jrn77478,
Please don't make me have to go back to my statistics classes and look for the many ways that statistical analysis can be used incorrectly and skew a result. There are just ways that if you have an idea of a result you are expecting or looking for that can cause you to ask a question in such a way as to reinforce your expectations. I am sure if I look I can find resent things in astrophysics where what was believed by many scientists was found to be incorrect after a new phenomena was found that went again previous thinking. Based on what was known at the time an incorrect principal is postulated and agreed upon by the body of science until something else comes along and disrupts that theory. So even though a paper has been vetted by the group and has gone through the scientific method, it can still be incorrect. Gladly that doesn't happen all that often or we would have real turmoil all the time. The discovery of the Higgs Boson is one of those things that will do just that now that supposedly it has been proven to exist. Theory will now have to be adjusted to take it into account.
Please don't make me have to go back to my statistics classes and look for the many ways that statistical analysis can be used incorrectly and skew a result. There are just ways that if you have an idea of a result you are expecting or looking for that can cause you to ask a question in such a way as to reinforce your expectations. I am sure if I look I can find resent things in astrophysics where what was believed by many scientists was found to be incorrect after a new phenomena was found that went again previous thinking. Based on what was known at the time an incorrect principal is postulated and agreed upon by the body of science until something else comes along and disrupts that theory. So even though a paper has been vetted by the group and has gone through the scientific method, it can still be incorrect. Gladly that doesn't happen all that often or we would have real turmoil all the time. The discovery of the Higgs Boson is one of those things that will do just that now that supposedly it has been proven to exist. Theory will now have to be adjusted to take it into account.
Member
Joined 2003
I once spent a couple of days trying to identify HOMs in measurements, including placing the mic very near the WG wall. No success, but one question has haunted me since then: Exactly how do HOMs differ from diffraction artifacts generated within a WG?
You know, I have been trying to look at horns/waveguides to understand what actually is going on, so my explanation may not in line with most terms used academically, but here goes.
1. Diffraction shows up as additional sources, so at different measuring locations, it seems that what may seem like mild comb effects shift in frequency location when you move the mic through the wave guide and out.
2. HOMs occurs when there is a geometry shape change as the wave travels along a duct till it hits open space, between any two shape change location, you have an impedance change, and there will be some reflected waves going back and forth between these to locations. I think something should show up in the CSD, but they can also show up as a very low level combing effect as well.
3. Honk. Well I am not going into this much here, but it seems to occur closer to the cutoff frequency of the horn/waveguide. It should show up in the CSD at that end of the spectrum as well.
To get the right optimized point between these, plus trying to shape a polar response for constant directivity is really hairsplitting.
1. Diffraction shows up as additional sources, so at different measuring locations, it seems that what may seem like mild comb effects shift in frequency location when you move the mic through the wave guide and out.
2. HOMs occurs when there is a geometry shape change as the wave travels along a duct till it hits open space, between any two shape change location, you have an impedance change, and there will be some reflected waves going back and forth between these to locations. I think something should show up in the CSD, but they can also show up as a very low level combing effect as well.
3. Honk. Well I am not going into this much here, but it seems to occur closer to the cutoff frequency of the horn/waveguide. It should show up in the CSD at that end of the spectrum as well.
To get the right optimized point between these, plus trying to shape a polar response for constant directivity is really hairsplitting.
Taken this understanding, 45deg or more prevents terminating waves from reflecting back in. So it reduces HOMs. Then you want to shape the throat so that it minimizes diffraction, but this shape also determines the type of honk it will have. Then you want to shape the mouth so that you can minimize diffraction from influencing the response. Tough job, I don't think a solution can be found without an unreasonable amount of modeling and verification. I'm trying to combine simplified modeling analysis with engineering intuition, then use measurement to gradually zoom in on one design specific to a driver.
They don't really, they are in a sense the same thing, but maybe a little different.
Consider a wave moving down a waveguide and that wave cannot stay in contact with the boundaries of the waveguide, a HOM develops as the wave propagates, to "fill" the need for the wavefront to stay normal to the walls, but this new HOM portion of the wavefront is not normal to the walls so it bounces off the walls. This is both diffraction and HOMs.
The difference is that an HOM can be created right at the throat by a poor phase plug design and would not have been created by diffraction Or it could be created by diffraction when the curvature of the boundary changes abruptly due to a slope change at some juncture.
