Speaker cone shape

For some reason, as to which one of you will no doubt enlighten me, they sound even better when the 6.5" are wired out of phase with the 8" & 4".

If you've copied an original crossover design then that driver would have been reverse polarity as well. Capacitors and Inductors alter the phase of the signal so it's not unusual to allow the signal for one driver to go 180˚ out and correct it at the driver. 

My only answer to your original question is that air doesn't flow through a driver so you can't apply the physics of a wing to a loudspeaker diaphragm. It needs to be stiff and light which is why a cone is a good choice of shape for a woofer or mid with a conventional voice coil. Electrostatic speakers are able to have flat diaphragms as the electromotive force is spread across the whole surface area.

If you don't already own a copy The Loudspeaker Design Cookbook by Vance Dickinson is a good primer for the subject... more practical than theory but a good jumping in point. If you really want to get into the mechanics of sound diffraction then the Master Handbook of Acoustics is as good a place as any to start.

"...Lincoln Walsh was a pioneering expert on radar design back in the Forties! I think he may have invented the perfect speaker!..."

A good example for this thread on speaker cone design. Walsh's full range driver was very interesting but the cone was so big that there were problems with cone break-up and distortion at high levels. As a mechanical engineer, you can quickly surmise that all electro-mechanical  drivers have trade-offs, nothing yet is the perfect radiator but the state of the art is still very very good. 

The Walsh Ohm speaker sounds awful. It's a novel design, but next to anything else it's terrible. Explain to me how a single voice coil driver made from three different materials firing downward can have a wideband, high fidelity frequency response. Short answer...it can't...and doesn't.

Sony has had flat diaphragms. Morel makes a dome drivers. Mount a woofer backwards, magnet out and the box gains some volume. Drivers designed with a round cone have the advantage of basic rigidity. Different frequency based cone geometries are chosen for dispersion characteristics.... everything is a compromise. 

Many new drivers have an inverted dome style for the diaphragm. Different materials and diaphragm treatments are also part of the mix.

The best motor design I've ever heard was the extreme underhung topology that was the NeoRadial developed by Aurasound back in the 1990s. Total voice coil immersion in the gap, very linear response, extremely low motor distortion...and very expensive to manufacture due to the amount of steel to house the motor. Over hung coils just cant do what underhung can do for low distortion control of the moving mass. The latest JBL Dual Differential motors is probably the closest with a braking effect from the coils as they reverse direction.

They are shaped that way to add strength and rigidity to the center coil or a more accurate pistonic motion during use to decrease distorion and flexing of the cone during movement.

I imagine many of you are not old enough to remember the Leak "Sandwich" loudspeakers from the early-1970’s; Leak was one of the British companies that never really took off in the U.S.A. in a big way.

Leak’s claim to fame was their flat-face drivers, very similar to the legendary KEF B-139 woofer (used by David Wilson in his mid-70’s WAMM, and ESS in their TranStatic 1), but with a round mounting frame rather than the B-139’s oval one. Leak argued that the cone shape of dynamic drivers causes them to have unacceptable levels of cone break-up, so they developed drivers which had flat front faces, the faces being created, as is that of the KEF woofer, out of expanded styrofoam.

One of the Leak models got a pretty enthusiastic review in 1971 by J. Gordon Holt in Stereophile (at the time, the only subjective hi-fi reviewer and magazine in the U.S.A., 1971 being a year before Harry Pearson started The Absolute Sound). I was in the market for new loudspeakers, and luckily for me there was a Leak dealer in San Jose, a little 1-man shop.

I gave the Leak an audition, but ended up choosing a different loudspeaker. I agreed with Holt’s assessment of the Leak, but found them to be no match for a couple of other the speaker I had also auditioned, both of which contained ESL tweeters: the Infinity 2000A and ESS Transtatic 1. I also heard the Infinity Servo-Static, but didn’t have the two thousand bucks they sold for.

Cone break-up is an important issue, but only one facing loudspeaker designers. And addressing the issue by making drivers with flat front faces only one way to do so. Richard Vandersteen goes to great lengths to minimize cone break-up, but the lack of that break-up does not by itself guaranty good sound.