# SIST-TP CEN/CLC/TR 17603-31-03:2021

(Main)## Space Engineering - Thermal design handbook - Part 3: Spacecraft Surface Temperature

## Space Engineering - Thermal design handbook - Part 3: Spacecraft Surface Temperature

Factors affecting the equilibrium temperature of a spacecraft surface are described in this Part 3 using simple geometrical configurations and basic assumptions.

Methods for conducting calculations on the affect of Solar, planetary and albedo radiation are given taking into consideration the internal and immediate environmental factors and incorporating the various configurations and dimensions of the constituent parts.

The Thermal design handbook is published in 16 Parts

TR 17603-31-01 Part 1

Thermal design handbook – Part 1: View factors

TR 17603-31-01 Part 2

Thermal design handbook – Part 2: Holes, Grooves and Cavities

TR 17603-31-01 Part 3

Thermal design handbook – Part 3: Spacecraft Surface Temperature

TR 17603-31-01 Part 4

Thermal design handbook – Part 4: Conductive Heat Transfer

TR 17603-31-01 Part 5

Thermal design handbook – Part 5: Structural Materials: Metallic and Composite

TR 17603-31-01 Part 6

Thermal design handbook – Part 6: Thermal Control Surfaces

TR 17603-31-01 Part 7

Thermal design handbook – Part 7: Insulations

TR 17603-31-01 Part 8

Thermal design handbook – Part 8: Heat Pipes

TR 17603-31-01 Part 9

Thermal design handbook – Part 9: Radiators

TR 17603-31-01 Part 10

Thermal design handbook – Part 10: Phase – Change Capacitors

TR 17603-31-01 Part 11

Thermal design handbook – Part 11: Electrical Heating

TR 17603-31-01 Part 12

Thermal design handbook – Part 12: Louvers

TR 17603-31-01 Part 13

Thermal design handbook – Part 13: Fluid Loops

TR 17603-31-01 Part 14

Thermal design handbook – Part 14: Cryogenic Cooling

TR 17603-31-01 Part 15

Thermal design handbook – Part 15: Existing Satellites

TR 17603-31-01 Part 16

Thermal design handbook – Part 16: Thermal Protection System

## Raumfahrttechnik - Handbuch für thermisches Design - Teil 3: Oberflächentemperatur von Raumfahrzeugen

## Ingénierie spatiale - Manuel de conception thermique - Partie 3: Température de surface des véhicules spatiaux

## Vesoljska tehnika - Priročnik o toplotni zasnovi - 3. del: Površinska temperatura vesoljskih plovil

### General Information

### Standards Content (sample)

SLOVENSKI STANDARD

SIST-TP CEN/CLC/TR 17603-31-03:2021

01-oktober-2021

Vesoljska tehnika - Priročnik o toplotni zasnovi - 3. del: Površinska temperatura

vesoljskih plovilSpace Engineering - Thermal design handbook - Part 3: Spacecraft Surface Temperature

Raumfahrttechnik - Handbuch für thermisches Design - Teil 3: Oberflächentemperatur

von RaumfahrzeugenIngénierie spatiale - Manuel de conception thermique - Partie 3: Température de surface

des véhicules spatiauxTa slovenski standard je istoveten z: CEN/CLC/TR 17603-31-03:2021

ICS:

49.140 Vesoljski sistemi in operacije Space systems and

operations

SIST-TP CEN/CLC/TR 17603-31-03:2021 en,fr,de

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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SIST-TP CEN/CLC/TR 17603-31-03:2021

TECHNICAL REPORT

CEN/CLC/TR 17603-31-

RAPPORT TECHNIQUE

TECHNISCHER BERICHT

August 2021

ICS 49.140

English version

Space Engineering - Thermal design handbook - Part 3:

Spacecraft Surface Temperature

Ingénierie spatiale - Manuel de conception thermique - Raumfahrttechnik - Handbuch für thermisches Design -

Partie 3 : Température de surface des véhicules Teil 3: von Oberflächen auf Raumfahrzeugen

spatiauxThis Technical Report was approved by CEN on 14 June 2021. It has been drawn up by the Technical Committee CEN/CLC/JTC 5.

CEN and CENELEC members are the national standards bodies and national electrotechnical committees of Austria, Belgium,

Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy,

Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Republic of North Macedonia, Romania, Serbia,

Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United Kingdom.CEN-CENELEC Management Centre:

Rue de la Science 23, B-1040 Brussels

© 2021 CEN/CENELEC All rights of exploitation in any form and by any means Ref. No. CEN/CLC/TR 17603-31-03:2021 E

reserved worldwide for CEN national Members and forCENELEC Members.

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CEN/CLC/TR 17603-31-03:2021 (E)

Table of contents

European Foreword ................................................................................................. 10

1 Scope ..................................................................................................................... 11

2 References ............................................................................................................ 12

3 Terms, definitions and symbols .......................................................................... 13

3.1 Terms and definitions ............................................................................................. 13

3.2 Symbols .................................................................................................................. 13

4 Solar radiation ...................................................................................................... 15

4.1 General ................................................................................................................... 15

4.2 Infinitely conductive planar surfaces ....................................................................... 19

4.2.1 Flat plate emitting on one or both sides ..................................................... 19

4.3 Infinitely conductive spherical surfaces ................................................................... 21

4.3.1 Sphere ...................................................................................................... 21

4.4 Infinitely conductive cylindrical surfaces .................................................................. 22

4.4.1 Two-dimensional circular cylinder ............................................................. 22

4.4.2 Three-dimensional circular cylinder ........................................................... 23

4.5 Infinitely conductive conical surfaces ...................................................................... 25

4.5.1 Semi-infinite circular cone ......................................................................... 25

4.5.2 Finite circular cone with insulated base. (axial configuration) .................... 27

4.5.3 Finite height circular cone ......................................................................... 29

4.6 Infinitely conductive cylindrical-conical surfaces ..................................................... 31

4.6.1 Cone-cylinder-cone ................................................................................... 31

4.7 Infinitely conductive prismatic surfaces ................................................................... 49

4.7.1 Prism with an n-sided regular polygonal section ........................................ 49

4.8 Infinitely conductive pyramidal surfaces .................................................................. 60

4.8.1 Pyramid with an n-sided regular polygonal section .................................... 60

4.9 Infinitely conductive prismatic-pyramidal surfaces................................................... 70

4.9.1.1 Pyramid-prism-pyramid with an n-sided regular polygonal ........................ 70

4.10 Thin-walled spherical bodies. Finite conductivity ..................................................... 80

4.10.1 Non-spinning sphere ................................................................................. 80

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4.10.2 Non-spinning sphere. Including internal radiation ...................................... 82

