Saturday, 6 November 2021

An easily-read planetary insolation table

Although of relatively marginal relevance to the actual climate of Earth today — and mainly in the field of glacial/interglacial cycles where small change have large effects — the relationship between planetary insolation and obliquity has been interesting to me ever since I read Darren M. Williams’ and David Pollard’s ‘Extraordinary Climates of Earth-Like Planets: Three-Dimensional Climate Simulations at Extreme Obliquity’. The article was originally published in 2003 by the International Journal of Astrobiology, but I first read it over a decade later and it was very interesting. Before reading ‘Extraordinary Climates of Earth-Like Planets’, I had circa 2000 read World-Building (Science Fiction Writing Series) by Stephen L. Gillett and Ben Bova, but, although I did find it somewhat interesting, I did not do any research related to it (although at the time I may not have had the resources to do so).

It was only when I read Alice Nadeau’s 2019 ‘Generalizations for Insolation and Albedo To Adapt an Energy Balance Model to Other Planets’ — originally published with Richard McGehee in 2015 in a much shorter form as ‘A Simple Formula for a Planet's Mean Annual Insolation by Latitude’ —that the subject attracted really serious attention. Basic studies of the topic usually simply note that equatorial insolation equals polar insolation at 54˚obliquity, and that beyond 54˚ the poles receive more insolation than the equator. Actually, though, when equatorial insulation equals polar insolation, as discussed explicitly by Anthony R. Dobrovolskis in ‘On a Planet’s Annual Mean Insolation’, the insolation has a “W” shape with peaks at the equator and the poles, and a shallow trough in the mid-latitudes. This “W” shape was noted by Nadeau, who mentioned that conventional approximations for Earthlike obliquities do not capture the shape well.

The graph below will provide an illustration of insolation at these obliquities:
Annual relative planetary insolation for obliquities 135˚ or 45˚ (green), arcsine(π/4) (orange), 126.103˚ or 53.897˚ (red dotted), 122.3747˚ or 57.6253˚ (red continuous line), and 114.645˚ or 65.355˚ (purple)
Originally when planning this post I intended to graph all the columns in the table below, but on Excel this proved impossible, because I could not find a way to graph the obliquity column (x-axis) by actual size (I may not have tried that hard to be frank). So I have provided a lengthy table with obliquities over 0.25 degrees from 0˚to 180˚, plus several other important obliquities where there is:
  • a transition between above- and below-average insolation at the equator or at the poles
    • these correspond to transitions between two and one latitude with average insolation
  • a transition between “W” shape and single insolation maximum
    • these occur at 45˚ and 135˚ which are the boundaries of the obliquities where the poles are the least insulated part of the planet
    • these also occur at approximately 65.355˚ and 114.645˚ between which the equator is the least insulated part of the planet, and outside which the equator is an insolation maximum
The columns in the table below show:
  1. obliquity in degrees
  2. the latitude of minimum annual insolation (Dobrovolskis’ “cold front”)
  3. the latitude or latitudes at which annual planetary insolation equals that for the planet as a whole
  4. the latitude, if any, of equal insolation to the equator
  5. the latitude, if any, of equal insolation to the poles
  6. the maximum percentage insolation for each obliquity
  7. the minimum percentage insolation for each obliquity
  8. the insolation of the secondary peak, if it exists, as a percentage of total planetary insolation
  9. the percentage above minimum planetary insolation of the secondary peak
  10. the percentage of the planet’s total surface receiving an insolation above the planetary average
Obliquity (˚) Latitude of minimum insolation (˚) Latitude(s) of average insolation (˚) Equal to equator Equal to poles Maximum percentage Minimum percentage Secondary peak % of surface above mean
0 90.000 38.24   127.32% 0.00%   61.90%
0.25 90.000 38.24 127.30% 0.56% 61.90%
0.5 90.000 38.24 127.32% 1.11% 61.90%
0.75 90.000 38.24 127.32% 1.67% 61.90%
1 90.000 38.24 127.31% 2.22% 61.90%
1.25 90.000 38.24 127.31% 2.78% 61.90%
1.5 90.000 38.23 127.30% 3.33% 61.88%
1.75 90.000 38.23 127.29% 3.89% 61.88%
2 90.000 38.23 127.28% 4.44% 61.88%
2.25 90.000 38.23 127.27% 5.00% 61.88%
2.5 90.000 38.23 127.26% 5.55% 61.88%
2.75 90.000 38.23 127.25% 6.11% 61.88%
3 90.000 38.22 127.24% 6.66% 61.87%
3.25 90.000 38.22 127.22% 7.22% 61.87%
3.5 90.000 38.21 127.21% 7.77% 61.85%
3.75 90.000 38.21 127.19% 8.33% 61.85%
4 90.000 38.21 127.17% 8.88% 61.85%
4.25 90.000 38.20 127.15% 9.44% 61.84%
4.5 90.000 38.20 127.13% 9.99% 61.84%
4.75 90.000 38.19 127.11% 10.54% 61.83%
5 90.000 38.19 127.08% 11.10% 61.83%
