Speaker cone shape

Why are speakers cone shaped, apart from rigidity? To my mind the air being pushed by a cone would radiate at an angle inward toward the axis of the speaker and collide in the centre, which seems inefficient to me, and likely to cause some distortion of the sound. This may also cause interference to adjacent speakers on the same baffle.  Would there be any advantage to having the surface flat, assuming you could maintain rigidity without increasing the mass? There must be modern capable materials out there.
Is the fact that the speaker is cone shaped that causes the volume to change counter intuitively as you move left and right in front of the speakers? What I mean by counter intuitively is when you move left the right speaker sounds louder and visa versa.
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Rigidity and mass. 

You could always go with ceramics. :)  They don't sound as good, but they are out there.

The thing that is wrong with your analysis is that the entire cone moves as 1 solid piece, therefore the inner and outer part of the cone have the same pressure at the same time.
But as the surface is at an angle the air can’t be pushed along the axis of the speaker only toward the centre. If you move something through the air at an angle the air doesn’t get pushed directly forward, it always moves in the direction of the trailing edge, which would be the centre of the cone.
There's all kinds of resonant modes in a given cone shape. If it's a standard typeish round cone, you can pretty well tell which modes it's experiencing when looking at the FFT plots/graphs with an educated eye.

This is a fairly deep subject. When exploring it, it is easy to hit the weeds. Meaning... lots of arguments, discussions, and complex nebulousness to be explored.
They're not all shaped as cones. There have been a number of flat drivers, and one current example is the top model from Vienna Acoustics. 
Hmm, seems to be a can of worms then?
I just had a look at Vienna Acoustics, even those are not completely flat, but very nearly, well that's how they come across in the images.

They say: "The plane surface of the spidercone offers the advantage of precise, piston-like movement. Any diaphragm should move in and out as one unit, not as a quivering mass of uncorrelated vibrations. It should move as a perfectly-solid piston. The flat cone is extremely stiff, with bracings of a height of 18 mm (bass) and 14 mm (mid), yet light, respectively, further reinforced by glass fibers in our new X4P mixture."
Interesting video. So there are advantages to flat drivers. How much difference you can actually hear is another question.
Hmm, seems to be a can of worms then?
Biggest can ever.

Loudspeaker design involves 7 branches of physics to be mastered at some high level to make a world class speaker...and they are all incomplete, like all reasonably considered branches of physics.

The loudspeaker may be one of the most common devices known to humanity, with a huge range of available designs, types and whatnot... but that does not mean it is simple. Oh no. Not at all.

When John Dunlavy of Duntech and then Dunlavy loudspeakers was asked about why he got into loudspeaker design at such a late age (approx 50) he said (I paraphrase) ’because it is the most difficult thing I know of’.

This was a man with about 30 patents to his name, some in black science and tech for quite some time and some might still be classified. Eg, a little thing called the spiral backed antenna is his design, and it is now everywhere. Originally designed for satellite use, IIRC.
You are thinking air movement as opposed to pressure wave. Sound is not moving air, not in a linear movement sense. Cones do provide rigidity, naturally, in the axis of movement which potentially allows them to be lighter. Unlike Eric, I am quite fond of some ceramic drivers, however, there are pluses and minuses like almost every driver.

Don’t let people over complicate a ham sandwich. There are a lot of things that go into a world class speaker, much tech buried in drivers, some in capacitors, some in cabinets, some in acoustics (not as much as you would think for many companies), and yet, Wilson speakers was started by a staff writer at an audio magazine. No one, Dunlavy included knows everything, hence why he used off the shelf drivers, and his speakers were relatively traditional construction, just well optimized for his particular design goal (time/phase alignment) and tightly controlled in manufacturing.
Don't let people under complicate it either, as that is the insanity of dunning-kreueger come to life in the limit ranges of the minds of all humans, as it is wont to. 

Hence the use of the word 'reasonable'.

The hoary common sense aspect.

A human is projected in and out of and filtered by the confines of a fleshy filter box that is animal based, so problems abound in that area...especially so, when exploring limits. Which was my point. To talk and tackle tech limits - is to talk and tackle human limits. 

Eg, at the limits, a ham sandwich is built out of myriad things we definitely don't understand.  Or one can roll it all back, and just eat the damned thing.
I'm beginning to realise there is enough known and unknown to keep your brain occupied for a lifetime :^).

I have just built a set of 3 way units with new 8" Kevlar - 6.5" Kevlar - 4" Silk, and better crossover units. They are rebuilt in a pair of cabinets I already had, I just relined the cabinets with acoustic absorbing material. 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".
There are far better forums to ask that question, many specifically on speaker design for DIYers, however, the most obvious answer would come down to phase angle introduced by your cross-over and the driver itself, such that the 6.5" wired in phase, is actually out of phase during the critical cross-over transition regions and is causing suck-out in the frequency response.  