4.11 Thin-walled cylindrical bodies. Finite conductivity. .................................................. 83

4.11.1 Non-spinning two-dimensional circular cylinder ......................................... 83

4.11.2 Spinning two-dimensional circular cylinder ................................................ 85

4.11.3 Circular cylinder. solar radiation parallel to axis of symmetry .................... 89

4.11.4 Cylindrical surface of rectangular cross section. Solar radiationnormal to face ........................................................................................... 90

4.12 Thin-walled conical bodies. Conductivity ................................................................. 95

4.12.1 Non-spinning cone .................................................................................... 95

5 Planetary radiation ............................................................................................... 99

5.1 General ................................................................................................................... 99

5.2 Infinitely conductive planar surfaces ..................................................................... 104

5.2.1 Flat plate absorbing and emitting on one side ......................................... 104

5.3 Infinitely conductive spherical surfaces ................................................................. 105

5.3.1 Sphere .................................................................................................... 105

5.3.2 Hemispherical surface absorbing and emitting on outer face .................. 106

5.4 Infinitely conductive cylindrical surfaces ................................................................ 108

5.4.1 Circular cylinder with insulated bases...................................................... 108

5.4.2 Finite height circular cylinder ................................................................... 109

5.5 Infinitely conductive conical surfaces .................................................................... 119

5.5.1 Circular cone with insulated base ............................................................ 119

5.5.2 Finite height circular cone ....................................................................... 122

6 Albedo radiation ................................................................................................. 125

6.1 General ................................................................................................................. 125

6.2 Infinitely conductive planar surfaces ..................................................................... 130

6.2.1 Flat plate absorbing and emitting on one side ......................................... 130

6.3 Infinitely conductive spherical surfaces ................................................................. 135

6.3.1 Sphere .................................................................................................... 135

6.4 Infinitely conductive cylindrical surfaces ................................................................ 139

6.4.1 Circular cylinder with insulated bases...................................................... 139

Bibliography ........................................................................................................... 144

Figures1/4

Figure 4-1: The function T (A /A ) vs. the distance to the Sun. Calculated by the

R E Icompiler. ............................................................................................................ 16

1/4Figure 4-2: The function TR(AE/AI) vs. the optical characteristics of the surface.

Shaded zone of a is enlarged in b. Calculated by the compiler. .......................... 17

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Figure 4-3: Temperature TR as a function of αs / ε and AI/AE for d = 1 AU. Shaded zone

of a is enlarged in b. Calculated by the compiler. ............................................... 18

1/4Figure 4-4: Ration (A /A ) as a function of γ, in the case of a flat plate. Calculated by

I Ethe compiler. ...................................................................................................... 20

1/4Figure 4-5: Ratio (A /A ) as a function of γ and H/R, in the case of a finite height

I Ecircular cylinder. Calculated by the compiler. ...................................................... 24

1/4Figure 4-6: Ratio (A /A ) as a function of δ, in the case of a semi-infinite circular cone.

I ECalculated by the compiler. ................................................................................ 26

1/4Figure 4-7: Ratio (A /A ) as a function of δ, in the case of a finite circular cone with

I Einsulated base (axial configuration). Calculated by the compiler. ........................ 28

1/4Figure 4-8: Ratio (A /A ) as a function of γ and δ, in the case of a finite height cone.

I ECalculated by the compiler. ................................................................................ 30

1/4Figure 4-9: Ratio (A /A ) as a function of γ and δ , in the case of a cone-cylinder-cone.

I ECalculated by the compiler. ................................................................................ 32

1/4Figure 4-10: Ratio (A /A ) as a function of γ and δ , in the case of a cone-cylinder-

I Econe. Calculated by the compiler. ...................................................................... 33

1/4Figure 4-11: Ratio (A /A ) as a function of γ and δ , in the case of a cone-cylinder-

I Econe. Calculated by the compiler. ...................................................................... 34

1/4Figure 4-12: Ratio (A /A ) as a function of γ and δ , in the case of a cone-cylinder-

I Econe. Calculated by the compiler. ...................................................................... 35

1/4Figure 4-13: Ratio (A /A ) as a function of γ and δ , in the case of a cone-cylinder-

I Econe. Calculated by the compiler. ...................................................................... 36

1/4Figure 4-14: Ratio (A /A ) as a function of γ and δ , in the case of a cone-cylinder-

I Econe. Calculated by the compiler. ...................................................................... 37

1/4Figure 4-15: Ratio (A /A ) as a function of γ and δ , in the case of a cone-cylinder-

I Econe. Calculated by the compiler. ...................................................................... 38

1/4Figure 4-16: Ratio (A /A ) as a function of γ and δ , in the case of a cone-cylinder-

I Econe. Calculated by the compiler. ...................................................................... 39

1/4Figure 4-17: Ratio (A /A ) as a function of γ and δ , in the case of a cone-cylinder-

I Econe. Calculated by the compiler. ...................................................................... 40

1/4Figure 4-18: Ratio (A /A ) as a function of γ and δ , in the case of a cone-cylinder-

I Econe. Calculated by the compiler. ...................................................................... 41

1/4Figure 4-19: Ratio (A /A ) as a function of γ and δ , in the case of a cone-cylinder-

I Econe. Calculated by the compiler. ...................................................................... 42

1/4Figure 4-20: Ratio (A /A ) as a function of γ and δ , in the case of a cone-cylinder-

I Econe. Calculated by the compiler. ...................................................................... 43

1/4Figure 4-21: Ratio (A /A ) as a function of γ for any value of Η/R, in the case of a

