# Engine balance

Engine balance refers to those factors in the design, production, tuning, maintenance and the operation of an engine that benefit from being balanced. Major considerations are:

• Structural and operational elements within an engine
• Longevity and performance
• Power and efficiency
• Performance and weight/size/cost
• Environmental cost and utility
• Noise/vibration and performance

## Overview

Piston engine balancing is a complicated subject that covers many areas in the design, production, tuning and operation. The engine considered to be well balanced in a particular usage may produce unacceptable level of vibration in another usage for the difference in driven mass and mounting method, and slight variations in resonant frequencies of the environment and engine parts could be big factors in throwing a smooth operation off balance. In addition to the vast areas that need to be covered and the delicate nature, terminologies commonly used to describe engine balance are often incorrectly understood and/or poorly defined not only in casual discussions but also in many articles on respected publications.

Internal combustion piston engines, by definition, are converter device to transform energy in intermittent combustion into energy in mechanical motion. Slider-crank mechanism is used in creating a chemical reaction on fuel with air (compression and ignition), and converting the energy into rotation (expansion). The intermittened energy source combined with the nature of this mechanism make the engine naturally vibration-prone. Multi-cylinder configuration and many of the engine design elements are reflections of the effort to reduce vibrations through the act of balancing.

lists the balancing elements to establish the basics on the causes of imbalance.
lists different kinds of vibration as the effects of imbalance.
discusses the term "Primary balance".
explains what Secondary balance is, and how the confusing terminologies 'Primary' and 'Secondary' came into popular use.
goes into engine balance discussions on various multi-cylinder configurations.
describes the wheel hammer effect unique to steam locomotives.

## Items to be balanced

There are many factors that could throw an engine off balance, and there are many ways to categorize them. The following is an example of categorizing the items that need to be balanced for a smooth running piston engine. In the category descriptions, 'Phase' refers to the timing on the rotation of crankshaft, 'Plane' refers to the location on the crankshaft rotating axis, and 'CG' refers to the center of gravity.

