Bd, Fd

calculated eV

Calculation

cosmic rays

observed eV

B8

1.7 × 1015

the first knee

3 × 1015

the midpoint between B8 and F9

2 × 1016

Equation (11)

the first ankle

2 × 1016

F9

2.4 × 1017

the second knee

3 × 1017

the midpoint between F9 and B9

2.8 × 1018

Equation (11)

the second ankle

3 × 1018

B9

3.2 × 1019

the toe

4 × 1019

F10

4.4 × 1021

beyond the GZK limit

not observed