Flywheel Theory   
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   By Cotten 
This workshop is a compilation of discussions from the Virtual Indian List relating to repair services on Indian crank assemblies. The discussion that led up to the Flywheel Workshop deals primarily with practical theory behind motor balancing for a V-twin. This is where you are now.
Extensive editing was necessary to condense the wealth of posts on these subjects. Juxtaposing posts and grammatical changes have been made in order to resemble syntax. My apologies for the liberties I have taken, and to those of you whose very pertinent posts were still squeezed out.

On this page: Basic Theory.
Page2: Balancing. Page 3: Chassis Stiffness. Page 4: Balance Factors. Page 5: Crankshaft Windup.
From: Cotten <>
When I read the military manual method, which was apparently the same as your 741/640B manual, I proceeded to back calculate factors whenever a Chief came in for rebuild. Usually they figured about 65%, which our posts last year confirmed as appropriate. The arbitrary addition of weight in the Q&A book is no more confusing than some of the primitive Milwaukee speed balancing recipes, where a prescribed number of holes of a given size were to be drilled, independent of piston mass, and actual knife-edge trials weren't even mentioned.
Bless the forgiving nature of the V-twin design! Harmonics and vibrations aside, balancing seems to affect the performance of a motor as much as anything. I have found that low factored Milwaukee machines jump like dirtbikes with a short powerband, while high factored ones pull rpm slower, but useable over a much larger range of rpm. Balancing is apparently a tuning procedure for simple single crankpin motors, whereas opposed or multiple throw motors require accurate factoring to prevent them from pulling themselves apart.
Anyone else see it this way?

From: Duff <>
Na, you (Cotten) are not the last to find this out! I'll give you a hint, you may take a set of Indian rods, weigh them by supporting the rod by the wrist pin. Let the big end sit on a gram scale and get it's weight, do the same for both rods. The weight is then used for the recip total
weight like piston complete etc. This get ya around 64% which is about what Indian's end's up with.

From: Cotten <>
That's been my experience also. There is a lot of methods of supporting the rod for weighing: platforms,thread, even roller bearings on a lab apparatus. I have even whipped up a spirit level with nylon pucks to slip into the rod ends to set up for perfect level when weighed. It's a bit of overkill, when I can often resort to what I call the "Clymer" method: After washing all lube out of the crank, I found that I can set the entire flywheel assembly on a v-block on my scale table, and then rotate the crankpin position to where the rod is level when laying on the scale pan. Care must be taken to center the rods, and the other rod must not interfere. And the rod end must sit square and center on the pan. I obtain rodtop weights that are quite close to readings on the disassembled rod. (Face it, a coupla grams inaccuracy isn't a lot of final factor)
Of course, I usually only resort to this when someone brings me a trued assembly, and then usually for a check of balance factor.
From: Matthias Elvenkemper <>
Listers, Cotten offers a good example with the comparison of low and high factored Milwaukie bikes. Multiple throw motors (e.g. four cylinder inline) have little problems with vibrations caused by first order momentum because these are balanced by the offset crank. What counts in multiple throw motors is picky choosing rods and pistons for equal weight because differences cause vibrations caused by second (and higher) order momentum that can be very nasty.
A single crankpin motor produces vibrations caused by reciprocating (up and down) forces and rotating (fore and aft) forces. The up and down forces are produced by the pistons (with pin, retainers, rings) and the reciprocating mass (upper part) of the rods. The longer the rods (weight equal) the higher the reciprocating mass.
The balance factor determines the ratio of "up and down" versus "fore and aft" vibrations.
In practice (apart from the r.p.m. range where the "worst" vibrations occur) the "desirable" ratio of up and down vs. fore and aft vibrations depends to a large extend on the frame design and how the motor is fixed to the frame.
In all single crankpin motors ALL of the rotating masses are balanced by the flywheel counterweight. Plus part of the reciprocating masses are balanced.

The "balance factor" is the percentage of the reciprocating masses being balanced by flywheel counterweight.

A motor with low balance factor thus vibrates up and down a lot and vibrates fore and aft a little. The extreme case would be a vertically mounted single cylinder motor with ZERO balance factor (only rotating masses balanced). This motor vibrates only up and down. The same motor 100% balanced would only vibrate fore and aft. The basics apply to V-Twins as well, with other things equal the wider the cylinder angle the more the motor vibrates fore and aft. Thus: An identical flywheel assembly put in different cylinder angle motors would have a different balance factor.
Kinematics (the angle of the rod on the downstroke) play the role here.
Practical example: Late Indian Sport Scouts have a balance factor of 82%. If you put Sport Scout flywheels rods and pistons in 45 degree cases the balance factor rises to a little over 84%. This small difference would be only noticable in racing motors if at all.