• Mechanical
• Static Balance - Static balance refers to the balancing of weight and the location of CG on moving parts.
1. Reciprocating mass - e.g. Piston and conrod weight and CG uniformity.
2. Rotating mass - e.g. Crank web weight uniformity and flywheel concentricity
• Dynamic Balance - In order for a mass to start moving or change its course in the motion, it needs to be accelerated. In order for a mass to be accelerated, a force is required, and that force needs to be countered (supported) in the opposite direction. Dynamic balance refers to the balancing of these forces and friction.
All accelerations of a mass can be divided into two components opposing in the direction. For example, in order for a piston in a single cylinder engine to be accelerated upward, something must receive (support) the downward force, and it is usually the mass of the entire engine that moves downward a bit as there is no counter-moving piston. This means one cause of engine vibration usually appears in two opposing directions. Often the movement or deflection in one direction appears on a moving mass, and the other direction appears on the entire engine, but sometimes both sides appear on moving parts, e.g. a torsional vibration killing a crankshaft, or a push-pull resonance breaking a chain. In other cases, one side is a deflection of a static part, the energy in which is converted into heat and dissipated into the coolant.
• Reciprocating mass - Piston mass needs to be accelerated and decelerated, resisting a smooth rotation of a crankshaft. In addition to the up-down movement of a piston, a conrod bigend swings left and right on top and bottom halves of a crank rotation.
3. Phase balance - e.g. Pistons on 60 or 90 degree V6 without an offset crankshaft reciprocate with unevenly spaced phases in a crank rotation
4. Plane balance - e.g. Boxer Twin pistons travel on two different rotational planes of the crankshaft, which creates forces to rock the engine on Z-axis[note 1]
• Rotating mass
5. Phase balance - e.g. Imbalance in camshaft rotating mass could generate a vibration with the frequency equal to once in 2 crank rotations in a 4 cycle engine
6. Plane balance - e.g. Boxer Twin crankshaft without counterweights rocks the engine on Z-axis[1]
7. Torsional balance - If the rigidity of crank throws on an inline 4 cylinder engine is uniform, the crank throw farthest to clutch surface (#1 cylinder) normally shows the biggest torsional deflections. It is usually impossible to make these deflections uniform across multiple cylinders except on a radial engine. See Torsional vibration
• 8. Static mass - A single cylinder 10 HP engine weighing a ton is very smooth, because the forces that comprise its imbalance in the operation must move a large mass to create a vibration. As power to weight ratio is important in the design of an engine, the weight of a crankcase, cylinder block, cylinder head, etc. (i.e. static mass) are usually made as light as possible within the limitations of strength, cost and safety margin, and are often excluded in the consideration of engine balance.
However, most vibrations of an engine are small movements of the engine itself, and are thus determined by the engine weight, rigidity, location of CG, and how much its mass is concentrated around the CG. So these are crucial factors in engine dynamic balance, which is defined for the whole engine in reciprocal and rotational movements as well as in bending and twisting deflections on X, Y and Z axis, all of which are important factors in the design of engine mounts and rigidity of static parts.
It is important to recognize that some moving mass must be considered a part of static mass depending on the kind of dynamic balance consideration (e.g. camshaft weight in analyzing the Y-axis[note 1] rotational vibration of an engine).
• Friction
9. Slide resistance balance - A piston slides in a cylinder with friction. A ball in a ball bearing also slides as the diameter of inner and outer laces are different and the distance of circumference differs from the inside and out. When a ball bearing is used as the main bearing on a crankshaft, eccentricity of the laces normally create phase imbalance in slide friction. Metal bearing diameter and width define its bearing surface area, which needs to be balanced for the pressure and the rotational speed of the load, but differing main bearing sizes on a crankshaft create plane imbalance in slide friction.
10. Rolling resistance balance - e.g. A ball in a ball bearing generates friction in rolling on a lace
• Fluid - Pressure, Flow and Kinetic balance on gas, oil, water, mist, air, etc.
• Torque Balance - Torque here refers to the torque applied to crankshaft as a form of power generation, which usually is the result of gas expansion. In order for the torque to be generated, that force needs to be countered (supported) in the opposite direction, so engine mounts are essential in power generation, and their design is crucial for a smooth running engine.
11. Amount of torque - Normally, the amount of torque generated by each cylinder is supposed to be uniform within a multi-cylinder engine, but often are not. This irregularity creates torque imbalance in phase and plane.
12. Timing/Direction of torque - The conrod of a cylinder with fast-burning mixture pushes the crankshaft most at a different angle when compared to a late-igniting or slow-burning cylinder.
13. Phase balance - e.g. Firings on a single cylinder 4 cycle engine occur at every 720 degrees in crankshaft rotation, which is not balanced from one rotation to another.
14. Plane balance - Torque is applied to the crankshaft on the crank rotational plane where the conrod is located, which are at different distances to power take off (clutch surface) plane on inline multi-cylinder engines.
• Drag - Negative torque that resists the turning of crankshaft that is caused by fluid elements in an engine.
• Pressure balance - Not only the compression in a cylinder, but also any creation of positive (as in oil pressure) and negative (as in intake manifold) pressure are sources of resistance, which benefit from being uniform.
15. Phase balance - e.g. Compression on a single cylinder 4 cycle engine occurs once every 720 degrees in crank rotation phase, which creates imbalance from one rotation to another.
16. Plane balance - e.g. Compression on a boxer twin engine occurs at different planes on the crankshaft at different distances to clutch surface. A single plane (single row) radial engine does not have this plane inbalance except for a short mismatch between the power generating plane where the conrods are, and the power take off plane where the propeller is.
• Flow resistance
17. Phase balance - e.g. If only one cylinder of a multi-cylinder engine has a restrictive exhaust port, this condition results in increased resistance every 720 degrees on crank rotation on a 4 cycle engine.
18. Plane balance - e.g. If only one cylinder of a multi-cylinder inline engine has a restrictive exhaust port, it results in increased resistance on the crank rotational plane where that cylinder/conrod is located.
• 19. Kinetic resistance - Oil, water, vapor, gas and air do have mass, that needs to be accelerated in order to be moved for the operation of an engine. Rolls Royce Merlin and Nakajima NK1F Sakae 21 received rear-facing stub exhaust pipes in their development, resulting in a measurable increase in the maximum speed of Supermarine Spitfire, De Havilland Mosquito and Mitsubishi A6M Zero. This is a form of jet propulsion using kinetic energy in the exhaust, implying that the balancing of kinetic resistance arising from fluid components of an engine is not insignificant. Crank webs partially hitting the oil in oil pan (accelerating the oil mass rapidly) could be a big source of vibration.
• 20. Shearing resistance - Metallic parts in an engine are normally designed not to touch each other by being separated by a thin film of oil. But a cam sometimes touches the tappet, and metal bearing surface wears with insufficient oil or with too much / too little clearance. A film of liquid (especially oil) resists being sheared apart, and this resistance could be a source of vibration as experienced on an over-heating engine that is nearing a seizure.
• 21. Thermal - Thermal balance is crucial for the longevity and durability of an engine, but also has a profound effect on many of the above balancing categories. For example, it is common for a longitudinally-mounted inline engines to have the front-most cylinder cooled more than the other cylinders, resulting in the temperature and torque generated on that cylinder less than on other phase and planes. Also, thermal imbalance creates variations in tolerance, creating varied sliding frictions.

