Abstract

No abstract available.

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. Buckley, “On the radiation from the inside of a circular cylinder,” Phil. Mag. 4, 753 (1927); Phil. Mag. 6, 447 (1928); Phil. Mag. 17, 576 (1934).
  2. Z. Yamauti, “Recherche d’un radiateur intégral au moyen d’un corps cylindrique,” Com. Int. Poids et Mésures, Procès-verbaux 16, 243 (1933).
  3. K. Hisano, “Light flux distribution in a rectangular parallelepiped and its simplifying scale,” Researches Electrotech. Lab., Tokyo, No. 394 (1936).
  4. H. C. Hottell and F. Keller, “Effect of reradiation on heat transmission in furnaces and through openings,” A. S. M. E. annual meeting (December, 1932).
  5. A. D. Moore, “Interreflection by the increment method as applied to a light court,” Trans. I. E. S. 24, 629 (1929).
  6. H. F. Meacock and G. E. V. Lambert, “Efficiency of lightwells,” (1930).
  7. See Parry Moon, “Interreflections in lightwells,” to appear in this journal.
  8. Parry Moon, “Basic principles in illumination calculations,” J. Opt. Soc. Am. 29, 108 (1939).
    [Crossref]
  9. Parry Moon, “On interreflections,” J. Opt. Soc. Am. 30, 195 (1940).
    [Crossref]

1940 (1)

1939 (1)

1933 (1)

Z. Yamauti, “Recherche d’un radiateur intégral au moyen d’un corps cylindrique,” Com. Int. Poids et Mésures, Procès-verbaux 16, 243 (1933).

1932 (1)

H. C. Hottell and F. Keller, “Effect of reradiation on heat transmission in furnaces and through openings,” A. S. M. E. annual meeting (December, 1932).

1929 (1)

A. D. Moore, “Interreflection by the increment method as applied to a light court,” Trans. I. E. S. 24, 629 (1929).

1927 (1)

H. Buckley, “On the radiation from the inside of a circular cylinder,” Phil. Mag. 4, 753 (1927); Phil. Mag. 6, 447 (1928); Phil. Mag. 17, 576 (1934).

Buckley, H.

H. Buckley, “On the radiation from the inside of a circular cylinder,” Phil. Mag. 4, 753 (1927); Phil. Mag. 6, 447 (1928); Phil. Mag. 17, 576 (1934).

Hisano, K.

K. Hisano, “Light flux distribution in a rectangular parallelepiped and its simplifying scale,” Researches Electrotech. Lab., Tokyo, No. 394 (1936).

Hottell, H. C.

H. C. Hottell and F. Keller, “Effect of reradiation on heat transmission in furnaces and through openings,” A. S. M. E. annual meeting (December, 1932).

Keller, F.

H. C. Hottell and F. Keller, “Effect of reradiation on heat transmission in furnaces and through openings,” A. S. M. E. annual meeting (December, 1932).

Lambert, G. E. V.

H. F. Meacock and G. E. V. Lambert, “Efficiency of lightwells,” (1930).

Meacock, H. F.

H. F. Meacock and G. E. V. Lambert, “Efficiency of lightwells,” (1930).

Moon, Parry

Moore, A. D.

A. D. Moore, “Interreflection by the increment method as applied to a light court,” Trans. I. E. S. 24, 629 (1929).

Yamauti, Z.

Z. Yamauti, “Recherche d’un radiateur intégral au moyen d’un corps cylindrique,” Com. Int. Poids et Mésures, Procès-verbaux 16, 243 (1933).

A. S. M. E. annual meeting (1)

H. C. Hottell and F. Keller, “Effect of reradiation on heat transmission in furnaces and through openings,” A. S. M. E. annual meeting (December, 1932).

Com. Int. Poids et Mésures, Procès-verbaux (1)

Z. Yamauti, “Recherche d’un radiateur intégral au moyen d’un corps cylindrique,” Com. Int. Poids et Mésures, Procès-verbaux 16, 243 (1933).

J. Opt. Soc. Am. (2)

Phil. Mag. (1)

H. Buckley, “On the radiation from the inside of a circular cylinder,” Phil. Mag. 4, 753 (1927); Phil. Mag. 6, 447 (1928); Phil. Mag. 17, 576 (1934).