However: Theory fits Cotten's Milwaukie bikes comparison perfectly. The low factored bike accelerates fast (other things equal due to the weight of flywheels being lower with less counterweight) but has a limited r.p.m. range because reciprocating masses cause bad up and down vibrations when reaching higher r.p.m. The same bike high factored accelerates slower (other things equal due to higher weight of flywheels with heavier counterweight) but has a broader usable r.p.m. range because bad vibrations occur at much higher r.p.m.
Also (I think) this explains why Indian had a lower balance factor on the Chief compared to the Sport Scout. The essence of the Chief is "you can't beat cubes" low end torque which makes it a good puller at low r.p.m. The long stroke of the Chief would prohibit high r.p.m anyway because of dangerous piston speeds. So it would not make sense to choose a high balance factor.

The essence of the 45 101 and Sport Scout is trading cubes and low end torque for power at high r.p.m. This is no threat for motor life because piston speed in a 45" Scout is approx. 27% lower than in a 74" Chief. So it was logical to choose a high balance factor to support the (piston speed wise) ability to stand high r.p.m.

From: Guy <>
Mat - thank you for your efforts, and you do a great job in English, so please don't take this as criticism, just a helping hand..."momentum" = mass x velocity, you may have meant "moment" (force x distance), but I think first order "couples" is a more proper terminology (actually I think V-twins have an engine vibration phenomena described as a "rocking couple")...

I looked up my info on balance factors, a dynamic shop used 52% to 56% (but I think this is apples & oranges)...S&S uses 60% for static...of course their wheels are lighter than it seems reasonable that "low" factors are used with lighter wheels for quicker revs, and vice-versa, heavy wheels and higher factor....I still have an unsettled feeling that some of these "factor" equations are using different input, so that 85% may be70% by a different definition.
From: "Dave Clements" <>
Guy: Rocking couple is only found in v twins that have the rods side by side not in engines with male and female rods.

From: Matthias Elvenkemper <>
It is clear that the balancing method shown in the Indian manuals is better than nothing. And it might be overengineering to do more on the low r.p.m. Chief motor if you are sure that both flywheel sides are a matching pair. If left and right flywheel have different center of gravity you can not find out with the static method. Even if you do the job perfect the flywheels will stagger when running and cause more vibrations than nessessary.

From: Cotten <>
I found a copy of a page out of a loose-bound Milwaukee manual that outlines a static balance method that requires the centerpoint of 'balance' for each rod be measured so as to determine the weight of the top of the rod by proportional distance. The rod is balanced upon a knife edge and marked at its center of gravity. The distance between this and the wristpin bore center is measured, as well as the total center-to-center (wristpin to crankpin) distance. The reciprocating weight of the rod is then determined by multiplying the total weight of the rod by the marked distance, and then dividing by the total center-to-center distance.
Am I the last to learn of this? It does not seem to reproduce my 'hanging' method of determining the weight of the rod. (Even more confusing is that it calls for a factor of 50%.) Any clues?

From: Guy <>
Good info, Cotten - I've not seen it....I think the problem with determining the rod centroid this way is with actually being able to balance it on a knife edge, marking it, and then measuring....before/during/after balancing my Shovelhead stroker, I was paying attention to my car hot rod mags....the hot rod aftermarket performance industry (per the photos - no text) uses
the hanging method....I was able to use the hanging method and weigh each end of the rod and the sum of those ends equalled the total rod weight - mathematically, both methods should give the same result....50% factor doesn't surprise me (the quoted 85% does!) some balance shops use 52-56% of reciprocating wt in dynamic balance approach,  S & S quotes 60% of recip wt for their wheels....I think there is still much confusion (in my mind anyway) as to whether these various static balance recipes use consistent definitions and, I'm still looking for some info to establish what static balance % to use on Indians when using what I consider to be a "correct" definition (ie, clear separation of rotating vs reciprocating wt....100% rotating wt plus  ____% recip wt, the sum divided by two and bob wt placed on each wheel).
Also, I'm unsure of the practical effect on balancing when we have a heavy drive-side wheel & lighter pinion-side wheel (stock HD) vs both wheels weighing the same (T&O, S&S, modified HD)...

From: Matthias Elvenkemper <>
Cotten, the formula you mention gives you the ROTATING mass of the rod not the reciprocating!
This method has been used for decades, it is a good approximation for determining reciprocating and rotating mass of rods though there are more accurate methods. Of course it does NOT call for a balance factor of 50%.

From: Cotten <>
Now I am really confused! Is not the top of the rods (in effect) the reciprocating mass, and the crank end (in effect) the rotating mass?

From: Matthias Elvenkemper <>
Cotten,you are right that top end of rod is (in effect) reciprocating mass and crank end is in (effect) rotating mass. I don't understand why you are confused. Let's put forth your formula mathematically:

You described the formula you found in the HD manual as follows:
"The rod is balanced upon a knife edge and marked at its center of gravity. The distance between this and the wristpin bore center is measured, as well as the total center-to-center (wristpin to crankpin) distance. The reciprocating weight of the rod is then determined by multiplying the total weight of the rod by the marked distance, and then dividing by the total center-to-center distance."