## Types of vibration

In contrast to the causes of imbalance listed above, effects of imbalance mainly appear as vibration. There are three major types of vibration caused by engine imbalances:

### Reciprocating

A single cylinder, 360°-crank parallel twin, or a 180°-crank inline-3 engine normally vibrates up and down because there are no counter-moving piston(s) or there is a mismatch in the number of counter-moving pistons. This is a 3. phase imbalance of reciprocating mass.

### Rocking

Boxer engines, 180°-crank parallel twin, 120°-crank inline-3, 90 degree V4, inline-5, 60 degree V6 and crossplane 90 degree V8 normally vibrate rotationally on Z or Y-axis. This is a result of plane imbalances (4., 6., 14. and 16) called the rocking couple.

Four stroke engines with 4 or less number of cylinders normally do not have overlapping power stroke, so tend to vibrate the engine back and forth rotationally on X-axis. Also, multi-cylinder engines with counter moving pistons have a CG height imbalance in a conrod swinging left on the top half of crank rotation, while another swings right on the bottom half, causing the top of the engine to move right while the bottom moves slightly to the left.[note 2] Engines with 13. phase imbalance on torque generation (e.g. 90 degree V6, 180°-crank inline-3, etc.) show the same kind of rocking vibration on X-axis.

### Torsional

Twisting forces on crankshaft cannot be avoided because conrods are normally located at a (often different) distance(s) to the power take-off plane (e.g. clutch surface) on the length of the crankshaft. The twisting vibrations caused by these (7.Torsional imbalance) forces normally cannot be felt outside of an engine, but are major causes of crankshaft failure.

## Primary Balance

The term "Primary balance" is a major source of confusion in the discussion of engine balance. Please see the below Secondary (Non-sinusoidal) Balance section for the underlying meaning and how this terminology came into popular use.
Primary, "first order" or "first harmonic" balance are supposed to indicate the balancing of items that could shake an engine once in every rotation of the crankshaft, i.e. having the frequency equal to one crank rotation. Secondary or "second order" balance should refer to those items with the frequency of twice in one crank rotation, so there could be tertiary (third order), quaternary (fourth order), quinary (fifth order), etc. balances as well.
The term 'harmonic' comes from simple harmonic motion, and is equivalent to the 'sinusoidal' concept described in the section below.

A cylinder in 4 cycle engines fires once in two crank rotations, generating forces with the frequency of a half the crankshaft speed, so the concept of "half order" vibrations, is sometimes used when the discussion is on the balances on torque generation and compression.

However, it is somewhat customary to discuss only two categories, primary and secondary, in the discussion of engine balance in which 'Primary' is often meant to be all non-secondary imbalance items lumped together regardless of frequency, and 'Secondary' is meant to be the effects of non-sinusoidal component of piston and conrod motions in slider-crank mechanism as described below.

