      # Inertia Forces and Moments in Racing Engines

8 replies to this topic

### #1 blueprint2002

blueprint2002
• • Member

• 142 posts
• Joined: May 19

Posted 10 July 2020 - 01:09

Those who have acquired an engineering degree or diploma, may recall the standard analysis of the inertia forces which result from the reciprocating motion of the piston. Briefly, the position of the piston along the line of stroke is described mathematically (using trigonometric ratios), and this is then differentiated twice to obtain expressions, first for the velocity, and finally the acceleration. The last when multiplied by the mass of the reciprocating parts gives the inertia force, acting along the line of stroke, and all these values may be calculated for any angular position of the crank. The exact mathematics is unmanageably cumbersome, so certain simplifying assumptions are made, which reduce the final form of the equations to just two terms, described as the primary and the secondary, respectively. Those assumptions are themselves based on the average values of certain engine dimensions, which are usual in the greatest number of cases (which means mostly automotive engines, numerically the overwhelming majority).

Using this expression for the inertia forces acting on one piston, the resultant for any number of cylinders, and for any configuration (in-line, V etc) can be calculated, and the best arrangement of the cranks (from the viewpoint of balance of forces) decided. This has been done for a century or more, and I believe still continues to be done.

But to the best of my knowledge, no analysis has been done for the force that acts transversely, or at right angles to the line of stroke. This force is of course the result of the angle which the connecting rod makes with the line of stroke, (which is zero only at TDC and BDC), and known as the side thrust of the piston. It is possible that when the analysis was first carried out, the rather long connecting rods that were then common, meant that the side thrust was too small to be of concern, at least in comparison with those described above.

However, it seems possible, or even probable, that the extremely short connecting rods that are used in modern racing engines make this assumption invalid, in which case there must now be a method to calculate it over the entire cycle. Anyone know of a text or a technical paper that addresses this subject? (I’m sure there must be software that does this, but “black box” solutions are not what I am looking for).

### #2 Greg Locock

Greg Locock
• • Member

• 5,870 posts
• Joined: March 03

Posted 10 July 2020 - 01:44

"I believe still continues to be done"

You bet

"But to the best of my knowledge, no analysis has been done for the force that acts transversely, or at right angles to the line of stroke"

Wrong.

Typically the piston manufacturer will be heavily involved, but any software such as MSC ADAMS/Engine can calculate the exact forces throughout the cycle, given cylinder pressure. If you don't like that do a co-sim with a combustion model.

https://www.scienced...888327014004610

is the first hit i got, don't know if it is any good. I'm away from my textbooks but I'd be surprised if Heywood doesn't mention it. Skirt design is crucial for piston slap, cooling and efficiency.

### #3 manolis

manolis
• • Member

• 924 posts
• Joined: May 03

Posted 10 July 2020 - 03:16

Hello Blueprint2002.

You write:

The exact mathematics is unmanageably cumbersome, so certain simplifying assumptions are made, which reduce the final form of the equations to just two terms, described as the primary and the secondary, respectively.

The mathematics are quite simple. You can’t imagine how simple they are (the Pythagorean theorem, some simple trigonometry and open mind is all it takes; we talk for arithmetic analysis).

And you do not need to limit yourself in just two terms (those of first and second order).

A couple of dozens of years ago the Balance program was written in Quick Basic (which means it requires DOS environment to run); and does exactly this: it calculates – step by step – all forces (along the cylinder axis, and normal to the cylinder axis), as well as the inertia torque and the inertia moments; for any cylinder arrangement; it makes also the Fourier analysis (and controlled re-synthesis) of the inertia forces, torque and moments; it also introduces external balance shafts rotating at various speeds and calculates the balancing of the engine with and without them.

The precision of the calculations is as high as you like (you can select steps of one crankshaft degree, or of, say, 0.01 crankshaft degrees).

The general idea is:

take the “piston – connecting rod – crankshaft” linkage at an initial position,

then turn the crankshaft for one degree (if one degree is the selected step), calculate the new position of the piston / connecting rod / crankpin and store the values in an array, repeat for one more step of crankshaft rotation,

and so on,

until a complete rotation of the crankshaft is done.

