# Driver force/inertia/momentum



## Benja (Jun 17, 2011)

I am curious as to how much force/inertia/momentum etc are in a driver.

Can a math guru help me out? I am not sure how much a typical cone weighs, 200g? I have no clue, nor do I know how to add and subtract.

My basic question is, as the cone reaches full excursion at any given frequency, how much force is required to stop it, or how much force is exerted on the basket/enclosure?

IE: you are holding a 15lb baby in a car crash at 30 mph, then the baby weights 300 lbs.

Something simple I can understand. Or am I not making any sense?


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## cmayo117 (Aug 14, 2009)

It depends on the frequency of the wave, how far the cone is moving, and the mass of the cone. As an example, a 200 gram cone playing a 50Hz sine wave with 20mm cone excursion would experience a maximum of about 200 newtons or 45 lbs of force. Sticking with your example, the 200 gram cone would weigh about half a pound at rest but experience up to 45 lbs of force playing the 50Hz tone. 

If you care about the math, maximum particle acceleration is amplitude*(2pi*frequency)^2. Amplitude is half of excursion in this case. This gives 987 m/s^2 acceleration. Plug this into force = mass*acceleration where mass is .2kg to get 197 newtons which is 44.3 lbs.


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## Spyke (Apr 20, 2012)

cmayo117 said:


> It depends on the frequency of the wave, how far the cone is moving, and the mass of the cone. As an example, a 200 gram cone playing a 50Hz sine wave with 20mm cone excursion would experience a maximum of about 200 newtons or 45 lbs of force. Sticking with your example, the 200 gram cone would weigh about half a pound at rest but experience up to 45 lbs of force playing the 50Hz tone.
> 
> If you care about the math, maximum particle acceleration is amplitude*(2pi*frequency)^2. Amplitude is half of excursion in this case. This gives 987 m/s^2 acceleration. Plug this into force = mass*acceleration where mass is .2kg to get 197 newtons which is 44.3 lbs.


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## Benja (Jun 17, 2011)

Awesome, that is exactly what I was looking for. Thank you!

I can't believe you are only 21 years old. Makes me feel old and stupid. But we all excel at one thing or another, math was not one of my strong suits. It makes me zone out.

So what would you say are the maximum forces in any given typical 10" or 12" sub? For this we could need more dimensions of cone mass, xmax and maximum velocity at a given freq, I would assume 80hz would induce move force just from a common sense standpoint.

I mean, 45 lbs is quite an astounding number when you think of it.


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## cmayo117 (Aug 14, 2009)

45 lbs sounds like a lot to me too, but I'm thinking 200 grams moving mass is a little high for the average 12 inch sub. At a given frequency for the same speaker, the maximum force just depends on excursion. Raising the frequency raises the max force a lot as it is squared in the equation, but excursion generally drops off pretty fast as frequency increases. 

If you did maintain 20mm of excursion with the 200 gram cone from the first example at 80Hz, the force would be about 112 lbs. I would think most speakers would burn up long before you got to that point though.


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## Benja (Jun 17, 2011)

I am beginning to see why baskets are cast so massive and rigid. The force of a little mass moving at high speed is greater than I anticipated. A .5 lb object is capable of exerting ~100 lbs. Just mind boggling.

So if a cone does indeed weigh 200g (don't remember where I got that figure) and inertial force is ~100 lbs, then the force needed to retain the basket in staticity must be greater than 100 lbs or the enclosure will resonate. Meaning the enclosure must not move if 100 lbs of force is applied to it in either direction laterally of drivers motion. Is that correct? 

Just trying to learn how much coupling is necessary to eliminate enclosure resonance from driver inertia. Pressure resonance is obviously different.

Are the calculations taking into account the distance from incursion to excursion into the acceleration equation? I would assume that if excursion is +20mm from 0 (idle) and incursion is -20mm, then the acceleration from -20mm to +20mm = 40mm should technically allow the cone to accelerate to a faster "speed"? Does speed play a part in force or just acceleration?