## Secondary (Non-sinusoidal) Balance

When a crank moves 90 degrees from the top dead center (TDC) in a single cylinder engine positioned upright, the bigend up-down position is exactly at the half-way point in the stroke, but the conrod is at the most tilted position at this time, and this tilt angle makes the small-end position to be lower than the half-way point in its stroke.

Because the small-end position is lower than the half-way point of the stroke at 90 degrees and at 270 degrees after TDC, the piston moves less distance when the crank rotates from 90 degrees to 270 degrees after TDC than during the crank rotation from 90 degrees before TDC to 90 degrees after TDC. In other words, a piston must travel a longer distance in its reciprocal movement on the top half of the crank rotation than on the bottom half.

Assuming the crank rotational speed to be constant, this means the reciprocating movement of a piston is faster on the top half than on the bottom half of the crank rotation. Consequently, the inertia force created by the mass of a piston (in its acceleration and deceleration) is stronger in the top half of crank rotation than on the bottom half.

So, an ordinary inline 4 cylinder engine with 180 degrees up-down-down-up crank throws may look like cancelling the upward inertia created by the #1-#4 piston pair with the downward inertia of the #2-#3 pair and vice versa, but in fact the upward inertia is always stronger, and the vibration caused by this imbalance is traditionally called the Secondary Vibration.

When a conrod bigend rotates, its up-down movement (like it is seen from the side of an inline 4 cylinder engine) can be plotted on a graph (with the position on the stroke on Y-axis, rotational position of the crank in degrees on X-axis) with a clean Sine curve, and so this is called the sinusoidal movement. Its left-right changes in position is exactly the same, as it is equivalent to just changing the view point from the side to the top of the engine. However, the up-down position of a conrod small-end (and the piston) does not move in this fashion as described above, thus is considered not sinusoidal.

The inertia force created by this non-sinusoidal reciprocating motion is equivalent to the mass times the acceleration of change in the position, which is expressed as:

$\Delta x = l + r \cos \Delta \alpha \,$

where $\Delta x$ is the change in up-down position, $l$ is the center-to-center conrod length, $r$ is the radius of the crank (i.e. a half of stroke), $\Delta \alpha$ is the change in crank rotational angle from TDC in degrees.

This means the imbalance is proportional to the ratio of conrod length to stroke, i.e. the longer the conrod in relation to stroke, the less this imbalance becomes. Also, inertia force is created not by a steady speed, but by acceleration and deceleration of mass movement, so the strength is proportional to the square of crankshaft rotational speed, making the imbalance particularly speed sensitive.

This non-sinusoidal motion can mathematically be considered as a combination of two hypothetical sinusoidal motions, one with the frequency equal to the crank rotation (equivalent to the piston motion with infinitely long conrod) which is called the 'primary' component, another with double the frequency[2] (equivalent to the effect of conrod tilting angle that lowers the small-end position from when it is upright), which is the 'secondary' component. Although pistons do not move in the fashion defined by either of these two components, it is easier to analyze the motion as a combination of the two. As this method of considering the piston motion in two components became widely accepted in the field of mathematical analysis, the use of the terms primary and secondary became popular outside of academia without a full grasp on the terminologies and the underlying theory.

The vibration caused by this inertia force (or the difference of its strength between the top and bottom half of crank rotation) is small at lower engine speed, but it grows exponentially with the increase in crank rotational speed, making it a major problem in high-revving engines.[note 3] Inline 4, inline 6 and 90 degree V8 engines with flat-plane crankshaft move two pistons always in synch, making the imbalance twice as large (and a half as frequent) as in other configurations that move all pistons in different, evenly spaced, reciprocal phases (e.g. Crossplane inline-four and crossplane V8).

Non-sinusoidal imbalance can almost never be completely cancelled (balanced) with a single-crankshaft multi-cylinder configuration without balancer shafts.[note 4] But boxer engines with many cylinders show the least effect by cancelling all but the (4.) plane imbalance in the cancelling forces.