Selecting the revs (rpm) the engine operates, the time required for one step is defined.

Then, using the values stored in the array, they are calculated the resulting velocities and accelerations of the moving parts by simply applying the definition of the velocity and acceleration: if the time for one step is t and the difference of two consecutive piston positions along the cylinder axis is d, the velocity of the piston during this transition is v=d/t; having the velocity for each step, the acceleration is calculated: it is the difference of the velocities in two successive steps divided by the time required for one step.

Having the acceleration of the piston for each step of crank rotation, the required inertia force on the piston is calculated: it is nothing but the product of the piston “mass” times the acceleration of the piston (“required", because it is the force that causes the calculated acceleration).

Calculating  the leaning (the angle) of the connecting rod with the cylinder axis for each step of crank rotation, the previously calculated inertia force acting on the piston gives the resulting trust force normal to the cylinder axis.

Knowing the force normal to the cylinder axis for each step of the crank rotation, the inertia torque is calculated by multiplying it by the distance of the piston pin from the crankshaft rotation axis.

The previous calculations are for all orders, not only for the first and second order.

Having the previous calculations for a single piston, we proceed easily to any multi-cylinder arrangement by applying simple maths. Think how.

Having the inertia forces, inertia torque and inertia moments for every step of crankshaft rotation, the Fourier analysis can be applied to focus only on one order (or a few orders) of them.

You also write:

But to the best of my knowledge, no analysis has been done for the force that acts transversely, or at right angles to the line of stroke. This force is of course the result of the angle which the connecting rod makes with the line of stroke, (which is zero only at TDC and BDC), and known as the side thrust of the piston. It is possible that when the analysis was first carried out, the rather long connecting rods that were then common, meant that the side thrust was too small to be of concern, at least in comparison with those described above.”

The balance program (at http://pattakon.com/pattakonEduc.htm ) does all these and presents them in animations.

For instance, it shows how the inertia thrust force (normal to the cylinder axis) increases and degrees as the crankshaft rotates, also what inertia torque results etc, etc.

If you want the code of the balance program (and even better, if you have the time and the background to transfer it to Visual Basic), just let me know.

Some slides from the BalanceEXE program explaining the previous:           Thanks

Manolis Pattakos

Edited by manolis, 10 July 2020 - 03:17.

### #4 manolis

manolis
• • Member

• 924 posts
• Joined: May 03

Posted 11 July 2020 - 03:39

Hello Blueprint2002

You write:

"However, it seems possible, or even probable, that the extremely short connecting rods that are used in modern racing engines make this assumption invalid, in which case there must now be a method to calculate it over the entire cycle. Anyone know of a text or a technical paper that addresses this subject? (I’m sure there must be software that does this, but “black box” solutions are not what I am looking for)."

Among the inputs of the balance program are the piston stroke and the connecting rod length (center to center length).

For instance you can use:

Conrod to stroke ratio 2.5.

Used in some Diesel engines and in some high revving (20,000rpm) racing (F1) engines (piston stroke 40mm, conrod length: 100mm).

Conrod to stroke ratio 2.0

Say, piston stroke 90mm, connecting rod length (from center to center) 180mm.

The relatively long connecting rods reduce the 2nd order inertia vibrations and the thrust loads between the cylinder and the piston.

Conrod to stroke ratio 1.0

Piston stroke 3,468mm, connecting rod length 3,468mm.

It is the Wartsila X92 (a moderrn giant 2-stroke cross-head Marine Diesel engine having over 50% BTE (Brake Thermal Efficiency)).

The extra-short connecting rod reduces the overall height of the engine without spoiling the fuel efficiency (cross-head design): Conrod to stroke ratio 1.5

Piston stroke 70mm, connecting rod length 105mm (conrod to stroke ratio 1.5) not unsusual in racing and (older) normal engines.

Con-rod to piston-stroke ratio 1.35

Piston stroke 30mm, connecting rod length 40.5mm, used in some OPRE Tilting Opposed Piston engines ( http://pattakon.com/...akonTilting.htm ) . The pulling rod architecture combined with the extra-short con-rod substantially increases (by some 40%) the piston dwell around the combustion dead center offering time for more efficient combustion (the combustion has time to complete at high-expansion-ratios): Conrod to piston stroke 1000.