I Econe-cylinder-cone. Calculated by the compiler. ................................................ 44

1/4Figure 4-22: Ratio (A /A ) as a function of γ and Η/R, in the case of a cone-cylinder-

I Econe. Calculated by the compiler. ...................................................................... 45

1/4Figure 4-23: Ratio (A /A ) as a function of γ and Η/R, in the case of a cone-cylinder-

I Econe. Calculated by the compiler. ...................................................................... 46

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1/4

Figure 4-24: Ratio (AI/AE) as a function of γ and Η/R, in the case of a cone-cylinder-

cone. Calculated by the compiler. ...................................................................... 47

1/4Figure 4-25: Ratio (A /A ) as a function of γ and Η/R, in the case of a cone-cylinder-

I Econe. Calculated by the compiler. ...................................................................... 48

1/4Figure 4-26: Ratio (A /A ) as a function of Η/R, in the case of a prism. The curves

I Eplotted are those corresponding to the largest and smallest areas projected

from the Sun. Circular cylinder, n = ∞. Calculated by the compiler. .................... 50

1/4Figure 4-27: Ratio (A /A ) as a function of Η/R, in the case of a prism. The curves

I Eplotted are those corresponding to the largest and smallest areas projected

from the Sun. The values corresponding to Η/R ≤1 are also plotted in the

previous figure. Circular cylinder, n = ∞. Calculated by the compiler. ................. 51

1/4Figure 4-28: Ratio (A /A ) as a function of Η/R, in the case of a prism. The curves

I Eplotted are those corresponding to the largest and smallest areas projected

from the Sun. Circular cylinder, n = ∞. Calculated by the compiler. .................... 52

1/4Figure 4-29: Ratio (A /A ) as a function of Η/R, in the case of a prism. The curves

I Eplotted are those corresponding to the largest and smallest areas projected

from the Sun. The values corresponding to Η/R ≤1 are also plotted in the

previous figure. Circular cylinder, n = ∞. Calculated by the compiler. ................. 53

1/4Figure 4-30: Ratio (A /A ) as a function of Η/R, in the case of a prism. The curves

I Eplotted are those corresponding to the largest and smallest areas projected

from the Sun. Circular cylinder, n = ∞. Calculated by the compiler. .................... 54

1/4Figure 4-31: Ratio (A /A ) as a function of Η/R, in the case of a prism. The curves

I Eplotted are those corresponding to the largest and smallest areas projected

from the Sun. The values corresponding to Η/R ≤1 are also plotted in the

previous figure. Circular cylinder, n = ∞. Calculated by the compiler. ................. 55

1/4Figure 4-32: Ratio (A /A ) as a function of Η/R, in the case of a prism. The curves

I Eplotted are those corresponding to the largest and smallest areas projected

from the Sun. Circular cylinder, n = ∞. Calculated by the compiler. .................... 56

1/4Figure 4-33: Ratio (A /A ) as a function of Η/R, in the case of a prism. The curves

I Eplotted are those corresponding to the largest and smallest areas projected

from the Sun. The values corresponding to Η/R ≤1 are also plotted in the

previous figure. Circular cylinder, n = ∞. Calculated by the compiler. ................. 57

1/4Figure 4-34: Ratio (AI/AE) as a function of Η/R, in the case of a prism. The curves

plotted are those corresponding to the largest and smallest areas projectedfrom the Sun. Circular cylinder, n = ∞. Calculated by the compiler. .................... 58

1/4Figure 4-35: Ratio (A /A ) as a function of Η/R, in the case of a prism. The curves

I Eplotted are those corresponding to the largest and smallest areas projected

from the Sun. The values corresponding to Η/R ≤ 1 are also plotted in the

previous figure. Circular cylinder, n = ∞. Calculated by the compiler. ................. 59

1/4Figure 4-36: Ratio (A /A ) as a function of Η/R, in the case of a pyramid. The curves

I Eplotted are those corresponding to the largest and smallest areas projected

from the Sun. Circular cone, n = ∞. Calculated by the compiler. ......................... 61

1/4Figure 4-37: Ratio (A /A ) as a function of Η/R, in the case of a pyramid. The curves

I Eplotted are those corresponding to the largest and smallest areas projected

from the Sun. The values corresponding to Η/R ≤1 are also plotted in the

previous figure. Circular cone, n = ∞. Calculated by the compiler. ...................... 62

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1/4

Figure 4-38: Ratio (AI/AE) as a function of Η/R, in the case of a pyramid. The curves

plotted are those corresponding to the largest and smallest areas projectedfrom the Sun. Circular cone, n = ∞. Calculated by the compiler. ......................... 63

1/4Figure 4-39: Ratio (A /A ) as a function of Η/R, in the case of a pyramid. The curves

I Eplotted are those corresponding to the largest and smallest areas projected

from the Sun. The values corresponding to Η/R ≤1 are also plotted in the

previous figure. Circular cone, n = ∞. Calculated by the compiler. ...................... 64

1/4Figure 4-40: Ratio (A /A ) as a function of Η/R, in the case of a pyramid. The curves

I Eplotted are those corresponding to the largest and smallest areas projected

from the Sun. Circular cone, n = ∞. Calculated by the compiler. ......................... 65

1/4Figure 4-41: Ratio (A /A ) as a function of Η/R, in the case of a pyramid. The curves

I Eplotted are those corresponding to the largest and smallest areas projected

from the Sun. The values corresponding to Η/R ≤1 are also plotted in the

previous figure. Circular cone, n = ∞. Calculated by the compiler. ...................... 66

1/4Figure 4-42: Ratio (A /A ) as a function of Η/R, in the case of a pyramid. The curves

I Eplotted are those corresponding to the largest and smallest areas projected

from the Sun. Circular cone, n = ∞. Calculated by the compiler. ......................... 67

1/4Figure 4-43: Ratio (A /A ) as a function of Η/R, in the case of a pyramid. The curves

I Eplotted are those corresponding to the largest and smallest areas projected

from the Sun. The values corresponding to Η/R ≤1 are also plotted in the

previous figure. Circular cone, n = ∞. Calculated by the compiler. ...................... 68

1/4Figure 4-44: Ratio (A /A ) as a function of Η/R, in the case of a pyramid. The curves

I Eplotted are those corresponding to the largest and smallest areas projected

from the Sun. Circular cone, n = ∞. Calculated by the compiler. ......................... 69

1/4Figure 4-45: Ratio (A /A ) as a function of Η/R, in the case of a pyramid. The curves

I Eplotted are those corresponding to the largest and smallest areas projected

from the Sun. The values corresponding to Η/R ≤1 are also plotted in the

previous figure. Circular cone, n = ∞. Calculated by the compiler. ...................... 70

1/4Figure 4-46: Ratio (A /A ) as a function of Η/R, in the case of a pyramid - prism -

I Epyramid. The curves plotted are those corresponding to the largest and

smallest areas projected from the Sun. Cone - cylinder - cone, n = ∞.