In designing a balancer for this purpose, it is common to create a sinusoidal force mirroring the hypothetical secondary component with two counter-rotating eccentric weights that rotate at twice the crankshaft speed, as the use of a counter-moving slider-crank as the balancer is less efficient.

## Inherent balance

When comparing piston engines with different configurations in the number of cylinders, the V angle, etc., the term "inherent balance" is used. This term often describes just two categories in the above list that are 'inherent' in the configuration, namely, 3. Phase balance on reciprocating mass, and 13. Phase balance on torque generation.

In rare cases when considering a boxer twin, the categories 4. Plane balance on reciprocating mass, 6. Plane balance on rotating mass and sometimes 14. Plane balance on torque generation are included, however, statements like "A flat-8 boxer engine has a perfect inherent balance"[3] ignore these three categories (as well as 16. Plane imbalance on compression) as flat-8 boxer configuration has inherent imbalance in these four categories by having the left and right banks staggered front to back (not positioned symmetrically in plan view) in the same manner as in boxer twin.

"Inherent mechanical balance" further complicates the discussion in the use of the word 'mechanical' by implying to exclude balances on torque generation and compression for some people (as in the above categorization) while not excluding them for others (as they are the results of mechanical interaction among piston, conrod and crankshaft).

While many items on the above category list are not inherent to a configuration of a multi-cylinder engine, it is safe for a meaningful discussion of inherent balance on multi-cylinder engine configurations to include at least the balances on:

• Reciprocating mass (3.Phase and 4.Plane)
• Rotating mass (6.Plane)
• Torque generation (13.Phase and 14.Plane) and
• Compression (15.Phase and 16.Plane)

### Two cylinder engines

There are three common configurations in two-cylinder engines: parallel-twin; V-twin; and boxer twin (a common form of flat engine).

Secondary imbalance is the strongest on a parallel twin with a 360 degree crankshaft[4] (that otherwise has the advantage of 13. an evenly spaced firing, and lack of 4. & 6. imbalances), which moves two pistons together. Parallel twin with a 180 degree crankshaft[5] (that has the disadvantage of 13. uneven firing spacing and strong 4., 6., 14. & 16. imbalance) produces the vibration a half as strong and twice as frequent. In a V-twin with a shared crank pin (e.g. Ducati 'L-twin'), the strong vibration of the 360°-crank parallel twin is divided into two different directions and phase separated by the same amount of degrees as in the V angle, with 13. unevenly spaced firing as well as the imbalances 4. Plane imbalance on reciprocating mass, 6. Plane imbalance on rotating mass, 14. Plane imbalance on torque generation and 16. Plane imbalance on compression. These four kinds of imbalance are also known as "rocking couple".

BMW R50/2 boxer-twin engine viewed from above, showing the left & right cylinders being offset

A boxer engine is a type of flat engine in which each of a pair of opposing cylinders is on separate crank throws, offset at 180° to its partner, with 13. an evenly spaced firing. If the pistons could lie on the same crank rotational plane, then the design is inherently balanced for the momentum of the pistons. But since they cannot, the design, despite having a perfect 3. phase balance largely cancelling the non-sinusoidal imbalance, inherently has 4., 6., 14. and 16. imbalances due to the crank pin rotating planes being offset.[6]

Fork and Blade conrods. This is the type used on Allison V-1710, which was retrofitted to many racing Merlins post-war.

This offset, the length of which partly determines the strength of the rocking vibration, is the largest on the parallel twin with a 180° crankshaft, and does not exist on a V or a flat engine that has a shared crank pin with "fork and blade" conrods (e.g. Harley-Davidson V-twin engine. See illustration on right). Other configurations fall in between, depending on the bigend and crank web thickness (if it exists in between the throws), and the main bearing width (if it exists in between the throws).

### Three cylinder engines

Inline 3 with 120° crankshaft is the most common three cylinder engine. They have 13. evenly spaced firing and perfect 3. phase balance on reciprocating mass, with 4., 6., 14. and 16. imbalances. Just like in a crossplane V8, these first order rocking couples can be countered with heavy counterweights, and the secondary balance is comparable to, or better than an ordinary inline 4 because there is no piston pairs that move together.