What Vienna Acoustics wrote is no more than marketing. I cone moves as a complete signal unit every bit as much as a flat surface. It is meant to impress people who don't know what they are writing is just market speak.  Sort of like the Phase Technology guy claiming that his drivers are acoustically opaque to the back wave (and others are not), and yet his cone is only 3.1 grams (ignores the weight of the flat piece). If you believe that, I have some swamp land for you in Florida. Don't tell me in marketing speak, show me actual measurements that prove what you claim. If you can't show your driver has lower distortion, more even dispersion, lacks resonances, and can truly block the back wave, then it is just market speak. 

Don't get me wrong, designing a good speaker takes work, but as you will see in DIY sites, people with limited physics knowledge, by building on the work of others, can achieve very significant results.

(Side note, there is technical merit in Dunlavy's time and phase aligned design, however, that does not necessarily translate into higher levels of listener satisfaction. It has technical merit, but it is not proven out to be psychoacoustically critical. <-- Not even 1 area of physics needed.   Dunlavy didn't push the boundaries of any physics in his implementation and most of what was accomplished was "math", i.e. the mathematically modelling to achieve time alignment, but I digress). 

“they sound even better when the 6.5" are wired out of phase with the 8" & 4”... I believe some companies actually do this sometimes to help with phase response in certain designs, not sure though.
A company named Phase Tech made speakers using FLAT woofers. In fact, the owner/designer invented the first dome tweeter!  
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Woe I wish I knew what you mean.
Manger makes flat diaphragm drivers that use the "bending wave" principle for phase coherence.
Don't forget the Quad 63 with its flat ESL panel driven concentrically by delay lines to approximate a point source. Now made in China by the IAG group!
Flat drivers? I didn’t read every line, BUT PLANAR. I been using them for over 25 years.. Small planars are "flat". 3" 8" 10" all real popular.

Strathearns are a wonderful FLAT ribbon driver.. Actually one of my all time favorites. Nothing is like a Strathearn, nothing..

300 hz and down round speakers and no planars for ME. There are planars that will play to 150 or so.. I couldn’t get use to it.

A lot of the music I listen to 150hz -300hz likes round cone speakers.

So the best of both worlds. Round larger sub drivers 10" med - high excursion for 100 hz or less with tunable phase plugs. Kevlar, and WCF are my preference for material. 8" or smaller cone style medium excursion, with cast basket and once again (adjustable if need be) phase plugs. 100-300hz Mid Bass duty...

The only thing I really change in the system IS for controlling the drivers.

Servo or DSP, I use both passive and plate amps with dsp. 100 hz <
I use Behringer 2496 and 12K class Ds, directly coupled to the drivers.. Guess what as accurate as GRs Servo system for controlling cone overshoot., IF you use an active XO and short heavy cables. The dampening actually works as good... Go figure... Not servo, but extremely well behaved with off the shelf PE sub drivers...

I used GR OB servo system for Sub duty too.. 100 hz < Great look and it pressures the room a completely different way...

The best speakers I ever heard were and ARE DIY.. The finest speakers in the whole world are DIY, onesies and twosies.. the only scientist in sight were the RED faced fools admiring them, IF thy were invited at all.

Sorry guys it ain’t rocket science, a good 6th grade education IF YOU LISTENED. Will build you the best speakers money can buy. Crack me up with all the tech talk... BLING ad whatever price you want.. In the 4th grade I learned how to repair an oscilloscope and built my first valve amp...

OH I like model railroading too, but it is a TAD more techy, ay...BUT the people there think it's real high on the tech list too.. CRACK ME UP... It is more techy than stereo gear, we use stereo gear in some of the setups..

Depends on the day, ay... :-)

The noble art of the "Audiophiler", expensive YES.. Rocket science NO...

Back to cones: how about the Walsh soeaker? Omnidirectional and phase coherent! I have a pair of the older Sound Cylinders and they do produce a 3-D room-filling sound field unlike the typical box speaker! Astounding is the best word to describe them! 
Lincoln Walsh was a pioneering expert on radar design back in the Forties! I think he may have invented the perfect speaker! 

396 posts
04-22-2021 1:21pm
Manger makes flat diaphragm drivers that use the "bending wave" principle for phase coherence.

Great transient response, but frequency response is all over the map. His website dedicates much time to transients and location by transients, but seems to ignore all the other mechanisms for location that are frequency based. I guess it comes with the marketing territory. I can certainly appreciate the engineering of the driver. I have only heard them at an audio show. They were good. Not great, good. I found them no more or less realistic than other implementations.
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.
I don't perceive flat speakers to have any inherent advantage in breakup. If anything a cone has more stiffness in the vector of movement.
Nobody's mentioned amt drivers yet, 'til now.

Absolutely effortless....*S*  

Oldhvymec, +1 on the 2496....sweet.

