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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Sunday, 31 October 2021

Oil states as an analog to the United States – and resource rather than settler status as key?

During the 1990s and 2000s, I was extremely aware that the working classes of the United States and Australia were radically different from the powerfully Communist working classes of Europe. The working classes of the United States and Australia, indeed, opposed Communism as anti-Christian.

More recent reading, especially since the 2016 presidential election, has seen a much darker side in that the conservatism of the United States lower class, at least of its white component, is largely or even wholly driven by racism. The fact that, despite massive increases in the wealth of the richest 1 percent, stagnating real wages, and major decreases in religious observance (although they remain much higher than of European workers 150 years ago), poor white Americans are voting for Republicans in larger proportions than they did for Richard Nixon in his 1972 landslide over George McGovern suggests that the role of religion is less marked than I had assumed.

In the 2010s – I think before the Trump victory – I looked online at a book titled Settlers: The Mythology of the White Proletariat by one J. Sakai. “J. Sakai” does not sound like a real name but web searches have failed to find out what his real name actually is. “J. Sakai” argued that the poor white population of America was much more different from the working classes of Europe, East Asia and Latin America than I had presumed previously. He argues that lower-class whites are essentially a petit bourgeois or a “labor aristocracy” and that as settlers they had the same interests as the ruling class.

Whilst I was sceptical of Sakai, I was much less sceptical of Michael Goldfield, who argued and argues that race has always been the mainspring of American politics. A recent article by Mitchell Peterson on medium.com demonstrating the the US is mapped towards a one-party authoritarian regime made me wish to look deeply at this. It is abundantly clear that poor whites are the critical group to reverse increasing income inequality and voter suppression. What I found was an (admittedly outdated, written in January 2010) article by Sebastian Lamb titled ‘J. Sakai’s Settlers and Anti-Racist Working-Class Politics’ which argued that defending the privilege of belonging to the dominant racial group is attractive to lower class whites and promoted constantly by the ruling class as a means of protecting itself. Concurrently the US ruling class invests heavily in making it as difficult as possible for white workers to unite with workers of color. Lamb argues that this emphasis on white supremacy has led to many distinctive traits of US politics and culture.

What Lamb did not discuss, but might, is why the US ruling class has been so much more able to do this than ruling classes in other Enriched nations. I think a relatively simple answer exists:

  1. that the US is vastly richer in natural resources than almost any other Enriched nation
  2. capitalists who own natural resources are uniquely vulnerable to a united lower class because their assets are so physically immovable
  3. ownership of natural resources gives capitalists more financial ability, as well as need, to divide lower classes
I believe that there exists a “hidden” and consistently ignored example elsewhere in the world of an analogous situation to the absence of a socialist party independent of the ruling class in the United States. This being the absence of any democratisation movement in the Gulf oil monarchies (except for an unsuccessful attempt in Baḥrain), as is noted by Sean L. Yom and F. Gregory Gause III in their 2012 ‘Resilient Royals: How Arab Monarchies Hang On’ which emphasises the role oil reserves play in preventing any democratisation movement in most of the oil states. That the United States’ vast and more diverse mineral resources could play an indispensable role in allowing the ruling class to so successfully and consistently divide white workers and workers of color is ignored by Lamb. So is the fact that the Gulf oil monarchies possess similar blood-based caste systems to the white/nonwhite racial classification in the United States. Once one sees this, it actually becomes logical to think that the racial caste system of the United States is more analogous to that of the Gulf Oil monarchies than of India or perhaps even South Africa. Yet writers like Michael Goldfield and Isabel Wilkerson (in Caste) never mention the Gulf oil states as a possible comparison to the United States, despite what I have said above.

If we look at the traits noted by Sebastian Lamb that distinguish the United states, and which he notes are due to racism, and then make a comparison with the Gulf States, one can in most cases see possible similarities as the table below shows 

US trait noted by Sebastian Lamb

Comparative Feature in Gulf Oil States

bad jobs

high frequency of low-paying jobs by expatriates in oil states

low pay

low-paying jobs taken by expatriates in oil states

extreme relative scarcity of jobs full stop in states from which oil state expatriates originate

low level of unionization

unions are banned by law in all oil monarchies

the dominance of bureaucratic business unionism

no mass workers’ party organizationally independent of the ruling class

complete absence of movements amongst citizens of oil states for any democratisation

almost no public health care or welfare

exception because segregation is sectorial (public v. private) rather than geographic as in the US

the influence of patriotic nationalism and narrow individualism

extremely strong nationalism is apparent amongst citizen populations in oil states
As the table shows, there is one key difference: the Gulf States do have large public health and welfare systems for their citizen populations. The reason for this difference is that caste segregation takes upon a different form in the oil states from the United States. Whereas in the United States caste segregation takes the form of confining nonwhites to urban ghettoes or impoverished reservations, in the Gulf States segregation takes the form of privileged citizens working in the public sector with much greater security than expatriates who dominate all but the highest positions in the private sector. This is possibly because in the United States the expansion of the public sector coincided with nonwhite civil rights movements. These in turn coincided with imperialist competition with Stalinist Russia that forced a degree of racial reform on the United States to avoid being viewed as a pariah internationally and prevent mass international support for Moscow over Washington.