5.25 90.000 38.18 127.06% 11.65% 61.81%
5.5 90.000 38.18 127.03% 12.20% 61.81%
5.75 90.000 38.17 127.00% 12.76% 61.80%
6 90.000 38.16 126.98% 13.31% 61.79%
6.25 90.000 38.16 126.95% 13.86% 61.79%
6.5 90.000 38.15 126.92% 14.41% 61.77%
6.75 90.000 38.15 126.88% 14.97% 61.77%
7 90.000 38.14 126.85% 15.52% 61.76%
7.25 90.000 38.13 126.82% 16.07% 61.74%
7.5 90.000 38.12 126.78% 16.62% 61.73%
7.75 90.000 38.12 126.74% 17.17% 61.73%
8 90.000 38.11 126.71% 17.72% 61.72%
8.25 90.000 38.10 126.67% 18.27% 61.70%
8.5 90.000 38.09 126.63% 18.82% 61.69%
8.75 90.000 38.08 126.58% 19.37% 61.68%
9 90.000 38.07 126.54% 19.92% 61.66%
9.25 90.000 38.06 126.50% 20.47% 61.65%
9.5 90.000 38.05 126.45% 21.01% 61.63%
9.75 90.000 38.04 126.41% 21.56% 61.62%
10 90.000 38.03 126.36% 22.11% 61.61%
10.25 90.000 38.02 126.31% 22.66% 61.59%
10.5 90.000 38.01 126.26% 23.20% 61.58%
10.75 90.000 37.99 126.21% 23.75% 61.55%
11 90.000 37.98 126.16% 24.29% 61.54%
11.25 90.000 37.97 126.10% 24.84% 61.52%
11.5 90.000 37.96 126.05% 25.38% 61.51%
11.75 90.000 37.95 125.99% 25.93% 61.50%
12 90.000 37.93 125.94% 26.47% 61.47%
12.25 90.000 37.92 125.88% 27.02% 61.46%
12.5 90.000 37.91 125.82% 27.56% 61.44%
12.75 90.000 37.89 125.76% 28.10% 61.41%
13 90.000 37.88 125.70% 28.64% 61.40%
13.25 90.000 37.86 125.63% 29.18% 61.37%
13.5 90.000 37.85 125.57% 29.72% 61.36%
13.75 90.000 37.84 125.51% 30.26% 61.35%
14 90.000 37.82 125.44% 30.80% 61.32%
14.25 90.000 37.80 125.37% 31.34% 61.29%
14.5 90.000 37.78 125.30% 31.88% 61.26%
14.75 90.000 37.77 125.23% 32.42% 61.25%
15 90.000 37.75 125.16% 32.95% 61.22%
15.25 90.000 37.74 125.09% 33.49% 61.21%
15.5 90.000 37.72 125.02% 34.03% 61.18%
15.75 90.000 37.70 124.95% 34.56% 61.15%
16 90.000 37.68 124.87% 35.10% 61.13%
16.25 90.000 37.67 124.79% 35.63% 61.11%
16.5 90.000 37.65 124.72% 36.16% 61.08%
16.75 90.000 37.63 124.64% 36.69% 61.06%
17 90.000 37.61 124.56% 37.23% 61.03%
17.25 90.000 37.59 124.48% 37.76% 61.00%
17.5 90.000 37.58 124.39% 38.29% 60.99%
17.75 90.000 37.55 124.31% 38.82% 60.95%
18 90.000 37.53 124.23% 39.35% 60.92%
18.25 90.000 37.51 124.14% 39.87% 60.89%
18.5 90.000 37.49 124.06% 40.40% 60.86%
18.75 90.000 37.47 123.96% 40.93% 60.83%
19 90.000 37.46 123.88% 41.45% 60.82%
19.25 90.000 37.43 123.79% 41.98% 60.78%
19.5 90.000 37.40 123.70% 42.50% 60.74%
19.75 90.000 37.38 123.61% 43.02% 60.71%
20 90.000 37.35 123.51% 43.55% 60.67%
20.25 90.000 37.32 123.42% 44.07% 60.63%
20.5 90.000 37.30 123.33% 44.59% 60.60%
20.75 90.000 37.28 123.23% 45.11% 60.57%
21 90.000 37.25 123.13% 45.63% 60.53%
21.25 90.000 37.23 123.03% 46.15% 60.50%
21.5 90.000 37.20 122.93% 46.66% 60.46%
21.75 90.000 37.18 122.83% 47.18% 60.43%
22 90.000 37.15 122.73% 47.70% 60.39%
22.25 90.000 37.12 122.63% 48.21% 60.35%
22.5 90.000 37.09 122.53% 48.72% 60.31%
22.75 90.000 37.07 122.42% 49.24% 60.28%
23 90.000 37.04 122.32% 49.75% 60.24%
23.25 90.000 37.01 122.21% 50.26% 60.20%
23.5 90.000 36.98 122.10% 50.77% 60.15%
23.75 90.000 36.95 121.99% 51.28% 60.11%
24 90.000 36.92 121.88% 51.79% 60.07%
24.25 90.000 36.89 121.77% 52.29% 60.03%
24.5 90.000 36.86 121.66% 52.80% 59.99%
24.75 90.000 36.83 121.55% 53.31% 59.94%
25 90.000 36.80 121.43% 53.81% 59.90%
25.25 90.000 36.77 121.32% 54.31% 59.86%
25.5 90.000 36.73 121.20% 54.81% 59.80%
25.75 90.000 36.70 121.08% 55.32% 59.76%
26 90.000 36.66 120.97% 55.82% 59.71%
26.25 90.000 36.63 120.85% 56.31% 59.66%
26.5 90.000 36.60 120.73% 56.80% 59.62%
26.75 90.000 36.56 120.61% 57.31% 59.57%
27 90.000 36.53 120.49% 57.80% 59.52%
27.25 90.000 36.49 120.36% 58.30% 59.47%
27.5 90.000 36.45 120.24% 58.79% 59.41%
27.75 90.000 36.41 120.11% 59.28% 59.36%
28 90.000 36.38 119.99% 59.77% 59.31%
28.25 90.000 36.34 119.86% 60.26% 59.26%
28.5 90.000 36.30 119.73% 60.75% 59.20%
28.75 90.000 36.26 119.61% 61.24% 59.15%
29 90.000 36.22 119.48% 61.73% 59.09%
29.25 90.000 36.18 119.35% 62.21% 59.03%
29.5 90.000 36.14 119.21% 62.70% 58.98%
29.75 90.000 36.09 119.08% 63.18% 58.91%
30 90.000 36.05 118.95% 63.66% 58.85%
30.25 90.000 36.01 118.81% 64.14% 58.79%
30.5 90.000 35.96 118.68% 64.62% 58.72%
30.75 90.000 35.92 118.54% 65.10% 58.67%
31 90.000 35.88 118.41% 65.58% 58.61%
31.25 90.000 35.83 118.27% 66.05% 58.54%
31.5 90.000 35.78 118.13% 66.53% 58.47%
31.75 90.000 35.73 117.99% 67.00% 58.40%
32 90.000 35.69 117.85% 67.47% 58.34%
32.25 90.000 35.64 117.71% 67.94% 58.27%
32.5 90.000 35.59 117.57% 68.41% 58.20%
32.75 90.000 35.54 117.42% 68.88% 58.13%
33 90.000 35.49 117.28% 69.35% 58.06%
33.25 90.000 35.44 117.13% 69.81% 57.99%
33.5 90.000 35.38 116.99% 70.27% 57.90%
33.75 90.000 35.33 116.84% 70.74% 57.83%
34 90.000 35.28 116.69% 71.20% 57.76%
34.25 90.000 35.22 116.55% 71.66% 57.67%
34.5 90.000 35.16 116.40% 72.12% 57.59%
34.75 90.000 35.11 116.25% 72.57% 57.51%
35 90.000 35.05 116.10% 73.03% 57.43%
35.25 90.000 34.99 115.95% 73.48% 57.34%
35.5 90.000 34.93 115.79% 73.94% 57.26%
35.75 90.000 34.87 115.64% 74.39% 57.17%
36 90.000 34.81 115.49% 74.84% 57.09%
36.25 90.000 34.74 115.33% 75.29% 56.99%
