All top engine builders recognize that the exhaust system exerts tremendous influence on engine performance, particularly with regard to breathing efficiency and torque curve positioning within the required RPM range. Thoughtful exhaust tuning can often promote additional torque production and the enormously valuable ability to position that torque in the most favorable part of an engine’s operating range based on the final application. Header primary tube cross-sectional area and length are the core contributors to this strategy and they must be sized accordingly to complement inlet tract dimensions, cam timing, and engine speed as they relate to the final application in terms of the overall powerband and the specific placement of torque and power within the vehicle’s required operating range.
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So how do you determine the correct header size for any given engine combination? Off-the-shelf headers are, at best, a compromise that can’t possibly meet the broad application specific requirements of all the engines they support. Wave tuning theory has long been a popular method, and there are many good engine simulation software programs designed to help you pinpoint the ideal dimensions for your particular application.
In short, wave tuning seeks to take advantage of oscillating pressure pulses within the exhaust stream to aid cylinder scavenging. The goal is to time the waves or pulses so that a reflected low-pressure pulse arrives at the cylinder at just the right time to lend its energy to discharging exhaust gases from the cylinder. The critical timing is a function of primary tube length, and is affected by the point at which the pulse reaches atmospheric pressure at the end of the tube. It is most effective at one particular engine speed, and its value is well illustrated in top-level engine simulation packages such as Performance Trend’s Engine Analyzer Pro, Motion Software’s Dynomation 5, and the PipeMax program that calculates the optimum pipe dimensions based on the engine builder’s specified parameters.
The quick and easy way to calculate the ideal primary header pipe diameter for effective performance is based on engine displacement, engine speed, and VE. Performance authority Jim McFarland provides a simple formula for calculating the optimum cross-sectional area (c/s) of a header primary tube or pipe. This method optimizes for the engine’s torque peak, which is the point of maximum VE and thus the point of maximum generated exhaust volume. At engine speeds above the torque peak, cylinder filling decays proportionately with RPM (time) because there is progressively less time available to fill the cylinder on each intake event. There are more power strokes per minute, but proportionately less exhaust volume to evacuate due to declining VE with increased engine speed.
Optimizing for the torque peak provides the ideal primary pipe diameter and since peak power is usually no more than 1,500 to 1,750 rpm above the torque peak, the selected pipe size has no trouble accommodating an exhaust volume that essentially flat lines and begins to fade rapidly. The RPM spread between the torque peak and the power peak is largely influenced by the engine’s rod to stroke (R/S) ratio. Shorter rods tend to broaden the separation between the torque peak and the power peak. Similarly, longer rods tends to move the peaks closer together. The previously stated range applies for most of the stroke lengths and rod lengths commonly used by performance enthusiasts.
A formula can be written two ways one to solve for primary pipe cross-sectional (c/s) area when the torque peak RPM is known or anticipated, and the other to predict torque peak engine speed based on a primary pipe cross section that is under consideration.
To accommodate specific cylinder volumes, the formula considers a single cylinder only, so you have to divide your known or anticipated displacement by the number of cylinders to determine single-cylinder volume.
Cylinder Volume = displacement ÷ number of cylinders c/s = (cylinder volume x RPM) ÷ 88,200 RPM = (c/s x 88,200) ÷ cylinder volume
Where: c/s = primary pipe cross-sectional area Cylinder volume = volume of a single cylinder 88,200 = mathematical constant RPM = RPM at torque peak
Once the calculated c/s area is known, the corresponding primary pipe diameter to the nearest available pipe size can be calculated.
If area = diameter2 x .7854, then pipe size equals the square root of the previously calculated c/s area times the reciprocal of the constant .7854.
Pipe Size = √[A x (1÷7854)] Pipe Size = √(A x 1.273)
If you’re solving for a torque peak RPM based on contemplated primary pipe size, calculate the c/s area by squaring the inside diameter (ID) of the pipe and multiplying by .7854. To determine the true inside diameter of a pipe for the purpose of calculating c/s area, use the measured outside diameter (OD) minus twice the wall thickness of the pipe.