Despite this difference, it does seem logical to me that the US is politically similar to the Gulf oil states to an extent unrecognised. I even suspect that for the Republican Party and its academic supporters, the oil monarchies may be a political model of “privately owned government” (Hans-Hermann Hoppe) regardless of the powerful anti-Islamic bent of the Republicans.

Even the radical left, as can be seen in Gabriel Kuhn’s 2017 ‘Oppressor and Oppressed Nations: Sketching a Taxonomy of Imperialism’, has failed to consider that the US (and Australia) may be much more critically “resource states” than “settler states”. Of the Gulf States, Saudi Arabia and the United Arab Emirates are undoubtedly true imperialist nations, as seen in their support for international Islamic terrorism and their ability to blockade greenhouse gas emissions reductions. Kuhn also does not recognise that New Zealand – although a settler state – has much more in common politically and economically with noncolonial European nations or the European periphery (especially Iceland) than with Australia or even perhaps the US.
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Sunday, 10 October 2021

‘Rolling Stone’’s Updated 500 Greatest Songs of All Time

  1. Aretha Franklin – ‘Respect’
  2. Public Enemy – ‘Fight the Power’
  3. Sam Cooke – ‘A Change Is Gonna Come’
  4. Bob Dylan – ‘Like a Rolling Stone’
  5. Nirvana – ‘Smells Like Teen Spirit’
  6. Marvin Gaye – ‘What’s Going On’
  7. The Beatles – ‘Strawberry Fields Forever’
  8. Missy Elliott – ‘Get Ur Freak On’
  9. Fleetwood Mac – ‘Dreams’
  10. Outkast – ‘Hey Ya!’
  11. The Beach Boys – ‘God Only Knows’
  12. Stevie Wonder – ‘Superstition’
  13. The Rolling Stones – ‘Gimme Shelter’
  14. The Kinks – ‘Waterloo Sunset’
  15. The Beatles – ‘I Want to Hold Your Hand’
  16. Beyoncé feat. Jay-Z – ‘Crazy in Love’
  17. Queen – ‘Bohemian Rhapsody’
  18. Prince and the Revolution – ‘Purple Rain’
  19. John Lennon – ‘Imagine’
  20. Robyn – ‘Dancing on My Own’
  21. Billie Holiday – ‘Strange Fruit’
  22. The Ronettes – ‘Be My Baby’
  23. David Bowie – ‘Heroes’
  24. The Beatles – ‘A Day in the Life’
  25. Kanye West feat. Pusha T – ‘Runaway’
  26. Joni Mitchell – ‘A Case of You’
  27. Bruce Springsteen – ‘Born to Run’
  28. Talking Heads – ‘Once in a Lifetime’
  29. Dr. Dre feat. Snoop Doggy Dogg – ‘Nuthing but a ‘G’ Thang’
  30. Lorde – ‘Royals’
  31. The Rolling Stones – ‘(I Can’t Get No) Satisfaction’
  32. Notorious B.I.G. – ‘Juicy’
  33. Chuck Berry – ‘Johnny B. Goode’
  34. James Brown – ‘Papa’s Got a Brand New Bag’
  35. Little Richard – ‘Tutti-Frutti’
  36. The White Stripes – ‘Seven Nation Army’
  37. Prince and the Revolution – ‘When Doves Cry’
  38. Otis Redding – ‘(Sittin’ On) the Dock of the Bay’
  39. Outkast – ‘B.O.B.’
  40. The Jimi Hendrix Experience – ‘All Along the Watchtower’
  41. Joy Division – ‘Love Will Tear Us Apart’
  42. Bob Marley and the Wailers – ‘Redemption Song’
  43. The Temptations – ‘My Girl’
  44. Michael Jackson – ‘Billie Jean’
  45. Kendrick Lamar – ‘Alright’
  46. M.I.A. – ‘Paper Planes’
  47. Elton John – ‘Tiny Dancer’
  48. Radiohead – ‘Idioteque’
  49. Lauryn Hill – ‘Doo Wop (That Thing)’
  50. Daddy Yankee – ‘Gasolina’
  51. Dionne Warwick – ‘Walk on By’
  52. Donna Summer – ‘I Feel Love’
  53. The Beach Boys – ‘Good Vibrations’
  54. Smokey Robinson and the Miracles – ‘The Tracks of My Tears’
  55. Madonna – ‘Like a Prayer’
  56. Missy Elliott – ‘Work It’
  57. Sly and the Family Stone – ‘Family Affair’
  58. The Band – ‘The Weight’
  59. Grandmaster Flash and the Furious Five – ‘The Message’
  60. Kate Bush – ‘Running Up That Hill’
  61. Led Zeppelin – ‘Stairway to Heaven’
  62. U2 – ‘One’
  63. Dolly Parton – ‘Jolene’
  64. Ramones – ‘Blitzkrieg Bop’
  65. Earth, Wind & Fire – ‘September’
  66. Simon and Garfunkel – ‘Bridge Over Troubled Water’
  67. Bob Dylan – ‘Tangled Up in Blue’
  68. Chic – ‘Good Times’
