Extending the Yagi to a boom length of a bit less than 2 X results in the azimuth pattern of Fig 19-12. Again the forward gain is close to that predicted in Fig 19-10. This analysis could be extended as far as desired; however, a few observations are in order.
If you were to place a six element combination broadside -collinear array in front of a back screen reflector (such as was shown earlier in Fig 17-5 in Chapter 17), the resulting reflector array provides a forward gain within about 0.5 dB of the longer 2 X Yagi array. The antenna with the back screen reflector, however, is about 1.5 X high, 1.5 X wide and 0.15 X deep, while the Yagi is 2 A. long, about 0.5 X wide, and not very high. You're trading, in effect, volume for area for two different arrays
Whatever you decide to call "optimum" for any particular installation depends on your specific requirements. I should also point out that the reflector array from Chapter 17 has much less sensitivity to dimensional tolerances or changes in frequency, while the long-boom Yagi is more sensitive to these effects.
You could keep extending the boom and gaining additional forward gain. Another alternative is to stack another copy of the array on top of the first. At the optimum stacking distance, you can increase the gain by almost 3 dB. Stacking compresses the elevation pattern, rather than further squeezing more gain out of the azimuth pattern, as happens when you lengthen the boom of a Yagi. Stacking is often a good method to get more gain, since doubling the boom length results in an increase of about 2 dB,
A Yagi antenna array can have significant gain and front-to-back ratio compared to other types of structures. It offers more gain per unit of wind- surface area than many other types of high -gain systems, at the cost of having tighter dimensional tolerances and correspondingly narrow operating bandwidth. Multiple Yagi arrays can often be combined into stacks of very effective antenna systems.