)
Spider top 0.2 4 -
Spider 0.8 4 -
LLT 0.8 4 Dissipation: 200 (W)
Top end electronics 0.8 4 Dissipation: 800 (W)
BTO duct top 0.2 4 -
BTO duct 0.8 4 -
M2 mirror surface 0.02 4 -
M2 rest 0.8 4 -
Hexapod 0.8 4 Dissipation: 90 (W)
EL journal surfaces in contact
with the HSB pads
0.8 - Temperature: TA+1 (K)
Remaining structure 0.8 4 -
Structure interior (if hollow) 0.8 0 -

5. The value of 1 W/m2
/K for everything between the M1 segments and the M1 cell platform is conservative. Typical
emissivity values of lo-emit paints are 0.15-0.2, but it is unclear whether they can meet the stray light requirement.
Therefore a worst case value of 0.8 is used for the surfaces of the spider. The top of the BTO and the spider can have
higher reflectivity, as high as 0.95. An emissivity value of 0.2 was used for these surfaces (also conservative). Finally it
is assumed that the M2 electronics cabinets are located at the top end and the M3 electronics cabinets are located at the
M3 tower. Note that these electronics cabinets have rather large power dissipations. There is an option to move most of
that heat load, off the telescope or at least the M1 cell. Figures 4 and 5 below show the locations of some of the
components included in Table 1.
Figure 4 – Top end thermal components
Figure 5 – Elevation structure thermal components

6. 2.6 Analysis cases studied
Even though we are interested in night-time performance, diurnal simulations are necessary to ensure that the final result
is independent of the initial conditions. The typical simulation lasts 36h (night-day-night, each 12h long). Only results
after the first 24h cycle are considered and reported.
An important parameter is the reference temperature of zero deformation (TREF). In this study the underlying
assumption is that after APS calibration the telescope is perfectly aligned. TMT is planning to calibrate every 30 days.
The median ambient temperature difference between calibrations is around ±1.5K, as shown in Figure 6. The optimum
time for calibration is 3h after sunset.
Figure 6 – Cumulative Distribution Function of the absolute difference between the ambient night-time temperature and
the temperature during calibration
Two cases will be studied. For the first case (C1) the simulation is repeated with a reference temperature of 275.5K and
the boundary conditions of Table 3. The assumption is that calibration occurred the night before and the night in
question is identical. Thus the sensitivity to thermal properties and loads will be inferred. The second case (C2) will be
using the same thermal conditions but assumes that calibration occurred 30 days ago, 3h after sunset. In our standard
ambient record input (Eq. 1) the temperature at 3h after sunset is 276.5 K. This results in a reference temperature median
range of 275-278 K, while the ambient temperature will vary between 277.6 K and 274 K (Eq. 1). For this case a TREF
value of 278 K was selected (the other option, 275K, would be very similar to C1).
To save time and preserve accuracy, the optimum combination of time-step and number of iterations within the time-step
were selected based on additional tests not presented here. Maximum displacement error relative to steady state is <=5%.
The 36h cycle was compared to a 60h cycle to ensure that the initial condition effect does not extend past 24h.
Maximum temperature deviations for period (24-36) h and period (48-60) h show very little difference (<0.1K).
3. RESULTS
3.1 CSD results
Maximum pointing errors occur at the end of the night, when the deviation from TREF is largest due to the telescope's
thermal inertia. C2 is the worst case of the two and it will be used to check the thermal performance of the structure
against requirements. Surface temperature and displacement magnitude contours (looking down the optical axis) are
shown in Figures 7 & 8 every two hours after sunset for case C1. For the temperature the variable shown is relative to
TREF (for C2 the contours will be identical with a 2.5K offset). The spatial distribution of the variables is shown clearer
for case C1 (as opposed to C2).

7. Figure 7 – C1: T-TREF (K) 12h after sunset
Figure 8 – C1: Displacement magnitude (m) 12h after sunset

8. 3.2 MFR results
The Merit Function Routine (MFR) is a TMT Telescope Structure Analysis tool which is used to evaluate displacement
results from single case type analysis, such as thermal and applied loads [2]. The night-time temporal behavior of certain
MFR variables after primary mirror alignment and phasing is reviewed for case C2. The RMS wave-front error due to
segment motions exhibits a flat behavior throughout the night at 10-12 nm. Figure 9 shows the maximum actuator
stroke. Figures 10 and 11 show the M1 translation and rotation respectively, relative to the original M1 coordinates after
alignment and phasing. Figures 12 and 13 show the M2 translation and rotation respectively, from M2 alignment
coordinates after alignment and phasing.
3.3 Pointing results
The pointing errors caused by the thermal distortion can be calculated from the mirror translations and rotations using
the pointing sensitivity coefficients from AD6. Figure 14 shows the temporal behavior of the telescope pointing error for
case C2 (the behavior of case C1 is qualitatively similar but the actual error is 0.6 arcsec smaller). Because thermal
distortion of the azimuth structure has not been included in this study, these pointing errors are likely underestimated.
Previous studies have indicated that the azimuth structure contributes less pointing error than the elevation structure.
However, it should be noted that no correction strategy has been applied.
4. DISCUSSION
Compared to the full range of site environmental data, the difference TA-TREF used in this study is a "median-worst",
not an "absolute-worst". Ambient temperature can vary by as much as 10K between calibrations. From Figure 6, 4K is
selected as a worst case, currently covering 90% of the time.
Figure 15 shows the temporal behavior of TA-TREF, the difference between the mean temperature of the M1 top chord
"TM1" and TREF and the difference between the mean temperature of the spider apex "TM2" and TREF for case C2
(case C1 is just a 2.5K shift). Comparing with Figure 14, it appears that the pointing error follows the deviation of TM1
mean temperature from TREF.
Figure 9 – C2: Temporal variation of maximum actuator stroke (microns)