  69. Taylor Swift – ‘All Too Well’
  70. Elvis Presley – ‘Suspicious Minds’
  71. Tracy Chapman – ‘Fast Car’
  72. The Beatles – ‘Yesterday’
  73. Beyoncé – ‘Formation’
  74. Leonard Cohen – ‘Hallelujah’
  75. Pulp – ‘Common People’
  76. Johnny Cash – ‘I Walk the Line’
  77. The Modern Lovers – ‘Roadrunner’
  78. The Four Tops – ‘Reach Out (I’ll Be There)’
  79. Amy Winehouse – ‘Back to Black’
  80. Ray Charles – ‘What’d I Say’
  81. The Velvet Underground – ‘I’m Waiting for the Man’
  82. Adele – ‘Rolling in the Deep’
  83. Bob Dylan – ‘Desolation Row’
  84. Al Green – ‘Let’s Stay Together’
  85. Prince – ‘Kiss’
  86. The Rolling Stones – ‘Tumbling Dice’
  87. LCD Soundsystem – ‘All My Friends’
  88. Guns N’ Roses – ‘Sweet Child O’ Mine’
  89. The Beatles – ‘Hey Jude’
  90. Aretha Franklin – ‘(You Make Me Feel Like) A Natural Woman’
  91. UGK feat. Outkast – ‘Int’l Players Anthem (I Choose You)’
  92. Little Richard – ‘Good Golly, Miss Molly’
  93. Kelly Clarkson – ‘Since U Been Gone’
  94. Whitney Houston – ‘I Will Always Love You’
  95. Oasis – ‘Wonderwall’
  96. Jay-Z – ‘99 Problems’
  97. Patti Smith – ‘Gloria’
  98. The Beatles – ‘In My Life’
  99. Bee Gees – ‘Staying Alive’
  100. Daddy Yankee – ‘Gasolina’
  101. Yeah Yeah Yeahs – ‘Maps’
  102. Chuck Berry – ‘Maybelline’
  103. Alanis Morissette – ‘You Oughta Know’
  104. The Jackson 5 – ‘I Want You Back’
  105. David Bowie – ‘Life on Mars?’
  106. The Rolling Stones – ‘Sympathy for the Devil’
  107. Wu-Tang Clan – ‘C.R.E.A.M.’
  108. The Cure – ‘Just Like Heaven’
  109. Sly and the Family Stone – ‘Everyday People’
  110. The Beatles – ‘Something’
  111. Bruce Springsteen – ‘Thunder Road’
  112. R.E.M. – ‘Losing My Religion’
  113. Stevie Wonder – ‘Higher Ground’
  114. Britney Spears – ‘Toxic’
  115. Etta James – ‘At Last’
  116. Rob Base and DJ E-Z Rock – ‘It Takes Two’
  117. Aretha Franklin – ‘I Say a Little Prayer’
  118. Radiohead – ‘Creep’
  119. Marvin Gaye – ‘I Heard It Through the Grapevine’
  120. X-Ray Spex – ‘Oh Bondage! Up Yours!’
  121. The Beatles – ‘Let It Be’
  122. The Impressions – ‘People Get Ready’
  123. Talking Heads – ‘This Must Be the Place (Naive Melody)’
  124. Buddy Holly – ‘That’ll Be the Day’
  125. Sex Pistols – ‘Anarchy in the U.K.’
  126. George Michael – ‘Freedom! ’90’
  127. TLC – ‘Waterfalls’
  128. Led Zeppelin – ‘Whole Lotta Love’
  129. Drake feat. Majid Jordan – ‘Hold On, We’re Going Home’
  130. Martha and the Vandellas – ‘Dancing in the Street’
  131. Ben E. King – ‘Stand by Me’
  132. Eric B. and Rakim – ‘Paid in Full’
  133. Journey – ‘Don’t Stop Believin’’
  134. Tina Turner – ‘What’s Love Got to Do With It’
  135. The Beatles – ‘She Loves You’
  136. Otis Redding – ‘Try a Little Tenderness’
  137. Ariana Grande – ‘Thank U, Next’
  138. Blondie – ‘Heart of Glass’
  139. Madonna – ‘Vogue’
  140. Bob Marley and the Wailers – ‘No Woman No Cry’
  141. Rod Stewart – ‘Maggie May’
  142. George Jones – ‘He Stopped Loving Her Today’
  143. The Clash – ‘London Calling’
  144. The Rolling Stones – ‘Jumping Jack Flash’
  145. Outkast – ‘Ms. Jackson’
  146. James Taylor – ‘Fire and Rain’
  147. Fats Domino – ‘Blueberry Hill’
  148. Led Zeppelin – ‘Kashmir’
  149. Elton John – ‘Rocket Man’
  150. Green Day – ‘Basket Case’
  151. The Shirelles – ‘Will You Love Me Tomorrow’
  152. Creedence Clearwater Revival – ‘Proud Mary’
  153. Rick James – ‘Super Freak’
  154. Howlin’ Wolf – ‘Spoonful’
  155. The Strokes – ‘Last Nite’
  156. The Kingsmen – ‘Louie Louie’
  157. Sonic Youth – ‘Teenage Riot’
  158. The Meters – ‘Cissy Strut’
  159. The Who – ‘Baba O’Riley’
  160. R.E.M. – ‘Nightswimming’
  161. Madonna – ‘Into the Groove’
  162. Nick Drake – ‘Pink Moon’
  163. Fleetwood Mac – ‘Landslide’
  164. Bob Dylan – ‘Mr. Tambourine Man’
  165. Hank Williams – ‘I’m So Lonesome I Could Cry’
  166. Mott the Hoople – ‘All the Young Dudes’
  167. Eminem – ‘Lose Yourself’
