Actually, that is not a good title, because I don't mean a port. What I mean is when the woofer is slot loaded, how do you know if the slot is "big enough." This has a few cases I can think of:
1) Woofer facing down onto a baffle or the floor or a back wall. (This might have some kind of airflow/anti-turbulence device like a cone or Polk's PowerPort curved cone). OK, this is not really a "slot" but the same problem really.
2) Woofer is facing into a rectangular slot, mounted on the side of the slot, only one skinny side of the slot is open.
3) Like #2, but the slot is actually tapered, so the opening height is X inches and the other end of the slot tapers to zero.
And there are two aspects of the question occurring to me:
a) Is the slot opening big enough to keep the airspeed low? This should be like a port calculation. At a given frequency, the woofer cone moves a volume of air with a maximum peak velocity...which calculation is totally escaping me at the moment.* In the crudest sense, if you have the cone velocity you could transform the velocity by the ratio (woofer area)/(slot area) to get airspeed in the slot, though that ignores
b) airflow and turbulence effects.
c) Oh, I guess there is also the question of if the port tapers to zero, does it get too "constipated" on the inside. I suppose one could do some kind of ugly integral of slot cross section versus intercepted area of the cone...but I wonder if the opening is OK for airflow, will it basically be OK.
By the way, the reason for the question is I just got a VW Golf Alltrack, which turns out to have a large spare tire cavity, which could maybe accommodate a tapered slot out the side. (The simplest install would be to replace the trunk floor with plywood with a woofer mounted in it, but then I'd need a strong grille, junk can get down in the cone, and any boxes on top of the cone would block the bass. A tapered slot could fire into the scooped cavity on a side of the trunk; trickier to build but nicer.
*I have a copy of Richard Small's thesis buried somewhere in the garage, I'm sure he derives that, guess I better start rooting around. That could get caught up in "what is the input power and frequency and the box and the radiation" and on and on. It seems to me if instead you first define maximum cone excursion, and the frequency thereof, the velocity should derive easily. It's just been too long since I've though about it!
1) Woofer facing down onto a baffle or the floor or a back wall. (This might have some kind of airflow/anti-turbulence device like a cone or Polk's PowerPort curved cone). OK, this is not really a "slot" but the same problem really.
2) Woofer is facing into a rectangular slot, mounted on the side of the slot, only one skinny side of the slot is open.
3) Like #2, but the slot is actually tapered, so the opening height is X inches and the other end of the slot tapers to zero.
And there are two aspects of the question occurring to me:
a) Is the slot opening big enough to keep the airspeed low? This should be like a port calculation. At a given frequency, the woofer cone moves a volume of air with a maximum peak velocity...which calculation is totally escaping me at the moment.* In the crudest sense, if you have the cone velocity you could transform the velocity by the ratio (woofer area)/(slot area) to get airspeed in the slot, though that ignores
b) airflow and turbulence effects.
c) Oh, I guess there is also the question of if the port tapers to zero, does it get too "constipated" on the inside. I suppose one could do some kind of ugly integral of slot cross section versus intercepted area of the cone...but I wonder if the opening is OK for airflow, will it basically be OK.
By the way, the reason for the question is I just got a VW Golf Alltrack, which turns out to have a large spare tire cavity, which could maybe accommodate a tapered slot out the side. (The simplest install would be to replace the trunk floor with plywood with a woofer mounted in it, but then I'd need a strong grille, junk can get down in the cone, and any boxes on top of the cone would block the bass. A tapered slot could fire into the scooped cavity on a side of the trunk; trickier to build but nicer.
*I have a copy of Richard Small's thesis buried somewhere in the garage, I'm sure he derives that, guess I better start rooting around. That could get caught up in "what is the input power and frequency and the box and the radiation" and on and on. It seems to me if instead you first define maximum cone excursion, and the frequency thereof, the velocity should derive easily. It's just been too long since I've though about it!
Keeping port length short (sq) will be the dominating factor.
Port velocity also depends on air volume, max. excursion, Sd and tuning frequency.
I'd say it is big enough when there's no noise or chuffing at the intended max. spl. But generally you want as much area as you can get especially with bandpass boxes.
Flared ports also help.
The more narrow the port the more losses or resistance.
I would not go below 1 inch on a slot port.
When it is too narrow it will be more of a closed box or a "hybrid".
Regarding the tuning you will need to find a synergy with the specific cabin gain and pressure chamber effect of your vehicle.
Therefore a test enclosure using telescope-like variable ports might come in handy to determine optimal tuning.
Port velocity also depends on air volume, max. excursion, Sd and tuning frequency.
I'd say it is big enough when there's no noise or chuffing at the intended max. spl. But generally you want as much area as you can get especially with bandpass boxes.
Flared ports also help.
The more narrow the port the more losses or resistance.
I would not go below 1 inch on a slot port.
When it is too narrow it will be more of a closed box or a "hybrid".
Regarding the tuning you will need to find a synergy with the specific cabin gain and pressure chamber effect of your vehicle.
Therefore a test enclosure using telescope-like variable ports might come in handy to determine optimal tuning.
A slot port uses a lot of volume.
It has the volume of air contained in the slot and it has the volume of the panel that separates the internal speaker volume from the slot volume.
It is usually more efficient in the use of space/volume to use a rigid plastic tube as the port, the plastic volume is usually much less than the timber panel.
Using a tube allows the Builder to experiment with different lengths of port to alter the "tuning".
It has the volume of air contained in the slot and it has the volume of the panel that separates the internal speaker volume from the slot volume.
It is usually more efficient in the use of space/volume to use a rigid plastic tube as the port, the plastic volume is usually much less than the timber panel.
Using a tube allows the Builder to experiment with different lengths of port to alter the "tuning".
Ah, not a bad idea...at home I have all Macs, though I have an extra Windoze machine at work, a pretty old Dell. How robust a machine do you need to do that?
In any case, a theoretical development should be simple, there must be a simple formula for the velocity of a cone given the excursion and frequency...
Good point! I've tended to use slots when a tube won't fit well, but it is true the timber can take up good space.
It's a fit thing, firing the woofer into the side scooped out part of the car's cargo area. You're raising another good issue, which is that if the space is tight it does load down the cone, and I don't know if that is easy to predict. Makes me think I should just use a normal grill.
Vd = Dd * 2 * Pi * f / Sqrt(2)
Where:
Vd = rms velocity
Dd = maximum displacement from mean position
f = frequency
Ah thanks for that!
I never did put the sub in the Alltrack as COVID intervened. However this topic has reared it's head in that one configuration of speakers I'm thinking to build is a horn with a slot/plenum underneath with opposed woofers. So this has come around to being a topic of interest for me.
Then again, I start thinking I should just mount the woofers on the outside, so less headache...except it would look a lot more boring...
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