I posted the following to the Ariel Owners Club, where there are a few more Black Ariel owners than here. Not a lot, mind you, but more than here. For completeness I'm posting it here as well since some of you may find the general procedure I used, if not the actual results, of interest.
As a reminder I wanted to determine the original balance factor used by the factory on my 1928 Ariel Model C so that I could rebalance the engine for one of the two new, +60 aftermarket pistons I've already purchased. My Ariel came with a worn +30 piston and with the small end rebushed to accept the 13/16" gudgeon pin of this newer-style piston rather than the 1" originally used. So, in addition to determining weights I had to correct for the weights of different bushes as well as for the socket head cap screws now locking the big end nuts in place. However, other than socket head cap screws used to lock the crankpin nuts, and the possible exception of four 5/16" holes discussed below, there are no other signs that the flywheels have been altered by additional drilling or plugging since they left the factory.
Since a search of the AOMCC web site shows the subject of balance factors has come up more than once, along with speculation on what value Ariel might have used, below I describe in some detail the measurements, uncertainties, calculations and assumptions leading to my determination so that others can decide for themselves if they want to accept the value I found. For those who don't want to read all of this, the executive summary is that the original balance factor used in my engine was either 56% or 60% (both +/-1%) depending on an assumption about four holes described below.
A seldom discussed but fundamental issue with the static balance method as usually described is it relies on the center of mass of the flywheels being on the axis defined by the crankpin and crankshaft. If an inhomogeneity in the flywheels places the center of mass off that axis then adding weight to the hanging connecting rod (which in effect places that weight at the center of the crankpin) will draw the center of mass close to the crankshaft axis but can never precisely balance the flywheels. To achieve perfect static balance requires applying weight to the connecting rod to draw the center of mass to its point of closest approach to the axis of the crankshaft, then adding (or subtracting) additional weight from the flywheels at 90-deg. from the crank-crankpin axis.
In all there are five 1/2"-dia. balancing holes drilled on the inside rims of the two flywheels. Because of the inaccessible location of these holes I speculate that the flywheels were balanced individually prior to being assembled into a complete crankshaft. There also are four 5/16"-dia. balancing holes drilled on the outside faces of the rims. There is no way to know if these were done by the factory at the time to tweak the crankshaft into the final balance factor after assembly, or if they were done during a later rebuild to keep the same balance factor for a heavier piston, or to change it to a higher balance factor. I address the quantitative effect of these possibilities on the calculated balance factor below.
In what follows I keep the precision of individual measurements (e.g. the 10 mg of one scale) although the final quoted uncertainty largely depends on the least sensitive measurement used in the calculation. I used the following tools:
200 g balance calibrated with weights accurate to 0.3 mg. Balance reads to +/-10 mg.
6 kg balance calibrated with weights accurate to 0.1 g. Balance reads to +/-0.5 g.
6-piece set of 5-50 g balance weights each accurate to 0.01 g.
Crown-brand balancing wheels of sensitivity 1 g-cm, equivalent to 0.2 g imbalance at the radius of the crankpin.
The four "external" 5/16" holes are at the crankpin end of the crankpin/crankshaft axis and have a total depth of 3.86" resulting in a volume of steel removed of 0.296 in.3. Using 0.29 lbs./in.3 for the density of steel, the total weight removed from these four holes was 0.086 lbs. (38.9 grams)
A formula for calculating the Balance Factor can be written in the form:
Balance Factor = (balance weight + small end weight) / (piston weight + small end weight)
As can be seen, to solve this requires determining three weights as well as having a fixture for holding the crankshaft so it can rotate freely when the balance weights are added.
Small end weight:
With the bushing to reduce it for a smaller gudgeon pin it weighs 267.5 +/-1 g. However, from this subtract 7.4 g for the "excess" weight of the bronze (see 'sidebar' below for details) so it originally would have weighed 260.0 +/-2 g.
