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Air volume for dual 40s


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That KW Alpina box is a beautiful piece of craftsmanship and I want one for my Touring but when you go from 4 separate intake runners/ sidedraft horns , to one enclosed  box and add to that a long dryer vent hose it's a definite restriction.I still want one.

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I suspect it's far more of a matter of

 

resonance

than

flow,

 

unless that thing

is a lot more restrictive inside than it looks.

The individual runner carbs are NOT constant flow,

of course, and become very sensitive to what happens to 

the resonance of their inlet path.  

 

As JimK says,

If you stuck an averaging manometer on the plenum, it would 

read almost atmospheric. 

If you stuck a manometer capable of reading instantaneous peaks,

it'd be all over the place.

 

t

uses a huge pleated filter as far from the trumpets as he can get it.

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10 minutes ago, TobyB said:

resonance

 

This was written about intakes on motorcycles, but this thread led me to it this morning.

https://motorcycleinfo.calsci.com/Airboxes.html

 

It includes a bit of math, for those who are so inclined.

 

Part I: Theory.

Here, from first principles we'll develop the theory of how an air box and an inlet tube form a coupled spring- mass system with a resonant frequency.

  • air box volume = V
  • inlet pipe = area * length = A * L
  • Air Mass = 1.25g / 1000 cc
  • Atmospheric Pressure = 104kg / cm sec2
  • PV = nkT (Ideal Gas Law)

If the air in the inlet tube moves X cm into the air box, then the volume of air inside the air box changes to:

V' = V + AX

Since Boltzman's constant and the air box volume don't change, that leaves only the temperature and the pressure. The gamma for air is 1.4, so

T' / T = (V' / V)^.4

T' / T = (1 + AX/V)^.4

We'll presume AX/V is small, so (1 + AX/V)^.4 = 1 + .4AX/V

The number of atoms in the air box changes to n' = (1 + AX/V)n. So, the new pressure is:

P'V = (1+AX/V) nk (1+.4AX/V) T

P' = (1 + AX/V) (1 + .4AX/V) P

P' = (1 + 1.4 AX/V) P

Now we can find the spring constant of the air box, K:

Force = Pressure*Area = Kx

Kx = 1.4 AX/V * A * 104 kg cm / sec2

K = AA/V * 146 kg / sec2

The mass of air in the inlet tube is:

M = AL * 1.25g / 1000

The resonant frequency w, in radians per second, of a spring-mass system is:

 

w = sqrt( K/M )
  = sqrt( AA/V * 146 kg / sec2 * 1000 / 1.25g AL )
  = sqrt( A/VL * 146*1000*1000 / 1.25 sec2 )
  = 1000 sqrt( 116.5 A/VL ) / sec

 

The resonant frequency is w / 2pi, and the resonant rpm is 30 * number of cylinders * f. For a V-twin, rpm = 60 * f.

f = w / 2pi = 160 sqrt( 116.5 A / VL )

resonant rpm = 4775 sqrt( 116.5 A / VL ) (single cylinder)

resonant rpm = 9550 sqrt( 116.5 A / VL ) (V-twin)

resonant rpm = 19100 sqrt( 116.5 A / VL ) (4 cylinder)

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On 6/15/2019 at 10:59 AM, jimk said:

Tom,

You are being too academic.  Car linguists won't understand.  They only speak in terms of some volume of flow at some magical pressure drop (that nobody seems to know what it is) thru an element of interest

 

Well that 200 CFM IS what the intake system needs to provide an fuel/air mixture for the motor to run.  Obviously the whole intake design - geometry, number and sizing of inlets, restrictions, etc. matters greatly too, to provide deliver the fuel/air mixture across all cylinders at that effective CFM.

 

So what's the average speed of the air that's being rhythmically gulped down my 40mm trumpet at 6500rpm?

 

More (simplified) fun maths...

  • 200 Cubic Feet/Min = 345,600 cu In/Min of air/fuel mixture required at 6500 rpm.
  • For a 4 cylinder, that's 86400 cu in/Min per cylinder.
  • In a dual sidedraught or ITB set-up that mixture for each cylinder is passing through a single inlet runner, with approximately a 2.0 sq in cross-section area.
  • 86400 cu in/Mi ÷ 2.0 sq in = 43,200 in/min.  That says the mixture is traveling at an average speed of 3600 feet/min (40 mph) in the intake tract when the motors at 6500rpm.  It's not a constant flow, though, but highly pulsed - stopped and restarted.  4-cycle, valves, compression waves, and such.  So peak intake velocities are actually much higher.

With CFM, area matters. For a typical single 100mm intake inlet (say at the end of an airbox or cone filter) feeding this motor 200 Cu Ft/Min, the average flow speed at that inlet would need to be capable of 2400 feet/min (27 mph).

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How about the reduction of air due to the volume stolen by the fuel vapor because that entering the cylinder is a mixture of air + fuel. Gasoline takes up a certain portion of the 200 cfm.  Toss in the calcs the voume change caused by the fuel heat of vaporization cooling the air.

I quit doing this stuff when I retired.:blink:

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The triangular Alpina setup is an air collector without a filter inside and was developed for the 3 series E21, not for 02.

 

Main reason was, that the 02 TI can didn't fit the E21 front wheel arch in the engine bay anymore. Second reason were the emission rules getting stricter concerning exhaust fumes and noise here in Germany all throughout the 70s.

 

If correctly jetted it works well with a 125hp A1/3 setup and a 150hp A2/3 setup with dual Solex DDH.

 

Best regards, Lars.

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7 minutes ago, LarsAlpina said:

The triangular Alpina setup is an air collector without a filter inside and was developed for the 3 series E21, not for 02.

 

Main reason was, that the 02 TI can didn't fit the E21 front wheel arch in the engine bay anymore. Second reason were the emission rules getting stricter concerning exhaust fumes and noise here in Germany all throughout the 70s.

 

If correctly jetted it works well with a 125hp A1/3 setup and a 150hp A2/3 setup with dual Solex DDH.

 

Best regards, Lars.

Thank you.  I will see how it compares to the ITG when we tune.  I plan to route the intake lines different and try to go solid line up to the air intake and maybe a few inches of silicone turbo hose for flex and vibration      Or

maybe just hang it on the wall

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For a data point.  From some of my logs at low elevation where baro is 98.9 kPa, the S14 2.3 with larger intake valves and a Portland Cam, stock air box and mufflers that are too loud, draws air flow at 6687 rpm, wot, AFR 12.4 of 306 cfm. 

 

This number was cross checked using two methods, one from the direct measurement at the MAF of 172 gmAir/sec flow and the second using the ECU recorded corrected air flow calculation of 0.78 gmAir/cylinder based on the wide band reading.

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