Helmholtz resonators and how this applies to your motorcycle?


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basically stole this from another site. Good reading.


Randy Norian's thoughts on
tuned inlet design for Motorcycles

thanks to Randy for letting me go public with this series of E-mails


Oddly enough, I am pursuing this very topic (design of a resonant airbox) on another forum. I'll let you know if I get any good responses!

Here is from a previous post on this topic

OK, this is regarding my diesel, but just so you know I'm still pondering airboxes and this one is a good example.

Typical helmholtz resonators are a volume (airbox), fed by a duct of certain length and cross section. these 3 things determine the resonant frequency of the airbox. look at an RGV250 and you see a pair of inlet ducts, a few inches in length, that feed the airbox. shortening those ducts raises airbox rez freq. anyhow--

My TLS has a little flapper in the inlet duct, it closes at low rpm. to provide restriction? nooope- read on!

OK, I gave the TLS airbox my best analysis. (sat and stared at it) just how does the flapper affect things? The airbox is a CLASSIC helmholtz resonator, complete with entry duct (that is the tube coming up from the floor) . stock, I figure (flapper open) the duct length is approx 2.4" and area is approx 5 sq in. with a box volume of 550 cu in it resonates at approx 120 Hz.

flapper closed, sectional open area of inlet duct approx 1 sq inch, airbox now resonates at 53 Hz (low end boost)

remove flapper, you lose that variable resonance

shorten the inlet duct to 1" in length, resonance goes up to 184 Hz. cut it off completely and I'm not sure what happens?? This is a very clever bit of work. The TL has a weird double-gulp intake event every other revolution. I'll treat it as a single for simplicity- with flapper closed, the airbox resonates approx 3200 cycles/min, so you'd have a weaker resonance at 1600 rpm and then a stronger resonance at 3200 rpm. once the flapper opens, you have airbox resonance at 7200 cycles/minute -- so you get a weak resonance at 3600 rpm --and a stronger resonance at 7200 rpm.

All these resonators use a box with inlet duct of certain length. it's never just an open hole. There has to be a better way to improve things than cutting everything out of there.

One could apply this to an RG500 airbox- one on each side of the engine- sufficiently large... the use of a flapper could seriously aid low rpm power

Say we want a boost at 3000 rpm, where we have 6000 intake events/min we can shoot for a helping wave every other revolution (3000 cycles/min D 50Hz) treat each side separately- I think one could make an airbox of 400 cu in (0.23 cu ft) on each side. feed this through an inlet duct of sufficient size, - say - 4 sq in (.0278 sq ft) , , with a flapper that blocks it down to 1 sq in (.007 sq ft) . and length of... 3.6" that gives a resonance at 52 Hz. with flapper open, resonance occurs at 104 Hz (6240 cycles/min) and you get a boost in the midrange at 6200. or juggle the inlet tube length to counteract the pre-pipe flat spot anyhow, I'm still working on stuff... but my next effort will have airboxes that work!

So long


and more from Kevin Cameron

The airbox used to be just an intake silencer and a place to put the air filter. Now it's much more than that, so read on before you gut or toss your box. Just as is being done on new cars and motorcycles, snowmobile airboxes and their intakes are being built as resonant systems. When the airbox is resonating strongly, driven by the engine's suction pulses, its rapid internal pressure fluctuation covers a range of plus and minus 10-15%. This is just like the resonance of a bottle when you hum into it. If your engine's intake events run in step with the positive side of this resonance, it's just like getting a 10-15% supercharge boost for free. That's worth having. And what if you modify your engine, raising its peak-power rpm beyond the range of the airbox resonant frequency? There is a simple relationship you can use to alter airbox frequency by changing the length and/or diameter of the airbox intake pipe(s). That's worth having.


Any hi-fi enthusiast knows that woofer enclosures work best when the resonant frequency of the enclosure is nicely centred on the speaker's response range. The enclosure usually consists of a sealed volume with the speaker installed in one of its walls, and an opening, called a reflex port, cut into the enclosure. A resonant system consists of a mass, which vibrates back and forth against the restraint of something flexible, like a spring, with an excitatory force to drive it. In the case of the speaker enclosure, the mass is the air in and within one diameter's distance of the reflex port. The spring is the compressible air inside the enclosure. The system is set into vibration by the amplifier, driving the speaker cone back and forth as a piston.