Calculated by the compiler. ................................................................................ 71

1/4Figure 4-47: Ratio (AI/AE) as a function of Η/R, in the case of a pyramid - prism -

pyramid. The curves plotted are those corresponding to the largest andsmallest areas projected from the Sun. The values corresponding to Η/R ≤

1 are also plotted in the previous figure. Cone - cylinder - cone, n = ∞.

Calculated by the compiler. ................................................................................ 72

1/4Figure 4-48: Ratio (A /A ) as a function of Η/R, in the case of a pyramid - prism -

I Epyramid. The curves plotted are those corresponding to the largest and

smallest areas projected from the Sun. Cone - cylinder - cone, n = ∞.

Calculated by the compiler. ................................................................................ 73

1/4Figure 4-49: Ratio (A /A ) as a function of Η/R, in the case of a pyramid - prism -

I Epyramid. The curves plotted are those corresponding to the largest and

smallest areas projected from the Sun. The values corresponding to Η/R ≤

1 are also plotted in the previous figure. Cone - cylinder - cone, n = ∞.

Calculated by the compiler. ................................................................................ 74

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1/4

Figure 4-50: Ratio (AI/AE) as a function of Η/R, in the case of a pyramid - prism -

pyramid. The curves plotted are those corresponding to the largest andsmallest areas projected from the Sun. Cone - cylinder - cone, n = ∞.

Calculated by the compiler. ................................................................................ 75

1/4Figure 4-51: Ratio (A /A ) as a function of Η/R, in the case of a pyramid - prism -

I Epyramid. The curves plotted are those corresponding to the largest and

smallest areas projected from the Sun. The values corresponding to Η/R ≤

1 are also plotted in the previous figure. Cone - cylinder - cone, n = ∞.

Calculated by the compiler. ................................................................................ 76

1/4Figure 4-52: Ratio (A /A ) as a function of Η/R, in the case of a pyramid - prism -

I Epyramid. The curves plotted are those corresponding to the largest and

smallest areas projected from the Sun. Cone - cylinder - cone, n = ∞.

Calculated by the compiler. ................................................................................ 77

1/4Figure 4-53: Ratio (A /A ) as a function of Η/R, in the case of a pyramid - prism -

I Epyramid. The curves plotted are those corresponding to the largest and

smallest areas projected from the Sun. The values corresponding to Η/R ≤

1 are also plotted in the previous figure. Cone - cylinder - cone, n = ∞.

Calculated by the compiler. ................................................................................ 78

1/4Figure 4-54: Ratio (A /A ) as a function of Η/R, in the case of a pyramid - prism -

I Epyramid. The curves plotted are those corresponding to the largest and

smallest areas projected from the Sun. Cone - cylinder - cone, n = ∞.

Calculated by the compiler. ................................................................................ 79

1/4Figure 4-55: Ratio (A /A ) as a function of Η/R, in the case of a pyramid - prism -

I Epyramid. The curves plotted are those corresponding to the largest and

smallest areas projected from the Sun. Cone - cylinder - cone, n = ∞.

Calculated by the compiler. ................................................................................ 80

Figure 4-56: Temperature distribution on sphere. No spin. No internal radiation.Calculated by the compiler. ................................................................................ 81

Figure 4-57: Temperature distribution on sphere including internal radiation. No spin.

Calculated by the compiler. ................................................................................ 83

Figure 4-58: Temperature distribution on a two-dimensional cylinder. No spin. Nointernal radiation. Calculated by the compiler. .................................................... 85

Figure 4-59: Temperature distribution on a two - dimensional spinning cylinder for

several µ an γ values. No internal radiation. Calculated by the compiler. ............ 87

Figure 4-60: Temperature distribution on a two - dimensional spinning cylinder for

several µ an γ values. No internal radiation. Calculated by the compiler. ............ 88

Figure 4-61: Temperature distribution on cylinder. No spin. No internal radiation. From

Nichols (1961) [11]. ............................................................................................ 90

Figure 4-62: Temperature distribution on a cylindrical surface whose cross section is a

rectangle of aspect - ratio λ = 0,5. No internal radiation. Calculated by thecompiler. ............................................................................................................ 92

Figure 4-63: Temperature distribution on a cylindrical surface whose cross section is a

rectangle on aspect - ration λ = 1. No internal radiation. Calculated by thecompiler. ............................................................................................................ 93

Figure 4-64: Temperature distribution on a cylindrical surface whose cross section is a

rectangle on aspect - ration λ = 2. No internal radiation. Calculated by thecompiler. ............................................................................................................ 94

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Figure 4-65: Temperature distribution on cone. No spin. No internal radiation. From

Nichols (1961) [11]. ............................................................................................ 96

Figure 4-66: Temperature distribution on cone. No spin. No internal radiation. From

Nichols (1961) [11]. ............................................................................................ 97

Figure 4-67: Temperature distribution on cone. No spin. No internal radiation. From

Nichols (1961) [11]. ............................................................................................ 98

Figure 5-1: The ratio Τ T vs. the optical characteristics of the surface for different

RP / Pvalues of F . Shaded zone of a is enlarged in b. Calculated by the

compiler. .......................................................................................................... 101

Figure 5-2: Radiation equilibrium temperature Τ vs. ratio Τ T . Incoming radiation