Trans. I. E. S. (1)

A. D. Moore, “Interreflection by the increment method as applied to a light court,” Trans. I. E. S. 24, 629 (1929).

Other (3)

H. F. Meacock and G. E. V. Lambert, “Efficiency of lightwells,” (1930).

See Parry Moon, “Interreflections in lightwells,” to appear in this journal.

K. Hisano, “Light flux distribution in a rectangular parallelepiped and its simplifying scale,” Researches Electrotech. Lab., Tokyo, No. 394 (1936).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Equations (122)

Equations on this page are rendered with MathJax. Learn more.

K 21 ( s ) = - 0 K 11 ( s - t ) d t .
K 31 ( s ) = l K 11 ( s - t ) d t .
K 23 ( l ) = - 0 K 13 ( t ) d t .
K 23 ( l ) = K 32 ( l ) .
d F 12 = ( K 12 d t ) S ,
d F 21 = K 21 ( p d t ) .
K 12 = K 21 α ,
K 13 = K 31 α .
K 21 ( 0 ) = 1 2             K 31 ( l ) = 1 2             K 23 ( 0 ) = 1 ,
L 1 ( s ) = L 01 ( s ) + ρ 1 { 0 l K 11 s - t L 1 ( t ) d t + K 21 ( s ) · L 2 + K 31 ( s ) · L 3 } L 2 = L 02 + ρ 2 { 0 l K 12 ( t ) L 1 ( t ) d t + K 32 ( l ) · L 3 } , L 3 = L 03 + ρ 3 { 0 l K 13 ( t ) L 1 ( t ) d t + K 23 ( l ) · L 2 } . }
L 1 ( s ) = L 0 ( s ) + ρ 1 0 l K ( s , t ) L 1 ( t ) d t ,
L 0 ( s ) = L 01 ( s ) + ρ 1 1 - ρ 2 ρ 3 K 23 2 × { [ K 21 ( s ) + ρ 3 K 31 ( s ) K 23 ( l ) ] L 02 + [ K 31 ( s ) + ρ 2 K 21 ( s ) K 23 ( l ) ] L 03 } ,
K ( s , t ) = K 11 ( s - t ) + α 1 - ρ 2 ρ 3 K 23 2 × { [ K 21 ( s ) + ρ 3 K 31 ( s ) K 23 ( l ) ] ρ 2 K 21 ( t ) + [ K 31 ( s ) + ρ 2 K 21 ( s ) K 23 ( l ) ] ρ 3 K 31 ( t ) } .
L 2 = 1 1 - ρ 2 ρ 3 K 23 2 { L 02 + ρ 2 K 23 ( l ) · L 03 + α ρ 2 0 l [ K 21 ( t ) + ρ 3 K 31 ( t ) × K 23 ( l ) ] L 1 ( t ) d t } ,
L 3 = 1 1 - ρ 2 ρ 3 K 23 2 { L 03 + ρ 3 K 23 ( l ) · L 02 + α ρ 3 0 l [ K 31 ( t ) + ρ 2 K 21 ( t ) × K 23 ( l ) ] L 1 ( t ) d t } .
K 11 s - t = A e - a s - t .
K 21 ( s ) = A - 0 e - a ( s - t ) d t = A a e - a s ,
K 31 ( s ) = A l e - a ( t - s ) d t = A a e - a ( l - s ) ,
K 23 ( l ) = K 32 ( l ) = α l K 21 ( t ) d t = α A a l e - a t d t = α A a 2 e - a l .
A = a / 2 ,             a = 2 a .
K 11 s - t = ( a / 2 ) e - a s - t ,
K 21 ( s ) = 1 2 e - a s ,