(*hmmmm* Initialed, 'o.h.m.'...ohm.....interesting....;)...)

The old Ohm Walsh's large cones were a breakthrough, but suffered from the tech of the era.  The newer ones are very good, but the interpretation of their designs 'cheat' a bit on the original concept......

I do too, but in a different fashion. *G*  Just got to go there...*S*
Having done some research on this when I was making custom speakers, I can tell you shape does not seem to effect radiation pattern. They all create a pressure wave that expands outward in all directions as it travels. It does not collapse inward. Think ripples on a pond. The waves you see are not in the same direction as the stone that caused them.  You can mount a woofer backwards and it still performs the same if polarity is reversed. I hope this helps you visualize what’s happening at the air/cone interface. 
Thank you vinylfan62! Someone finally came up with the right answer. Talking about lay instinct gone awry. Air is not moving. It is pressure fronts that are moving. A flat woofer radiates exactly the same way as a conical one. The physical characteristics of the drivers are different but that is all. This might lead to different driver behaviors and distortion characteristics. Nobody has been able to out perform the conical driver in bass and midrange applications for dynamic drivers.  It is an inherently stiff structure so it is easier to keep it light. Attempts at using alternative  structures have been relative failures. The old paper cone still reigns supreme but you also have composites, metal, ceramic and diamond cones and domes. You also have various suspension types, voice coil formers, methods of ventilation and voice coil cooling (ferrofluid), and basket structure. There is no magic in any of this.

The real problem for dynamic drivers is that their dispersion characteristics change dramatically with frequency relative to the size of the driver. The frequency band is not dispersing uniformly but continuously changing. Some people believe speakers that disperse uniformly over a narrower area have better imaging characteristics as opposed to speakers that will disperse widely but unevenly across the frequency band. 
mijostyn, that was pointed out about 20 posts ago ...
Put a whole bunch of small...say 3"...full range drivers in an array of some sort that will move enough air to get to 85+ dB and be prepared at the amazing sound...with no crossover interference...that all these little drivers working in unison can create. 

Faital Pro makes some pretty killer little full range drivers for about $20 each.
Essentially the old Infinity. They had some good ... and some bad. I am a fan of midranges in this size. Not many really good. 
Well this has been interesting.  So though there is science involved and calculations to make, and I dare say the implementation of aspects of others previous design successes to assist with the design of a good speaker system, the bottom line is once you have done all that and built your speaker, suck it and see seems to be the final process.
I’m not sure what you mean by “suck it and see”. Your post was about cone shape. Good speaker design is full of challenges. But cone shape isn’t one of them. Buy what sounds best to you. 
What I meant by "suck it and see", is reading the posts, despite any science or past design experiments, be that of cone shape, cabinet or any other aspect of the speaker design, the bottom line seems to be you have no guarantee that it will sound any better to you than something put together in your garage out of available parts. You design it, build it, take all the available measurements, but it's not until you listen to it, do you find out how good or bad it is. Just like a new recipe, despite having all the best ingredients you don't know until you taste it. Add to that the fact that tastes in how speakers sound vary, along with all the other variables, and what you said becomes the deciding factor be they $$$ latest tech or not, if they sound good to you, they are good.
to the OP,
Let's go back to understand what physically is happening to the cone. The voice coil attached to a cone will move the cone when the voice coil moves forward and backward. The entire cone does not respond all at once. Instead, a compression wave and a bending wave is launched into the cone by the voice coil. The compression wave causes no sound. The bending wave travels down the cone and induces a compression wave in the air.

As the bending wave travels to the far edge of the cone (at the surround), the air compression wave travels away from the cone surface. Due to the difference of the wave speed in the cone and the wave speed in the air, the effective wavefront at the plane of the cone surround can vary from a concave shape to a convex shape, with a plane wave between the two extremes.

Since the speed of the wave in the cone is typically slower than in the air, the cone angle can be designed to produce a convex spherical wavefront from the cone, propagating out  of the speaker into the forward half-space.

In the specific case of the Walsh speaker design with the apex of the cone pointed upward, the cone radiates sound from the convex side of the diaphragm. Since the sonic velocity in the cone much higher than in the air, a cylindrical wavefront is propagated in a 360-degree horizontal direction. With appropriate control of sound speed variation in the diaphragm, a waveform can be made to be spherical, radiating like a point source over a wideband of frequencies, without crossovers.

The reason most electromagnetic speakers use multiple drivers is that the designer wants each cone to move a if it were a rigid surface, which it's not. So the cone is restricted in frequency range where it acts as if it were moving all at once. For higher frequencies, a smaller driver is used to act as if it were moving all at once, because the wavelength in the cone (and in the air) is much shorter than for lower frequencies. And, so forth, which means you need crossovers to direct the right frequency range to each driver.

Many thanks,

I have a better idea of what's going on, and it gives me more to research.