RP RP / Pfrom different planets. After NASA - SP - 3051 (1965). ..................................... 102

Figure 5-3: Different estimates of radiation equilibrium temperature Τ vs. Τ T , for

RP RP / Pradiation from the Earth. Plotted from data by Johnson (1965) [9]. ................... 103

Figure 5-4: F as a function of λ and h / R in the case of a flat plate absorbing and

SP Pemitting on one side. Calculated by the compiler. ............................................. 105

Figure 5-5: F as a function of h / R in the case of a sphere. Calculated by theSP P

compiler. .......................................................................................................... 106

Figure 5-6: F as a function of λ and h / R in the case of a hemispherical surface

SΡ Pabsorbing and emitting on outer face. Calculated by the compiler. ................... 107

Figure 5-7: F as a function of λ and h / R in the case of a circular cylinder with

SΡ Pinsulated bases. Calculated by the compiler. .................................................... 109

Figure 5-8: F as a function of λ and h / R in the case of a finite height circular

SΡ Pcylinder. Calculated by the compiler. ................................................................ 110

Figure 5-9: F as a function of λ and h / R in the case of a finite height circular

SΡ Pcylinder. Calculated by the compiler. ................................................................ 111

Figure 5-10: F as a function of λ and h / R in the case of a finite height circular

SΡ Pcylinder. Calculated by the compiler. ................................................................ 112

Figure 5-11: F as a function of λ and h / R in the case of a finite height circular

SΡ Pcylinder. Calculated by the compiler. ................................................................ 113

Figure 5-12: F as a function of λ and h / R in the case of a finite height circular

SΡ Pcylinder. Calculated by the compiler. ................................................................ 114

Figure 5-13: F as a function of λ and h / R in the case of a finite height circular

SΡ P**...**

SLOVENSKI STANDARD

kSIST-TP FprCEN/CLC/TR 17603-31-03:2021

01-maj-2021

Vesoljska tehnika - Priročnik za toplotno zasnovo - 3. del: Površinska temperatura

vesoljskih plovilSpace Engineering - Thermal design handbook - Part 3: Spacecraft Surface Temperature

Raumfahrttechnik - Handbuch für thermisches Design - Teil 3: Oberflächentemperatur

von RaumfahrzeugenIngénierie spatiale - Manuel de conception thermique - Partie 3: Température de surface

des véhicules spatiauxTa slovenski standard je istoveten z: FprCEN/CLC/TR 17603-31-03

ICS:

49.140 Vesoljski sistemi in operacije Space systems and

operations

kSIST-TP FprCEN/CLC/TR 17603-31- en,fr,de

03:2021

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

---------------------- Page: 1 ----------------------kSIST-TP FprCEN/CLC/TR 17603-31-03:2021

---------------------- Page: 2 ----------------------

kSIST-TP FprCEN/CLC/TR 17603-31-03:2021

TECHNICAL REPORT

FINAL DRAFT

FprCEN/CLC/TR 17603-

RAPPORT TECHNIQUE

31-03

TECHNISCHER BERICHT

February 2021

ICS 49.140

English version

Space Engineering - Thermal design handbook - Part 3:

Spacecraft Surface Temperature

Ingénierie spatiale - Manuel de conception thermique - Raumfahrttechnik - Handbuch für thermisches Design -

Partie 3: Température de surface des véhicules Teil 3: Oberflächentemperatur von Raumfahrzeugen

spatiauxThis draft Technical Report is submitted to CEN members for Vote. It has been drawn up by the Technical Committee

CEN/CLC/JTC 5.CEN and CENELEC members are the national standards bodies and national electrotechnical committees of Austria, Belgium,

Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy,

Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Republic of North Macedonia, Romania, Serbia,

Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United Kingdom.Recipients of this draft are invited to submit, with their comments, notification of any relevant patent rights of which they are

aware and to provide supporting documentation.Warning : This document is not a Technical Report. It is distributed for review and comments. It is subject to change without

notice and shall not be referred to as a Technical Report.CEN-CENELEC Management Centre:

Rue de la Science 23, B-1040 Brussels

© 2021 CEN/CENELEC All rights of exploitation in any form and by any means Ref. No. FprCEN/CLC/TR 17603-31-03:2021 E

reserved worldwide for CEN national Members and forCENELEC Members.

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Table of contents

European Foreword ................................................................................................. 10

1 Scope ..................................................................................................................... 11

2 References ............................................................................................................ 12

3 Terms, definitions and symbols .......................................................................... 13

3.1 Terms and definitions ............................................................................................. 13

3.2 Symbols .................................................................................................................. 13

4 Solar radiation ...................................................................................................... 15

4.1 General ................................................................................................................... 15

4.2 Infinitely conductive planar surfaces ....................................................................... 19

4.2.1 Flat plate emitting on one or both sides ..................................................... 19

4.3 Infinitely conductive spherical surfaces ................................................................... 21

4.3.1 Sphere ...................................................................................................... 21

4.4 Infinitely conductive cylindrical surfaces .................................................................. 22

4.4.1 Two-dimensional circular cylinder ............................................................. 22

4.4.2 Three-dimensional circular cylinder ........................................................... 23

4.5 Infinitely conductive conical surfaces ...................................................................... 25

4.5.1 Semi-infinite circular cone ......................................................................... 25

4.5.2 Finite circular cone with insulated base. (axial configuration) .................... 27

4.5.3 Finite height circular cone ......................................................................... 29

4.6 Infinitely conductive cylindrical-conical surfaces ..................................................... 31

4.6.1 Cone-cylinder-cone ................................................................................... 31

4.7 Infinitely conductive prismatic surfaces ................................................................... 49

4.7.1 Prism with an n-sided regular polygonal section ........................................ 49

4.8 Infinitely conductive pyramidal surfaces .................................................................. 60

4.8.1 Pyramid with an n-sided regular polygonal section .................................... 60

4.9 Infinitely conductive prismatic-pyramidal surfaces................................................... 70

4.9.1.1 Pyramid-prism-pyramid with an n-sided regular polygonal ........................ 70

4.10 Thin-walled spherical bodies. Finite conductivity ..................................................... 80

4.10.1 Non-spinning sphere ................................................................................. 80

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4.10.2 Non-spinning sphere. Including internal radiation ...................................... 82