I hope this shows how they can be similar and yet definitely different at the same time.
This is not true
Quite correct, but precisely what my several papers have done. It is complicated and hard to follow (takes some serious knowledge of math), but it has stood the test of time (more than 20 years now) and several attempts at debunking it. You would be wise to read what is available rather than starting from scratch, others have been there already. Learn what they have left as knowledge.
Hi Earl,
There is one question I have been thinking about asking for some time. Is it correct that any wave front can be decomposed into a given set of modes, but if you want to say that "waveguide A has less HOM than waveguide B", you need to describe the sound field in those waveguides in their "native" orthogonal system?
Put another way, a spherical wave front can be described as a sum of cylindrical modes, and a flat (axisymmetric) wave front can be described as a sum of spherical modes. But if you want to compare, say, a conical horn and an OS waveguide, the modes in the first have to be described in spherical coordinates, while the modes in the second have to be described in OS coordinates. Only then can the modal amplitudes be compared in a way that makes sense. Is this correct?
Regards,
Bjørn
There is one question I have been thinking about asking for some time. Is it correct that any wave front can be decomposed into a given set of modes, but if you want to say that "waveguide A has less HOM than waveguide B", you need to describe the sound field in those waveguides in their "native" orthogonal system?
Put another way, a spherical wave front can be described as a sum of cylindrical modes, and a flat (axisymmetric) wave front can be described as a sum of spherical modes. But if you want to compare, say, a conical horn and an OS waveguide, the modes in the first have to be described in spherical coordinates, while the modes in the second have to be described in OS coordinates. Only then can the modal amplitudes be compared in a way that makes sense. Is this correct?
Regards,
Bjørn
Yes, that is basically correct. Only separable coordinates can expand a wavefront into modes, it is not possible in any other coordinate systems. But all separable wave solutions can be expanded in any other wave solution. This is the core of the Green's Function. The Green's Function in any coordinate system is the expansion of a spatial impulse in that coordinate system. Setting these expansions equal to each other results in one coordinate system in terms of the other one.
I believe that if the wave equation could be shown in a Tensor form as General Relativity is, then a waveguide solution could be done that is independent of the coordinate system, just like relativity. But such an approach is beyond me at this point in my life - I can follow General Relativity, but I could not derive it.
To compare a conical horn (a spherical waveguide) to an OS waveguide one would have to consider the shape of the wave at the throat. What works for one works completely different for the other - how then are you to make this comparison? What throat wave shape do you assume? Talking about horns or waveguides without a discussion of the wavefront at the throat is basically throwing away a large part of the problem. Since the horn equation cannot do this problem at all it is inherently inadequate for the task.
I believe that if the wave equation could be shown in a Tensor form as General Relativity is, then a waveguide solution could be done that is independent of the coordinate system, just like relativity. But such an approach is beyond me at this point in my life - I can follow General Relativity, but I could not derive it.
To compare a conical horn (a spherical waveguide) to an OS waveguide one would have to consider the shape of the wave at the throat. What works for one works completely different for the other - how then are you to make this comparison? What throat wave shape do you assume? Talking about horns or waveguides without a discussion of the wavefront at the throat is basically throwing away a large part of the problem. Since the horn equation cannot do this problem at all it is inherently inadequate for the task.
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Thank you very much for your answers, Earl.
Then what about the solution given by Stevenson (1951) that gives the sound field of arbitrarily shaped horns in terms of an infinite set of coupled modes? I don't know if you are familiar with that paper. I can send it to you if you are interested.
That is partly what I have been working on lately; sound fields in horns described in cylindrical modes. It has been very enlightening to look at horns and waveguides in this way.
That is a very interesting thought. It is beyond me, but one of my acoustics professors has a PhD (IIRC) in General Relativity...
Of course. I did not have a particular comparison in mind, it was rather that I wanted to see if I had understood the concept correctly, that you need to describe the modes in the coordinate system native to the waveguide to actually judge the modal levels.
I imagine it would be enlightening to look at the modal frequency responses at the mouth for different wave shapes at the throat, and for various geometries. This would mabye make the concept of HOMs easier to grasp for many.