9. Figure 10 – C2: Temporal variation of M1 translation errors (microns)
Figure 11 – C2: Temporal variation of M1 rotation errors (mas)

10. Figure 12 – C2: Temporal variation of M2 translation errors (microns)
Figure 13 – C2: Temporal variation of M2 rotation errors (mas)

11. Figure 14 – Telescope pointing error for case C2
Figure 15 – C2: Difference between TREF and ambient, mean top chord, and mean spider apex temperature
The worst MFR results from this study, as mentioned in 4.2, occurred for case C2, 12 h after sunset (C2-12). At the time
TA-TREF = -4.00K
TM1-TA = 1.25K
TM1-TREF = -2.75K
Using TA-TREF = ±4K, assuming TM1-TA = +2K as a max value and extrapolating the results for |TM1-TREF| = 6K,
using a factor of 2.17, we can estimate worst case errors.
We have yet to compare these results to actual requirements. Some key requirements related to STR thermal deformation
are presented below.

12. 1. The primary mirror cell shall be designed such that relative in-plane motion between any two adjacent segments
shall not cause the inter-segment gap to decrease by more than 0.44 mm at any point along the gap.
2. The M1CS actuator range of travel budgeted for the thermal deflection of telescope elevation structure and M1
optics system is limited to 0.42 mm.
3. Telescope pointing error budget for the Structure/M1 thermal drift: 0.5 arcsec
Table 2 – Requirements vs. Estimates
Requirement Value
Estimate
C2-12h
Estimate
"worst case"
Comments
1 0.109 mm 0.046 mm 0.100 mm Requirement met
2 0.42 mm 0.025 mm 0.054 mm
Effects not included < 0.010 mm
Requirement met
3 0.5 arcsec 0.89 arcsec 1.93 arcsec Before correction strategy
Table 2 summarizes the key required and expected errors. TMT plans to measure the temperature of the main structural
members and use this information to calculate pointing corrections. Compensation for thermally-induced pointing errors
may also be possible using information from previous pointing corrections on the same night. Under the assumption that
a correction strategy would compensate for a large part of the pointing error due to uniform expansion/contraction, then
the residual pointing error would behave closer to case C1. That case exhibits a maximum pointing error of 0.37 arcsec,
a maximum tracking error of 0.015 arcsec over any 10min period and a night-time rms of 0.20 arcsec. For C2 these
values are 1.13 arcsec, 0.083 arcsec and 0.89 arcsec respectively.
5. CONCLUSION
A new Telescope Structure thermal model was developed to account for design and heat load changes. Pointing errors
appear acceptable. This has to be weighed against the additional expected errors from the azimuth structure and more
benign/realistic thermal boundary conditions. It can also allow for a lower thermal resistance between subsystem
components and the structure, in order to minimize their expected temperature deviation from ambient through
conduction.
ACKNOWLEDGMENTS
The TMT Project gratefully acknowledges the support of the TMT collaborating institutions. They are the Association
of Canadian Universities for Research in Astronomy (ACURA), the California Institute of Technology, the University of
California, the National Astronomical Observatory of Japan, the National Astronomical Observatories of China and their
consortium partners, and the Department of Science and Technology of India and their supported institutes. This work
was supported as well by the Gordon and Betty Moore Foundation, the Canada Foundation for Innovation, the Ontario
Ministry of Research and Innovation, the National Research Council of Canada, the Natural Sciences and Engineering
Research Council of Canada, the British Columbia Knowledge Development Fund, the Association of Universities for
Research in Astronomy (AURA) and the U.S. National Science Foundation.
REFERENCES
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[2] Roberts, S., Sun, S., Kerley, D., "Optical performance analysis and optimization of large telescope structural
designs", SPIE 5867, p. 200-211, Optical Modeling and Performance Predictions II, (2005).
[3] Vogiatzis, K., & Angeli, G. Z., "Monte Carlo Simulation Framework for TMT", SPIE 7017(29), (2008).
[4] Vogiatzis, K., “Aero-thermal modeling framework for TMT,” SPIE 8336(10), (2011).
[5] Vogiatzis, K., "Thermal modeling environment for TMT", SPIE 7738(11), (2010).