# Port output in hornresp

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#### Droco

When looking at some different horn configurations I came to the realisation that hornresp doesnt lineairly model its port output and velocity.
When keeping internal volume and tuning equal in winISD there is no difference in port velocity or output, which is supported by the mathematics.
In hornresp this is a totally different story. I get drastically different (and not linear) differences in output, velocity AND port length when doubling port area, but keeping tuning equal (by also changing porth length). I also dont see a mathematical trend that explains it.

Anyone who knows what causes this? Do they also implement other factors to calculate the values? Maybe they also include port compression etc?

#### David McBean

When keeping internal volume and tuning equal in winISD there is no difference in port velocity or output, which is supported by the mathematics.

What mathematics are you using?

#### Droco

Wow, didnt realize at first I was talking to THE hornresp man

In any case, I got some deeper into the math because you asked me, and I clearly missed a lot of the 'complexities' so I will not be pursuing the math. I don't like math that much, that's why I love software like yours!

So lets aside the math, and just focus on what perplexes me the most.

'I get drastically different (and not linear) differences in output, velocity AND port length when doubling port area, but keeping tuning equal (by also changing porth length). I also dont see a mathematical trend that explains it.'

I dont have the exact numbers anymore, but I dont remember seeing any logical trend. I figure there will be one, and it could just be the actual math that was too complex for me. On the other hand, winISD didnt show this.

Could you explain me some of the factors that determine the output of the ports? And why I would get largely different results although the tuning and box volume stays the same?
I'm in the process of understanding port compressing, chuffing so I would need to know if its somehow already included in HR.

Thanks in any case for your wonderful software!

#### David McBean

I get drastically different (and not linear) differences in output, velocity AND port length when doubling port area, but keeping tuning equal (by also changing port length).

Hi Droco,

If the chamber was a perfect acoustic compliance and the port tube a perfect acoustic mass, and end corrections were not added in separately, then theoretically, if the chamber volume remains unchanged, doubling the port area would require that the port length be doubled also, to retain the same acoustic mass value and therefore the same system resonance frequency or "tuning".

In reality though, because the chamber is not a perfect acoustic compliance and the port tube is not a perfect acoustic mass, if the port area is doubled, the port length will not be exactly doubled to achieve the same system resonance frequency.

To illustrate:

The grey line in the attached screenprint is for a port area of 50cm^2 and a port length of 10cm. The pink line is for a port area of 100cm^2 (doubled) and a port length of 22.2 cm (slightly more than doubled) to retain the same resonance frequency of 68.4 Hz.

Increasing the length of the port tube introduces a secondary resonance, seen as a "blip" in the response around 600Hz. This is exactly what I would expect to see - there are no drastic differences in the results.

Kind regards,

David

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#### Droco

Hi Droco,

In reality though, because the chamber is not a perfect acoustic compliance and the port tube is not a perfect acoustic mass, if the port area is doubled, the port length will not be exactly doubled to achieve the same system resonance frequency.

To illustrate:

The grey line in the attached screenprint is for a port area of 50cm^2 and a port length of 10cm. The pink line is for a port area of 100cm^2 (doubled) and a port length of 22.2 cm (slightly more than doubled) to retain the same resonance frequency of 68.4 Hz.

Increasing the length of the port tube introduces a secondary resonance, seen as a "blip" in the response around 600Hz. This is exactly what I would expect to see - there are no drastic differences in the results.

Kind regards,

David

What kind of formula is used to predict this disproportionate change in required port length?

Also, do you also take port compression into account? Or what would explain my change in port output (several dBs) when increasing area (with same tuning and internal volume).

Thanks in any case, lovely to see real life is incorporated into the modelling, not only dry formulas.

#### Droco

Also, quick question. How is the spatial loading incorporated into tuning frequency? I noticed the tuning lowers when going from 2 to 1pi etc.

#### David McBean

What kind of formula is used to predict this disproportionate change in required port length?

If the chamber was a perfect acoustic compliance Ca and the port tube was a perfect acoustic mass Ma, then the system resonance frequency would be given by the formula:

f = 1 / (2 * Pi * Sqrt(Ma * Ca))

In your example, the chamber size and therefore Ca remain the same, with the cross-sectional area of the port being doubled and the length of the port tube adjusted to keep the value of Ma constant so that the resonance frequency remains unchanged.

Ma = rho * Lpt / Ap

Where rho is the density of air.

If Ap is doubled then Lpt has to be doubled also to keep the value of Ma the same as before. Note that this idealised example ignores end corrections, and that the Hornresp model does not actually use these simple formulas.

Or what would explain my change in port output (several dBs) when increasing area (with same tuning and internal volume).

An example showing the above behaviour would be helpful.

I noticed the tuning lowers when going from 2 to 1pi etc.

Going from 2 Pi to 1 Pi alters the radiation impedance load at the port tube outlet. In effect the outlet "end correction" changes. In other words, going from 2 Pi to 1 Pi increases the effective length of the port tube and therefore lowers the resonance frequency of the system.

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