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## cmayo117 (Aug 14, 2009)

Well, as I said, I don't think most drivers are capable of 20mm of excursion at 80Hz. That would take a lot of power. The original example already took into account that amplitude is half of excursion in this case(I plugged in .01m for amplitude not .02m). So the example is for 20mm total excursion. 

Speed alone doesn't really play any part in the force; the force at the maximum cone speed, which occurs at 0 excursion, is theoretically 0. It's the change in speed, or acceleration, that requires the force. That's where force = mass*acceleration comes from.


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## Benja (Jun 17, 2011)

Thanks for the help, it makes total sense now. A driver at 80hz is changing direction before it has a chance to move through the total travel available.

Curious, how fast does a driver move? Let's say at 80hz, in mph?


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## cmayo117 (Aug 14, 2009)

max velocity = displacement * 2pi*frequency = .01*2pi*80 = 5.03m/s = 11.3mph for 20mm, which again I think is unreasonable. It's important to notice that this depends on both frequency and excursion(2*displacement). At say 5mm excursion, which seems more reasonable, it would only be 2.82 mph. 

I know this seems very slow, but the large forces come from changing from 3mph in one direction to 3mph in the opposite direction in .00625 seconds(at 80Hz).


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## Spyke (Apr 20, 2012)

Really gives an understanding as to why bracing and damping is so important.


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## Jimi77 (Jul 4, 2005)

FYI, a CSS SDX 10 has MMS of 112 grams (xmax is 18.4 mm). 

Baskets are also stout because there is a heavy motor attached to them. In car audio, that motor is getting vibrated and occassionally bounced down the road.


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## Benja (Jun 17, 2011)

Ok last one. lol

What kinds of forces do you think are possible in a Jackhammer?

T9922-22
Fs = 24 Hz
Qms = 5.044
Vas = 5.776 cu.ft
Cms = 0.039 mm/N
Mms = 1140.0 g
Rms = 33.92 kg/S
Xmax = 1 in
Xmech = 3 in
P-Dia = 18.49 in
Sd = 267.84 sq.in
P-Vd = 0.155 cu.ft
Qes = 0.441
Re = 0.87 ohms
BL = 18.41 Tm
Qts = 0.406
no = 0.487 %
2.83V SPL = 98.8 dB


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## Benja (Jun 17, 2011)

Spyke said:


> Really gives an understanding as to why bracing and damping is so important.


Yes, I have to keep reminding myself that anything that vibrates creates sound, no matter how small the vibration.

I was researching how much air pressure is in a sealed enclosure and found it was ~1psi. If it were, and your enclosure was a square 1 cu ft, each side would have 144 lbs of force pushing and pulling on it, or 864 lbs total for all surfaces.


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## cmayo117 (Aug 14, 2009)

Benja said:


> Ok last one. lol
> 
> What kinds of forces do you think are possible in a Jackhammer?
> 
> ...


It really depends on the limits of the speaker. From what I read, excursion for a given spl increases with the inverse square of frequency. In other words, if the excursion is 3in at 20Hz, at 40Hz it's 3 in*(20/40)^2 = .75 in. 

This means that the maximum force for a given speaker at a given spl is the same at any frequency, assuming the speaker can produce the frequency at that spl. The frequency squared part of the equation balances out with the inverse excursion squared as frequency rises(excursion drops just as fast a frequency squared rises). 

To calculate the force, we just need to estimate the maximum excursion for a certain frequency. Let's estimate that the speaker is capable of its 3 in = 7.6 mm mechanical limit at 35Hz. Plugging that into the earlier equation, I get 3685 N or 828 lbs. Remember that this is at the mechanical limit of the sub(xmech). I'm really not sure if that's an accurate estimate. It seems like a rediculous amount, but that's the best I can figure out.