This secondary balance advantage is beneficial for making the engine compact, for there is not as much need for longer conrods, which is one of the reasons for the popularity of modern and smooth turbo-charged inline 3 cylinder engines on compact cars. However, the crankshaft with heavy counterweights tend to make it difficult for the engine to be made sporty (i.e. quick revving up and down) because of the strong flywheel effect.

Unlike in a crossplane V8, the bank of three cylinders have evenly spaced exhaust pulse 240° (120° if two stroke) crank rotational angle apart, so a simple three-into-one exhaust manifold can be used for uniform scavenging of exhaust (needed for uniform intake filling of cylinders, which is important for 11. Uniform amount of torque generated and 12. Uniform timing of torque generation), further contributing to the size advantage.

### Four cylinder engines

Inline-4, flat-4 and V4 are the common types of four cylinder engine. Normal inline-4 configuration[note 5] has very little rocking couples that often results in smooth middle rpm range, but the secondary imbalance, which is undesirable for high rpm, is large due to two pistons always moving together. The rotational vibration on X-axis, which is often felt during idling, tend to be large because, in addition to the non-overlapping power stroke inherent in engines with 4 or less number of cylinders, the height imbalance on conrods' CG swinging left and right[note 2] is amplified due to two conrods moving together.

Ordinary Flat-4 boxer engines[note 6] have excellent secondary balance at the expense of rocking couples due to opposing pistons being staggered (offset front to back). The above mentioned rotational vibration on X-axis[note 2] is much smaller than an inline-4 because the pairs of conrods swinging up and down together move at different CG heights (different left-right position in this case). Another important imbalance somewhat inherent to boxer-four that is often not dialed out in the design is its irregular exhaust pulse on one bank of two cylinders. Please see flat-four burble explanation part of flat-four article on this exhaust requirement similar to the crossplane V8 exhaust peculiarity.

V4 engines come in vastly different configurations in terms of the 'V' angle and crankshaft shapes. Lancia Fulvia V4 engines with narrow V angle have crank pin phase offset corresponding to the V angle, so the firing spacing (phase pattern) is exactly like an ordinary inline-four. But some V4s have irregular firing spacing, and each design needs to be considered separately in terms of all the balancing items.
For example, Honda VFR1200F engine basically is a transversely mounted 76° V4 with a 360° shared-crank-pin crankshaft, but the conrod orientation is an unusual front-rear-rear-front (as opposed to the normal fore-aft-fore-aft) with much wider bore spacing (distance between cylinder centers) on the front bank than on the rear, which results in significantly reduced rocking couples at the expense of wider engine width. Furthermore, the shared crank pin is split and has 28° phase offset, resulting in 256°-104°-256°-104° firing spacing, which is irregular within a 360° crankshaft rotation but evenly distributed from one rotation to another. This compares to a 90° V4 with 180° crankshaft (e.g. Honda RC36 engine) that has 180°-270°-180°-90° firing spaced unevenly within 360 degrees and within 720 degrees of crankshaft rotation.[7]

### Five cylinder engines

Inline five cylinder (L5) engine, with crank throws at 72° phase shift to each other, is the common five cylinder configuration. (Notable exceptions are Honda racing V5, and Volkswagen VR5 engine.) These typical L5 engines have 13. Evenly spaced firing and perfect 3. Phase balance on reciprocating mass, with 4. Plane imbalance on reciprocating mass, 6. Plane imbalance on rotating mass, 14. Plane imbalance on torque generation, and 16. Plane imbalance on compression. Just like in inline 3 engines above, these first order rocking couples can be countered with heavy counterweights, and the secondary balance is comparable to, or better than an ordinary inline 6 because there is no piston pairs that move together.

Compared to three and four cylinder designs, a major advantage in 4-stroke format is the overlap in power stroke, where the combustion at every 144° of crank rotation ensures a continuous driving torque, which, while not as much noticeable at high rpm, translates to a much smoother idle.

