Dan Jacobson wrote:
"Just curious, what is the result of computer modeling for the ideal
shape of Yagi elements?"

Advantage of a Yagi is gain in a small space due to close element
spacing. This also results in lower radiation resistance as the size
goes down with increased coupling and gain. To get a more convenient
Yagi drivepoint impedance (5 ohms is not usually convenient), a folded
dipole is often used as the driven element. That can multiply the
impedance by 4. See "Multi-Element V-H-F Beam Antennas" section of
Editors and Engineers "The Radio Handbook", William I. Orr, W6SAI,
Editor 15th Edition.

The tapered elements, large at the boom and small at the tip as shown in
the "ARRL Antenna Book", are mechanically sound but the taper is the
reverse of that needed for wide bandwidth.

Cones which grow in size from feedpoint to open ends have an advantage
of more uniform characteristic impedance.

Kraus says on page 229 of his 1950 edition:
"Whereas the characteristic impedance of a biconical antenna is uniform,
the impedance of antennas of shapes other than conical is nonuniform."

Terman says on page 921 of his 1955 edition:
"A particularly effective manner of utilizing the thick antenna
principle to obtain a wideband is to employ a cone antenna. Excitation
at the apex starts a spherical wave, as illustrated in Fig. 23-56, which
spreads out along the cone and in adjacent space without reflection
until reaching the end of the cone."

I don`t know what a computer program indicates as an ideal shape for a
Yagi`s driven element. The conical element shape may be a candidate for
computer optimization. Kraus and Terman have suggestions about the apex
angle and length of the cone.

Best regards, Richard Harrison, KB5WZI