36.5 90.000 34.67 115.18% 75.74% 56.88%
36.75 90.000 34.61 115.02% 76.18% 56.80%
37 90.000 34.55 114.86% 76.63% 56.71%
37.25 90.000 34.48 114.71% 77.07% 56.61%
37.5 90.000 34.42 114.55% 77.51% 56.53%
37.75 90.000 34.34 114.39% 77.95% 56.41%
38 90.000 34.27 114.23% 78.39% 56.31%
38.25 90.000 34.20 114.07% 78.83% 56.21%
38.5 90.000 34.12 113.91% 79.26% 56.09%
38.75 90.000 34.05 113.74% 79.70% 55.99%
39 90.000 33.97 113.58% 80.13% 55.88%
39.25 90.000 33.90 113.42% 80.56% 55.77%
39.5 90.000 33.81 113.25% 80.99% 55.64%
39.75 90.000 33.74 113.09% 81.42% 55.54%
40 90.000 33.66 112.92% 81.84% 55.43%
40.25 90.000 33.57 112.76% 82.27% 55.30%
40.5 90.000 33.49 112.59% 82.69% 55.18%
40.75 90.000 33.40 112.42% 83.11% 55.05%
41 90.000 33.30 112.25% 83.53% 54.90%
41.25 90.000 33.21 112.09% 83.95% 54.77%
41.5 90.000 33.12 111.92% 84.37% 54.64%
41.75 90.000 33.03 111.75% 84.78% 54.51%
42 90.000 32.93 111.58% 85.20% 54.36%
42.25 90.000 32.83 111.40% 85.61% 54.21%
42.5 90.000 32.73 111.23% 86.02% 54.07%
42.75 90.000 32.62 111.06% 86.43% 53.91%
43 90.000 32.51 110.89% 86.83% 53.74%
43.25 90.000 32.40 110.71% 87.24% 53.58%
43.5 90.000 32.30 110.54% 87.64% 53.44%
43.75 90.000 32.18 110.36% 88.05% 53.26%
44 90.000 32.07 110.19% 88.45% 53.10%
44.25 90.000 31.94 110.01% 88.85% 52.90%
44.5 90.000 31.82 109.83% 89.24% 52.73%
44.75 90.000 31.70 109.66% 89.64% 52.55%
45 90.000 31.56   90.00 109.48% 90.03% 90.03% 0.00% 52.34%
45.125 82.458 31.50 79.35 109.390% 90.226% 90.228% 0.002% 52.25%
45.25 79.372 31.43 75.01 109.301% 90.417% 90.424% 0.008% 52.15%
45.5 75.076 31.30 69.02 109.122% 90.787% 90.814% 0.030% 51.95%
45.75 71.848 31.15 64.56 108.943% 91.143% 91.202% 0.065% 51.73%
46 69.183 31.01 60.92 108.763% 91.485% 91.589% 0.114% 51.52%
46.25 66.881 30.86 57.81 108.583% 91.813% 91.974% 0.175% 51.29%
46.5 64.841 30.70 55.09 108.402% 92.129% 92.358% 0.249% 51.05%
46.75 63.001 30.54 52.68 108.22% 92.43% 92.74% 0.34% 50.81%
47 61.321 30.38 50.50 108.04% 92.72% 93.12% 0.43% 50.57%
47.25 59.772 30.21 48.53 107.86% 93.00% 93.50% 0.54% 50.32%
47.5 58.334 30.04 46.74 107.67% 93.27% 93.87% 0.64% 50.06%
47.75 56.990 29.86 45.11 107.49% 93.52% 94.25% 0.78% 49.79%
48 55.729 29.67 43.62 107.31% 93.77% 94.62% 0.91% 49.50%
48.25 54.540 29.48 42.28 107.12% 94.00% 94.99% 1.05% 49.21%
48.5 53.416 29.28 41.10 106.94% 94.22% 95.36% 1.21% 48.91%
48.75 52.349 29.07 40.02 106.75% 94.44% 95.73% 1.37% 48.59%
49 51.335 28.86 38.97 106.57% 94.64% 96.09% 1.53% 48.27%
49.25 50.368 28.63 37.92 106.38% 94.84% 96.46% 1.71% 47.92%
49.5 49.444 28.40 36.86 106.20% 95.02% 96.82% 1.89% 47.56%
49.75 48.560 28.16 35.78 106.01% 95.20% 97.18% 2.08% 47.19%
50 47.712 27.91 34.69 105.82% 95.36% 97.54% 2.29% 46.81%
50.25 46.898 27.65 33.56 105.64% 95.52% 97.89% 2.48% 46.41%
50.5 46.116 27.37 32.41 105.45% 95.67% 98.25% 2.70% 45.97%
50.75 45.363 27.10 31.20 105.26% 95.82% 98.60% 2.90% 45.55%
51 44.638 26.80 29.97 105.07% 95.95% 98.95% 3.13% 45.09%
51.25 43.938 26.49 28.66 104.88% 96.08% 99.30% 3.35% 44.60%
51.5 43.262 26.17 27.30 104.70% 96.20% 99.64% 3.58% 44.10%
51.75 42.610 25.83 25.86 104.51% 96.31% 99.99% 3.82% 43.57%
51.7575 42.590 25.81 90.00   25.81 104.50% 96.32% 100.00% 3.82% 43.54%
51.875 42.291 25.65 82.59 25.11 104.41% 96.36% 100.16% 3.94% 44.12%
52 41.978 25.47 79.34 24.33 104.32% 96.41% 100.33% 4.07% 44.73%
52.25 41.368 25.10 74.93 22.70 104.13% 96.51% 100.67% 4.31% 45.86%
52.5 40.776 24.70 71.65 20.93 103.94% 96.60% 101.01% 4.57% 46.87%
52.75 40.203 24.29 68.97 18.99 103.75% 96.68% 101.35% 4.83% 47.80%
53 39.648 23.85 66.67 16.81 103.56% 96.76% 101.69% 5.10% 48.61%
53.25 39.110 23.39 64.64 14.30 103.37% 96.83% 102.02% 5.36% 49.34%
53.5 38.588 22.90 62.83 11.21 103.17% 96.90% 102.35% 5.62% 49.95%
53.75 38.082 22.38 61.20 6.82 102.98% 96.96% 102.68% 5.90% 50.44%
53.8225 37.938 22.22 60.75 4.85 102.93% 96.97% 102.77% 5.98% 50.57%
53.8962 37.793 22.06 60.31 90.00 0.00 102.87% 96.99% 102.87% 6.06% 50.69%
53.9375 37.712 21.98 60.09 85.47   102.93% 97.00% 102.84% 6.02% 50.75%
54 37.590 21.82 59.71 82.35 103.01% 97.01% 102.79% 5.96% 50.82%
54.25 37.114 21.24 58.33 75.94 103.33% 97.06% 102.60% 5.71% 51.12%
54.5 36.652 20.61 57.06 71.71 103.66% 97.10% 102.41% 5.47% 51.28%
54.75 36.204 19.94 55.90 68.34 103.98% 97.13% 102.22% 5.24% 51.30%
55 35.770 19.21 54.80 65.43 104.30% 97.16% 102.02% 5.00% 51.19%
55.25 35.350 18.43 53.77 62.94 104.62% 97.19% 101.83% 4.77% 50.95%
55.5 34.944 17.59 52.82 60.66 104.93% 97.21% 101.64% 4.56% 50.55%
55.75 34.552 16.64 51.92 58.60 105.24% 97.22% 101.45% 4.35% 49.92%
56 34.177 15.65 51.08 56.66 105.56% 97.23% 101.25% 4.13% 49.17%
56.25 33.820 14.51 50.29 54.88 105.87% 97.24% 101.06% 3.93% 48.13%
56.5 33.492 13.24 49.55 53.20 106.17% 97.24% 100.87% 3.73% 46.81%
56.75 33.153 11.78 48.85 51.62 106.48% 97.24% 100.68% 3.54% 45.12%
57 32.791 10.04 48.18 50.12 106.78% 97.23% 100.48% 3.34% 42.91%
57.25 32.411 7.85 47.56 48.69 107.08% 97.22% 100.29% 3.16% 39.86%
57.5 32.016 4.57 46.96 47.34 107.38% 97.20% 100.10% 2.98% 34.88%