Regarding the measurement of HOMs mentioned some posts back, is it so that you would prefer to measure in the far field, to consider only the propagating modes? Could you then decompose the sound field in spherical modes, or do you need the "native" modal description of the waveguide that is measured?
Regards,
Bjørn
Then what about the solution given by Stevenson (1951) that gives the sound field of arbitrarily shaped horns in terms of an infinite set of coupled modes? I don't know if you are familiar with that paper. I can send it to you if you are interested.
That is partly what I have been working on lately; sound fields in horns described in cylindrical modes. It has been very enlightening to look at horns and waveguides in this way.
That is a very interesting thought. It is beyond me, but one of my acoustics professors has a PhD (IIRC) in General Relativity...
Of course. I did not have a particular comparison in mind, it was rather that I wanted to see if I had understood the concept correctly, that you need to describe the modes in the coordinate system native to the waveguide to actually judge the modal levels.
I imagine it would be enlightening to look at the modal frequency responses at the mouth for different wave shapes at the throat, and for various geometries. This would mabye make the concept of HOMs easier to grasp for many.
Regarding the measurement of HOMs mentioned some posts back, is it so that you would prefer to measure in the far field, to consider only the propagating modes? Could you then decompose the sound field in spherical modes, or do you need the "native" modal description of the waveguide that is measured?
Regards,
Bjørn
I am not familiar with the Stevenson paper, I'd like to see it.
If one calculates the wave shape at the mouth of a waveguide this wave shape can be expanded in the internal modes of the device (assuming that they are known and orthogonal). The mouth wave shape can be done in spherical coordinates or it can be done as a aperture in an infinite baffle. The spherical is more direct but the infinite baffle is the easier experimental setup.
What do you mean by "cylindrical modes"? Hankel functions? How can these modes be applied to situations where the boundary does not meet the boundary requirements?
You can do an arbitrary axi-symmetric waveguide as a sum of spherical waves - this is shown in my book - as most of this stuff is.
If one calculates the wave shape at the mouth of a waveguide this wave shape can be expanded in the internal modes of the device (assuming that they are known and orthogonal). The mouth wave shape can be done in spherical coordinates or it can be done as a aperture in an infinite baffle. The spherical is more direct but the infinite baffle is the easier experimental setup.
What do you mean by "cylindrical modes"? Hankel functions? How can these modes be applied to situations where the boundary does not meet the boundary requirements?
You can do an arbitrary axi-symmetric waveguide as a sum of spherical waves - this is shown in my book - as most of this stuff is.
Is there an easy way to calculate (or rule-of-thumb predict) the actual acoustic phase response of a waveguide?
My thought after trying to get a broad region well-adding sum of a 10" mid and a cheap 10" WG with a 25mm dome tweeter is that the resulting acoustic phase of the WG section is somewhere in between the calculated phase response of the naked driver (calculated by on-axis response) and the calculated phase response of the dome-WG combination (also theoretical acoustic phase calculated from on-axis response).
At first I was trying to match phase by the tweeter total system response (with WG), but could not get the system to sum together well just outside of the x-over point - at the x-over point, I optimized by digital delay.
I couldn't get the system to match between calculated impulse response and measured impulse response either.
I wrote a small program that averages the last 100 pulse front ends on a square wave, and the program seems to work perfectly - but it doesn't match up with the result I get from using either swept-sine inverse or MLS FFT. My first though was that I was getting reflection interference in the average, but this worked out to be very low in magnitude after trying several different measurement positions that should give very different reflection contamination. This leads me to think that the actual pulse response does not actually follow the "normal" theories.
Or am I just "doing it wrong"?
My thought after trying to get a broad region well-adding sum of a 10" mid and a cheap 10" WG with a 25mm dome tweeter is that the resulting acoustic phase of the WG section is somewhere in between the calculated phase response of the naked driver (calculated by on-axis response) and the calculated phase response of the dome-WG combination (also theoretical acoustic phase calculated from on-axis response).
At first I was trying to match phase by the tweeter total system response (with WG), but could not get the system to sum together well just outside of the x-over point - at the x-over point, I optimized by digital delay.
I couldn't get the system to match between calculated impulse response and measured impulse response either.
