In-depth way of calculating the required length of a flared port

[DevilDriver 28]

This is a routinely asked question:

"How long does the vent tube need to be if I use an n" flared port?"

Granted, there are a few calculators out there that will calculate this for you, particularly if you're using some of the widely available manufactured ports. Here's a good example of a calculator available to you:

http://psp-inc.com/psp-inc.com/public_html..._calculator.cgi

But what if you have hand-formed your flared ends? Better yet, let's assume you are a dork like me and prefer to hand calculate a lot of things (believe it or not, the extra effort is worthwhile in the long run, but that's a rant for another day).

Without getting too into depth on the actual derivation of the formula, here's what you need to know.

Where:

Lv = length of the vent tube (in meters)

N = number of ports (unitless)

c = speed of sound (in meters/second)

Rm = mouth radius of the flare (in meters)

Rt = throat radius of the flare (in meters)

Rf = flare radius (in meters)

Fb = frequency of port resonance (in Hertz)

Vb = size of enclosure (in cubic meters)

V = Volume of air in the flare

Rm = Rf + Rt

and

V = pi*Rf*Rm*Rm - (pi*pi*Rm*Rf*Rf/2) + (2*pi*Rf*Rf*Rf/3)

and for a vent with two flared ends:

Lv = N*c*c*Rt*Rt / (4*pi*Fb*Fb*Vb) - 0.85*Rm - 0.613*Rm - 2*V / (pi*Rt*Rt)

and for a vent with one flared end:

Lv = N*c*c*Rt*Rt / (4*pi*Fb*Fb*Vb) - 0.85*Rm - 0.613*Rt - 2*V / (pi*Rt*Rt)

I KNOW you are happy to have a lot of equations thrown at you, but this is actually relatively simple to sort out, as far as equations go. First, let's fill in the blanks I know the answer to in our simulation. We'll assume I have already measured or calculated the radius of the flare, throat, and mouth.

Lv = length of the vent tube (in meters)

N = 1 port

c = 340 m/s at sea level

Rm = mouth radius of the flare (in meters)

Rt = 0.05m (approximately 2 inches)

Rf = 0.025m (approximately 1 inch)

Fb = 10 Hz

Vb = 0.284m^3 (approximately 1 cubic foot)

V = Volume of air in the flare

As you can see, we are down to only three things that need solving! First, let's solve for Rm. As mentioned previously:

Rm = Rt + Rf

Rm = 0.05m + 0.025m

Rm = 0.075m

Now we move on to solving for V. This one is a bit more complicated, but still easy when we know all of the variables.

V = pi*Rf*Rm*Rm - (pi*pi*Rm*Rf*Rf/2) + (2*pi*Rf*Rf*Rf/3)

V = 3.14*0.025*0.075*0.075 - (3.14*3.14*0.075*0.025*0.025/2) + (2*3.14*0.025*0.025*0.025/3)

V = 0.0004415625 - 0.000231084375 + 0.0000327083

V = 0.0002432

Ok, now we're getting somewhere! Let's get to solving for Lv where both ends are flared!

Lv = N*c*c*Rt*Rt / (4*pi*Fb*Fb*Vb) - 0.85*Rm - 0.613*Rm - 2*V / (pi*Rt*Rt)

Lv = 1*340*340*0.05*0.05 / (4*3.14*10*10*0.284) - 0.85*0.075 - 0.613*0.075 - 2*0.0002432 / (3.14*0.05*0.05)

Lv = 289 / 356.704 - 0.06375 - 0.045975 - 0.0004864 / 0.00785

Lv = 0.81020 - 0.06375 - 0.04597 - 0.06196

Lv = 0.63852m

Lv = 25.15"

At last, we know how long the vent tube must be. There is one last step which you might find interesting.

Let's say you model up an enclosure (who hasn't?). Using a straight port with a 2" radius, you notice that the vent speed is approximately 15m/s. What will be the new vent speed, now that we have flared ports? Using the values for Rt and Rm that we determined previously, we can easily calculate the change in exit velocity.

Vt = 15m/s

Vm = Rt*Rt*Vt / Rm*Rm

Vm = 0.05*0.05*15 / 0.075*0.075

Vm = 0.0375 / 0.005625

Vm = 6.67m/s

That's quite a change! From % perspective standpoint, that's a decrease of approximately 56%!

Hopefully you enjoyed the little math lesson. Whether this is practical for you to learn in depth or not, it is definitely worth reading and maybe picking up some theory. If someone asks you any questions about calculating flared ports, you can answer intelligibly.

Cheers!

[///M5 2,833]

Nice post. I was going to double check your math even though I can say with 100% confidence I am sure it is right, but dang it is hard to read equations on without some sort of software that allows superscripts. You did a great job making it readable considering, but pi*pi just doesn't have quite the meaning as "pi squared" written out the classical way.

[DevilDriver 28]

Nice post. I was going to double check your math even though I can say with 100% confidence I am sure it is right, but dang it is hard to read equations on without some sort of software that allows superscripts. You did a great job making it readable considering, but pi*pi just doesn't have quite the meaning as "pi squared" written out the classical way.

I agree so much. Going back through the equations was painful to make sure I was looking at the right part; I greatly prefer doing things in paper. If I get a chance, I'll do up some gifs of the math to make it a tad easier to follow.

Oh, and it wouldn't be the first time I calculated things wrong. I did this late at night, so I wouldn't be surprised

[helotaxi 46]

Question: Is the value of Lv given by the equation the length of the vent from the mouth of the flare or from the throat? Kinda important to know, ya know...