57.5625 31.915 3.24 46.82 47.00 107.46% 97.20% 100.05% 2.93% 32.73%
57.6 31.854 2.06 46.73 46.81 107.50% 97.20% 100.02% 2.90% 30.78%
57.6253 31.813 0.00 46.68 46.68 107.53% 97.19% 100.00% 2.89% 27.25%
57.6875 31.710   46.54 46.36 107.61% 97.19% 99.95% 2.84% 27.41%
57.75 31.606 46.40 46.04 107.68% 97.18% 99.90% 2.80% 27.58%
58 31.183 45.87 44.79 107.98% 97.16% 99.71% 2.62% 28.22%
58.25 30.745 45.36 43.59 108.27% 97.13% 99.52% 2.46% 28.85%
58.5 30.293 44.88 42.44 108.56% 97.09% 99.32% 2.30% 29.44%
58.75 29.827 44.43 41.33 108.85% 97.05% 99.13% 2.14% 30.00%
59 29.346 43.99 40.25 109.14% 97.01% 98.94% 1.99% 30.55%
59.25 28.850 43.58 39.21 109.42% 96.96% 98.74% 1.84% 31.06%
59.5 28.337 43.18 38.20 109.71% 96.90% 98.55% 1.70% 31.57%
59.75 27.080 42.81 37.22 109.99% 96.84% 98.36% 1.57% 32.04%
60 27.261 42.45 36.27 110.27% 96.78% 98.16% 1.43% 32.51%
60.25 26.696 42.11 35.34 110.54% 96.71% 97.97% 1.30% 32.94%
60.5 26.110 41.78 34.43 110.82% 96.63% 97.78% 1.19% 33.37%
60.75 25.504 41.47 33.54 111.09% 96.55% 97.59% 1.08% 33.78%
61 24.875 41.17 32.67 111.36% 96.46% 97.39% 0.96% 34.17%
61.25 24.221 40.88 31.81 111.63% 96.37% 97.20% 0.86% 34.55%
61.5 23.541 40.61 30.96 111.89% 96.27% 97.01% 0.77% 34.91%
61.75 22.831 40.34 30.13 112.16% 96.17% 96.82% 0.68% 35.27%
62 22.090 40.09 29.28 112.42% 96.06% 96.62% 0.58% 35.60%
62.25 21.314 39.85 28.45 112.680% 95.951% 96.432% 0.501% 35.92%
62.5 20.498 39.61 27.57 112.937% 95.832% 96.239% 0.425% 36.24%
62.75 19.638 39.39 26.60 113.193% 95.707% 96.048% 0.356% 36.54%
63 18.728 39.17 25.51 113.446% 95.578% 95.857% 0.292% 36.84%
63.25 17.966 38.96 24.31 113.698% 95.442% 95.666% 0.235% 37.12%
63.5 16.721 38.75 23.00 113.947% 95.301% 95.475% 0.183% 37.41%
63.75 15.600 38.56 21.55 114.193% 95.154% 95.285% 0.138% 37.67%
64 14.377 38.38 19.94 114.438% 95.001% 95.094% 0.098% 37.91%
64.25 13.022 38.20 18.13 114.680% 94.824% 94.904% 0.084% 38.16%
64.5 11.490 38.02 16.06 114.921% 94.677% 94.715% 0.040% 38.41%
64.75 9.695 37.85 13.60 115.159% 94.506% 94.525% 0.020% 38.64%
65 7.449 37.69 10.49 115.395% 94.330% 94.336% 0.006% 38.86%
65.25 4.063 37.53 5.74 115.628% 94.147% 94.148% 0.001% 39.08%
65.3 2.942 37.50 4.16 115.675% 94.1098% 94.1100% 0.0002% 39.12%
65.35496 0.000 37.47 0.00 115.726% 94.070% 94.070% 0.000% 39.17%
65.5 0.000 37.37   115.86% 93.96%   39.30%
65.75 0.000 37.23 116.09% 93.77% 39.50%
66 0.000 37.08 116.32% 93.58% 39.71%
66.25 0.000 36.96 116.54% 93.40% 39.87%
66.5 0.000 36.81 116.76% 93.21% 40.08%
66.75 0.000 36.68 116.98% 93.02% 40.27%
67 0.000 36.56 117.20% 92.84% 40.43%
67.25 0.000 36.42 117.42% 92.65% 40.63%
67.5 0.000 36.30 117.63% 92.47% 40.80%
67.75 0.000 36.19 117.84% 92.28% 40.95%
68 0.000 36.08 118.05% 92.10% 41.11%
68.25 0.000 35.96 118.26% 91.92% 41.28%
68.5 0.000 35.86 118.46% 91.73% 41.42%
68.75 0.000 35.76 118.67% 91.55% 41.56%
69 0.000 35.66 118.87% 91.37% 41.70%
69.25 0.000 35.56 119.07% 91.19% 41.84%
69.5 0.000 35.46 119.26% 91.01% 41.99%
69.75 0.000 35.37 119.45% 90.83% 42.11%
70 0.000 35.28 119.65% 90.65% 42.24%
70.25 0.000 35.18 119.83% 90.47% 42.39%
70.5 0.000 35.10 120.02% 90.30% 42.50%
70.75 0.000 35.02 120.21% 90.12% 42.61%
71 0.000 34.94 120.39% 89.94% 42.73%
71.25 0.000 34.85 120.57% 89.77% 42.86%
71.5 0.000 34.76 120.74% 89.59% 42.99%
71.75 0.000 34.70 120.92% 89.42% 43.07%
72 0.000 34.62 121.09% 89.25% 43.19%
72.25 0.000 34.55 121.26% 89.08% 43.29%
72.5 0.000 34.48 121.43% 88.91% 43.39%
72.75 0.000 34.40 121.60% 88.74% 43.50%
73 0.000 34.34 121.76% 88.57% 43.59%
73.25 0.000 34.27 121.92% 88.40% 43.69%
73.5 0.000 34.21 122.08% 88.23% 43.78%
73.75 0.000 34.15 122.24% 88.07% 43.86%
74 0.000 34.08 122.39% 87.90% 43.97%
74.25 0.000 34.03 122.54% 87.74% 44.04%
74.5 0.000 33.96 122.69% 87.57% 44.14%
74.75 0.000 33.91 122.84% 87.41% 44.21%
75 0.000 33.85 122.99% 87.25% 44.30%
75.25 0.000 33.80 123.13% 87.09% 44.37%
75.5 0.000 33.74 123.27% 86.93% 44.46%
75.75 0.000 33.69 123.41% 86.77% 44.53%
76 0.000 33.64 123.54% 86.62% 44.60%
76.25 0.000 33.59 123.68% 86.46% 44.68%
76.5 0.000 33.55 123.81% 86.31% 44.73%
76.75 0.000 33.50 123.93% 86.16% 44.81%
77 0.000 33.46 124.06% 86.01% 44.86%
77.25 0.000 33.41 124.18% 85.86% 44.94%
77.5 0.000 33.37 124.31% 85.71% 45.00%
77.75 0.000 33.33 124.42% 85.56% 45.05%
78 0.000 33.29 124.54% 85.42% 45.11%
78.25 0.000 33.25 124.66% 85.27% 45.17%
78.5 0.000 33.21 124.77% 85.13% 45.23%
78.75 0.000 33.17 124.88% 84.99% 45.29%
79 0.000 33.13 124.98% 84.85% 45.35%
79.25 0.000 33.10 125.09% 84.71% 45.39%
79.5 0.000 33.07 125.19% 84.58% 45.43%
79.75 0.000 33.03 125.29% 84.44% 45.49%
80 0.000 33.00 125.39% 84.31% 45.54%
80.25 0.000 32.96 125.48% 84.18% 45.59%
80.5 0.000 32.93 125.58% 84.05% 45.64%
80.75 0.000 32.90 125.67% 83.92% 45.68%
81 0.000 32.87 125.76% 83.80% 45.73%
81.25 0.000 32.84 125.84% 83.67% 45.77%
81.5 0.000 32.82 125.93% 83.55% 45.80%
81.75 0.000 32.79 126.01% 83.43% 45.84%
82 0.000 32.77 126.08% 83.31% 45.87%
82.25 0.000 32.74 126.16% 83.20% 45.92%
82.5 0.000 32.72 126.23% 83.09% 45.95%