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## Oliver (Jun 25, 2007)

> JBL W15GTi 15" subwoofer driver. This is an automotive 15" woofer that uses JBL's *differential drive coil geometry* for low distortion and high xmax.


These were very* nicely designed *subwoofers, it would actually brake itself as it moved froward and backward !


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## 14642 (May 19, 2008)

Oliver said:


> These were very* nicely designed *subwoofers, it would actually brake itself as it moved froward and backward !


Only at really high excursion where one coil moved into the other coil's gap.


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## Oliver (Jun 25, 2007)

Andy Wehmeyer said:


> Only at really high excursion where one coil moved into the other coil's gap.


*So, only @ the levels most listen to *


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## Benja (Jun 17, 2011)

This was a fun thread, thanks for the math lessons although I never will have the desire to learn them. Failed algebra 3 times in high school, but I got all A's in my hands on classes.

This really enlightened me as to how mechanical forces in a driver can affect efficiency. A vibrating basket/enclosure = lost db and increased resonance.


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## thehatedguy (May 4, 2007)

Nothing in car audio.

Not too many new ones in home audio- Focal had one a few years back and that's about it in terms of OEM stuff.



cajunner said:


> out of all commercially viable motor designs, which one comes closest to a field coil motor?


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## Benja (Jun 17, 2011)

I just read up on field coils in audio for a few minutes. It makes sense to me but it seems that it would still equal a normal driver.

I am thinking that in order to create forces necessary to have complete driver control you would need 2 field coils, one for incursion and one for excursion. The coils would oscillate by alternating voltage between the coils, instead of the voice coil voltage oscillating. A highly magnetic material would be replace the traditional voice coil.

By utilizing the field coils to control the motion of the driver, DC to both coils would suspend the driver in the rest position. This would result in the ability to go from driver oscillations to full suspension of oscillations in fractions of a second maybe?

I'm sure it has been thought of before so it's probably nothing new.


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## minbari (Mar 3, 2011)

Benja said:


> I just read up on field coils in audio for a few minutes. It makes sense to me but it seems that it would still equal a normal driver.
> 
> I am thinking that in order to create forces necessary to have complete driver control you would need 2 field coils, one for incursion and one for excursion. The coils would oscillate by alternating voltage between the coils, instead of the voice coil voltage oscillating. A highly magnetic material would be replace the traditional voice coil.
> 
> ...


so would this eliminate the need for magnets?


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## Benja (Jun 17, 2011)

Yes, the coils would become the magnetic field.


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## Benja (Jun 17, 2011)

This would also decrease MMs by replacing the voice coil with a thin, lighter material, reducing inertia.


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## thehatedguy (May 4, 2007)

You still need voice coils. You can adjust the strength of the magentic field though.

You are just replacing the perment ceramic magent with an energized coil...you will need a power supply to make this all work.


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## Benja (Jun 17, 2011)

One of us doesn't understand, it could be me.

The 2 field coils would be at each end of the metal piece that is replacing the voice coil. The field coils oscillate in freq, instead of the voice coil oscillating in freq.

In a single field coil design the coil is the magnetic field and the voice coil oscillates freq by way of voltage.

In the dual configuration the field coils become alternating magnets, pushing and pulling a piece of metal. When both coils are energized the metal would become suspended at rest with equal force applied to it, creating a lot of cone resistance. Resistance to unwanted cone movements enabling immediate response from cone oscillations.

Some kind of processor would be necessary to determine 0hZ and apply DC to both coils at the exact moment the frequency is no longer present.

This would eliminate cone resonance from the inertia inherent in common designs, which rely on the spider and surround to slow the cone to 0hZ.


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## thehatedguy (May 4, 2007)

Historically field coil speakers are no different internally than permenate magnet speakers. The only difference being the magentic assembly. Way back when, it was near impossible to source quality ceramic/permenant magnets, and the only way to get the field strength was to use an electromagnet...you know like the ones you made as a kid with a piece of wire, a nail, and a small battery. 