[helotaxi 46]

If anyone wants it, I made a spreadsheet out of this complete with conversion from imperial units. It does both single and double flares. I also included a velocity ratio to give you an idea of how much the flare will reduce port velocity. It's not fancy but it is functional.

[bdawson72 0]

If anyone wants it, I made a spreadsheet out of this complete with conversion from imperial units. It does both single and double flares. I also included a velocity ratio to give you an idea of how much the flare will reduce port velocity. It's not fancy but it is functional.

You should post it here

[subwoofery 0]

That might sound stupid but does it mean that using a flared port only require you to use a 3" port instead of a 4" port?

SS RL-i8 (as per Mike's quote: moves a lot of air) needs 10 square inches of port area. 4" port will provide around 12.56 square inches of port area (but the port will be longer).

Using flared port will help reduce the need for a 4" port or not at all?

[DevilDriver 28]

That might sound stupid but does it mean that using a flared port only require you to use a 3" port instead of a 4" port?

SS RL-i8 (as per Mike's quote: moves a lot of air) needs 10 square inches of port area. 4" port will provide around 12.56 square inches of port area (but the port will be longer).

Using flared port will help reduce the need for a 4" port or not at all?

You've got the idea, for sure. I have some more to add in the morning, though.

[subwoofery 0]

Sweet, can't wait to read what you have to add.

Not that I go on every forum waiting for you to post something useful

[DevilDriver 28]

The reason a flared port works in the first place is because the flare causes the air in the boundary layer (air close to the walls of the port) to expand and loose speed in a controlled manner, the amount of expansion obviously depending on the various radiuses I listed above.

The problem is that the flare effect is most predominant on the boundary layer and has little to no effect on the air in the center of the port. As the velocity increases, this air becomes increasingly turbulent (for a given diameter port) and the flare does nothing to help this. This is port compression at it's finest, where there is a little loss of output and the helmholtz resonator shifts in frequency (the tuning frequency of the port changes).

For a given port diameter and throat velocity, you will encounter problems regardless of the flare radiuses. Flared ports work with reason....if a design would call for 4 4" ports, you probably won't get away with one flared 4" port. But in the example you suggested, I would say yes, a flared 3" port will work just fine over a straight 4" port.

[///M5 2,833]

If you do a 3 instead of a 4, I'd flare both ends though.

[dmz2711 0]

devildriver, just curious as to where you found those equations/formulas? I'm always trying to learn more, any links you would recommend?? or are those your own formulas??? thanks...

[Megalomaniac 0]

wow thats lot of math

what i do is use that psp calculator and subtract 6" from "Flare Length Port required", like the instructions say, to get the length of center piece required.

[subwoofery 0]

Flare both ends? Sure can do

[mrray13 30]

If anyone wants it, I made a spreadsheet out of this complete with conversion from imperial units. It does both single and double flares. I also included a velocity ratio to give you an idea of how much the flare will reduce port velocity. It's not fancy but it is functional.

You should post it here

x2

please

wheeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

[BKOLFO4 29]

I have used the Lv calculator on the PSP website you reference above a couple of times, but it looks like all it does is add 1" to the standard calculated port length. . . .Does not matter what port size, box volume, # ports, etc. you use. Did I miss something?

[DevilDriver 28]

I have used the Lv calculator on the PSP website you reference above a couple of times, but it looks like all it does is add 1" to the standard calculated port length. . . .Does not matter what port size, box volume, # ports, etc. you use. Did I miss something?

That's because of the radiuses they use on all their flares. It's the same, so the length required is always an inch longer. This is for more of a DIY approach and just the general theory behind port flares.

[BKOLFO4 29]

I do not have a PSP flare in front of me to measure, so I was just curious if all their flares worked out that way, or if that calculator was just an approximation. . . .

Nice reading. . .I just designed a flare and am having it tooled for a 3.5" tube. Now I can calculate how long the port needs to be!!!!

Brian

[Megalomaniac 0]

the psp calculator calculates everything gross.

"The Vb measurement is the total volume of the enclosure. Most people use

the gross volume to make things easier. You can subtract out all "internal"

items if you like.

Depending on your application (Home or Auto), I would determine what the

maximum size of enclosure you want to build and then do the math from there.

Please let me know if you have any other questions.

Thank You,

Steve

Precision Sound Products

Phone: 815-599-0662

Fax: 309-279-0359

www.psp-inc.com"

[helotaxi 46]

If anyone wants it, I made a spreadsheet out of this complete with conversion from imperial units. It does both single and double flares. I also included a velocity ratio to give you an idea of how much the flare will reduce port velocity. It's not fancy but it is functional.

You should post it here

x2

please

wheeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

I'll head upstairs right now. It's on the other computer.

[helotaxi 46]

denim- Anywhere I can upload the file to link to here. It's only about 14k.

[DevilDriver 28]

Here is the spreadsheet. Thanks for emailing it to me, Rich.

[Miles 128]

I have a quick question. I have a box that is 2.26 cubes before displacement, and 2.1 after the sub is in. Which volume do I use to determine the port length. I ordered one of their 3 inch ports(tube, both flairs) and I just want to know how long I should cut the tube to get the tune to 32 hz.

Thanks,

Miles

[helotaxi 46]

You have to account for the air displaced by the sub AND the port. The volume displaced by the port is "dead air" for tuning purposes. You're going to be looking at around 1.9 or smaller once you install the port.

[Miles 128]

I used the PSP port calculator and used 1.9 cubes, tune of 32 hz, and 1 3" flared port. It says that the port should be 8.6 inches long, but that seems too short for what I think it should be. Is this right?