ID = OD – (2 x wall thickness)
For example, the ID of a pipe with a 1.75-inch OD and a wall thickness of .040 inch is calculated to be:
ID = 1.75 – (2 x .040) = 1.67 inches
For many applications header pipe size selection based on manipulating peak torque RPM outweighs the pursuit of absolute peak power. This often suggests erring on the small side of primary pipe selection to preserve velocity with the minimum c/s required to service maximum exhaust volume at peak torque, hence the formula for c/s area is based on engine speed, cylinder volume, and VE. Additionally, tuned induction systems generate their own torque curves that contribute independently and proportionately to an engine’s “net” torque curve.
PipeMax Header Software
Meaux Racing Heads PipeMax program is a popular exhaust system dimension calculator. It is primarily a header design program, but it incorporates enough user data to also function as a partial engine simulation program. It also calculates torque and horsepower output based on VE and the recommended header specs. It provides a wealth of information about header dimensions and the proper design of headers to accommodate wave tuning.
You input all the usual engine information along with details about the cylinder heads and camshaft and it calculates the optimum primary pipe diameters, cross-sectional areas, primary tube lengths, and collector specifications for optimum performance. The results screen displays dimensions for a single primary pipe or a two- and three-step header designs. It provides recommended pipe diameters and lengths for the primary pipes and the collectors. It also displays the best and worst specifications (so you can avoid them). It calculates primary pipe harmonics for the first through eighth reflected wave and collector harmonics with mufflers and tailpipes.
All of these specs are delivered in standard (U.S.) and metric units automatically. The program is based on projected VE and consequent exhaust volume and it can estimate VE for your particular engine specs. It allows you to select a dyno acceleration rate for the simulation and you can specify the mean flow velocity to be used in cross-sectional area calculations.
It is inexpensive, very thorough, and makes a perfect complement to other simulators you might be using. It pinpoints ideal header dimensions for an engine and simplifies header design. It teaches you a lot about the effects of pressure wave activity in the engine’s exhaust system.
The steps in a stepped header design tend to reduce flow resistance along the specific length of the pipe, but they must be strategically placed to take maximum advantage of pulse reflections and minimize velocity loss within the pipe. Considerably more effort is currently being directed at understanding the dynamics of stepped header performance and how it applies to specific applications. Each step presents an area change that reflects a smaller-magnitude, negative pressure pulse back toward the valve while diminishing the intensity of the positive pulse that continues down the pipe toward the next step or the collector.
Steps also function the opposite way, returning both positive and negative waves down the pipe. This disrupts their strength, speed, and overall effect. They are commonly thought to constitute functional reversion dams on milder applications with a broader RPM range and are generally considered unnecessary on higher-powered applications with narrow powerbands.
Larger steps intended to reduce flow restriction are typically more effective when employed on a 4-into-1 system than on a 4-into-2- into-1 arrangement. In effect, however, it is relatively easy to get lost in the dimensional mathematics of pulse tuning so it is often more beneficial to size the cross section to adequately service maximum exhaust volume based on actual VE at the torque peak RPM. Hence, the growing popularity of merge collectors, which provide a restriction or choke to attenuate the pulses and minimize their effect in favor of dimensionally correct collectors that optimize the effectiveness of properly sized primary pipes.
The merge collector works by maintaining maximum system velocity until the exhaust encounters atmospheric pressure. Maintaining exhaust velocity and pulse strength in the pipe is often more beneficial than using steps to reduce flow restriction. Larger steps tend to require longer primaries to compensate for velocity loss regardless of powerband width.
The position of the first step provides an area increase that generates the first reflected pulse and influences how quickly the pulse arrives at the valve the closer the step, the lower the mean velocity in the pipe.
Exhaust gas temperature also influences pulse timing. Higher EGTs (within reason) increase the speed of the pulse and improve scavenging if the pulse can be properly timed. This is relatively critical to calculate and I believe that optimizing the cross-sectional area with a single-dimension (no step) pipe length that tunes to the second or third reflected pulse adequately services 90 percent of most racing applications.
