In Figure 2, we see that the elements near the half-wavelength dipole will contribute to the radiation of the LPDA, however the other elements will not. The elements that are too short will be too capacitive to radiate; the elements much longer than a half-wavelength will also not radiate well. Note that this is somewhat of an approximation, as if elements are 1.5 wavlengths, they will tend to radiate well. However, this should give a bit of intuition.