Excerpted from The ARRL Radio Amateur's VHF Manual, 3rd Edition p. 160

In stacking horizontal Yagis one above the other on a single support, certain considerations apply whether the bays are for different bands or for the same band. As a rule of thumb, the minimum desirable spacing is one‑half the boom length for two bays on the same band, or half the boom length of the higher frequency array where two bands are involved.

This example shows 6- and 2-meter antennas however the procedure holds true for the HF bands also. [View larger]

In the stacked two‑band array of the figure, the 50‑MHz 4‑element Yagi is going to "look like ground" to the 7‑element 144‑MHz Yagi above it, if it has any effect at all. It is well known that the impedance of an antenna varies with height above ground, passing through the free‑space value at a quarter wavelength and multiples thereof. At one­ quarter wavelength and at the odd multiples thereof, ground also acts like a reflector, causing considerable radiation straight up. This effect is least at the half‑wave points, where the impedance also passes through the free‑space value. Preferably, then, the spacing S should be a half wavelength, or multiple thereof, at the frequency of the smaller antenna. The half‑the‑boom‑length rule gives about the same answer in this example. For this length of 2‑meter antenna, 40 inches would be the minimum desirable spacing, but 80 inches would be better.

The effect of spacing on the larger array is usually negligible. If spacing closer than half the boom length or a half wavelength must be used, the principal thing to watch for is variation in feed impedance of the smaller antenna. If the smaller antenna has an adjustable matching device, closer spacings can be used in a pinch, if the matching is adjusted for minimum SWR. Very close spacing and interlacing of elements should be avoided, unless the builder is prepared to go through an extensive program of adjustments of both elements lengths and matching.