In the case of an engine's intake airbox, the mass is the air in the airbox inlet pipe(s). The "spring" is the compressibility of the air in the box. The excitatory force - a very powerful one - is the endless sequence of strong engine intake suction pulses from the carburettors. The airbox must not have any significant leaks, as the throttled, back-and-forth airflow through them acts like a hand on a vibrating bell (anyone who's ever tried to play low notes on a valved wind instrument knows what a killer leakage is). The airbox inlet pipe is usually made with a smooth bellmouth on either end to reduce flow losses. Carburettors or throttle bodies must likewise seal positively to the box. When a system like this gets to humming, the pressure inside it vibrates rapidly plus and minus 10-15% of atmospheric pressure. In fact, the humming is so powerful that in many cases a sub-resonator is placed near the atmosphere end of the inlet, to prevent radiation of this powerful honking sound to the outside. EPA objectors are always waiting there with calibrated sound meters and spectrum analysers at the ready.

How can you adjust the resonant frequency of your airbox if you raise your engine's peak-torque rpm with pipes or porting? One way is to invest $30,000 or so in professional wave dynamics software like Ricardo "Wave", running on a $10,000 Sun workstation. Probably on the right back street in Hong Kong you can pick up a pirate copy for $25, but which street is it?

The airbox inlet tubes, or 93horns 94, are specifically designed to provide a resonance that can increase the total airflow by up to 10-15%. Removing these can cause the engine to loose power and increase the intake noise.

We're so used to the idea that problems have to be solved with silicon logic that we forget about steel and aluminium solutions. 93Wave 94 is great if you have a tricky fuel mixture glitch with #7 cylinder in your Ford NASCAR engine. But with a simple formula that tells us which variables push the airbox frequency which way, and by approximately how much, we can devise dyno experiments that will get us the answers we need - without those expensive Cathay-Pacific coach tickets.

Here is the formula.

(Airbox * Frequency), squared, is proportional to inlet pipe area/(airbox volume X inlet length)

This is useful because it shows us that if we want to raise airbox resonant frequency, we must increase inlet pipe area or decrease airbox volume or inlet pipe length


If our present engine is a twin, giving peak torque at 8200 rpm, that is 8200/60 D 137 revolutions per second, or 137 X 2 D 273 suction pulses per second. Unless there is some special problem, the airbox will be designed to resonate near that frequency. If we now want to raise peak torque revs by 10%, to 9020 rpm, we must also raise airbox frequency by a similar amount. If we raise airbox frequency by 10%, its square will increase by 1.1 X 1.1 D 1.21 times, or 21%. That means that whatever is on the right-hand side of the equation must also increase by a factor of 1.21. Take your pick.(a) increase inlet pipe area 21% (that is, increase its diameter by 10%) or,(b) decrease airbox volume by 21% or,(c) decrease inlet pipe length by 21%

Because these systems generally work better the bigger you make the airbox, we won't try (b). Since we are raising revs and power, increasing inlet area looks pretty good, so we could choose option (a), increasing inlet pipe area. However, option (c) would appear to be the easiest. Before we go to the dyno, we'll make up a few airbox inlet pipes to give us some test choices. Then we can run through our tests quickly and zero in on the sweet spot. Each end of the box inlet pipe should have a smooth bellmouth. Likewise, go carefully before removing internal airbox "furniture". Assume nothing, but test with each change to understand its effect. Airbox designs are sophisticated now, so their internal features often have functions. Any resonant system always has anti-resonance. In the case of an airbox, that is an rpm at which the engine breathes from the box when pressure is at the low part of its cycle. What if there's an anti-resonance right where you want your clutch to engage? Of course you could imagine a system with a variable-length inlet pipe to deal with this, but the easy way is just to kill the anti-resonance by opening a big hole in the airbox. Systems of this type are in use on certain sports motorcycles. When the engine runs near the rpm of the anti-resonance, the engine control computer tells a little motor to open the airbox port. When it revs up, the motor closes the port.

So long

Randy Norian
Is the XS airbox large enough for being resonant at the fairly low peak power rpm of an XS? Which would be around 60 hz for a 4stroke at 7200 rpm.
Look at an early Buell Lightning airbox, which is designed as a resonant box. It is pretty large, and the Buell version of the Sportster engine operates pretty much at similar rpm as an XS.
since we ride 360 twins wouldn't we be able to get results at 1/2 the RPM with a shared airbox? Not so possible on a Vee Twin.
since we ride 360 twins wouldn't we be able to get results at 1/2 the RPM with a shared airbox? Not so possible on a Vee Twin.
As I understand it, a shared airbox on an XS should be resonating at twice the frequency of two individual boxes, since intake events occur twice as often. Additionally, a shared airbox would have a larger volume, thus allowing larger intake opening for the same resonant frequency. I wonder if the design changes you illustrated so well has more to do with noise regulations getting stricter over time.
Another way to look at it.
https://www.enginebasics.com/Advanced Engine Tuning/Intake Runner Length.html
Intake Runner Length Tuning
Contributed by: Unknown

The intake system on a four-stroke car engine has one main goal, to get as much air-fuel mixture into the cylinder as possible. One way to help the intake is by tuning the lengths of the pipes.