I wrote a small program that averages the last 100 pulse front ends on a square wave, and the program seems to work perfectly - but it doesn't match up with the result I get from using either swept-sine inverse or MLS FFT. My first though was that I was getting reflection interference in the average, but this worked out to be very low in magnitude after trying several different measurement positions that should give very different reflection contamination. This leads me to think that the actual pulse response does not actually follow the "normal" theories.
Or am I just "doing it wrong"?
I have never looked at the phase response of a waveguide as a stand alone transfer function.
I am not quite sure what you are trying to do either. I measure the impulse response with HolmImpulse and use that in models to simulate the crossover and the results are quite good. I suspect that you are doing something wrong, but I can't tell from your description what that would be.
I am not quite sure what you are trying to do either. I measure the impulse response with HolmImpulse and use that in models to simulate the crossover and the results are quite good. I suspect that you are doing something wrong, but I can't tell from your description what that would be.
This is another phenomena, which requires distance for this to build up which not only relates with surface quality but also surface shape. You see these more evidently with steady flow. But pour phase plug + throat design match creates what we more associate to the term "diffraction", which acts like a new point source(s).
It seems that HOM would more appropriately be a collective terms describing generated waves higher than the fundamental wave transmitted regardless how. From my assessment of the variation of phenomena, there are vary contradicting solutions depending on the band of the frequency passing through a horn/waveguide. So the final optimization is more likely to result heavily on phycho acoustics and actually listening where the combination of HOM harmonics at various frequencies come to play since it is highly improbable or cost effective to model the surface properties.
Maybe I should say it minimizes ...
Based on design procedures I have been through, we are used to the process of using the past knowledge to predict measureable result that match our goal, then after a build, verify hoe closely the match is, and adjust it with user perception in design change consideration. In the research field, I see each sector just claiming to be correct much ignorance in bringing other fields into factor. So basically, yes, I do spend time to integrate knowledge and user perception, but I don't pick sides. As you may have seen in other posts I have made, I look into blending views from different people as well as my own findings.
If you are using a soft dome tweeter, you can dump it for a rigid dome tweeter first. What is the purpose of the mid in this?Is there an easy way to calculate (or rule-of-thumb predict) the actual acoustic phase response of a waveguide?
My thought after trying to get a broad region well-adding sum of a 10" mid and a cheap 10" WG with a 25mm dome tweeter is that the resulting acoustic phase of the WG section is somewhere in between the calculated phase response of the naked driver (calculated by on-axis response) and the calculated phase response of the dome-WG combination (also theoretical acoustic phase calculated from on-axis response).
....
Or am I just "doing it wrong"?
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Tanks again.
I've sent it to the email address on your webpage. Any comments would be highly appreciated.
I mean the radial modes in cylindrical ducts, described by cylindrical Bessel functions. The waveguide is approximated by a series of short cylinders, with a mode coupling matrix at the interface between each cylinder. The method is described in the PhD thesis by Jonathan Kemp: Jonathan Kemp PhD Thesis 2002. By using enough modes and segments, the results are very close to the results produced by BEM simulations, and are computed faster.
Yes, I have wanted to implement that method too. And I have to add, your book is probably the single most useful book on electroacoustics that I have. I use it all the time.
Regards,
Bjørn
I've sent it to the email address on your webpage. Any comments would be highly appreciated.
I mean the radial modes in cylindrical ducts, described by cylindrical Bessel functions. The waveguide is approximated by a series of short cylinders, with a mode coupling matrix at the interface between each cylinder. The method is described in the PhD thesis by Jonathan Kemp: Jonathan Kemp PhD Thesis 2002. By using enough modes and segments, the results are very close to the results produced by BEM simulations, and are computed faster.
Yes, I have wanted to implement that method too. And I have to add, your book is probably the single most useful book on electroacoustics that I have. I use it all the time.
Regards,
Bjørn
Thanks, I read through the paper briefly enough to understand the premise. The way I read it is as follows - by breaking up the expansion into different layers the transfer between the layers can be done using orthogonal modes that are defined by the 2-dimensional boundary with the layer. I would completly agree wth this and it is a good insight given the date of the publication. However, not much is done with this and so it leaves a great many details unresolved. It is significant how early the EM people realized what a problem it was not having a way to calculate the waveshape across the waveguide. Clearly in EM theory this would be a significant drawback, but the acoustics community still doesn't seem to have a full appreciation of this limitation.