4.11 Thin-walled cylindrical bodies. Finite conductivity. .................................................. 83

4.11.1 Non-spinning two-dimensional circular cylinder ......................................... 83

4.11.2 Spinning two-dimensional circular cylinder ................................................ 85

4.11.3 Circular cylinder. solar radiation parallel to axis of symmetry .................... 88

4.11.4 Cylindrical surface of rectangular cross section. Solar radiationnormal to face ........................................................................................... 89

4.12 Thin-walled conical bodies. Conductivity ................................................................. 94

4.12.1 Non-spinning cone .................................................................................... 94

5 Planetary radiation ............................................................................................... 98

5.1 General ................................................................................................................... 98

5.2 Infinitely conductive planar surfaces ..................................................................... 103

5.2.1 Flat plate absorbing and emitting on one side ......................................... 103

5.3 Infinitely conductive spherical surfaces ................................................................. 104

5.3.1 Sphere .................................................................................................... 104

5.3.2 Hemispherical surface absorbing and emitting on outer face .................. 105

5.4 Infinitely conductive cylindrical surfaces ................................................................ 107

5.4.1 Circular cylinder with insulated bases...................................................... 107

5.4.2 Finite height circular cylinder ................................................................... 108

5.5 Infinitely conductive conical surfaces .................................................................... 118

5.5.1 Circular cone with insulated base ............................................................ 118

5.5.2 Finite height circular cone ....................................................................... 121

6 Albedo radiation ................................................................................................. 124

6.1 General ................................................................................................................. 124

6.2 Infinitely conductive planar surfaces ..................................................................... 129

6.2.1 Flat plate absorbing and emitting on one side ......................................... 129

6.3 Infinitely conductive spherical surfaces ................................................................. 134

6.3.1 Sphere .................................................................................................... 134

6.4 Infinitely conductive cylindrical surfaces ................................................................ 138

6.4.1 Circular cylinder with insulated bases...................................................... 138

Bibliography ........................................................................................................... 143

Figures1/4

Figure 4-1: The function T (A /A ) vs. the distance to the Sun. Calculated by the

R E Icompiler. ............................................................................................................ 16

1/4Figure 4-2: The function T (A /A ) vs. the optical characteristics of the surface.

R E IShaded zone of a is enlarged in b. Calculated by the compiler. .......................... 17

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Figure 4-3: Temperature T as a function of / and A /A for d = 1 AU. Shaded zone

R s I Eof a is enlarged in b. Calculated by the compiler. ............................................... 18

1/4Figure 4-4: Ration (A /A ) as a function of , in the case of a flat plate. Calculated by

I Ethe compiler. ...................................................................................................... 20

1/4Figure 4-5: Ratio (A /A ) as a function of and H/R, in the case of a finite height

I Ecircular cylinder. Calculated by the compiler. ...................................................... 24

1/4Figure 4-6: Ratio (A /A ) as a function of , in the case of a semi-infinite circular cone.

I ECalculated by the compiler. ................................................................................ 26

1/4Figure 4-7: Ratio (A /A ) as a function of , in the case of a finite circular cone with

I Einsulated base (axial configuration). Calculated by the compiler. ........................ 28

1/4Figure 4-8: Ratio (A /A ) as a function of and , in the case of a finite height cone.

I ECalculated by the compiler. ................................................................................ 30

1/4Figure 4-9: Ratio (A /A ) as a function of and , in the case of a cone-cylinder-cone.

I ECalculated by the compiler. ................................................................................ 32

1/4Figure 4-10: Ratio (A /A ) as a function of and , in the case of a cone-cylinder-

I Econe. Calculated by the compiler. ...................................................................... 33

1/4Figure 4-11: Ratio (AI/AE) as a function of and , in the case of a cone-cylinder-

cone. Calculated by the compiler. ...................................................................... 34

1/4Figure 4-12: Ratio (A /A ) as a function of and , in the case of a cone-cylinder-

I Econe. Calculated by the compiler. ...................................................................... 35

1/4Figure 4-13: Ratio (A /A ) as a function of and , in the case of a cone-cylinder-

I Econe. Calculated by the compiler. ...................................................................... 36

1/4Figure 4-14: Ratio (A /A ) as a function of and , in the case of a cone-cylinder-

I Econe. Calculated by the compiler. ...................................................................... 37

1/4Figure 4-15: Ratio (A /A ) as a function of and , in the case of a cone-cylinder-

I Econe. Calculated by the compiler. ...................................................................... 38

1/4Figure 4-16: Ratio (A /A ) as a function of and , in the case of a cone-cylinder-

I Econe. Calculated by the compiler. ...................................................................... 39

1/4Figure 4-17: Ratio (A /A ) as a function of and , in the case of a cone-cylinder-

I Econe. Calculated by the compiler. ...................................................................... 40

1/4Figure 4-18: Ratio (A /A ) as a function of and , in the case of a cone-cylinder-

I Econe. Calculated by the compiler. ...................................................................... 41

1/4Figure 4-19: Ratio (A /A ) as a function of and , in the case of a cone-cylinder-

I Econe. Calculated by the compiler. ...................................................................... 42

1/4Figure 4-20: Ratio (A /A ) as a function of and , in the case of a cone-cylinder-

I Econe. Calculated by the compiler. ...................................................................... 43

1/4Figure 4-21: Ratio (A /A ) as a function of for any value of /R, in the case of a

I Econe-cylinder-cone. Calculated by the compiler. ................................................ 44

1/4Figure 4-22: Ratio (A /A ) as a function of and /R, in the case of a cone-cylinder-

I Econe. Calculated by the compiler. ...................................................................... 45

1/4Figure 4-23: Ratio (A /A ) as a function of and /R, in the case of a cone-cylinder-

I Econe. Calculated by the compiler. ...................................................................... 46

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1/4

Figure 4-24: Ratio (A /A ) as a function of and /R, in the case of a cone-cylinder-

I Econe. Calculated by the compiler. ...................................................................... 47

