Online calculator precision re box volume? Plus some box tuning ideas...
I think I have found the reason for the curious coincidence of similar frequency response curves a fellow member had with the same driver in two different boxes. Assuming his comparison was done according to the "rules of the art", then some calculator "Gremlins" ? Maybe not...
While having a second look at the curves and calculator data presented, I clicked the MH Audio link referred to and used to calculate box parameters. The red flag (for those who know it) is in the calculator title: "Vented box calculator, according to W. J. J. Hoge" "This set-up provides the highest precision and a flat frequency response". Mh Audio (mh-audio.nl) is a vendor from the Netherlands (nothing wrong with that in itself). However, they don't mention what exactly they are using from John Hoge who produced a number of things (e.g. Articles and BB4 and SBB4 woofer alignments).
Those who have been in audio for quite some time like me, will remember John Hoge (then speaker engineer at CTS) and his famous articles in Audio Magazine (which I still have) that started the wave of DIY subwoofers: "Switched-on bass", Audio, August 1976, p. 34 (based on the work of Thiele/Small) and "Confessions of a Loudspeaker Engineer", Audio, August 1978, p. 47 (based on the work of D. B. Keele). In the latter, Hoge says "I will describe one method I use for vented-box woofer design. It was originally developed by Keele and represents an approximation of the charts given by Small for systems with an enclosure loss factor of QL = 7. In order to use this method, we must have the following information about the driver: Fs, Qts and Vas..." (p. 50) Further, he adds regarding box Vb: "This is the enclosure volume which will come close to giving maximally-flat response." (p. 50) "highest precision" as claimed by Mh audio? If, as it appears, they used that Hoge/Keele method, approximations are necessarily less accurate than the charts given by Small or others (simplied method means approximate which means less accurate).
With his equations/formulas Don Keele tried to simplify the work of Thiele/Small for designing a vented-box and he never officially published these equations/formulas, but he did circulate them privately to other scientists in the audio industry and they have appeared right and left in books, calculators, etc. I suppose because these were not the exact thing, but rather worthy approximations, he preferred not to publish them. I've used these myself many times in the past to design vented boxes, until books, then software replaced them...
It seems the Mh audio calculator is using Hoge's description of Keele's method of approximate vented box design (which I also have from Bolt, Beranek and Newman, dated June 1977) when it requires only the same three parameters (Fs, Qts, Vas) for "a flat frequency response"(so not Hoge's BB4 and SBB4 alignments). Mh audio's mention of Qms and Qes is solely to calculate Qts if you don't have it: "needed to calculate Qts" beside each of these two, indicated in red letters. The formula to calculate Qts with Qms and Qes is well known. Many other softwares require much more data for the box design process, such as Win ISD pro which additionnaly needs the data entered in a certain sequence to work properly...
Robert Bullock (Bullock on boxes, 1991), a mathematician, examined the work of Thiele, Small and Hoge. "Formulas also exist for Small alignments; for example, Hoge provides formulas for QL = 7. These formulas can be off by as much as 25 percent for some alignments. (...) If you like to play with formulas, I have included some of my own construction for QL = 5, 7, 10 in table IV. I make no claims about their accuracy except to say that they should be as accurate as those Hoge used. You can get an idea yourself by comparing formula values with the table values." (p. 8) The least accurate of his own three formulas (for Vb, Fb and F3), according to Bullock himself, is the one for Vb (-17% to + 25%), ± 2% for Fb and ± 6% for F3 usually (p. 6). For the alignments sample analysed by experts (e.g. max-flat response), among all of alignments possible, alignment tables such as those provided by Bullock or Vance Dickason (The Loudspeaker Design Cookbook), yield the highest precision.
With regards to enclosure volume tolerances, in view of Bullock's above stated inaccuracies in Vb formulas, and in the absence of such mention from JBL, its competitor Electro-Voice says "Variations of ± 5% of the specified net internal volume will not materially affect performance." (Pro Sound Facts, no. 7, October 1984, P. 7). So, 5% tolerance VS up to 25% error margin on some alignments for the same Vb parameter may affect performance...
Speaker builders should use online box design calculators with caution, trying to assess what calculation method is used. This does NOT mean that they are bad or worthless. They can be useful for a driver's "trial run" to assess its initial suitability, or even for the final box if you know and agree to an approximate design method, if that is the case. This may result in variances from ideal numbers, and an approximately fine box.
SOME BOX TUNING IDEAS TO FOLLOW IN AN UP-COMING NEXT POST HERE.
Richard