Modern examples such as the 2013 Audi RS3 engine have undersquare design, because the advantage in secondary balance allows it to have longer stroke without sacrificing the higher rpm smoothness, which is desirable for a smaller bore that results in shorter engine length. Honda G20A also with an undersquare design, was originally introduced with a balance shaft driven at the crankshaft speed to counter the wiggling vibration caused by the 6. Plane imbalance on rotating mass, but it evolved into 2.5 Liter G25A with heavier counterweights that does not have the balancer.

### Inline six cylinder engines

Inline 6 normally has crank throws at 120° phase shift to each other with two pistons at about equal distance to the center of the engine (#1 and #6 cylinders, #2 and #5, #3 and #4) always moving together, which results in superb plane balance on reciprocating mass (4.) and rotating mass (6.) in addition to the perfect phase balances 3., 5., 13. and 15.. Combined with the overlapping torque generation at every 120° of crankshaft rotation, it often results in a very smooth engine at idle. However, the piston pairs that move together tend to make secondary imbalance strong at high rpm, and the long length configuration can be a cause for crankshaft and camshaft torsional vibration, often requiring a torsional damper. The long length of the engine often calls for a smaller bore and longer stroke for a given cylinder displacement, which is another cause for large secondary imbalance unless designed with otherwise-unnecessary long conrods that further increase engine height. Moreover, 4-stroke inline 6 engines inherently have 14. (Plane imbalance on torque generation) and 16. (Plane imbalance on compression), which are typically more or less balanced on V12 and Flat-12 configurations.

In terms of firing spacing, these typical inline 6 are like two inline 3 engines connected in the middle, so the firing interval is evenly distributed within the front three cylinders and within the back three, with equal 240° spacing within the trio and 120° phase shift to each other. So three-into-one exhaust manifolds on the front and on the rear three cylinders, with each of them then connected with a two-into-one pipe results in 120° (240° if not merged in a dual exhaust system) evenly distributed exhaust pulse.
Intake pulse, which is also important to have equal spacing for evenly filling the cylinders with the same volume and mixture of intake charge for 11. (uniform amount of torque) and 12. (uniform timing in torque generation), is formed the same way, so two carburetors or throttle bodies on two one-into-three intake manifolds each on the front and the rear three cylinders (strictly speaking when the three runner lengths are equal) results in evenly spaced intake pulse. Jaguar XK inline 6 had three SU carburettors each serving the front two, middle two and the rear two cylinders in the later models, which resulted in unevenly distributed intake pulse at the front and the rear carburetors (the middle carb gets an evenly spaced pulse at 360° interval). This configuration, while resulting in higher power due to the increased total flow capacity of the carburetors than the earlier evenly-spaced-pulse twin carburetor configuration, may have contributed to the later 4.2 Liter version's "rougher running" reputation compared to the legendary 3.4 and 3.8 Liter versions.
Modern inline six engines with fuel injection (including Diesels) normally have equal length intake runners connecting the intake ports to (often protruding into) a plenum (See Inlet manifold for parts descriptions) to keep intake pulse evenly spaced.

### V6 engines

V6 engines with un-split shared crank pin can have equally spaced firing when the V-angle is at 120° (60° or 120° for 2-stroke). However, the 120° bank angle makes the engine rather wide, so production V6 tend to use 60° angle with a crank pin that is offset 60° for the opposing cylinders. As offsetting the crank pin for as much as 60° no longer provides overlap in the diameter of the crank pin, the actual pin is not really an offset 'split' pin, but normally is completely separate in two parts with a thin crank web connecting the two individual pins. This makes the crankshaft structurally weaker, much more so than in the crankshaft with slight offset seen on the Lancia Fulvia V4 with 10.5° to 13° offset, so racing V6 engines from Carlo Chiti-designed 1961 Ferrari 156 engine to Cosworth GBA for Formula One often used the 120° bank angle to avoid this weakness, unless required by the formula as in all the 2014 - 2015 Formula One 1.6 Liter turbo V6 engines that has 90° bank angle according to the regulation.[8]

60° V6 is compact in length, width and height, which is advantageous for rigidity and weight. The short crankshaft length mitigates the torsional vibration problem, and secondary balance is better than in an inline 6 because there is no piston pair that move together. Furthermore, each bank of three cylinders have evenly spaced induction/ignition interval, so the intake/exhaust system advantage is shared with inline 3. However, these advantages come at the price of having plane imbalances on 4. rotating mass, 6. reciprocating mass, 14. torque generation, and 16. compression. Also, the left and the right banks being staggered (for the thickness of a conrod plus the thin crank web) makes the reciprocating mass plane imbalance more difficult to be countered with heavy counterweights than in inline 3. But when the engine and engine mounts are properly designed, it makes a smooth powerplant like Alfa Romeo V6 engines which have counterweighted webs in between the 'split' crank pins that are as thick as crank arms.