1/4Figure 4-25: Ratio (A /A ) as a function of and /R, in the case of a cone-cylinder-

I Econe. Calculated by the compiler. ...................................................................... 48

1/4Figure 4-26: Ratio (A /A ) as a function of /R, in the case of a prism. The curves

I Eplotted are those corresponding to the largest and smallest areas projected

from the Sun. Circular cylinder, n = . Calculated by the compiler. .................... 50

1/4Figure 4-27: Ratio (A /A ) as a function of /R, in the case of a prism. The curves

I Eplotted are those corresponding to the largest and smallest areas projected

from the Sun. The values corresponding to /R 1 are also plotted in the

previous figure. Circular cylinder, n = . Calculated by the compiler. ................. 51

1/4Figure 4-28: Ratio (A /A ) as a function of /R, in the case of a prism. The curves

I Eplotted are those corresponding to the largest and smallest areas projected

from the Sun. Circular cylinder, n = . Calculated by the compiler. .................... 52

1/4Figure 4-29: Ratio (A /A ) as a function of /R, in the case of a prism. The curves

I Eplotted are those corresponding to the largest and smallest areas projected

from the Sun. The values corresponding to /R 1 are also plotted in the

previous figure. Circular cylinder, n = . Calculated by the compiler. ................. 53

1/4Figure 4-30: Ratio (A /A ) as a function of /R, in the case of a prism. The curves

I Eplotted are those corresponding to the largest and smallest areas projected

from the Sun. Circular cylinder, n = . Calculated by the compiler. .................... 54

1/4Figure 4-31: Ratio (A /A ) as a function of /R, in the case of a prism. The curves

I Eplotted are those corresponding to the largest and smallest areas projected

from the Sun. The values corresponding to /R 1 are also plotted in the

previous figure. Circular cylinder, n = . Calculated by the compiler. ................. 55

1/4Figure 4-32: Ratio (A /A ) as a function of /R, in the case of a prism. The curves

I Eplotted are those corresponding to the largest and smallest areas projected

from the Sun. Circular cylinder, n = . Calculated by the compiler. .................... 56

1/4Figure 4-33: Ratio (A /A ) as a function of /R, in the case of a prism. The curves

I Eplotted are those corresponding to the largest and smallest areas projected

from the Sun. The values corresponding to /R 1 are also plotted in the

previous figure. Circular cylinder, n = . Calculated by the compiler. ................. 57

1/4Figure 4-34: Ratio (A /A ) as a function of /R, in the case of a prism. The curves

I Eplotted are those corresponding to the largest and smallest areas projected

from the Sun. Circular cylinder, n = . Calculated by the compiler. .................... 58

1/4Figure 4-35: Ratio (A /A ) as a function of /R, in the case of a prism. The curves

I Eplotted are those corresponding to the largest and smallest areas projected

from the Sun. The values corresponding to /R 1 are also plotted in the

previous figure. Circular cylinder, n = . Calculated by the compiler. ................. 59

1/4Figure 4-36: Ratio (A /A ) as a function of /R, in the case of a pyramid. The curves

I Eplotted are those corresponding to the largest and smallest areas projected

from the Sun. Circular cone, n = . Calculated by the compiler. ......................... 61

1/4Figure 4-37: Ratio (A /A ) as a function of /R, in the case of a pyramid. The curves

I Eplotted are those corresponding to the largest and smallest areas projected

from the Sun. The values corresponding to /R 1 are also plotted in the

previous figure. Circular cone, n = . Calculated by the compiler. ...................... 62

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1/4

Figure 4-38: Ratio (A /A ) as a function of /R, in the case of a pyramid. The curves

I Eplotted are those corresponding to the largest and smallest areas projected

from the Sun. Circular cone, n = . Calculated by the compiler. ......................... 63

1/4Figure 4-39: Ratio (A /A ) as a function of /R, in the case of a pyramid. The curves

I Eplotted are those corresponding to the largest and smallest areas projected

from the Sun. The values corresponding to /R 1 are also plotted in the

previous figure. Circular cone, n = . Calculated by the compiler. ...................... 64

1/4Figure 4-40: Ratio (A /A ) as a function of /R, in the case of a pyramid. The curves

I Eplotted are those corresponding to the largest and smallest areas projected

from the Sun. Circular cone, n = . Calculated by the compiler. ......................... 65

1/4Figure 4-41: Ratio (A /A ) as a function of /R, in the case of a pyramid. The curves

I Eplotted are those corresponding to the largest and smallest areas projected

from the Sun. The values corresponding to /R 1 are also plotted in the

previous figure. Circular cone, n = . Calculated by the compiler. ...................... 66

1/4Figure 4-42: Ratio (A /A ) as a function of /R, in the case of a pyramid. The curves

I Eplotted are those corresponding to the largest and smallest areas projected

from the Sun. Circular cone, n = . Calculated by the compiler. ......................... 67

1/4Figure 4-43: Ratio (A /A ) as a function of /R, in the case of a pyramid. The curves

I Eplotted are those corresponding to the largest and smallest areas projected

from the Sun. The values corresponding to /R 1 are also plotted in the

previous figure. Circular cone, n = . Calculated by the compiler. ...................... 68

1/4Figure 4-44: Ratio (A /A ) as a function of /R, in the case of a pyramid. The curves

I Eplotted are those corresponding to the largest and smallest areas projected

from the Sun. Circular cone, n = . Calculated by the compiler. ......................... 69

1/4Figure 4-45: Ratio (A /A ) as a function of /R, in the case of a pyramid. The curves

I Eplotted are those corresponding to the largest and smallest areas projected

from the Sun. The values corresponding to /R 1 are also plotted in the

previous figure. Circular cone, n = . Calculated by the compiler. ...................... 70

1/4Figure 4-46: Ratio (A /A ) as a function of /R, in the case of a pyramid - prism -

I Epyramid. The curves plotted are those corresponding to the largest and

smallest areas projected from the Sun. Cone - cylinder - cone, n = .

Calculated by the compiler. ................................................................................ 71

1/4Figure 4-47: Ratio (A /A ) as a function of /R, in the case of a pyramid - prism -

I Epyramid. The curves plotted are those corresponding to the largest and

smallest areas projected from the Sun. The values corresponding to /R

1 are also plotted in the previous figure. Cone - cylinder - cone, n = .

