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Intake
Runner Length
Have you ever wondered why modern car intake runners take a long curved path from the plenum to the head? Why make them that long instead of just making a short direct tube? The way the early model 1UZ is presented in the engine bay to looks as though the intake runners go from the plenum directly down to each head but they actually curve underneath the plenum and cross over to the head on the opposite side, so they're longer than they appear.
As a rule of thumb you may have heard that short wide runners are good for high RPM power and longer narrower runners are better for low RPM torque. The later VVTi 1UZ makes use of this by having dual length runners which it can switch between based on RPM. The length of the runner (total length from the valve seat to the plenum or end of the trumpet) is not arbitrary - it's calculated to maximise volumetric efficiency (ability to fill the cylinders with fuel/air) for a given RPM range.In a road car the runners are generally tuned to maximise efficiency where peak torque occurs and for race cars it's tuned for where peak power occurs. Note that the runner diameter and cams dictate where peak power and RPM occur - the runner length is used as a tuning tool to alter the shape of the curve. Say you change your camshafts and you want to maximise volumetric efficiency at 6000 RPM - what length should the intake runners be? This is a pointless question with a standard intake plenum as the runners are cast but if you're installing Individual Throttle Bodies then you can specify whatever trumpet length you like if you have enough clearance under the bonnet.
The theory is that the sudden action of the valve closing against the incoming air creates a pressure wave which bounces back towards the open end of the runner. This isn't a slug of air moving back towards the opening, but a compression wave moving back up the column of air. When the pressure wave reaches the open end this acts as a boundary where some of the pressure wave escapes and some bounces back down the runner towards the valve. If that can be timed so it reaches the valve just when it re-opens, a higher density of air/fuel can enter the cylinder to create a bigger bang. The calculations to give you the optimum length for the intake runner are long but not difficult to follow. Pressure waves travel at a constant depending on the material they are travelling through and for compression waves in air it's most commonly know as the speed of sound. So what do we need to know?
The speed of sound in air is dependant on a few things like temperature, humidity and barometric pressure but temperature is the main influence so it can be approximated as follows:
So, let's work out the optimum runner length for a stock 1UZ. The quoted RPM where peak torque occurs is a bit rubbery and is said to be 4400 RPM to 4600 RPM so we'll take 4500 to be safe. Here are our constants:
In a 4 stroke engine there are 2 complete revolutions (720°) between one intake stroke and the next and if the intake is open for 232°, then there is 488° (720-232) of rotation from when it closes to when it opens. With the engine spinning at 4500 RPM we need to work out how far the pressure wave will travel while the engine turns 488° after which time the intake valves start to open. Now we have to work out how long it takes for the engine to rotate 488° at 4500 RPM.
To work out how many seconds per revolution we just want to invert the above units, so:
Next we want to work out how many seconds for 488°. Given that we know it takes 0.0133 seconds to cover 360° let's work out the time for 1°:
So for 488°:
0.0181 of a second is how long it takes for the valve to close then start to reopen, so how far does the pressure wave travel in that time?
If we want it to travel up and back then we'll have to halve that length:
Having a 3.136m intake runner length isn't very practical - this is where we use harmonics to find a shorter length.
Harmonics are normally associated with musical instruments but we're dealing with the same principles here - a tuned length tube with a closed end, an open end and a pressure wave bouncing up and down. At the closed end is a wave node (ie. high pressure) and at the open end is a wave anti-node (ie. low pressure). This shows how the wave form fits in the runner with the full wavelength completed in dotted lines.
Obviously having an intake runner length of 3.136m is too long but if we halve the length of the runner, and therefore halve the wavelength of the pressure wave, we get the 2nd harmonic.
With a tube only half as long as we need, the pressure waves bounces up and back twice before the valves open. We can continue to halve the length to get the 3rd & 4th harmonics.
1st Harmonic = 3.136m
2nd Harmonic = 1.568m
3rd Harmonic = 0.784m
4th Harmonic = 0.392m
Each time the pressure wave bounces back from the open end some energy will be lost to the atmosphere so there will be less pressure at the valves on the 4th harmonic than the 3rd.
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