  168. Dusty Springfield – ‘Son of a Preacher Man’
  169. Tom Petty and the Heartbreakers – ‘American Girl’
  170. The Five Satins – ‘In the Still of the Night’
  171. Louis Armstrong – ‘What a Wonderful World’
  172. Nina Simone – ‘Mississippi Goddam’
  173. Television – ‘Marquee Moon’
  174. R.E.M. – ‘Radio Free Europe’
  175. The Flamingos – ‘I Only Have Eyes for You’
  176. The Kinks – ‘You Really Got Me’
  177. Van Halen – ‘Jump’
  178. Billie Eilish – ‘Bad Guy’
  179. Pink Floyd – ‘Comfortably Numb’
  180. Lou Reed – ‘Walk on the Wild Side’
  181. The Byrds – ‘Eight Miles High’
  182. Simon and Garfunkel – ‘The Sounds of Silence’ 
  183. Stevie Wonder – ‘You Are the Sunshine of My Life’
  184. Sinéad O’Connor – ‘Nothing Compares 2 U’ 
  185. Michael Jackson – ‘Beat It’
  186. The Staple Singers – ‘I’ll Take You There’
  187. Bob Dylan – ‘Subterranean Homesick Blues’
  188. The Jimi Hendrix Experience – ‘Little Wing’
  189. David Bowie – ‘Space Oddity’
  190. N.W.A – ‘[expletive] tha Police’
  191. Bobbie Gentry – ‘Ode to Billie Joe’
  192. Geto Boys – ‘Mind Playing Tricks on Me’
  193. The Rolling Stones – ‘Wild Horses’
  194. PJ Harvey – ‘Rid of Me’
  195. Patsy Cline – ‘Crazy’
  196. James Brown – ‘Get Up (I Feel Like Being A) Sex Machine’
  197. Ann Peebles – ‘I Can’t Stand the Rain’
  198. Marvin Gaye – ‘Sexual Healing’
  199. Aerosmith – ‘Dream On’
  200. David Bowie – ‘Changes’
  201. Johnny Cash – ‘Ring of Fire’
  202. Elton John – ‘Your Song’
  203. Stevie Wonder – ‘Signed, Sealed, Delivered I’m Yours’
  204. David Bowie – ‘Young Americans’
  205. Britney Spears – ‘…Baby One More Time’
  206. Glen Campbell – ‘Wichita Lineman’
  207. Rage Against the Machine – ‘Killing in the Name’
  208. Hole – ‘Doll Parts’
  209. Don Henley – ‘Boys of Summer’
  210. Funkadelic – ‘One Nation Under a Groove’
  211. U2 – ‘With or Without You’
  212. Boston – ‘More Than a Feeling’
  213. The Rolling Stones – ‘Paint It, Black’
  214. Steely Dan – ‘Deacon Blues’
  215. Mobb Deep – ‘Shook Ones, Pt. II’
  216. Elvis Presley – ‘Jailhouse Rock’
  217. Stevie Nicks – ‘Edge of Seventeen’
  218. Wilson Pickett – ‘In the Midnight Hour’
  219. Tom Petty – ‘Free Falling’
  220. New Order – ‘Bizarre Love Triangle’
  221. Ike and Tina Turner – ‘River Deep, Mountain High’
  222. David Crosby – ‘Suite: Judy Blue Eyes’
  223. Eminem feat. Dido – ‘Stan’
  224. Derek and the Dominos – ‘Layla’
  225. Joni Mitchell – ‘Both Sides Now’
  226. The Smiths – ‘There Is a Light That Never Goes Out’
  227. Creedence Clearwater Revival – ‘Fortunate Son’
  228. Beyoncé – ‘Single Ladies (Put a Ring On It)’
  229. Woody Guthrie – ‘This Land Is Your Land’
  230. The Byrds – ‘Mr. Tambourine Man’
  231. Whitney Houston – ‘I Wanna Dance With Somebody (Who Loves Me)’
  232. The Who – ‘My Generation’
  233. Deee-Lite – ‘Groove Is in the Heart’
  234. The Supremes – ‘You Keep Me Hanging On’
  235. New Order – ‘Blue Monday’
  236. Bill Withers – ‘Lean on Me’
  237. Hank Williams – ‘Your Cheating Heart’
  238. Aaliyah – ‘Are You That Somebody?’
  239. Big Star – ‘September Gurls’
  240. Backstreet Boys – ‘I Want It That Way’
  241. Digital Underground – ‘The Humpty Dance’
  242. Jerry Lee Lewis – ‘Great Balls of Fire’
  243. The Beatles – ‘Eleanor Rigby’
  244. Pavement – ‘Summer Babe (Winter Version)’
  245. Beastie Boys – ‘Sabotage’
  246. Faces – ‘Ooh La La’
  247. Joni Mitchell – ‘River’
  248. N.W.A – ‘Straight Outta Compton’
  249. Joan Jett – ‘Bad Reputation’
  250. The Jimi Hendrix Experience – ‘Purple Haze’
  251. Gloria Gaynor – ‘I Will Survive’
  252. Parliament – ‘Flash Light’
  253. Willie Nelson – ‘Blue Eyes Crying in the Rain’
  254. The Supremes – ‘Stop! In the Name of Love’
  255. Loretta Lynn – ‘Coal Miner’s Daughter’
  256. Metallica – ‘Master of Puppets’
  257. Martha Reeves and the Vandellas – ‘Heat Wave’
  258. Gil-Scott Heron – ‘The Revolution Will Not Be Televised’
  259. Neil Young – ‘Heart of Gold’