82.75 0.000 32.69 126.31% 82.97% 45.99%
83 0.000 32.67 126.37% 82.87% 46.02%
83.25 0.000 32.65 126.44% 82.76% 46.05%
83.5 0.000 32.63 126.51% 82.65% 46.08%
83.75 0.000 32.61 126.57% 82.55% 46.11%
84 0.000 32.59 126.63% 82.45% 46.14%
84.25 0.000 32.57 126.68% 82.36% 46.17%
84.5 0.000 32.56 126.74% 82.26% 46.18%
84.75 0.000 32.54 126.79% 82.17% 46.21%
85 0.000 32.53 126.84% 82.08% 46.23%
85.25 0.000 32.51 126.89% 82.00% 46.26%
85.5 0.000 32.50 126.93% 81.91% 46.27%
85.75 0.000 32.49 126.97% 81.83% 46.28%
86 0.000 32.47 127.01% 81.76% 46.31%
86.25 0.000 32.46 127.05% 81.68% 46.33%
86.5 0.000 32.45 127.09% 81.61% 46.34%
86.75 0.000 32.44 127.12% 81.55% 46.36%
87 0.000 32.43 127.15% 81.48% 46.37%
87.25 0.000 32.42 127.18% 81.42% 46.39%
87.5 0.000 32.41 127.20% 81.37% 46.40%
87.75 0.000 32.40 127.22% 81.31% 46.42%
88 0.000 32.40 127.25% 81.27% 46.42%
88.25 0.000 32.39 127.26% 81.22% 46.43%
88.5 0.000 32.39 127.28% 81.18% 46.43%
88.75 0.000 32.39 127.29% 81.15% 46.43%
89 0.000 32.38 127.30% 81.12% 46.45%
89.25 0.000 32.38 127.31% 81.09% 46.45%
89.5 0.000 32.38 127.32% 81.07% 46.45%
89.75 0.000 32.37 127.32% 81.06% 46.46%
90 0.000 32.37 127.32% 81.06% 46.46%
90.25 0.000 32.37 127.32% 81.06% 46.46%
90.5 0.000 32.38 127.32% 81.07% 46.45%
90.75 0.000 32.38 127.31% 81.09% 46.45%
91 0.000 32.38 127.30% 81.12% 46.45%
91.25 0.000 32.39 127.29% 81.15% 46.43%
91.5 0.000 32.39 127.28% 81.18% 46.43%
91.75 0.000 32.39 127.26% 81.22% 46.43%
92 0.000 32.40 127.25% 81.27% 46.42%
92.25 0.000 32.40 127.22% 81.31% 46.42%
92.5 0.000 32.41 127.20% 81.37% 46.40%
92.75 0.000 32.42 127.18% 81.42% 46.39%
93 0.000 32.43 127.15% 81.48% 46.37%
93.25 0.000 32.44 127.12% 81.55% 46.36%
93.5 0.000 32.45 127.09% 81.61% 46.34%
93.75 0.000 32.46 127.05% 81.68% 46.33%
94 0.000 32.47 127.01% 81.76% 46.31%
94.25 0.000 32.49 126.97% 81.83% 46.28%
94.5 0.000 32.50 126.93% 81.91% 46.27%
94.75 0.000 32.51 126.89% 82.00% 46.26%
95 0.000 32.53 126.84% 82.08% 46.23%
95.25 0.000 32.54 126.79% 82.17% 46.21%
95.5 0.000 32.56 126.74% 82.26% 46.18%
95.75 0.000 32.57 126.68% 82.36% 46.17%
96 0.000 32.59 126.63% 82.45% 46.14%
96.25 0.000 32.61 126.57% 82.55% 46.11%
96.5 0.000 32.63 126.51% 82.65% 46.08%
96.75 0.000 32.65 126.44% 82.76% 46.05%
97 0.000 32.67 126.37% 82.87% 46.02%
97.25 0.000 32.69 126.31% 82.97% 45.99%
97.5 0.000 32.72 126.23% 83.09% 45.95%
97.75 0.000 32.74 126.16% 83.20% 45.92%
98 0.000 32.77 126.08% 83.31% 45.87%
98.25 0.000 32.79 126.01% 83.43% 45.84%
98.5 0.000 32.82 125.93% 83.55% 45.80%
98.75 0.000 32.84 125.84% 83.67% 45.77%
99 0.000 32.87 125.76% 83.80% 45.73%
99.25 0.000 32.90 125.67% 83.92% 45.68%
99.5 0.000 32.93 125.58% 84.05% 45.64%
99.75 0.000 32.96 125.48% 84.18% 45.59%
100 0.000 33.00 125.39% 84.31% 45.54%
100.25 0.000 33.03 125.29% 84.44% 45.49%
100.5 0.000 33.07 125.19% 84.58% 45.43%
100.75 0.000 33.10 125.09% 84.71% 45.39%
101 0.000 33.13 124.98% 84.85% 45.35%
101.25 0.000 33.17 124.88% 84.99% 45.29%
101.5 0.000 33.21 124.77% 85.13% 45.23%
101.75 0.000 33.25 124.66% 85.27% 45.17%
102 0.000 33.29 124.54% 85.42% 45.11%
102.25 0.000 33.33 124.42% 85.56% 45.05%
102.5 0.000 33.37 124.31% 85.71% 45.00%
102.75 0.000 33.41 124.18% 85.86% 44.94%
103 0.000 33.46 124.06% 86.01% 44.86%
103.25 0.000 33.50 123.93% 86.16% 44.81%
103.5 0.000 33.55 123.81% 86.31% 44.73%
103.75 0.000 33.59 123.68% 86.46% 44.68%
104 0.000 33.64 123.54% 86.62% 44.60%
104.25 0.000 33.69 123.41% 86.77% 44.53%
104.5 0.000 33.74 123.27% 86.93% 44.46%
104.75 0.000 33.80 123.13% 87.09% 44.37%
105 0.000 33.85 122.99% 87.25% 44.30%
105.25 0.000 33.91 122.84% 87.41% 44.21%
105.5 0.000 33.96 122.69% 87.57% 44.14%
105.75 0.000 34.03 122.54% 87.74% 44.04%
106 0.000 34.08 122.39% 87.90% 43.97%
106.25 0.000 34.15 122.24% 88.07% 43.86%
106.5 0.000 34.21 122.08% 88.23% 43.78%
106.75 0.000 34.27 121.92% 88.40% 43.69%
107 0.000 34.34 121.76% 88.57% 43.59%
107.25 0.000 34.40 121.60% 88.74% 43.50%
107.5 0.000 34.48 121.43% 88.91% 43.39%
107.75 0.000 34.55 121.26% 89.08% 43.29%
108 0.000 34.62 121.09% 89.25% 43.19%
108.25 0.000 34.70 120.92% 89.42% 43.07%
108.5 0.000 34.76 120.74% 89.59% 42.99%
108.75 0.000 34.85 120.57% 89.77% 42.86%
109 0.000 34.94 120.39% 89.94% 42.73%
109.25 0.000 35.02 120.21% 90.12% 42.61%
109.5 0.000 35.10 120.02% 90.30% 42.50%
109.75 0.000 35.18 119.83% 90.47% 42.39%
110 0.000 35.28 119.65% 90.65% 42.24%
110.25 0.000 35.37 119.45% 90.83% 42.11%
110.5 0.000 35.46 119.26% 91.01% 41.99%
110.75 0.000 35.56 119.07% 91.19% 41.84%
111 0.000 35.66 118.87% 91.37% 41.70%
111.25 0.000 35.76 118.67% 91.55% 41.56%
111.5 0.000 35.86 118.46% 91.73% 41.42%
111.75 0.000 35.96 118.26% 91.92% 41.28%
112 0.000 36.08 118.05% 92.10% 41.11%
112.25 0.000 36.19 117.84% 92.28% 40.95%
112.5 0.000 36.30 117.63% 92.47% 40.80%
112.75 0.000 36.42 117.42% 92.65% 40.63%
113 0.000 36.56 117.20% 92.84% 40.43%
113.25 0.000 36.68 116.98% 93.02% 40.27%
113.5 0.000 36.81 116.76% 93.21% 40.08%
113.75 0.000 36.96 116.54% 93.40% 39.87%
114 0.000 37.08 116.32% 93.58% 39.71%