I used the following symbols:
"REC.W" means reciprocating weight (of rod)
"ROT.W" means rotating weight (of rod)
"TW" means total weight
"D-REC" means distance from center of gravity to center of wristpin bore
"TL" means total length of rod (from center to center of bores)

Thus your formula is:

Assume rod A of my example: TW = 500 grams, TL = 20 cm
D-REC = 14 cm

With your formula you get:
ROT.W = 500 grams x 14 / 20
ROT.W = 350 grams

For reciprocating weight you get the same as in my "direct" formula for REC.W :
REC.W = 500 grams - 350 grams
REC.W = 150 grams

The "direct" formula for calculating the reciprocating weight of the rod which is widely used gives (of course the same results):

REC.W = TW x ( 1 - D-REC / TL )
REC.W = 500 grams x ( 1 - 14 / 20 )
REC.W = 500 grams x 0.3
REC.W = 150 grams

quod erat demonstrandum

So as I said the formula you mentioned gives rotating mass of rod. Subtract from total rod weight and you have reciprocating mass of rod. Get the same result from the "direct" formula for reciprocating mass I mentioned.

Hope this stops the confusion...Mat

From: Cotten <>
Mat! My confusion hits me at this step:
The H-D method figured "The reciprocating weight of the rod is then determined by multiplying the total weight of the rod by the marked distance, and then dividing by the total center-to-center distance."

But you symbolized it as:
Thus your formula is:

It seems like I said:

From: Matthias Elvenkemper <>
The formula in your HD manual has a typo (slip). This error is the source of confusion and I should have pointed out the slip.
You are right if you formalize what the HD manual says as:

But this is wrong! TW x D-REC / TL gives the rotating mass!
Each rod that I know of has higher rotating mass than reciprocating mass which is logical because more mass is concentrated near and around the massive (rotating) crankpin. A lot less mass is concentrated near and around the skinny (reciprocating) wristpin.
Again, I am sure the source of the confusion is the typo in the
HD manual.

Cotten wrote:
> Mat! I did overlook the obvious! D-REC will always be the longer portion of the rod. (and thanx for saving my self-esteem!)

From: Guy <>
Thanks, we're getting somewhere....This is exactly the  method that I use as recommended by S&S (except I use "hanging" method of rod weighing)...I then multiply the recip wt by 60%, add it to 100% of the rotating wt, divide the sum by 2 and put that wt on each flywheel via bob wts to balance them separately....

As an engineer I appreciate that this is the most "scientific" approach to STATIC balancing, but we must keep in mind that underlying assumptions - such as that the lower 50% of the rod wt is rotating wt and not reciprocating wt are not strictly true but useful simplifications so we can solve the problem.....and with those assumptions, as well as other engine component characteristics and RPM range, we EMPIRICALLY determine acceptable balance factors....
So, now that we know we're both using the term "balance factor" the same questions remain:

what is there about Indian Chiefs that requires an 85% balance factor when HD, T&O, S&S, and others use 50% to 55% to 60% on HD big twins (and sporties)??

What does S&S recommend for big Indians??

Do Scouts really need to be balanced differently from Chiefs?

If the referenced "50%" is not a balance factor, what is it?

From: Matthias Elvenkemper <>
Guy, many misunderstandings are due to a wrong understanding of the term "balance factor". The one and only worldwide used definition is: The percentage of total reciprocating weight balanced by the counterweight in the flywheels.

Total reciprocating weight is both pistons (plus rings, pins, retaining rings) plus the reciprocating weight of the rods.

This is the process:
It is essential that you know the balance factor that the motor should have.

- weigh the rods
- measure length of rods (from center of
    crankpin bore to center of wristpin bore)
- balance rod on knife edge
- mark the center of gravity
- measure distance between this and center of wristpin bore

"REC.W" means reciprocating weight (of rod)
"ROT.W" means rotating weight (of rod)
"TW" means total weight
"D-REC" means distance from center of gravity to center of wristpin bore
"TL" means total length of rod (from center to center of bores)

The formula for calculating the reciprocating weight of the rod is:

REC.W = TW x ( 1 - D-REC / TL )

Subtract reciprocating weight from total weight gives you rotating weight:


Calculate reciprocating weight of both rods.
Total reciprocation weight is the sum of REC.W of both rods
plus the weight of both pistons with wristpin, rings, retaining rings.

The BALANCE FACTOR is the percentage of total reciprocating weight balanced by the flywheel counterweight.

It is clear that when you balance a rod on a knife edge 50% of the weight will be on the left and the other 50% will be on the right, don't get it wrong here: What counts is the weight distribution of the rod!

For example: Imagine two rods of identical weight:
TW = 500 grams
and identical length:
TL = 20 cm (centimeters).
You put both rods on a knife edge and measure D-REC 14 cm for rod A and D-REC 12 cm for rod B.

Calculate reciprocating weight of rod A and rod B with the formula:

rod A:
REC.W = 500g x ( 1 - 14 / 20 )
REC.W = 500g x ( 1 - 0.7 )
REC.W = 500g x 0.3
REC.W = 150g

rod B:
REC.W = 500g x ( 1 - 12 / 20 )
REC.W = 500g x ( 1 - 0.6 )
REC.W = 500g x 0.4
REC.W = 200g

The results are intuitively evident. Rod A  has a lower reciprocating weight because more of its weight is distributed around the big end (thus higher rotating weight)

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