K 31 ( s ) = 1 2 e - a ( l - s ) ,
K 23 ( l ) = e - a l .
L 0 ( s ) = L 01 ( s ) + ( ρ 1 / 2 M ) [ N 23 ( s ) · L 02 + N 32 ( s ) · L 03 ] ,
K ( s , t ) = ( a / 2 ) { e - a s - t + ( 1 / M ) [ N 23 ( s ) ρ 2 e - a t + N 32 ( s ) ρ 3 e - a ( l - t ) ] } ,
M = 1 - ρ 2 ρ 3 e - 2 a l ,
N 23 ( s ) = e a ( l - s ) + ρ 3 e - a ( l - s ) ,
N 32 ( s ) = e a s + ρ 2 e - a s .
L 2 ( l ) = 1 M { L 02 + ρ 2 e - a l × [ L 03 + a 0 l N 23 ( t ) · L 1 ( t ) d t ] } ,
L 3 ( l ) = 1 M { L 03 + ρ 3 e - a l × [ L 02 + a 0 l N 32 ( t ) · L 1 ( t ) d t ] } .
L 1 ( s ) = B cosh k s + C sinh k s + D .
B = 2 ( a 2 - k 2 ) a ν σ - μ τ λ σ - ρ μ ,
C = 2 ( a 2 - k 2 ) a λ τ - ν ρ λ σ - ρ μ ,
D = L 01 / ( 1 - ρ 1 ) ,
k = a ( 1 - ρ 1 ) 1 2 ,
λ = ( 1 + ρ 2 ) { [ ( a + k ) - ρ 3 ( a - k ) ] e k l + [ ( a - k ) - ρ 3 ( a + k ) ] e - k l } + 2 a ( 1 - ρ 2 ) ( e a l + ρ 3 e - a l ) , ρ = ( 1 - ρ 2 ) { [ ( a + k ) - ρ 3 ( a - k ) ] e k l + [ ( a - k ) - ρ 3 ( a + k ) ] e - k l } - 2 a ( 1 - ρ 2 ) ( e a l - ρ 3 e - a l ) , μ = ( 1 + ρ 2 ) { [ ( a + k ) - ρ 3 ( a - k ) ] e k l - [ ( a - k ) - ρ 3 ( a + k ) ] e - k l } - 2 k ( 1 + ρ 2 ) ( e a l + ρ 3 - a l ) , σ = ( 1 - ρ 2 ) { [ ( a + k ) - ρ 3 ( a - k ) ] e k l - [ ( a - k ) - ρ 3 ( a + k ) ] e - k l } + 2 k ( 1 + ρ 2 ) ( e a l - ρ 3 e - a l ) , ν = L 02 ( e a l + ρ 3 e - a l ) + L 03 ( 1 + ρ 2 ) - D { ( 1 - ρ 2 ) ( e a l + ρ 3 e - a l ) + ( 1 + ρ 2 ) ( 1 - ρ 3 ) } , τ = - L 02 ( e a l - ρ 3 e - a l ) + L 03 ( 1 - ρ 2 ) + D { ( 1 - ρ 2 ) ( e a l - ρ 3 e - a l ) - ( 1 - ρ 2 ) ( 1 - ρ 3 ) } .
B = ρ 1 { L 02 n + ( 1 - ρ 1 ) 1 2 ( 1 + ρ 2 ) L 03 - D [ ( 1 - ρ 2 ) n + ( 1 - ρ 1 ) 1 2 ( 1 + ρ 2 ) ( 1 - ρ 3 ) ] } ( 1 - ρ 2 ) n + ( 1 - ρ 1 ) 1 2 ( 1 + ρ 2 ) m ,
C = ρ 1 { - L 02 m + ( 1 - ρ 2 ) L 03 + D [ ( 1 - ρ 2 ) m - ( 1 - ρ 2 ) ( 1 - ρ 3 ) ] } ( 1 - ρ 2 ) n + ( 1 - ρ 1 ) 1 2 ( 1 + ρ 2 ) m ,
m = ( 1 - ρ 3 ) cosh k l + ( 1 - ρ 1 ) 1 2 ( 1 + ρ 3 ) sinh k l ,
n = ( 1 - ρ 3 ) sinh k l + ( 1 - ρ 1 ) 1 2 ( 1 + ρ 3 ) cosh k l .
L 2 ( l ) = 1 M { L 02 e a l + ρ 2 [ L 03 + a 0 l ( e a ( l - t ) + ρ 3 e - a ( l - t ) ) · ( D + B cosh k t + C sinh k t ) d t ] } ,