114.25 0.000 37.23 116.09% 93.77% 39.50%
114.5 0.000 37.37 115.86% 93.96% 39.30%
114.645 0.000 37.47 0.00   115.726% 94.070% 94.070% 0.000% 39.17%
114.7 2.942 37.50 4.16 115.675% 94.1098% 94.1100% 0.0002% 39.12%
114.75 4.063 37.53 5.74 115.628% 94.147% 94.148% 0.001% 39.08%
115 7.449 37.69 10.49 115.395% 94.330% 94.336% 0.006% 38.86%
115.25 9.695 37.85 13.60 115.159% 94.506% 94.525% 0.020% 38.64%
115.5 11.490 38.02 16.06 114.921% 94.677% 94.715% 0.040% 38.41%
115.75 13.022 38.20 18.13 114.680% 94.824% 94.904% 0.084% 38.16%
116 14.377 38.38 19.94 114.438% 95.001% 95.094% 0.098% 37.91%
116.25 15.600 38.56 21.55 114.193% 95.154% 95.285% 0.138% 37.67%
116.5 16.721 38.75 23.00 113.947% 95.301% 95.475% 0.183% 37.41%
116.75 17.966 38.96 24.31 113.698% 95.442% 95.666% 0.235% 37.12%
117 18.728 39.17 25.51 113.446% 95.578% 95.857% 0.292% 36.84%
117.25 19.638 39.39 26.60 113.193% 95.707% 96.048% 0.356% 36.54%
117.5 20.498 39.61 27.57 112.937% 95.832% 96.239% 0.425% 36.24%
117.75 21.314 39.85 28.45 112.680% 95.951% 96.432% 0.501% 35.92%
118 22.090 40.09 29.29 112.42% 96.06% 96.62% 0.58% 35.60%
118.25 22.831 40.34 30.13 112.16% 96.17% 96.82% 0.68% 35.27%
118.5 23.541 40.61 30.96 111.89% 96.27% 97.01% 0.77% 34.91%
118.75 24.221 40.88 31.81 111.63% 96.37% 97.20% 0.86% 34.55%
119 24.875 41.17 32.67 111.36% 96.46% 97.39% 0.96% 34.17%
119.25 25.504 41.47 33.54 111.09% 96.55% 97.59% 1.08% 33.78%
119.5 26.110 41.78 34.43 110.82% 96.63% 97.78% 1.19% 33.37%
119.75 26.696 42.11 35.34 110.54% 96.71% 97.97% 1.30% 32.94%
120 27.261 42.45 36.27 110.27% 96.78% 98.16% 1.43% 32.51%
120.25 27.080 42.81 37.22 109.99% 96.84% 98.36% 1.57% 32.04%
120.5 28.337 43.18 38.20 109.71% 96.90% 98.55% 1.70% 31.57%
120.75 28.850 43.58 39.21 109.42% 96.96% 98.74% 1.84% 31.06%
121 29.346 43.99 40.25 109.14% 97.01% 98.94% 1.99% 30.55%
121.25 29.827 44.43 41.33 108.85% 97.05% 99.13% 2.14% 30.00%
121.5 30.293 44.88 42.44 108.56% 97.09% 99.32% 2.30% 29.44%
121.75 30.745 45.36 43.59 108.27% 97.13% 99.52% 2.46% 28.85%
122 31.183 45.87 44.79 107.98% 97.16% 99.71% 2.62% 28.22%
122.25 31.606 46.40 46.04 107.68% 97.18% 99.90% 2.80% 27.58%
122.3125 31.710 46.54 46.36 107.61% 97.19% 99.95% 2.84% 27.41%
122.3747 31.813 0.00 46.68 46.68 107.53% 97.19% 100.00% 2.89% 27.25%
122.4 31.854 2.06 46.73 46.81 107.50% 97.20% 100.02% 2.90% 30.78%
122.4375 31.915 3.24 46.82 47.00 107.46% 97.20% 100.05% 2.93% 32.73%
122.5 32.016 4.57 46.96 47.34 107.38% 97.20% 100.10% 2.98% 34.88%
122.75 32.411 7.85 47.56 48.69 107.08% 97.22% 100.29% 3.16% 39.86%
123 32.791 10.04 48.18 50.12 106.78% 97.23% 100.48% 3.34% 42.91%
123.25 33.153 11.78 48.85 51.62 106.48% 97.24% 100.68% 3.54% 45.12%
123.5 33.492 13.24 49.55 53.20 106.17% 97.24% 100.87% 3.73% 46.81%
123.75 33.820 14.51 50.29 54.88 105.87% 97.24% 101.06% 3.93% 48.13%
124 34.177 15.65 51.08 56.66 105.56% 97.23% 101.25% 4.13% 49.17%
124.25 34.552 16.64 51.92 58.60 105.24% 97.22% 101.45% 4.35% 49.92%
124.5 34.944 17.59 52.82 60.66 104.93% 97.21% 101.64% 4.56% 50.55%
124.75 35.350 18.43 53.77 62.94 104.62% 97.19% 101.83% 4.77% 50.95%
125 35.770 19.21 54.80 65.43 104.30% 97.16% 102.02% 5.00% 51.19%
125.25 36.204 19.94 55.90 68.34 103.98% 97.13% 102.22% 5.24% 51.30%
125.5 36.652 20.61 57.06 71.71 103.66% 97.10% 102.41% 5.47% 51.28%
125.75 37.114 21.24 58.33 75.94 103.33% 97.06% 102.60% 5.71% 51.12%
126 37.590 21.82 59.71 82.35 103.01% 97.01% 102.79% 5.96% 50.82%
126.0625 37.712 21.98 60.09 85.47 102.93% 97.00% 102.84% 6.02% 50.75%
126.1038 37.793 22.06 60.31 90.00 0.00 102.87% 96.99% 102.87% 6.06% 50.69%
126.1775 37.938 22.22 60.75   4.85 102.93% 96.97% 102.77% 5.98% 50.57%
126.25 38.082 22.38 61.20 6.82 102.98% 96.96% 102.68% 5.90% 50.44%
126.5 38.588 22.90 62.83 11.21 103.17% 96.90% 102.35% 5.62% 49.95%
126.75 39.110 23.39 64.64 14.30 103.37% 96.83% 102.02% 5.36% 49.34%
127 39.648 23.85 66.67 16.81 103.56% 96.76% 101.69% 5.10% 48.61%
127.25 40.203 24.29 68.97 18.99 103.75% 96.68% 101.35% 4.83% 47.80%
127.5 40.776 24.70 71.65 20.93 103.94% 96.60% 101.01% 4.57% 46.87%
127.75 41.368 25.10 74.93 22.70 104.13% 96.51% 100.67% 4.31% 45.86%
128 41.978 25.47 79.34 24.33 104.32% 96.41% 100.33% 4.07% 44.73%
128.125 42.291 25.65 82.59 25.11 104.41% 96.36% 100.16% 3.94% 44.12%
128.2425 42.590 25.81 90.00 25.81 104.50% 96.32% 100.00% 3.82% 43.54%
128.25 42.610 25.83   25.86 104.51% 96.31% 99.99% 3.82% 43.57%
128.5 43.262 26.17 27.30 104.70% 96.20% 99.64% 3.58% 44.10%
128.75 43.938 26.49 28.66 104.88% 96.08% 99.30% 3.35% 44.60%
129 44.638 26.80 29.97 105.07% 95.95% 98.95% 3.13% 45.09%
129.25 45.363 27.10 31.20 105.26% 95.82% 98.60% 2.90% 45.55%
129.5 46.116 27.38 32.41 105.45% 95.67% 98.25% 2.70% 45.99%
129.75 46.898 27.65 33.56 105.64% 95.52% 97.89% 2.48% 46.41%
130 47.712 27.91 34.69 105.82% 95.36% 97.54% 2.29% 46.81%
130.25 48.560 28.16 35.78 106.01% 95.20% 97.18% 2.08% 47.19%
130.5 49.444 28.40 36.86 106.20% 95.02% 96.82% 1.89% 47.56%
130.75 50.368 28.63 37.92 106.38% 94.84% 96.46% 1.71% 47.92%
131 51.335 28.86 38.97 106.57% 94.64% 96.09% 1.53% 48.27%