  260. The Wailers – ‘Get Up, Stand Up’
  261. Curtis Mayfield – ‘Pusherman’
  262. Paul Simon – ‘American Tune’
  263. Dolly Parton – ‘Coat of Many Colors’
  264. Marvin Gaye – ‘Let’s Get It On’
  265. The Replacements – ‘Left of the Dial’
  266. Augustus Pablo – ‘King Tubby Meets the Rockers Uptown’
  267. Drake feat. Rihanna – ‘Take Care’
  268. The Isley Brothers – ‘Shout (Parts 1 and 2)’
  269. The Righteous Brothers – ‘Unchained Melody’
  270. Nine Inch Nails – ‘Closer’
  271. Procol Harum – ‘A Whiter Shade of Pale’
  272. Thin Lizzy – ‘The Boys Are Back in Town’
  273. Roberta Flack – ‘Killing Me Softly With His Song’
  274. Al Green – ‘Love and Happiness’
  275. Randy Newman – ‘Sail Away’
  276. Buzzcocks – ‘Ever Fallen in Love (With Someone You Shouldn’t Have)’
  277. Bo Diddley – ‘Bo Diddley’
  278. Toots and the Maytals – ‘Pressure Drop’
  279. Radiohead – ‘Karma Police’
  280. The Beatles – ‘Penny Lane’
  281. Clipse – ‘Grinding’
  282. INXS – ‘Never Tear Us Apart’
  283. Ray Charles – ‘Georgia on My Mind’
  284. Leonard Cohen – ‘Suzanne’
  285. Destiny’s Child – ‘Say My Name’
  286. ABBA – ‘Dancing Queen’
  287. AC/DC – ‘You Shook Me All Night Long’
  288. The Funky 4 + 1 – ‘That’s the Joint’
  289. Bruce Springsteen – ‘Atlantic City’
  290. Usher feat. Lil Jon and Ludacris – ‘Yeah!’
  291. Phil Collins – ‘In the Air Tonight’
  292. A Tribe Called Quest – ‘Can I Kick It?’
  293. Alice Cooper – ‘School’s Out’
  294. The Velvet Underground – ‘Sweet Jane’
  295. The Who – ‘Won’t Get Fooled Again’
  296. Bikini Kill – ‘Rebel Girl’
  297. Beach Boys – ‘Wouldn’t It Be Nice’
  298. Bruce Springsteen – ‘Jungleland’
  299. Screamin’ Jay Hawkins – ‘I Put a Spell on You’
  300. The B-52’s – ‘Rock Lobster’
  301. Bob Seger – ‘Night Moves’
  302. Pink Floyd – ‘Wish You Were Here’
  303. TLC – ‘No Scrubs’
  304. Kraftwerk – ‘Trans-Europe Express’
  305. The Police – ‘Every Breath You Take’
  306. Aretha Franklin – ‘Chain of Fools’
  307. Gnarls Barkley – ‘Crazy’
  308. Liz Phair – ‘Divorce Song’
  309. Bill Withers – ‘Ain’t No Sunshine’
  310. The Doors – ‘Light My Fire’
  311. The Eagles – ‘Hotel California’
  312. Isaac Hayes – ‘Walk on By’
  313. Smokey Robinson and the Miracles – ‘The Tears of a Clown’
  314. The Stooges – ‘I Wanna Be Your Dog’
  315. John Coltrane – ‘Pt. 1-Acknowledgement’
  316. The Shangri-Las – ‘Leader of the Pack’
  317. Bob Dylan – ‘Visions of Johanna’
  318. Big Mama Thornton – ‘Hound Dog’
  319. Tears for Fears – ‘Everybody Wants to Rule the World’
  320. 2Pac – ‘California Love’
  321. U2 – ‘I Still Haven’t Found What I’m Looking For’
  322. Neil Young – ‘After the Gold Rush’
  323. Everly Brothers – ‘All I Have to Do Is Dream’
  324. Billy Joel – ‘Scenes From an Italian Restaurant’
  325. Iggy Pop – ‘Lust for Life’
  326. Rilo Kiley – ‘Portions for Foxes’
  327. Mary J. Blige – ‘Real Love’
  328. Red Hot Chili Peppers – ‘Under the Bridge’
  329. Bad Bunny – ‘Safaera’
  330. The Notorious B.I.G. – ‘Big Poppa’
  331. The Marvelettes – ‘Please Mr. Postman’
  332. Rihanna feat. Jay-Z – ‘Umbrella’
  333. The Temptations – ‘Papa Was a Rollin’ Stone’
  334. The Grateful Dead – ‘Ripple’
  335. Marshall Jefferson – ‘Move Your Body (The House Music Anthem)’
  336. Hall and Oates – ‘She’s Gone’
  337. Cher – ‘Believe’
  338. Black Sabbath – ‘Paranoid’
  339. Prince – ‘1999’
  340. The Clash – ‘(White Man) in Hammersmith Palais’
  341. The Monkees – ‘I’m a Believer’
  342. Chuck Berry – ‘Promised Land’
  343. The Doobie Brothers – ‘What a Fool Believes’
  344. Black Sabbath – ‘Iron Man’
  345. Carole King – ‘It’s Too Late’
  346. BTS – ‘Dynamite’
  347. Elvis Presley – ‘Heartbreak Hotel’
  348. Roxy Music – ‘Virginia Plain’
  349. The Zombies – ‘Time of the Season’
  350. John Prine – ‘Angel From Montgomery’
  351. Jorge Ben – ‘Ponta de Lança Africano (Umbabarauma)’
  352. Ice Cube – ‘It Was a Good Day’
  353. Eurythmics – ‘Sweet Dreams (Are Made of This)’