L 2 ( l ) = ( 1 - ρ 2 ρ 3 e - 2 a l ) - 1 { L 02 + ρ 2 e - a l [ L 03 + L 01 1 - ρ 1 { v 3 - ( 1 - ρ 3 ) } + B ρ 1 { v 3 - ( 1 - ρ 3 ) cosh k l - ( 1 - ρ 1 ) 1 2 ( 1 + ρ 3 ) sinh k l } + C ρ 1 { ( 1 - ρ 1 ) 1 2 u 3 - ( 1 - ρ 3 ) sinh k l - ( 1 - ρ 1 ) 1 2 ( 1 + ρ 3 ) cosh k l } ] } .
L 3 ( l ) = ( 1 - ρ 2 ρ 3 e - 2 a l ) - 1 { L 03 + ρ 3 e - a l [ L 02 + L 01 1 - ρ 1 { v 2 - ( 1 - ρ 2 ) } + B ρ 1 { v 2 cosh k l - ( 1 - ρ 1 ) 1 2 u 2 sinh k l - ( 1 - ρ 2 ) } + C ρ 1 { u 2 sinh k l - ( 1 - ρ 1 ) 1 2 u 2 cosh k l + ( 1 - ρ 1 ) 1 2 ( 1 + ρ 2 ) } ] } ,
u 2 = e a l + ρ 2 e - a l ,             v 2 = e a l - ρ 2 e - a l ,             u 3 = e a l + ρ 3 e - a l ,             v 3 = e a l - ρ 3 e - a l .
L 02 = L 03 = 0 ,             ρ 2 = ρ 3 = 0.
B = - L 01 ρ 1 1 - ρ 1 ( 1 - ρ 1 ) 1 2 ( cosh k l + 1 ) + sinh k l 2 ( 1 - ρ 1 ) 1 2 cosh k l + ( 2 - ρ 1 ) sinh k l ,
C = L 01 ρ 1 1 - ρ 1 ( cosh k l - 1 ) + ( 1 - ρ 1 ) 1 2 sinh k l 2 ( 1 - ρ 1 ) 1 2 cosh k l + ( 2 - ρ 1 ) sinh k l ,
D = L 01 / ( 1 - ρ 1 ) ,
k = a ( 1 - ρ 1 ) 1 2 .
l = 2 l ,             s = s + l .
B = - L 01 ρ 1 1 - ρ 1 cosh k l cosh k l + ( 1 - ρ 1 ) 1 2 sinh k l ,
C = L 01 ρ 1 1 - ρ 1 sinh k l cosh k l + ( 1 - ρ 1 ) 1 2 sinh k l .
L 1 ( s ) = D + [ B cosh k l + C sinh k l ] cosh k s + [ B sinh k l + C cosh k l ] sinh k s ,
L 1 ( s ) = L 01 1 - ρ 1 { 1 - ρ 1 cosh k s cosh k l + ( 1 - ρ 1 ) 1 2 sinh k l } .
B = - L 01 1 - ρ 1 [ 1 - ( 1 - ρ 1 ) 1 2 ] ,             C = L 01 1 - ρ 1 [ 1 - ( 1 - ρ 1 ) 1 2 ]
L 1 ( s ) = L 01 1 - ρ 1 { 1 - [ 1 - ( 1 - ρ 1 ) 1 2 ] e - k s } ,
L 01 ( s ) = ρ 1 K 21 ( s ) L u .
L 02 = L u ,             L 01 = L 03 = 0 ,             ρ 2 = ρ 3 = 0 ,
L 0 ( s ) = 0 + ρ 1 K 21 ( s ) L u .
B = ρ 1 L u ( 1 - ρ 1 ) 1 2 cosh k l + sinh k l 2 ( 1 - ρ 1 ) 1 2 cosh k l + ( 2 - ρ 1 ) sinh k l ,
C = - ρ 1 L u cosh k l + ( 1 - ρ 1 ) 1 2 sinh k l 2 ( 1 - ρ 1 ) 1 2 cosh k l + ( 2 - ρ 1 ) sinh k l , D = 0 ,             K = a ( 1 - ρ 1 ) 1 2 .
L 1 ( s ) = ρ 1 L u 2 ( 1 - ρ 1 ) 1 2 cosh k l + ( 2 - ρ 1 ) sinh k l { [ ( 1 - ρ 1 ) 1 2 cosh k l + sinh k l ] cosh k s - [ cosh k l + ( 1 - ρ 1 ) 1 2 sinh k l ] sinh k s } .