When the intake valve is open on the engine, air is being sucked into the engine, so the air in the intake runner is moving rapidly toward the cylinder. When the intake valve closes suddenly, this air slams to a stop and stacks up on itself, forming an area of high pressure. This high-pressure wave makes its way up the intake runner away from the cylinder. When it reaches the end of the intake runner, where the runner connects to the intake manifold, the pressure wave bounces back down the intake runner.

If the intake runner is just the right length, that pressure wave will arrive back at the intake valve just as it opens for the next cycle. This extra pressure helps cram more air-fuel mix into the cylinder -- effectively acting like a turbocharger. The problem with this technique is that it only provides a benefit in a fairly narrow speed range. The pressure wave travels at the speed of sound (which depends on the density of the air) down the intake runner. The speed will vary a little bit depending on the temperature of the air and the speed it is moving, but a good guess for the speed of sound would be 1,300 feet per second (fps). Let's try to get an idea how long the intake runner would have to be to take advantage of this effect.

Let's say the engine is running at 5,000 rpm. The intake valve opens once every two revolutions (720 degrees), but let's say they stay open for 250 degrees. That means that there are 470 degrees between when the intake valve closes and when it opens again. At 5,000 rpm it will take the engine 0.012 seconds to turn one revolution, and 470 degrees is about 1.31 revolutions, so it takes 0.0156 seconds between when the valve closes and when it opens again. At 1,300 fps multiplied by 0.0156 seconds, the pressure wave would travel about 20 feet. But, since must go up the intake runner and then come back, the intake runner would only have to be half this length or about 10 feet.

Two things become apparent after doing this calculation:

1. The tuning of the intake runner will only have an effect in a fairly narrow RPM range. If we redo the calculation at 3,000 rpm, the length calculated would be completely different.

2. Ten feet is too long. You can't fit pipes that long under the hood of a car very easily. There is not too much that can be done about the first problem.

A tuned intake has its main benefit in a very narrow speed range. But there is a way to shorten the intake runners and still get some benefit from the pressure wave. If we shorten the intake runner length by a factor of four, making it 2.5 feet, the pressure wave will travel up and down the pipe four times before the intake valve opens again. But it still arrives at the valve at the right time.

There are a lot of intricacies and tricks to intake systems. For instance, it is beneficial to have the intake air moving as fast as possible into the cylinders. This increases the turbulence and mixes the fuel with the air better. One way to increase the air velocity is to use a smaller diameter intake runner. Since roughly the same volume of air enters the cylinder each cycle, if you pump that air through a smaller diameter pipe it will have to go faster.

The downside to using smaller diameter intake runners is that at high engine speeds when lots of air is going through the pipes, the restriction from the smaller diameter may inhibit airflow. So for the large airflows at higher speeds it is better to have large diameter pipes. Some carmakers attempt to get the best of both worlds by using dual intake runners for each cylinder -- one with a small diameter and one with a large diameter. They use a butterfly valve to close off the large diameter runner at lower engine speeds where the narrow runner can help performance. Then the valve opens up at higher engine speeds to reduce the intake restriction, increasing the top end power output.
So I've been turning this resonant thing around in my head for the past couple of days. For all people complain about the airbox, mine is still on and the power delivery (when the bike runs) is nice and smooth.

Is the airbox for the later models a resonant airbox? If so, has anyone figured out their working frequency (its on my to-do list)?

I've read mentions of "still air airbox" - I presume this is different, or is it a different name for the same thing?

Will vacuum carbs work with a resonant airbox, or would you need slide carbs (or something else) to take advantage of the resonance?
Yep, Crash, air box=still air box, same thing, and yep, vac carbs benefit from a tuned air box, and so do EFI systems. Unfortunately, there's only so much space for the air box on the XS650. Most modern bikes are built around a perimeter frame, which provides room for a bigass tuned air box under the gas tank. You're absolutely right to leave the OE air box in place with OE vacuum carbs.
I have noticed the later models,1980-till the production end, run hotter. 34mm carbs with this and the air box combo, run leaner? Machines are engineered, R&D to run with every OEM part in place. Take one out, and there goes the quality control. I will say, these Yamaha parallel twins are the AK 47 of twins. Rugged. Tough. Throw them down in the mud and they'll still run. Lol I just totally dumbed this conversation down. Lol
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Just ran into this while researching a bike purchase. :sneaky: (who me?) A BMW K1200S, but this is pretty universal.

"The thing breathes mixture through Bosch fuel injection and an airbox slightly smaller than the S model’s. That smaller airbox is the only major difference between the S and R motors. It costs the bike about four horsepower and two foot-pounds of torque,"