  354. Michael Jackson – ‘Rock With You’
  355. Thelma Houston – ‘Don’t Leave Me This Way’
  356. Cheap Trick – ‘Surrender’
  357. Taylor Swift – ‘Blank Space’
  358. Patti Smith – ‘Because the Night’
  359. Fugees – ‘Killing Me Softly With His Song’
  360. Prince – ‘Little Red Corvette’
  361. Jimmy Cliff – ‘The Harder They Come’
  362. Kacey Musgraves – ‘Merry Go ‘Round’
  363. Bob Marley and the Wailers – ‘Could You Be Loved’
  364. The Grateful Dead – ‘Box of Rain’
  365. Sex Pistols – ‘God Save the Queen’
  366. The Crystals – ‘Da Doo Ron Ron’
  367. Frank Ocean – ‘Thinking ‘Bout You’
  368. Soundgarden – ‘Black Hole Sun’
  369. The Cars – ‘Just What I Needed’
  370. Buddy Holly – ‘Peggy Sue’
  371. Elton John – ‘Bennie and the Jets’
  372. Bonnie Raitt – ‘I Can’t Make You Love Me’
  373. Drake – ‘Hotline Bling’
  374. William DeVaughn – ‘Be Thankful for What You Got’
  375. The Drifters – ‘Up on the Roof’
  376. Merle Haggard – ‘Mama Tried’
  377. The Cure – ‘Pictures of You’
  378. The Killers – ‘Mr. Brightside’
  379. D’Angelo – ‘Untitled (How Does It Feel)’
  380. Fountains of Wayne – ‘Radiation Vibe’
  381. The Slits – ‘Typical Girls’
  382. Fiona Apple – ‘Paper Bag’
  383. Childish Gambino – ‘Redbone’
  384. Cardi B Ft. Bad Bunny & J Balvin – ‘I Like It’
  385. Diana Ross – ‘I’m Coming Out’
  386. The Kinks – ‘Lola’
  387. New York Dolls – ‘Personality Crisis’
  388. DMX – ‘Party Up (Up in Here)’
  389. Pretenders – ‘Brass in Pocket’
  390. Metallica – ‘Enter Sandman’
  391. Eric Church – ‘Springsteen’
  392. Coldplay – ‘Fix You’
  393. James Brown – ‘Say It Loud (I’m Black and I’m Proud)’
  394. Jeff Buckley – ‘Grace’
  395. Afrika Bambaataa and the Soulsonic Force – ‘Planet Rock’
  396. Elvis Costello – ‘Alison’
  397. Public Enemy – ‘Bring the Noise’
  398. Duran Duran – ‘Hungry Like the Wolf’
  399. Sylvester – ‘You Make Me Feel (Mighty Real)’
  400. David Bowie – ‘Station to Station’
  401. Fleetwood Mac – ‘Go Your Own Way’
  402. Bill Withers – ‘Lovely Day’
  403. Rufus and Chaka Khan – ‘Ain’t Nobody’
  404. Kiss – ‘Rock and Roll All Nite’
  405. Selena – ‘Amor Prohibido’
  406. Run-DMC – ‘Sucker MC’s’
  407. Lynyrd Skynyrd – ‘Free Bird’
  408. Cat Stevens– ‘Father and Son’
  409. Foo Fighters – ‘Everlong’
  410. Allman Brothers Band – ‘Whipping Post’
  411. Wilco – ‘Heavy Metal Drummer’
  412. Neneh Cherry – ‘Buffalo Stance’
  413. Them – ‘Gloria’
  414. Blondie – ‘Dreaming’
  415. Depeche Mode – ‘Enjoy the Silence’
  416. Pearl Jam – ‘Alive’
  417. Mark Ronson feat. Bruno Mars – ‘Uptown Funk’
  418. Booker T. and the MGs – ‘Green Onions’
  419. Mariah Carey – ‘Fantasy’
  420. The Mamas and the Papas – ‘California Dreaming’
  421. The Smiths – ‘How Soon Is Now?’
  422. Craig Mack featuring Notorious B.I.G. – ‘Flava in Ya Ear (Remix)’
  423. Fiona Apple – ‘Criminal’
  424. Blackstreet feat. Dr. Dre and Queen Pen – ‘No Diggity’
  425. Muddy Waters – ‘Mannish Boy’
  426. Nicki Minaj – ‘Super Bass’
  427. Sugar Hill Gang – ‘Rapper’s Delight’
  428. Harry Styles – ‘Sign of the Times’
  429. Queen and David Bowie – ‘Under Pressure’
  430. Pete Rock and CL Smooth – ‘They Reminisce Over You’
  431. Prince – ‘Adore’
  432. Eddie Cochran – ‘Summertime Blues’
  433. Pet Shop Boys – ‘West End Girls’
  434. Ramones – ‘Sheena Is a Punk Rocker’
  435. Rush – ‘Limelight’
  436. Carly Rae Jepsen – ‘Call Me Maybe’
  437. Lucinda Williams – ‘Passionate Kisses’
  438. Megan Thee Stallion featuring Beyoncé – ‘Savage (Remix)’
  439. Celia Cruz – ‘La Vida Es un Carnaval’
  440. Alicia Keys – ‘If I Ain’t Got You’
  441. Miranda Lambert – ‘The House That Built Me’
  442. Motörhead – ‘Ace of Spades’
  443. Fall Out Boy – ‘Sugar, We’re Going Down’
  444. 50 Cent – ‘In Da Club’
  445. T. Rex – ‘Cosmic Dancer’
  446. Bruce Springsteen – ‘Rosalita (Come Out Tonight)’
  447. The Beatles – ‘Help!’
  448. Erykah Badu – ‘Tyrone’
  449. Blue Öyster Cult – ‘(Don’t Fear) The Reaper’