The use of "steps" to model horns is very old, going back to Mapes-Riordan or earlier. It works, given enough steps to get the desired accuracy.
The question that I asked myself was what solution "modal layers" would yield the fastest convergence. I think that this would clearly be the approach that I proposed and use in my book and in my software and that is to use the conical bounded spherical solution. This has to converge the most rapidly because the shapes of the elements boundary and the wavefronts are the closest to the actual shapes. This technique is shown in my book and there is an Appendix (not in the book but on my website) which solves a classic problem using this approach.
Any of the approaches will work, of course, one need not even assume any modes to find a solution - this is BEM, but if speed of convergence is a criteria then the conical spheres will certainly be the fastest for any axisymmetric device.
Non-axi-symmetric is a different situation and one would have to supply more details about the boundary shape in order to evaluate the best approach for convergence. They are an infinite number of ways that something can be non-axisymmetric.
A square waveguide could use sines and cosines for example and maybe even use the hard-wired very fast 2'D cosine transforms built into many graphics chips - a sort of JPeg horn calculation.
Thanks for the compliemt on my book. I am rather surprised however as it has been my impression that "horn" people all but ignore it. My theory is kind of a problem for them and I suppose that just ignoring it is the easiest way out.
The use of "steps" to model horns is very old, going back to Mapes-Riordan or earlier. It works, given enough steps to get the desired accuracy.
The question that I asked myself was what solution "modal layers" would yield the fastest convergence. I think that this would clearly be the approach that I proposed and use in my book and in my software and that is to use the conical bounded spherical solution. This has to converge the most rapidly because the shapes of the elements boundary and the wavefronts are the closest to the actual shapes. This technique is shown in my book and there is an Appendix (not in the book but on my website) which solves a classic problem using this approach.
Any of the approaches will work, of course, one need not even assume any modes to find a solution - this is BEM, but if speed of convergence is a criteria then the conical spheres will certainly be the fastest for any axisymmetric device.
Non-axi-symmetric is a different situation and one would have to supply more details about the boundary shape in order to evaluate the best approach for convergence. They are an infinite number of ways that something can be non-axisymmetric.
A square waveguide could use sines and cosines for example and maybe even use the hard-wired very fast 2'D cosine transforms built into many graphics chips - a sort of JPeg horn calculation.
Thanks for the compliemt on my book. I am rather surprised however as it has been my impression that "horn" people all but ignore it. My theory is kind of a problem for them and I suppose that just ignoring it is the easiest way out.
Earl,
I haven't read your book but would be very interested in that. Is that the book on transducers on your website also including your waveguide theory and measurement or is that a separate writing? I see you have a paper on horn theory, but what of your AES papers or pre-prints. How do I get my hands on those papers without going down to UCLA and looking through the stacks?
I haven't read your book but would be very interested in that. Is that the book on transducers on your website also including your waveguide theory and measurement or is that a separate writing? I see you have a paper on horn theory, but what of your AES papers or pre-prints. How do I get my hands on those papers without going down to UCLA and looking through the stacks?
Thanks for your comments. Most of the comments I have seen on the Stevenson paper is that the infinite set of equations is not solvable.
There's a lot of work on modal solutions in waveguides done by EM people, it seems. Some work is also done in acoustics, but surprisingly little compared to EM. (the reason could be that the EM research was better funded and with better access to computers in those early times, while horn development were mainly done by engineering companies. If WE and BTL had not opted out of the sound business in the late 30s, things could have been different). Here are the references I have found:
Hoersch, V. A.
Non-Radial Vibrations Within a Conical Horn
Phys. Rev., 1925, 25, 218-224
Stevenson, A. F.
Exact and Approximate Wave Equations for Wave Propagation in Acoustic Horns
J. App. Phys., 1951, 22, 1461-1463
Holtsmark, J.; Lothe, J.; Tjøtta, S. & Romberg, W.
Theoretical Investigation of Sound Transmission Through Horns of Small Flare, with Special Emphasis on the Exponential Horn
Universitetet i Oslo, 1955
(Norwegian, the Romberg is the man behind Romberg numerical integration).
Maezawa, S. On the Three-dimensional Corrections for One-dimensional Theory of Acoustic Horn
Reports of the Faculty of Engineering, Yamanashi University, The Faculty of Engineering, Yamanashi University, 1957, 69-79
Alfredson, R. J.
