BTB Technical article on header design - Jan/01/02
The design of exhaust manifolds is governed by two basic principles. The first calls for the efficient extraction of exhaust gases from the cylinder after combustion. The second is the controlled development of a standing pressure wave in the manifold pipe to encourage over filling of the combustion chamber with inlet charge.
The first is the easiest to understand if we merely think of the engine as a pump. After the combustion stroke has taken place the piston has to return to top dead centre. As it returns, the hot exhaust gas has to be expelled past the open exhaust valve into the exhaust pipe. At this point the objective is the efficient expulsion of exhaust gas to allow the piston to return as quickly as possible. The pressure against the piston as it rises determines the speed of its movement, this is known as the pumping loss and is simply the work done by the piston against the exhaust gas. In order to minimise pumping losses, the flow of exhaust gas has to be maximised. This does not necessarily mean the largest diameter pipe. Because the gas travels as a fluid, too large a duct will lose gas velocity and the gas flow will stall, (imagine a small stream reaching a large lake, the energy of the flow is lost as the stream decides where to go, and silts up the lake).
Conversely, too small a duct will restrict the flow and increase the pressure (damming up our analogous stream). Determining the optimum size of the exhaust duct largely depends on the capacity of the engine, and the amount of revolutions per minute at which it is operating. Supercharged engines will need bigger exhaust pipes as they effectively have a greater capacity. We can determine the theoretical perfect size for the exhaust through a series of calculations. Ironically, in the most widely used formula, these calculations rely on us already knowing the theoretical perfect length. Also very important is the need for a smooth parallel-sided duct with the minimum number of bends on the largest possible bend radius, because hot exhaust gases do not like to change direction too abruptly. We must also avoid sudden changes in diameter or mismatched ports, and encourage smooth transitions where one pipe meets another. So, in summary, this aspect of exhaust design is essentially a fluid dynamics exercise and is usually heavily compromised by packaging restraints once an engine is mounted in the chassis.
The rather more scientific wave tuning aspect of exhaust manifold design requires us to understand standing waves. For an acoustical analogy consider the case of a pipe organ, where different notes are formed from blowing air across the open ended mouth of different diameters and lengths of tubes. If we consider the case of a single cylinder engine with a straight exhaust pipe exiting to atmosphere, the pulsing flow of gas causes a standing wave to be formed in the pipe. A standing wave is best illustrated by stretching a "Slinky" spring between two people, if one end is oscillated at a consistent frequency a clear pattern can be seen in the coils where bunching indicates a high pressure zone and stretching shows low pressure. We have already seen how important it is for an engine to be expelling gases into a low-pressure pipe, but for a high performance engine a standing wave can be especially beneficial. This is because at high rpm in a tuned engine both the inlet and exhaust valves are open at the same time as the piston approaches TDC to begin its inlet stroke. At this point if we can ensure that a low pressure zone exits just behind the exhaust valve, inlet charge can start to be drawn into the cylinder even before the piston starts to travel downwards on its "sucking cycle". This ram effect is crucial to the "over filling" of the cylinder prior to combustion that leads to increased engine power. Of course these days most engines have more than one cylinder and therefore the interaction of the ram effect between the cylinders is paramount. A typical formula for calculating lengths and therefore diameters is as written in A.Graham Bell's excellent book 4 stroke Performance Tuning in Theory and Practice, published by Haynes.
850 x ED
P= ---------------- - 3
rpm
Where P is primary pipe length in inches
ED is 180 + the number of degrees that the exhaust valve opens before bottom dead centre Rpm is the tuned engine speed in revolutions per minute.
This gives an excellent starting point to exhaust manifold design by suggesting a primary length for a theoretical 4-1 design. Using this we can then calculate the Inside Diameter of the primary using the formula:
cc
ID = S ----------------------- x 2.1
(P+3) x 25
Mr Bell goes on to suggest a way of calculating lengths for a 4-2-1 design. This relies on a theory that the length of the primary pipes for a 4-2-1 should always be 15 inches. Whilst again this may be a good starting point it is generalising too much to suggest that all 4-2-1 exhausts should have the same primary length. Over the years we have tried many alternatives to this with sometimes surprising results. The most popular capacity range for race engines in the UK is from 1300-2000cc and in this range almost always a 4-2-1 design has proved to be better than 4-1. It should however be emphasised that, long primaries of the length calculated for a 4-1 but subsequently merging into two short secondaries appear to give the top end performance of a 4-1, without the flat spot at low revs that a 4-1 usually has.
The best way to establish the exact optimum layout and dimension for a specific engine is by trial and error on an engine dyno. This gives the tuner ample opportunity to try many different iterations of length, diameter, collector design and tailpipe size. Not to be forgotten of course is the inlet tract, which also will generate a standing wave and its length including plenums, trumpets and butterflies has to be tuned in conjunction with the exhaust. It is clear that exhaust pipe length and diameter dimension will be a function of the quantity of exhaust gas that is being expelled and the length of time that it is being expelled (period of stroke). Hence a short stroke, big bore engine will require a shorter and larger diameter pipe than a longer stroke narrow bore one. Altering the design of the inlet and exhaust can have a dramatic effect on the characteristics of the engine and often just looking for one peak power figure at a specific rpm doesn't produce as competitive an engine as considering the performance across the whole usable power band of the engine. The successful engine designer's holy grail is to get the maximum area under the torque curve, as this will provide the most opportunity for accelerating the car for the longest period. This partly explains the emergence of quirky manifold designs where theoretically the wrong cylinders are linked together in the layout of the manifold. This seems particularly to be the case in highly tuned motorcycle engines where instead of linking cylinders 1 & 4, and 2 & 3 into a 4-2-1 design, pipes are paired 1 & 2, 3 & 4.
Although initially this would appear to be so that the pipes can sweep under or around the engine frame more easily, it also gives a more even spread of torque with less peakiness. This unusual design layout has also been favoured in Touring Cars, where (in common with motor bikes) traction is at a premium and therefore a nice progressive power delivery is more desirable than a peaky wheel spin inducing one.
If it is not possible to optimise the exhaust manifold design on the dyno, then it is a good idea to make the pipes with slip joints between the pipes and collectors, so that different lengths can be experimented with during testing. It may be found that on a track with a high proportion of long straights a shorter primary that will give more power at higher revs provides a quicker lap time. Equally, on a tight track or a hillclimb with a standing start, a longer primary will boost acceleration from low revs.
The reason that a 4-2-1 works better over a wide range of rpm's than a 4-1 is that each combination of pipes will work best at a specific rpm and therefore the more combinations that are available the more possible solutions arise. A current trend in Formula 1 is to have steps in diameter at certain lengths along the primary.
Again, each step will create a standing wave at its own rpm, and these steps can be made to magnify existing waveforms at certain revs. Whatever the design, the object is the same. Sudden steps in the primary will contradict my earlier smooth gas flow theory, but it has obviously proved itself to be a compromise that the designer is willing to make. High revving short stroke racing engines have a very short time available to fill the cylinder with air fuel mixture and as such rely on ram tuning from the combined effects of the inlet and exhaust tracts to achieve their high specific outputs.