L 1 ( s ) = L u [ 1 - ( 1 - ρ 1 ) 1 2 ] e - k s .
L 02 = L u ,             L 01 = L 03 = 0 ,             ρ 2 = 0 ,
B = ρ 1 L u [ ( 1 - ρ 1 ) 1 2 ( 1 + ρ 3 ) cosh k l + ( 1 - ρ 3 ) sinh k l ] 2 ( 1 - ρ 1 ) 1 2 cosh k l + [ ( 1 - ρ 3 ) + ( 1 - ρ 1 ) ( 1 + ρ 3 ) ] sinh k l ,
C = - ρ 1 L u [ ( 1 - ρ 1 ) 1 2 ( 1 + ρ 3 ) sinh k l + ( 1 - ρ 3 ) cosh k l ] 2 ( 1 - ρ 1 ) 1 2 cosh k l + [ ( 1 - ρ 3 ) + ( 1 - ρ 1 ) ( 1 + ρ 3 ) ] sinh k l , D = 0 ,             K = a ( 1 - ρ 1 ) 1 2 .
U = ( 1 - ρ 1 ) 1 2 ( 1 + ρ 3 ) cosh k l + ( 1 - ρ 3 ) sinh k l , V = ( 1 - ρ 1 ) 1 2 ( 1 + ρ 3 ) sinh k l + ( 1 - ρ 3 ) cosh k l , W = 2 ( 1 - ρ 1 ) 1 2 cosh k l + [ ( 1 - ρ 3 ) + ( 1 - ρ 1 ) ( 1 + ρ 3 ) ] sinh k l ,
L 1 ( s ) = ( L u ρ 1 / W ) [ U cosh k s - V sinh k s ] .
M = e a l ,             N 32 ( t ) = e a t .
L 3 = ρ 3 e - a l { L u + a 0 l e a t [ B cosh k t + C sinh k t ] d t } ,
L 3 = ρ 3 L u e - a l { 1 + 1 W [ U { e a l [ cosh k l - ( 1 - ρ 1 ) 1 2 sinh k l ] - 1 } - V { e a l [ sinh k l - ( 1 - ρ 1 ) 1 2 cosh k l ] + ( 1 - ρ 1 ) 1 2 } ] } .
L 2 = L u .
cosh k l sinh k l 1 2 e k l
U = V = e k l 2 [ ( 1 - ρ 1 ) 1 2 ( 1 + ρ 3 ) + ( 1 - ρ 3 ) ] , W = e k l 2 [ 1 + ( 1 - ρ 1 ) 1 2 ] [ ( 1 - ρ 1 ) 1 2 ( 1 + ρ 3 ) + ( 1 - ρ 3 ) ] .
U W = 1 1 + ( 1 - ρ 1 ) 1 2 = 1 ρ 1 [ 1 - ( 1 - ρ 1 ) 1 2 ]
L 1 ( s ) = L u [ 1 - ( 1 - ρ 1 ) 1 2 ] e - k s ,
L 3 = ρ 3 L u [ 1 + ( 1 - ρ 1 ) 1 2 ] U W [ cosh k l - sinh k l ] = ρ 3 L u e - k l .
ρ 3 = 0 ,             L 01 = L 03 = 0 ,             D = 0.
B = ( L 02 ρ 1 / T ) [ ( 1 - ρ 1 ) 1 2 cosh k l + sinh k l ] ,
C = - ( L 02 ρ 1 / T ) [ cosh k l + ( 1 - ρ 1 ) 1 2 sinh k l ]
L 1 ( s ) = ( L 02 ρ 1 / T ) [ R cosh k s - S sinh k s ] ,
R = ( 1 - ρ 1 ) 1 2 cosh k l + sinh k l , S = cosh k l + ( 1 - ρ 1 ) 1 2 sinh k l , T = 2 ( 1 - ρ 1 ) 1 2 cosh k l + [ ( 1 - ρ 2 ) + ( 1 - ρ 1 ) ( 1 + ρ 2 ) ] sinh k l , k = a ( 1 - ρ 1 ) 1 2 .
L 2 = L 02 { 1 + ρ 1 ρ 2 sinh k l / T }
L 3 = 0.
R ( 1 - ρ 1 ) 1 2 ,             T 2 ( 1 - ρ 1 ) 1 2 .
L 1 ( s ) L 02 ρ 1 R / T = L 02 ρ 1 / 2.
L 2 = L 02 { 1 + ρ 1 ρ 2 sinh k l 2 ( 1 - ρ 1 ) 1 2 } L 02 .
