Just to jump in and talk about cone area for just a second..
In terms of speaker parameters, the measuremend of Sd shown in Thiele - Small parameters is the effective cone area of a driver, expressed in sq. in. or some other measure of area. You guys are measureing diameter only and not considering area.
The way we typically measure Sd is to take the diameter as measured from the middle of the speaker surround roll to the middle of the surround roll 180 degrees away. There is a mathematical reason we measure from the middle of the surround roll, (has to do with differences in excursion at extreme edge vs. at the surround - cone joint but will will not go into that). Take that linear dimension and plug it into the equation PI*D^2/4, (pi times the diameter squared, divided by 4). Some know the equation as PI*R^2 but sometimes it is easier to just use the diameter as a value in the first equation. Mathematically they are the same.
Assuming KG's numbers above are actuall roll-to roll diameters, (they are not, but lets use them since he did) we can do the math and show the following:
PI*(6.5^2)/4 = 3.14x42.25/4 = 33.16 sq. in. for each 6.5" speaker. That means roughly 199 sq. in. of cone area for 6 drivers, not 39
PI*(8.25^2)/4 = 3.14x68.06/4 = 53.43 sq. in. for each 8" speaker. That means roughly 214 sq. in. of cone area for 4 drivers, not 33
Mathematically, when you account for cone area instead of cone diameter you find they are about the same...
Just thought I would bring a little math to the table... Based on the logic presented in previous posts on the previous page , the math would suggest two 6" drivers were equal to a single 12" driver, and I think we can all visualize that would not be the case!!
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12-07-2011, 12:46 PM #51
12-07-2011, 12:56 PM #52
And to bring Dusty's numbers into play, just to be fair, and assuming 10" in his post was a roll-to-roll diameter measurement:
PI*(10^2)/4 = 3.14x100/4 = 78.5 sq. in. for each 10" driver. That means roughly 314 sq in. for 4 10" drivers
Again, this just uses diameters provided in previous posts. The roll-to-roll diameter of a 10" driver is going to be more like 8.5", (I went and measured a woofer just now to be sure) so these numbers are only theoretical, but they show how quicky cone area can go up when speaker diameters go up; it is exponential...
Also, to be fair, when considering coaxial drivers, and comparing cone area, you REALLY need to consider doing the math to remove the part of the cone that is missing where the pole mounted tweeter or horn go through. A sealed cone with no hole in the middle and nothing poking through it will have more radiating area than the same diameter cone that has a hole in the middle.
Last edited by philwsailz; 12-07-2011 at 01:01 PM.
12-07-2011, 12:57 PM #53
Great information there Phil. I never realized how complicated it could become!!06 Supra 24 Gravity Games
12-07-2011, 01:07 PM #54
Consider this. If you have a speaker that is 50 sq.in. you would expect a speaker that was 100 sq. in. to play twice as loud, right? Well, not nccessarily.
If the 50 Sq. in. speaker is 93 dB efficient, and the 100 sq. in speaker is 90 dB efficient, (and assuming identical frequency response, which would be difficult, but let's assume it) you would hear zero difference!
There is a LOT that goes into it!
12-07-2011, 01:19 PM #55
Yea, the number 3.141592653589793238462643383279502884197169399375 ... never came into my equation, lol.
I was merely trying to pass the winter away. Good reading, though, as its nice to learn more of the science side of the equation opposed to the "hype".
Plus you even worked in a Carpenter's reference!!2006 Supra 24SSV
12-07-2011, 01:50 PM #56
The weight of the cone is generally determined by adding the cone to 50 percent of the surround. For calculating surface area, personally I like to stick with edge of the cone to edge of the cone. Some cones terminate underneath the surround while others are over the top. Take that into consideration also. And surrounds can greatly vary in their contribution to moving surface area depending on their compliance.
Strictly from outside cone to cone edge here is what you have.
A hybrid consisting of four SXT65s and two XM7s is 105.10 sq in collective surface area.
Four XM9s would be 122.72 sq in collective surface area.
A hybrid consisting of four SXT65s and two XM9s is 132.60 sq in collective surface area.
Four REV10s would be 176.72 sq in collective surface area.
The surface area number will have a strong correlation to output and to a large degree the bass extension. However, past a point it is the pod/enclosure that is largely impacting the bass extension with any woofer or speaker. In other words, you can put a larger speaker in an undersized pod/enclosure and see a diminished benefit as compared to the potential of the larger speaker's bass response. So ideally the pod/enclosure should grow in proportion to the speaker increase.
Just a little info added to Phil's. Hope this helps in understanding how things work.
Multiple speaker surface area can sum for output but will not combine to extend the bass or midbass response. It can certainly add to the impact but the bass response of one speaker versus a quantity of identical speakers will essentially be the same.
12-07-2011, 02:43 PM #57
The reason why acoustical engineers measure cone diameter from the middle of the surround is as follows:
When looking at the rubber surround, the part of the surround that is directly glued to the cone is moving in and out at the same amplitude, (distance in and out) as the cone; it must, as it is attached. Similarly, when we look at the very outside edge of the surround, it is glued to the basket, and CANNOT move. Between these two points of reference, the surround does move in and out some, and the in-and-out excursion at any given point is a function of the distance between the surround/basket joint and the surround/come joint. SInce the surround moves in and out, and it has area, it does contribute to the output of the speaker, and when we start talking about moving mass, the mass of the cone.
Since the outside edge is not moving at all, and the inside edge is moving fully with the cone, we can mathematically determine that on average, the surround as a whole is moving in and out at basically half the distance of the cone, or put another way, half of the surround is contributing to the sound output, (and moving mass) of the cone. So, this is why we use half of the surround as a reference point for cone diameter measurement.
Just a little propeller-head rambling, still WAY off topic from the original post, and sorry, no Carpenters reference with this post...
12-07-2011, 02:49 PM #58
So basically, you guys both agree we should have two amazing sounding setups!
Ha!06 Supra 24 Gravity Games
12-07-2011, 02:56 PM #59
12-07-2011, 03:48 PM #6006 Supra 24 Gravity Games