Hoffman's Iron Law

[DevilDriver 28]

I love Iron Laws. Why? Well, they are so succinctly and aptly named: they are infact, iron. Good luck breaking them!

If you've been a browsing member of the online audio community for a while, you have no doubt heard about Hoffman's Iron Law. What's it all about? Well, it is quite simple. Forgive me if I am misquoting here, but I think JimJ put it best when he said:

"You can have low end extension, high efficiency, or small enclosure size. Pick two."

Please note that while many people use this statement related to enclosures, it applies to the speaker you're using as well So what does that mean? And why is that the case? Well, as you may have heard me say once before, speaker design and engineering is a game of compromises. The best speaker (if there truly is such a thing) is the one that has the lowest impacting compromises.

Let's say you you drive a little Dodge Sprint or another vehicle with a relatively small cabin and little-to-no room for an enclosure. Of course, you're a bass head and you want to hear those lower notes banged out with some authority. To top it off, you're a cheap bugger and want a lot of sound without buying an expensive amplifier. You build your miracle enclosure, install everything, power it up, and surprise! Those low notes just aren't there. You tried to have your cake and eat it too, which just doesn't work in the real world. Naturally, you think there must be something wrong with the sub or amplifier. Now you have switched every product imaginable in and out. The good news is that an amplifier rated much higher than the RMS of your sub has given you that low end beat you're looking for. The bad news is that you just cooked a voice coil.

And this is Hoffman's Iron Law at it's finest. If you want a low end monster, you had better step up the power or build a behemoth enclosure. If you want to keep your amplifier costs to a minimum, you had better build a huge enclosure or accept a very high rolloff with very little low end. If you want a small enclosure, be prepared to buy a big amp or give up that low end you love.

What is the specific relation between these by-products? Simply put, the efficiency of any speaker system is directly proportional to the enclosure volume and the cube of the f3 (the frequency at which SPL is down 3dB). If you halve the efficiency of your speaker system, you may also halve the volume of the enclosure. However, if you decrease the f3 of your speaker system by a factor of two while retaining the same efficiency, you would have to increase the enclosure volume by a factor of 8 (2^3=8). Let's say you have an enclosure with an efficiency of 90dB/w/m that is 2 cubic feet in size. Suppose the f3 of this system is 30hz. However, you've decided you want a heavy bottom end and wish to drop the f3 to 15hz. Without decreasing efficiency, this change would require an enclosure measuring 16 cubic feet in size! That is quite a change, and hardly affordable in a vehicle.

With a lot of preamble, I think that adequately explains how things work on the enclosure side. But as I mentioned earlier, this applies to a normal speaker prior to installation as well. I'll cover this when I get a chance, but to provide a starting point:

where n0 = reference efficiency (% based)

Fs = the resonant frequency of the driver (measured in Hz)

Vas = Volume of air which, when acted upon by a piston of area Sd, has the same compliance as the driver's suspension (measured in m^3)

Qes = electrical "Q" of the driver at Fs (unitless)

n0 = (9.614 * 10^-7 * Fs^3 * Vas)/Qes * 100

Edited February 24, 2007 by DevilDriver

[JimJ 11]

Excellent info!

My journey down the road of single ended triodes has taught me this all too well...getting reference levels with a lightbulb's worth of watts is no place for puny, stand-mounted "bookshelf" speakers

[bdawson72 0]

good read

[filtor1 13]

I have always "known" a little bit about this topic, but am definitely happy you posted this thread. It gives "meat" to the subject of necessary comprimise when deciding which driver, enclosure, and amount of power to use.

[CBFryman 2]

Good write up. I especially like the 5th paragraph.

You see that with noobs all the time.

I have a big enclosure, two big speakers, and a lot of power...Got low-end?

[Aaron Clinton 2,372]

This is something everyone on here should read. Heck I need to read it again.

[tejcurrent 13]

Great info. Nicely written too.

[sqguy 0]

Very nice write up!

If you happen to have a trunk you can cheat with IB (free-air) subs and get that 30Hz, but it has its drawbacks as well so it is not for everyone. You can use less wattage and then use more drivers to increase output. Since you can't lay the power to IB subs like with a box, you don't need super high power subs either. Problem is finding drivers that will work properly as that is a large extent of your tuning ability, though a great eq would help. Also IB tends to work better for SQ with its ability to produce low Hz tones more easily and its limited power capacity. If done properly you can make a stout IB setup with a moderate level of amp and sub wattage that can produce powerful 30Hz for music listening --and have no box in your car at all.

You would need to (very roughly) use twice the subs and half the wattage of an average box setup. Most subs that manufacturers say can do IB will say at half the rated wattage. Maximum applied amp power will be at the point the subs are playing near xmax, not any rating. Research this before you do it. I just put in 4 12" and they work well but I don't have it all sorted out yet.

[Naledge503 0]

Very good info. This helps answer questions that I have now and have had in the past.

[almond 0]

how does this relate to t-lines and rear loading horns??

[DevilDriver 28]

how does this relate to t-lines and rear loading horns??

Same rules apply, in general. They just apply in different ways. With a horn, for example, you generally limit low frequency extension if you keep the length of the throat short, and limit efficiency if you keep the mouth area small. You simply must build a large enclosure if you want to keep either of those two, which is why true horn enclosures are usually very big.

[woodguy 0]

Good Info. A must read.

[Aaron Clinton 2,372]

Good Info. A must read.

Thats for sure, if more people understood this, there would be less topics coming back saying that their speakers don't sound right or don't "hit" like they expected them to.

[yjbliz 0]

wow very informative answers a few questions............nice piece

[Aaron Clinton 2,372]

I hope you don't mind, I shared the topic on CYV also.

[Moon 0]

Yeah,the same to me here.I hope you don't mind, I shared the topic on CYV also.

[Aaron Clinton 2,372]

Cited and pinned on CA-F.

[j-roadtatts 1,129]

Get the biggest box you can and be done with it! I follow the laws.

[sq_mgb 21]

Thank you for stating what a lot of people have forgotten....there is no free lunch!

[Dexter Chaos 14]

this was a good read just found it thought it could help others.