131.25 52.349 29.07 40.02 106.75% 94.44% 95.73% 1.37% 48.59%
131.5 53.416 29.28 41.10 106.94% 94.22% 95.36% 1.21% 48.91%
131.75 54.540 29.48 42.28 107.12% 94.00% 94.99% 1.05% 49.21%
132 55.729 29.67 43.62 107.31% 93.77% 94.62% 0.91% 49.50%
132.25 56.990 29.86 45.11 107.49% 93.52% 94.25% 0.78% 49.79%
132.5 58.334 30.04 46.74 107.67% 93.27% 93.87% 0.64% 50.06%
132.75 59.772 30.21 48.53 107.86% 93.00% 93.50% 0.54% 50.32%
133 61.321 30.38 50.50 108.04% 92.72% 93.12% 0.43% 50.57%
133.25 63.001 30.54 52.68 108.22% 92.43% 92.74% 0.34% 50.81%
133.5 64.841 30.70 55.09 108.402% 92.129% 92.358% 0.249% 51.05%
133.75 66.881 30.86 57.81 108.583% 91.813% 91.974% 0.175% 51.29%
134 69.183 31.01 60.92 108.763% 91.485% 91.589% 0.114% 51.52%
134.25 71.848 31.15 64.56 108.943% 91.143% 91.202% 0.065% 51.73%
134.5 75.076 31.30 69.02 109.122% 90.787% 90.814% 0.030% 51.95%
134.75 79.372 31.43 75.01 109.301% 90.417% 90.424% 0.008% 52.15%
134.875 82.458 31.50 79.35 109.390% 90.226% 90.228% 0.002% 52.25%
135 90.000 31.56 90.00 109.48% 90.03% 90.03% 0.00% 52.34%
135.25 90.000 31.70   109.66% 89.64%   52.55%
135.5 90.000 31.82 109.83% 89.24% 52.73%
135.75 90.000 31.94 110.01% 88.85% 52.90%
136 90.000 32.07 110.19% 88.45% 53.10%
136.25 90.000 32.18 110.36% 88.05% 53.26%
136.5 90.000 32.30 110.54% 87.64% 53.44%
136.75 90.000 32.40 110.71% 87.24% 53.58%
137 90.000 32.51 110.89% 86.83% 53.74%
137.25 90.000 32.62 111.06% 86.43% 53.91%
137.5 90.000 32.73 111.23% 86.02% 54.07%
137.75 90.000 32.83 111.40% 85.61% 54.21%
138 90.000 32.93 111.58% 85.20% 54.36%
138.25 90.000 33.03 111.75% 84.78% 54.51%
138.5 90.000 33.12 111.92% 84.37% 54.64%
138.75 90.000 33.21 112.09% 83.95% 54.77%
139 90.000 33.30 112.25% 83.53% 54.90%
139.25 90.000 33.40 112.42% 83.11% 55.05%
139.5 90.000 33.49 112.59% 82.69% 55.18%
139.75 90.000 33.57 112.76% 82.27% 55.30%
140 90.000 33.66 112.92% 81.84% 55.43%
140.25 90.000 33.74 113.09% 81.42% 55.54%
140.5 90.000 33.81 113.25% 80.99% 55.64%
140.75 90.000 33.90 113.42% 80.56% 55.77%
141 90.000 33.97 113.58% 80.13% 55.88%
141.25 90.000 34.05 113.74% 79.70% 55.99%
141.5 90.000 34.12 113.91% 79.26% 56.09%
141.75 90.000 34.20 114.07% 78.83% 56.21%
142 90.000 34.27 114.23% 78.39% 56.31%
142.25 90.000 34.34 114.39% 77.95% 56.41%
142.5 90.000 34.42 114.55% 77.51% 56.53%
142.75 90.000 34.48 114.71% 77.07% 56.61%
143 90.000 34.55 114.86% 76.63% 56.71%
143.25 90.000 34.61 115.02% 76.18% 56.80%
143.5 90.000 34.67 115.18% 75.74% 56.88%
143.75 90.000 34.74 115.33% 75.29% 56.99%
144 90.000 34.81 115.49% 74.84% 57.09%
144.25 90.000 34.87 115.64% 74.39% 57.17%
144.5 90.000 34.93 115.79% 73.94% 57.26%
144.75 90.000 34.99 115.95% 73.48% 57.34%
145 90.000 35.05 116.10% 73.03% 57.43%
145.25 90.000 35.11 116.25% 72.57% 57.51%
145.5 90.000 35.16 116.40% 72.12% 57.59%
145.75 90.000 35.22 116.55% 71.66% 57.67%
146 90.000 35.28 116.69% 71.20% 57.76%
146.25 90.000 35.33 116.84% 70.74% 57.83%
146.5 90.000 35.38 116.99% 70.27% 57.90%
146.75 90.000 35.44 117.13% 69.81% 57.99%
147 90.000 35.49 117.28% 69.35% 58.06%
147.25 90.000 35.54 117.42% 68.88% 58.13%
147.5 90.000 35.59 117.57% 68.41% 58.20%
147.75 90.000 35.64 117.71% 67.94% 58.27%
148 90.000 35.69 117.85% 67.47% 58.34%
148.25 90.000 35.73 117.99% 67.00% 58.40%
148.5 90.000 35.78 118.13% 66.53% 58.47%
148.75 90.000 35.83 118.27% 66.05% 58.54%
149 90.000 35.88 118.41% 65.58% 58.61%
149.25 90.000 35.92 118.54% 65.10% 58.67%
149.5 90.000 35.96 118.68% 64.62% 58.72%
149.75 90.000 36.01 118.81% 64.14% 58.79%
150 90.000 36.05 118.95% 63.66% 58.85%
150.25 90.000 36.09 119.08% 63.18% 58.91%
150.5 90.000 36.14 119.21% 62.70% 58.98%
150.75 90.000 36.18 119.35% 62.21% 59.03%
151 90.000 36.22 119.48% 61.73% 59.09%
151.25 90.000 36.26 119.61% 61.24% 59.15%
151.5 90.000 36.30 119.73% 60.75% 59.20%
151.75 90.000 36.34 119.86% 60.26% 59.26%
152 90.000 36.38 119.99% 59.77% 59.31%
152.25 90.000 36.41 120.11% 59.28% 59.36%
152.5 90.000 36.45 120.24% 58.79% 59.41%
152.75 90.000 36.49 120.36% 58.30% 59.47%
153 90.000 36.53 120.49% 57.80% 59.52%
153.25 90.000 36.56 120.61% 57.31% 59.57%
153.5 90.000 36.60 120.73% 56.80% 59.62%
153.75 90.000 36.63 120.85% 56.31% 59.66%
154 90.000 36.66 120.97% 55.82% 59.71%
154.25 90.000 36.70 121.08% 55.32% 59.76%
154.5 90.000 36.73 121.20% 54.81% 59.80%
154.75 90.000 36.77 121.32% 54.31% 59.86%
155 90.000 36.80 121.43% 53.81% 59.90%
155.25 90.000 36.83 121.55% 53.31% 59.94%
155.5 90.000 36.86 121.66% 52.80% 59.99%
155.75 90.000 36.89 121.77% 52.29% 60.03%
156 90.000 36.92 121.88% 51.79% 60.07%
156.25 90.000 36.95 121.99% 51.28% 60.11%
156.5 90.000 36.98 122.10% 50.77% 60.15%
156.75 90.000 37.01 122.21% 50.26% 60.20%
157 90.000 37.04 122.32% 49.75% 60.24%
157.25 90.000 37.07 122.42% 49.24% 60.28%
157.5 90.000 37.09 122.53% 48.72% 60.31%
157.75 90.000 37.12 122.63% 48.21% 60.35%
158 90.000 37.15 122.73% 47.70% 60.39%
158.25 90.000 37.18 122.83% 47.18% 60.43%
158.5 90.000 37.20 122.93% 46.66% 60.46%
158.75 90.000 37.23 123.03% 46.15% 60.50%