Calculated by the compiler. ................................................................................ 72

1/4Figure 4-48: Ratio (A /A ) as a function of /R, in the case of a pyramid - prism -

I Epyramid. The curves plotted are those corresponding to the largest and

smallest areas projected from the Sun. Cone - cylinder - cone, n = .

Calculated by the compiler. ................................................................................ 73

1/4Figure 4-49: Ratio (A /A ) as a function of /R, in the case of a pyramid - prism -

I Epyramid. The curves plotted are those corresponding to the largest and

smallest areas projected from the Sun. The values corresponding to /R

1 are also plotted in the previous figure. Cone - cylinder - cone, n = .

Calculated by the compiler. ................................................................................ 74

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1/4

Figure 4-50: Ratio (A /A ) as a function of /R, in the case of a pyramid - prism -

I Epyramid. The curves plotted are those corresponding to the largest and

smallest areas projected from the Sun. Cone - cylinder - cone, n = .

Calculated by the compiler. ................................................................................ 75

1/4Figure 4-51: Ratio (A /A ) as a function of /R, in the case of a pyramid - prism -

I Epyramid. The curves plotted are those corresponding to the largest and

smallest areas projected from the Sun. The values corresponding to /R

1 are also plotted in the previous figure. Cone - cylinder - cone, n = .

Calculated by the compiler. ................................................................................ 76

1/4Figure 4-52: Ratio (AI/AE) as a function of /R, in the case of a pyramid - prism -

pyramid. The curves plotted are those corresponding to the largest andsmallest areas projected from the Sun. Cone - cylinder - cone, n = .

Calculated by the compiler. ................................................................................ 77

1/4Figure 4-53: Ratio (A /A ) as a function of /R, in the case of a pyramid - prism -

I Epyramid. The curves plotted are those corresponding to the largest and

smallest areas projected from the Sun. The values corresponding to /R

1 are also plotted in the previous figure. Cone - cylinder - cone, n = .

Calculated by the compiler. ................................................................................ 78

1/4Figure 4-54: Ratio (AI/AE) as a function of /R, in the case of a pyramid - prism -

pyramid. The curves plotted are those corresponding to the largest andsmallest areas projected from the Sun. Cone - cylinder - cone, n = .

Calculated by the compiler. ................................................................................ 79

1/4Figure 4-55: Ratio (A /A ) as a function of /R, in the case of a pyramid - prism -

I Epyramid. The curves plotted are those corresponding to the largest and

smallest areas projected from the Sun. Cone - cylinder - cone, n = .

Calculated by the compiler. ................................................................................ 80

Figure 4-56: Temperature distribution on sphere. No spin. No internal radiation.Calculated by the compiler. ................................................................................ 81

Figure 4-57: Temperature distribution on sphere including internal radiation. No spin.

Calculated by the compiler. ................................................................................ 83

Figure 4-58: Temperature distribution on a two-dimensional cylinder. No spin. Nointernal radiation. Calculated by the compiler. .................................................... 85

Figure 4-59: Temperature distribution on a two - dimensional spinning cylinder for

several an values. No internal radiation. Calculated by the compiler. ............ 86

Figure 4-60: Temperature distribution on a two - dimensional spinning cylinder for

several an values. No internal radiation. Calculated by the compiler. ............ 87

Figure 4-61: Temperature distribution on cylinder. No spin. No internal radiation. From

Nichols (1961) [11]. ............................................................................................ 89

Figure 4-62: Temperature distribution on a cylindrical surface whose cross section is a

rectangle of aspect - ratio = 0,5. No internal radiation. Calculated by thecompiler. ............................................................................................................ 91

Figure 4-63: Temperature distribution on a cylindrical surface whose cross section is a

rectangle on aspect - ration = 1. No internal radiation. Calculated by thecompiler. ............................................................................................................ 92

Figure 4-64: Temperature distribution on a cylindrical surface whose cross section is a

rectangle on aspect - ration = 2. No internal radiation. Calculated by thecompiler. ............................................................................................................ 93

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Figure 4-65: Temperature distribution on cone. No spin. No internal radiation. From

Nichols (1961) [11]. ............................................................................................ 95

Figure 4-66: Temperature distribution on cone. No spin. No internal radiation. From

Nichols (1961) [11]. ............................................................................................ 96

Figure 4-67: Temperature distribution on cone. No spin. No internal radiation. From

Nichols (1961) [11]. ............................................................................................ 97

Figure 5-1: The ratio T vs. the optical characteristics of the surface for different

RP / Pvalues of F . Shaded zone of a is enlarged in b. Calculated by the

SP

compiler. .......................................................................................................... 100

Figure 5-2: Radiation equilibrium temperature vs. ratio T . Incoming radiation

RP RP / Pfrom different planets. After NASA - SP - 3051 (1965). ..................................... 101

Figure 5-3: Different estimates of radiation equilibrium temperature vs. T , for

RP RP / Pradiation from the Earth. Plotted from data by Johnson (1965) [9]. ................... 102

Figure 5-4: F as a function of and h / R in the case of a flat plate absorbing and

SP Pemitting on one side. Calculated by the compiler. ............................................. 104

Figure 5-5: F as a function of h / R in the case of a sphere. Calculated by theSP P

compiler. .......................................................................................................... 105

Figure 5-6: F as a function of and h / R in the case of a hemispherical surface

S Pabsorbing and emitting on outer face. Calculated by the compiler. ................... 106

Figure 5-7: F as a function of and h / R in the case of a circular cylinder with

S Pinsulated bases. Calculated by the compiler. .................................................... 108

Figure 5-8: F as a function of and h / R in the case of a finite height circular

S Pcylinder. Calculated by the compiler. ................................................................ 109

Figure 5-9: F as a function of and h / R in the case of a finite height circular

S Pcylinder. Calculated by the compiler. ................................................................ 110

Figure 5-10: F as a function of and h / R in the case of a finite height circular

S Pcylinder. Calculated by the compiler. ................................................................ 111

**...**

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