Piston stroke: 100mm, connecting rod length 100,000mm (100m). It simulates a pure sinusoidal (harmonic) engine that eliminates the thrust loads and the 2nd order free inertia forces (as the following PatTwo engine / more at http://pattakon.com/pattakonPatTwo.htm ) : All above cases (in any cylinder arrangement) can be presented / analyzed with the BalanceEXE program.

Thanks

Manolis Pattakos

### #5 blueprint2002

blueprint2002
• • Member

• 142 posts
• Joined: May 19

Posted 12 July 2020 - 01:17

Thanks Greg and Manolis. Appreciate your responses.

You have both confirmed what I only suspected: that software exists to tackle this otherwise difficult task.

And Manolis has explained in detail how this is achieved: by repeated calculation at successive crank positions, based on the linkage geometry.

No doubt at all that the results thus obtained are sufficiently accurate, but I would still like to know if there is an analytical way of doing it!

### #6 manolis

manolis
• • Member

• 924 posts
• Joined: May 03

Posted 12 July 2020 - 04:37

Hello Blueprint2002

You write:

"No doubt at all that the results thus obtained are sufficiently accurate, but I would still like to know if there is an analytical way of doing it! "

As you decrease the size of the step, the arithmetic method gets as precise as you like.

With one degree “crankshaft angle” steps, it is already more precise than the analytical method if you limit the latter in a few lower “orders” (or terms).

For instance, if you keep only the first and second orders of the analytical method, you miss the third and fourth orders of the Inertia Torque as calculated with the arithmetic method: Any difference or error (in either method) has to do not with the method used, but with the assumptions made.

For instance, how “exactly” is distributed the mass of the connecting rod?

For instance, how the clearance between the piston and the bore affects piston’s motion?

For instance, are the oil droplets on the piston taken into account?

The "Internal Combustion Engine in Theory and Practice" of Charles Fayette Taylor (MIT / Sloan Laboratories) describes the analytical method you are looking for.

The following image is taken from Taylor’s book: If you think that the combustion itself has a lot of “uncertainty” (when and where it exactly starts? how long (in crankshaft degrees) it takes to burn the first 2% of the fuel trapped in the cylinder? how the peak pressure “plays” from cycle to cycle? how the combustion front expands and where it fades out? etc, etc), the above “pressure vs crankshaft angle” plot from Taylor’s book is just indicative of the reality.

So, do you really need more accuracy?

To put it differently:

If you reply: “it is 72.86536858998Kg”, something is wrong; it may seem precise, but it is meaningless.

More correct is to say: it is 72.9Kg.

Thanks

Manolis Pattakos

Edited by manolis, 12 July 2020 - 04:38.

### #7 blueprint2002

blueprint2002
• • Member

• 142 posts
• Joined: May 19

Posted 13 July 2020 - 14:53

To put it differently:

If you reply: “it is 72.86536858998Kg”, something is wrong; it may seem precise, but it is meaningless.

More correct is to say: it is 72.9Kg.

Or 73 Kg. Thank you, Manolis.

### #8 gruntguru

gruntguru
• • Member

• 7,079 posts
• Joined: January 09

Posted 14 July 2020 - 03:25

No way. I definitely weigh less than 73 kg.

### #9 manolis

manolis
• • Member

• 924 posts
• Joined: May 03

Posted 15 July 2020 - 03:42

Hello Gruntguru.

Most people don't really get how the "a little less than 73Kg" and the "73Kg" and the "72.9Kg" are all more "correct" than the "72.86536858998Kg".

For the arithmentic method it would be interesting to demonstrate how precise it is by writing "a dozen lines program" to calculate and present the path of a planet moving around the sun, given its initial distance from the sun and its initial velocity.

And even more interesting it would be to extend the "short" (high school) program in calculating the paths of two or more interacting-with-each-other planets as they orbit around the sun.

Isaak Newton did try to solve such a case by applying "his own laws", but he dropped the project because the calculations required were too many and time consuming: at his time there were no computers to make the "stupid" wotk: the arithmetic calculations). But since there is no interest, let's forget it.

By the way, another discussion waits for your response.

Thanks

Manolis Pattakos