The voice coil still drives the speaker and a power supply supplies the coils to energize the field.

There are several people retrofitting fixed magnets in things like compression drivers and fullrange speakers with field coils...some say they can hear the differences between alinco, field coils, and ferrite magnets. But the big thing with field coils is the ability to change the field strength and manipulate the T/S parameters in the process.


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## thehatedguy (May 4, 2007)

But what you are suggesting would be done much easier with a servo motor driving the cone.


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## Benja (Jun 17, 2011)

Wouldn't a servo motor induce moving parts to manipulate movement?

My idea would not have any moving parts besides the moving mass.

Efficiency could be doubled by inverting polarity on each coil.

Imagine a magnet with a + charge and it attracts a piece of metal. Reverse polarity and it repels it.

This could be accomplished with a simple 2 channel amplifier by connecting one coil in normal polarity and reversing polarity on the other channel, effectively creating one magnet at one end of the metal pushing it away, and the other magnet pulling it towards it.

Am I right or just completely nuts?


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## Benja (Jun 17, 2011)

The assembly would essentially become a solenoid.


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## thehatedguy (May 4, 2007)

I don't know how you would get a solenoid to vary both amplitude and frequency.


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## 14642 (May 19, 2008)

Oh, this idea of the baby in a plane crash doesn't really apply here. That's what the spider and surround are for. Try holding a 15" woofer in your hand and playing 20Hz sine waves. No bruising. I promise.


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## Benja (Jun 17, 2011)

thehatedguy said:


> I don't know how you would get a solenoid to vary both amplitude and frequency.


By varying the power to the coils for amplitude and varying the phase to the coils in frequency.


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## Benja (Jun 17, 2011)

cajunner said:


> balanced armature
> 
> one about 12" in diameter, 3 feet long, jus' right to fit in the parcel shelf space in the trunk, with ports extending to the rear...
> 
> it might be a little heavy, but you could make it using field coil and neo-impregnated resin, what a deal..


So you're saying it would take a tremendous amount of power to get something the equivalent of standard drivers? I don't know much about magnetic fields.


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## Benja (Jun 17, 2011)

Andy Wehmeyer said:


> Oh, this idea of the baby in a plane crash doesn't really apply here. That's what the spider and surround are for. Try holding a 15" woofer in your hand and playing 20Hz sine waves. No bruising. I promise.


I understand that. But could you please explain the dB loss between me holding the basket in me hands versus the basket bolted down to an object that doesn't move?


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## Benja (Jun 17, 2011)

That's exactly what I'm talking about but in a totally different configuration, not using foil but a traditional cone. Also instead of the magnet config it would use 2 coils to move a metal tube in between the 2.

Just Try and Make Your Own Coil-Gun (Accelerator) - YouTube

Like this but with 2 coils butted up against one another.


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## Benja (Jun 17, 2011)

It's been done before. Just found a patent. Dammit.


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## chad (Jun 30, 2005)

Andy Wehmeyer said:


> Oh, this idea of the baby in a plane crash doesn't really apply here. That's what the spider and surround are for. Try holding a 15" woofer in your hand and playing 20Hz sine waves. No bruising. I promise.


What if you were in space, on a merry-go-round?


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## chad (Jun 30, 2005)

Andy Wehmeyer said:


> Oh, this idea of the baby in a plane crash doesn't really apply here. That's what the spider and surround are for. Try holding a 15" woofer in your hand and playing 20Hz sine waves. No bruising. I promise.


What if you were in space, on a merry-go-round?


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## Benja (Jun 17, 2011)

And a plane crashes into you..


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## chad (Jun 30, 2005)

Benja said:


> And a plane crashes into you..


while you are wearing a funky space diaper.

You know, like that guitar player from Parliment....

Just dated myself.


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## Oliver (Jun 25, 2007)

Benja said:


> It's been done before. Just found a patent. Dammit.


keep trying


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