The Propagation of Sound in a Circular Duct of Continuously Varying Cross-Sectional Area
J. Sound Vibr., 1972, 23, 433-442
(First numerical computation of the sound radiated from a horn speaker by a modal method that I'm aware of, uses the stepped approximation).
Shindo, T.; Yoshioka, T. & Fukuyama, K.
Calculation of Sound Radiation from an Unbaffled, Rectangular-Cross-Section Horn Loudspeaker Using Combined Analytical and Boundary-Element Methods
J. Audio Eng. Soc., 1990, 38, 340-349
Pagneux, V.; Amir, N. & Kergomard, J.
A study of wave propagation in varying cross-section waveguides by modal decomposition. Part I. Theory and validation
J. Acoust. Soc. Am., 1996, 100, 2034-2048
And then there is some more recent work by the last authors.
I would assume the conical/spherical segment method would converge faster, but it is limited to axisymmetric waveguides. I'm currently working on applying the stepped method to rectangular waveguides, and I can then use the same framework. Thanks for the tip on using the 2D cosine transform. I'll see if I can apply that in some way to my work.
While I can probably be counted among the "horn people", I'm also very interested in numerical acoustics, sound radiation, and sound propagation in "flaring ducts" in general. I want to understand as much as possible of what is going on, and your book has helped me quite a lot in that regard.
Kindhornman, the book can be bought from Earl's homepage, and it contains much more than what you get from the JAES papers and preprints - check the contents. You may have to brush up your math, though...
Regards,
Bjørn
There's a lot of work on modal solutions in waveguides done by EM people, it seems. Some work is also done in acoustics, but surprisingly little compared to EM. (the reason could be that the EM research was better funded and with better access to computers in those early times, while horn development were mainly done by engineering companies. If WE and BTL had not opted out of the sound business in the late 30s, things could have been different). Here are the references I have found:
Hoersch, V. A.
Non-Radial Vibrations Within a Conical Horn
Phys. Rev., 1925, 25, 218-224
Stevenson, A. F.
Exact and Approximate Wave Equations for Wave Propagation in Acoustic Horns
J. App. Phys., 1951, 22, 1461-1463
Holtsmark, J.; Lothe, J.; Tjøtta, S. & Romberg, W.
Theoretical Investigation of Sound Transmission Through Horns of Small Flare, with Special Emphasis on the Exponential Horn
Universitetet i Oslo, 1955
(Norwegian, the Romberg is the man behind Romberg numerical integration).
Maezawa, S. On the Three-dimensional Corrections for One-dimensional Theory of Acoustic Horn
Reports of the Faculty of Engineering, Yamanashi University, The Faculty of Engineering, Yamanashi University, 1957, 69-79
Alfredson, R. J.
The Propagation of Sound in a Circular Duct of Continuously Varying Cross-Sectional Area
J. Sound Vibr., 1972, 23, 433-442
(First numerical computation of the sound radiated from a horn speaker by a modal method that I'm aware of, uses the stepped approximation).
Shindo, T.; Yoshioka, T. & Fukuyama, K.
Calculation of Sound Radiation from an Unbaffled, Rectangular-Cross-Section Horn Loudspeaker Using Combined Analytical and Boundary-Element Methods
J. Audio Eng. Soc., 1990, 38, 340-349
Pagneux, V.; Amir, N. & Kergomard, J.
A study of wave propagation in varying cross-section waveguides by modal decomposition. Part I. Theory and validation
J. Acoust. Soc. Am., 1996, 100, 2034-2048
And then there is some more recent work by the last authors.
I would assume the conical/spherical segment method would converge faster, but it is limited to axisymmetric waveguides. I'm currently working on applying the stepped method to rectangular waveguides, and I can then use the same framework. Thanks for the tip on using the 2D cosine transform. I'll see if I can apply that in some way to my work.
While I can probably be counted among the "horn people", I'm also very interested in numerical acoustics, sound radiation, and sound propagation in "flaring ducts" in general.
I want to understand as much as possible of what is going on, and your book has helped me quite a lot in that regard. Kindhornman, the book can be bought from Earl's homepage, and it contains much more than what you get from the JAES papers and preprints - check the contents. You may have to brush up your math, though...
Regards,
Bjørn