R = S = ( e k l / 2 ) [ 1 + ( 1 - ρ 1 ) 1 2 ] , T = ( e k l / 2 ) [ 2 ( 1 - ρ 1 ) 1 2 + ( 1 - ρ 2 ) + ( 1 - ρ 1 ) ( 1 + ρ 2 ) ] .
L 1 ( s ) = L 02 ρ 1 R T e - k s
L 2 = L 02 { 1 + ρ 1 ρ 2 2 ( 1 - ρ 1 ) 1 2 + ( 1 - ρ 2 ) + ( 1 - ρ 1 ) ( 1 + ρ 2 ) } .
ρ 3 = 0 ,             L 02 = L 03 = 0
B = - ρ 1 L 01 1 - ρ 1 [ ( 1 - ρ 2 ) R + ( 1 - ρ 1 ) 1 2 ( 1 + ρ 2 ) ] T ,
C = ρ 1 L 01 1 - ρ 1 ( 1 - ρ 2 ) ( S - 1 ) T ,
D = L 01 / ( 1 - ρ 1 ) .
L 1 ( s ) = L 01 1 - ρ 1 { 1 + ρ 1 T [ - [ ( 1 - ρ 2 ) R + ( 1 - ρ 1 ) 1 2 ( 1 + ρ 2 ) ] cosh k s + ( 1 - ρ 2 ) ( S - 1 ) sinh k s ] } .
L 2 ( l ) = L 01 1 - ρ 1 { [ 1 + ρ 1 T ( 1 - ρ 2 ) ( R - S ) ] - e - a l [ 1 + ρ 1 T ( ( 1 - ρ 1 ) 1 2 ( 1 + ρ 2 ) S + ( 1 - ρ 2 ) R ] } .
L 1 ( s ) = 0.
L 2 ( l ) = L 02 + ρ 2 e - a l L 03 1 - ρ 2 ρ 3 e - 2 a l ,
L 3 ( l ) = L 03 + ρ 3 e - a l L 02 1 - ρ 2 ρ 3 e - 2 a l .
L 2 ( l ) = L 02 + ρ 2 K 32 ( l ) · L 3 L 3 ( l ) = L 03 + ρ 3 K 23 ( l ) · L 2 } ,
K 32 ( l ) = K 23 ( l ) = ( α A / a 2 ) e - a l .
L 2 ( l ) = L 02 + ρ 2 L 3 e - a l L 3 ( l ) = L 03 + ρ 3 L 2 e - a l } .
L 1 ( s ) = L 01 ( s ) + ρ 1 E 1 ( s )             or             E 1 ( s ) = [ L 1 ( s ) - L 01 ( s ) ] / ρ 1 .
E 2 ( l ) = ( L 2 ( l ) - L 02 ) / ρ 2 ,
E 3 ( l ) = ( L 3 ( l ) - L 03 ) / ρ 3 .
E Av ( h ) = K 23 ( h ) · L 2 + 0 h K 13 ( t ) · L 1 ( t ) d t ,
K 13 ( t ) = α K 31 ( t ) = ( α A / a ) e - a ( h - t ) ,
K 23 ( h ) = ( α A / a 2 ) e - a h .
E Av ( h ) = L 2 e - a h + a e - a h 0 h e a t [ D + B cosh k t + C sinh k t ] d t .
E Av ( h ) = L 2 e - a h + L 01 1 - ρ 1 ( 1 - e - a h ) + B ρ 1 { [ cosh k h - ( 1 - ρ 1 ) 1 2 sinh k h ] - e - a h } + C ρ 1 { [ sinh k h - ( 1 - ρ 1 ) 1 2 cosh k h ] + ( 1 - ρ 1 ) 1 2 e - a h } .
a = p / 2 S ,
a = 1.
K ( s - t ) = 1 2 e - s - t
S = π b p π [ 2 ( 1 + b 2 ) ] 1 2
a [ ( 1 + b 2 ) / 2 b 2 ] 1 2 .
S = 3 3 / 2 ,             p = 6 ,             a = 2 / 3 = 1.155.
S = w / 2 p = 1 + w + ( 1 + w 2 ) 1 2 , a = ( 1 / w ) [ 1 + w + ( 1 + w 2 ) 1 2 ] .
S = w ,             p = 2 ( 1 + w ) ,             a = ( 1 + w ) / w .
a l = ( W 2 + W 3 ) W 1 / W 2 W 3 ,
l = ( W 2 + W 3 ) W 1 / 2 W 2 W 3 .
s = ( W 2 + W 3 ) h / 2 W 2 W 3 .