  In the cosmic ray spectrum, there are two knees (abrupt changes of slopes)
located around the energies $E_{th}=10^{15.5}$ eV and $10^{17.8}$ eV
respectively. Based on the pioneering work by Kostelecky and Ehrlich, we
ascribe the first knee to a sudden opening of the reaction channel
$\tilde{\nu}_e+p\to n+e^+$ when the proton has a velocity just exceeding a
critical value and so can absorb a tachyonic neutrino $\nu_e$ in the form of an
antineutrino $\tilde{\nu}_e$. Similarly, the second knee is triggered by the
reaction $\tilde{\nu}_\mu+p\to \Lambda+\mu^+$. The fitting of these two values
of $E_{th}$ gives the tachyon mass of $\nu_e$ and $\nu_\mu$ being 0.54 eV/$c^2$
and 0.48 eV/$c^2$ respectively, which are in favor of a minimal three-flavor
model for tachyonic neutrino with one parameter $\delta$ being estimated to be
$\delta=0.34$ eV.