90° V6 sometimes were designed like chopping 2 cylinders off common V8 engines to share production tooling (e.g. General Motors 90° V6 engines up to 229 CID with 18° offset crankshaft and uneven firing interval), but newer examples (e.g. Honda C Series engines that evolved from not having a balancer to the 3.5 Liter version with a balance shaft.) are dedicated designs with 30° offset crank pins that result in even combustion spacing. Compared to 60° V6, the offset crank pins could have overlap in the diameter of the pin, and the V angle coincides with the angle of mean directions of conrods swinging left and right in each bank. It also shares the four (4., 6., 14. and 16.) plane imbalances and the staggered cylinders, but there is the secondary balance advantage over inline 6 as well.

## Steam locomotives

Steam locomotives commonly have balancing weights on the driving wheels to control wheel hammer caused by the up and down motion of the coupling rods and, to some degree, the connecting rods.

## Notes

1. ^ a b Crankshaft rotating axis is referred to as the X-axis, the horizontal line perpendicular to it is referred to as the Y-axis, and the up-down line perpendicular to X and Y axis is called the Z-axis
2. ^ a b c When a conrod swings left on the top half of crank rotation, another swings right on the bottom half, with the conrod CG heights located as much as the piston stroke apart. When the CG is located at different heights, the swing motion to the left cannot cancel the swing motion to the right, and a rotational vibration is introduced.
3. ^ In an early BRM study, a longer conrod design accounted for up to 5% increase in maximum horse power on a 1.5L GP engine due to the energy wasted in the vibration.
4. ^ It is theoretically possible to completely cancel secondary imbalance with unusual flat-4, flat-8, flat-16, etc. boxer configurations where one bank of cylinders are divided equally into two groups, with one group staggered to the front, and the other group staggered to the rear in mating with the opposite bank. But this arrangement leaves a large gap in between the two groups of cylinders, which is not desirable for size and thermal balance points of view.
5. ^ Normal inline-four has up-down-down-up crank throws. See crossplane inline-four for unusual up-left-right-down or similar crank throws.
6. ^ 'Ordinary' means left-right-right-left crank throws.

## References

Citations
1. ^ Foale, Tony, Some science of balance p. 2, Fig. 2a
2. ^ Foale, Tony, Some science of balance p. 4, Fig. 4. Reciprocating Forces, Piston motion = Red, Primary = Blue, Secondary = Green
3. ^
4. ^ Foale, Tony, Some science of balance, p. 6, Fig. 13. 360°-crank parallel twin
5. ^ Foale, Tony, Some science of balance p. 6, Fig. 13. 180°-crank parallel twin
6. ^ Foale, Tony, Some science of balance p. 17, Fig. 14. Plane offset
7. ^ Sagawa, Kentaro. "VFR1200F, Real value of the progress (in Japanese)". Retrieved 2014-02-09.
8. ^ Fédération Internationale de l’Automobile (2014-01-23). "2014 FORMULA ONE TECHNICAL REGULATIONS". Article 5.1.7 on p.21. Retrieved 2014-02-27.
Sources
• Foale, Tony. "Some science of balance" (pdf). Tony Foale Designs: Benidoleig, Alicante, Spain. Archived from the original on 2013-12-27. Retrieved 2013-11-04.
• Taylor, Charles Fayette (1985). The Internal Combustion Engine in Theory and Practice. Vol. 2: Combustion, Fuels, Materials, Design. Massachusetts: The MIT Press. p. 299. ISBN 0-262-70027-1.