Why? More elements provide higher gain. The returns diminish at some point, however. Let us discover where that point is.
* Leading Half-Angle. Ref. Definition
Ref: How I define saw teeth ☞Link
Zin near 300Ω, 1/𝜏 = 1.06740, LHA = 18.629°
Zin near 300Ω, 1/𝜏 = 1.05969, LHA = 16.737°
Zin near 300Ω, 1/𝜏 = 1.05357, LHA = 15.186°
Zin near 300Ω, 1/𝜏 = 1.04444, LHA = 12.799°
Zin near 300Ω, 1/𝜏 = 1.03798, LHA = 11.052°
Zin between 200Ω & 300Ω, 1/𝜏 = 1.03315, LHA = 9.720°
Zin near 300Ω, 1/𝜏 = 1.02941, LHA = 8.673°
Zin between 200Ω & 300Ω, 1/𝜏 = 1.02643, LHA = 7.828°
Conclusions: 10 elements provided the smoothest SWR. Gain increased with more elements, but only by a tiny amount. More elements clearly helps out F/R at the bottom-frequency end.
Conclusions: Max gain for 24.89MHz is got with 18 elements. Maybe not enough extra, though, to risk that bump in the SWR chart for 18 elements. Split the difference and go with either 14 or 15?