159 90.000 37.25 123.13% 45.63% 60.53%
159.25 90.000 37.28 123.23% 45.11% 60.57%
159.5 90.000 37.30 123.33% 44.59% 60.60%
159.75 90.000 37.32 123.42% 44.07% 60.63%
160 90.000 37.35 123.51% 43.55% 60.67%
160.25 90.000 37.38 123.61% 43.02% 60.71%
160.5 90.000 37.40 123.70% 42.50% 60.74%
160.75 90.000 37.43 123.79% 41.98% 60.78%
161 90.000 37.46 123.88% 41.45% 60.82%
161.25 90.000 37.47 123.96% 40.93% 60.83%
161.5 90.000 37.49 124.06% 40.40% 60.86%
161.75 90.000 37.51 124.14% 39.87% 60.89%
162 90.000 37.53 124.23% 39.35% 60.92%
162.25 90.000 37.55 124.31% 38.82% 60.95%
162.5 90.000 37.58 124.39% 38.29% 60.99%
162.75 90.000 37.59 124.48% 37.76% 61.00%
163 90.000 37.61 124.56% 37.23% 61.03%
163.25 90.000 37.63 124.64% 36.69% 61.06%
163.5 90.000 37.65 124.72% 36.16% 61.08%
163.75 90.000 37.67 124.79% 35.63% 61.11%
164 90.000 37.68 124.87% 35.10% 61.13%
164.25 90.000 37.70 124.95% 34.56% 61.15%
164.5 90.000 37.72 125.02% 34.03% 61.18%
164.75 90.000 37.74 125.09% 33.49% 61.21%
165 90.000 37.75 125.16% 32.95% 61.22%
165.25 90.000 37.77 125.23% 32.42% 61.25%
165.5 90.000 37.78 125.30% 31.88% 61.26%
165.75 90.000 37.80 125.37% 31.34% 61.29%
166 90.000 37.82 125.44% 30.80% 61.32%
166.25 90.000 37.84 125.51% 30.26% 61.35%
166.5 90.000 37.85 125.57% 29.72% 61.36%
166.75 90.000 37.86 125.63% 29.18% 61.37%
167 90.000 37.88 125.70% 28.64% 61.40%
167.25 90.000 37.89 125.76% 28.10% 61.41%
167.5 90.000 37.91 125.82% 27.56% 61.44%
167.75 90.000 37.92 125.88% 27.02% 61.46%
168 90.000 37.93 125.94% 26.47% 61.47%
168.25 90.000 37.95 125.99% 25.93% 61.50%
168.5 90.000 37.96 126.05% 25.38% 61.51%
168.75 90.000 37.97 126.10% 24.84% 61.52%
169 90.000 37.98 126.16% 24.29% 61.54%
169.25 90.000 37.99 126.21% 23.75% 61.55%
169.5 90.000 38.01 126.26% 23.20% 61.58%
169.75 90.000 38.02 126.31% 22.66% 61.59%
170 90.000 38.03 126.36% 22.11% 61.61%
170.25 90.000 38.04 126.41% 21.56% 61.62%
170.5 90.000 38.05 126.45% 21.01% 61.63%
170.75 90.000 38.06 126.50% 20.47% 61.65%
171 90.000 38.07 126.54% 19.92% 61.66%
171.25 90.000 38.08 126.58% 19.37% 61.68%
171.5 90.000 38.09 126.63% 18.82% 61.69%
171.75 90.000 38.10 126.67% 18.27% 61.70%
172 90.000 38.11 126.71% 17.72% 61.72%
172.25 90.000 38.12 126.74% 17.17% 61.73%
172.5 90.000 38.12 126.78% 16.62% 61.73%
172.75 90.000 38.13 126.82% 16.07% 61.74%
173 90.000 38.14 126.85% 15.52% 61.76%
173.25 90.000 38.15 126.88% 14.97% 61.77%
173.5 90.000 38.15 126.92% 14.41% 61.77%
173.75 90.000 38.16 126.95% 13.86% 61.79%
174 90.000 38.16 126.98% 13.31% 61.79%
174.25 90.000 38.17 127.00% 12.76% 61.80%
174.5 90.000 38.18 127.03% 12.20% 61.81%
174.75 90.000 38.18 127.06% 11.65% 61.81%
175 90.000 38.19 127.08% 11.10% 61.83%
175.25 90.000 38.19 127.11% 10.54% 61.83%
175.5 90.000 38.20 127.13% 9.99% 61.84%
175.75 90.000 38.20 127.15% 9.44% 61.84%
176 90.000 38.21 127.17% 8.88% 61.85%
176.25 90.000 38.21 127.19% 8.33% 61.85%
176.5 90.000 38.21 127.21% 7.77% 61.85%
176.75 90.000 38.22 127.22% 7.22% 61.87%
177 90.000 38.22 127.24% 6.66% 61.87%
177.25 90.000 38.23 127.25% 6.11% 61.88%
177.5 90.000 38.23 127.26% 5.55% 61.88%
177.75 90.000 38.23 127.27% 5.00% 61.88%
178 90.000 38.23 127.28% 4.44% 61.88%
178.25 90.000 38.23 127.29% 3.89% 61.88%
178.5 90.000 38.23 127.30% 3.33% 61.88%
178.75 90.000 38.24 127.31% 2.78% 61.90%
179 90.000 38.24 127.31% 2.22% 61.90%
179.25 90.000 38.24 127.32% 1.67% 61.90%
179.5 90.000 38.24 127.32% 1.11% 61.90%
179.75 90.000 38.24 127.30% 0.56% 61.90%
180 90.000 38.24 127.32% 0.00% 61.90%

Converting Insolation by Obliquity To Insolation By Latitude:

The table above is of insolation with latitude by obliquity.

However, one can use the table above to see how insolation varies with obliquity for a constant latitude thus:
  1. Add 90˚ to the absolute value of the required latitude
  2. Add 90˚ to all the latitudinal values in the above table.
    • if one desires obliquity to be less than 90˚, then subtract the resulting obliquity from 180˚
      • I generally prefer to quote retrograde obliquities because in out solar system high obliquities are always retrograde, and theoretical astronomy suggests that high obliquities are much more likely to be retrograde owing to the instability of high direct obliquities
  3. “Equal to Equator” becomes “Equal to 90˚ obliquity”
  4. “Equal to Poles” becomes “Equal to 180˚ or 0˚ obliquity”
For example, at 37.75˚ (approximately the latitude of Melbourne):
  1. we see the table for 127.75˚ and by adding 90˚, we see that:
    1. the lowest insolation will be for an obliquity of 131.368˚ (or 48.642˚)
    2. planetary average insolation will occur at 115.10˚ and 164.93˚ (or 64.90˚ and 15.07˚)
      • insolation will be above average below 15.07˚, between 64.90˚ and 115.10˚, and above 164.93˚
    3. no value will equal the insolation at 90˚ obliquity (90˚ give the maximum possible insolation)
    4. an insolation equal to that at 180˚ or 0˚ obliquity will occur at 112.70˚ (or 67.30˚) obliquity
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