  450. Neil Young – ‘Powderfinger’
  451. Migos feat. Lil Uzi Vert – ‘Bad and Boujee’
  452. Toto – ‘Africa’
  453. Missy Elliot – ‘The Rain (Supa Dupa Fly)’
  454. Sister Nancy – ‘Bam Bam’
  455. Jefferson Airplane – ‘White Rabbit’
  456. Lana Del Rey – ‘Summertime Sadness’
  457. Bon Jovi – ‘Living on a Prayer’
  458. Beck – ‘Loser’
  459. Sade – ‘No Ordinary Love’
  460. Steel Pulse – ‘Ku Klux Klan’
  461. Roy Orbison – ‘Crying’
  462. Van Morrison – ‘Into the Mystic’
  463. John Lee Hooker – ‘Boom Boom’
  464. Joni Mitchell – ‘Help Me’
  465. Daft Punk feat. Pharrell Williams – ‘Get Lucky’
  466. Luther Vandross – ‘Never Too Much’
  467. Nirvana – ‘Come as You Are’
  468. Mazzy Star – ‘Fade Into You’
  469. Dixie Chicks – ‘Goodbye Earl’
  470. Gladys Knight and the Pips – ‘Midnight Train to Georgia’
  471. The Animals – ‘The House of the Rising Sun’
  472. Peter Gabriel – ‘Solsbury Hill’
  473. Tammy Wynette – ‘Stand by Your Man’
  474. Curtis Mayfield – ‘Move On Up’
  475. Janet Jackson – ‘Rhythm Nation’
  476. Kris Kristofferson – ‘Sunday Morning Comin’ Down’
  477. The Go-Gos – ‘Our Lips Are Sealed’
  478. Juvenile feat. Lil Wayne and Mannie Fresh – ‘Back That Azz Up’
  479. Santana – ‘Oye Como Va’
  480. Biz Markie – ‘Just a Friend’
  481. Robert Johnson – ‘Cross Road Blues’
  482. Lady Gaga – ‘Bad Romance’
  483. The Four Tops – ‘I Can’t Help Myself (Sugar Pie, Honey Bunch)’
  484. Weezer – ‘Buddy Holly’
  485. Azealia Banks – ‘212’
  486. Lil Wayne – ‘A Milli’
  487. Solange – ‘Cranes in the Sky’
  488. The Weeknd – ‘House of Balloons’
  489. The Breeders – ‘Cannonball’
  490. Lil Nas X – ‘Old Town Road’
  491. Guns N’ Roses – ‘Welcome to the Jungle’
  492. Miles Davis – ‘So What’
  493. The Pixies – ‘Where Is My Mind?’
  494. Cyndi Lauper – ‘Time After Time’
  495. Carly Simon – ‘You’re So Vain’
  496. Harry Nilsson – ‘Without You’
  497. Lizzo – ‘Truth Hurts’
  498. Townes Van Zandt – ‘Pancho and Lefty’
  499. The Supremes – ‘Baby Love’
  500. Kanye West – ‘Stronger’
Taking into account my lack of knowledge of commercial music after the 1994 Republican Revolution – due to both my own dislike and the criticism of the likes of Joe S. Harrington and Piero Scaruffi – there are not many songs I would be likely to include in a “best-of” of my own:
  • #12 – ‘Superstition’ – is a definite exception that I wholeheartedly agree could be almost as high as it is
  • #28 – ‘Once in a Lifetime’ – is also exceptional but its predecessor on Remain in Light – ‘The Great Curve’ – is even better
  • #40 – ‘All Along the Watchtower’ – is another that fully deserves its place here and which I might include myself
  • #60 – ‘Running Up That Hill’ – is truly deserving, although third track ‘The Big Sky’ is even better
  • #61 – ‘Stairway to Heaven’ – is deserving, although ‘The Battle of Evermore’, ‘Four Sticks’ and ‘When the Levee Breaks’ are better to my mind
  • #68 – ‘Good Times’ – I have recently listened to and feel fully deserves its place, although why ‘Le Freak’ is not there at all is a big question
  • #172 – ‘Mississippi Goddamn’ – is probably the greatest civil rights protest song and would have to be on any list I make
  • #358 – ‘Because the Night’ – is a deserved selection but not necessarily the best from its parent album
  • #410 – ‘Whipping Post’ – is an equal must to ‘Superstition’
  • #462 – ‘Into the Mystic’ – I also would have to include, although on a top-10 album probably it would have to be alongside the title tune and several others
  • #210, #235, #289, #371, #468, #495, and Aretha’s several late-1960s and early 1970s songs would also be considerations, and if I thought carefully I could certainly add to this list further
However, what is apparent to me is that it is much more difficult to make a list of best songs than best albums. In many cases, I would certainly have chosen a different song, or one of several different songs, from the same or nearby albums:

Artist

Song

Song(s) I would have included myself

Fleetwood Mac

 ‘Dreams’

‘Rhiannon’

‘Sisters of the Moon’

‘Sara’

 ‘Landslide’

 ‘Go Your Own Way’

Patti Smith

 ‘Gloria’

‘Birdland’

‘Ain’t It Strange’

‘Poppies’

Stevie Wonder

 ‘Higher Ground’

‘Living for the City’

Elton John

 ‘Rocket Man’

‘Honky Cat’

Television

 ‘Marquee Moon’

‘See No Evil’

‘Venus’

‘Friction’

‘Torn Curtain’

‘Foxhole’

Parliament

 ‘Flash Light’

‘Sir Nose D‘Void‘Of Funk’

‘Funkentelechy’

‘Bop Gun (Endangered Species)’

The Police

 ‘Every Breath You Take’

‘Message in a Bottle’

‘Don’t Stand So Close to Me’

‘Every Little Thing She Does Is Magic’

‘Spirits in the Material World’

Steely Dan

 ‘Deacon Blues’ (in my view one of their worst songs)

‘Josie’

‘Black Friday’

‘Hey Nineteen’

‘Glamour Profession’

The Doors

 ‘Light My Fire’

‘Break On Through’

‘Twentieth Century Fox’

‘Alabama Song (Whisky Bar)’

Roxy Music

 ‘Virginia Plain’

‘Do the Strand’

‘Re Make/Re Model’

‘Psalm’

The Slits

 ‘Typical Girls’

‘Spend, Spend, Spend’

‘Shoplifting’

‘Earthbeat’

‘Animal Space/Spacier’

Bruce Springsteen

 ‘Rosalita (Come Out Tonight)’

‘The E Street Shuffle’

‘Kitty’s Back’
These cases really do make me think a lot. The fact that Rolling Stone have so often not chosen what I think of as the best songs on even those albums I would rate most highly really makes me feel that it must be more difficult to list best songs than best albums. I say this despite the fact that I rarely listen non-stop through even what I consider the best albums like Moondance, Country Life, Spiderland, Hejira, The Milk-Eyed Mender, alongside other lesser-known masterpieces. (The lack of full album listens may be influenced by lack of opportunity under record COVID numbers for long periods of non-stop listening as I formerly obtained via extended bus rides).

Even with my knowledge limitations, I am not willing to discredit entirely Rolling Stone’s list, and the possibly greater difficulty might call for more lenience than with their Top 500 Albums.
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