A cross section that satisfies the discharge requirement of the engine’s exhaust volume at peak VE provides an ideal header dimension to position the torque peak for maximum effect. Beyond that, primary pipe length can be adjusted accordingly to provide a torque boost above or below the peak as required by the specific application.
When multiple steps are positioned at various lengths along the primary pipe the area increase at each step creates another reflection point. There are typically only one or two steps in most stepped header designs. Each reflection point along the pipe delivers progressively weaker pulses returning to the valve. The closer the first step is to the valve the sooner it returns a pulse, which is typically the highest-intensity pulse with the greatest scavenging effect. Pulse strength diminishes accordingly at each successive step, making it critical to properly locate the first step to take maximum advantage of its strength. Where there is only one step, the step is typically positioned approximately halfway along the total length of the pipe.
On two-step systems, the pipe lengths after the first step usually split the difference of the remaining length. So you might have an initial step at something like 11 to 12 inches and two secondary steps approximately 6 inches long. One reason for this is to reflect more pulses sooner because it takes progressively longer for each pulse to reach the valve, primarily because they are weakened when they encounter the first step. Hence, multiple pulses are continuously reflected up and down the pipe at supersonic speed that varies according to specific exhaust gas temperature.
You can do more harm than good here if you’re not careful. That’s why I recommend a properly sized (cross-section) non-stepped pipe for most applications. If you run a stepped header, consult PipeMax to calculate the optimum step lengths.
Another thing to consider is the initial cross section of the pipe relative to the size of the exhaust port. If the cross section of the pipe is considerably larger than the port, it tends to function as a very short first step, or what is commonly thought of as a reversion dam. The large area change reduces flow velocity, particularly if it departs too far from the mathematically correct cross section required to process the engine’s exhaust volume at maximum VE.
Many applications, particularly those with broader powerbands, are better served by closely matching pipe size to port size to preserve flow energy at lower engine speeds. This often requires altering the cam specs to deal with any reversion tendencies. Wave tuning software such as Dynomation 5 graphically predicts reversion problems if provided with very precise camshaft data. You can use this to successfully choose alternate cam timing that helps reduce or eliminate reversion.
Header Design Kit
Once the importance of constructing exhaust headers with dimensions specifically targeted to improve and position torque is recognized, you must construct dimensionally correct headers that actually fit the chassis. To help accomplish this, icengineworks offers a header design and modeling kit to help build headers to fit any particular chassis requirement. These clever kits are like nothing you’ve seen before. They provide a complete set of ABS plastic modeling blocks shaped exactly like header tubing of the appropriate size. Each block is exactly 1 inch long and they come in straight and curved versions that provide 2-, 3-, 4-, and 6-inch-radius bends at the centerline. You snap these blocks together in any desired combination and rotate the curved pieces to achieve the required configuration and radius.
The kits allow you to piece together a full-scale model header that exactly fits your engine and chassis combination. Each individual piece is clearly marked with multiple indexing arrows and witness marks so you can easily duplicate the sections in metal tubing using lengths of straight, J-bend, or U-bend tubing.
The witness marks are spaced 30 degrees apart providing exact positioning references for transferring the design to metal. The Pro Kit version includes block adapters, which lock the blocks in expandable starter tubes so the initial blocks do not move during the process. The beauty of this system is that it allows you infinite freedom to rotate, extend, or shorten any segment into the desired shape and length you need. This makes it particularly easy to model your way around various chassis obstructions and still achieve an equal-length header or a multiple-length header with perfectly aligned joints and bends.
The company also offers construction aids in the form of a special pivot table for making precise tubing cuts, starter block accessories, and special tack welding clamps that facilitate precise joints for final welding.
You can purchase a kit for just one side or both sides of a V-8 engine. Once you have created a perfect model header and transferred it to metal, you can disassemble the model and store the kit until the next header project comes along. The math involved is easy and straightforward, consisting primarily of counting the segments and noting the appropriate lengths and radii. It can turn an amateur into a first-class header designer almost overnight.
Written by John Baechtel and Posted with Permission of CarTechBooks