-- Current small end weight = 267.5 +/-1 g
-- Original small end weight = 260.0 +/-1 g
The "piston weight" is that of the complete assembly of piston, gudgeon pin, circlips and rings. Although it doesn't enter into the calculations shown here I'll note that the weight of the additional Al used in a, say, +30 piston is not negligible. It can be calculated from the annular volume of a piston of stock diameter and one 0.03" larger than that.
-- weight of +30 piston assembly that was currently in my bike 467.5 +/-0.5g
I was lucky to find two people with original piston assemblies for the Ariel. The one in Australia is used and weighs 507.2 g and the one in Canada is new and weighs 503.5 g.
-- weight of original piston assembly weight (average of above) = 505 +/-2 g
-- weight of aftermarket +60 Gandini piston assembly 516.5 +/-0.5 g
-- weight of aftermarket +60 Omega piston assembly 435.0 +/-0.5 g
I hung balance weights and washers from a wire attached to the small end until the crankshaft was in balance and weighed the final total mass. It took 196.59 g plus 10 g on the rim at 90o. Taking into account the off-axis imbalance I estimate the uncertainty in balancing the crank using only weights hanging from the connecting rod and none at 90o is +/-3 g.
The weight of the heads of the two 1/4" cap screws pinning the big end is 2 x 2.74 grams = 5.48 g. Without the cap screws it would have required that much additional weight to balance the crank originally, offset somewhat by the 7.4 g "excess" of the current bronze reducing bushing, i.e. 196.6 + 5.5 - 7.4 = 194.7 grams.
-- weight to originally balance crankshaft = 195 +/-3 g
If the 5/16" holes were added sometime later the original weight required to balance it would have been 38.9 grams less.
-- weight to balance crankshaft without the four 5/16" holes =165 +/-3 g
-- total weight to balance crankshaft in its current form = 196.6 +/-0.1 g
Original factory balance factor:
If the crankshaft in its current form (less the cap screws) is how it left the factory, the original balance factor was:
294.7 + 260.0 / 505.0 + 260.0 = 455 / 765 = 60.2 +/-1%
If the four 5/16" holes were added later it would have required 38.9 grams less to balance it originally. In this case the original balance factor would have been
165 + 260 / 505 + 260 = 425 / 765 = 55.6 +/-1%
For comparison, a 1960 BSA Service Bulletin shows 60% for the 250cc 'C' series, 58% for Gold Stars, 55% for the essentially identical 'B' series singles in the same frame as the Gold Star, and 55% for both the 500cc and 650cc 'A' series twins, also in the same frame as the Gold Star. A 1930s Vincent Comet used 66% (claimed weight 390 lbs. vs. 290 for the Ariel) but this had to be reduced to 61% in a lightweight speedway frame.
Current Balance Factor:
With current piston in it:
196.6 + 267.5 / 467.5 + 267.5 = 464.1 / 735 = 63.1% +/-0.3%
With Gandini piston in it:
196.6 + 267.5 / 516.5 + 267.5 = 464.1 / 784 = 59.2 +/-0.3%
With Omega piston in it:
196.6 + 267.5 / 435.0 + 267.5 = 464.1 / 702.5 = 66.1 +/-0.3%
To reduce the balance factor to 60% in order to use the Omega piston in it would require reducing the required balance weight by 43 g which in turn would mean removing roughly half that weight from the rim of the flywheel. This could be achieved by, for example, drilling two additional 5/16" holes approx. 1" deep each.
If the Omega offered a significant advantage over the Gandini I would modify the crankshaft accordingly. However, since the Gandini piston could be used with the crankshaft as-is, I'm particularly interested in any experiences people have with these aftermarket pistons.
Sidebar: The difference in weight of the bronze in an original 1" ID bushing and the current 13/16" reducing bushing in the small end:
Density of steel = 7.75-8.05 gram/cm3
Density of bronze = 8.7 grams/cm3
Width of connecting rod = 0.87"
Width of current reducing bush = 1.065" (tapered)
OD of bush = 1.1875"
ID of original bush = 1.000"
ID of current bush = 0.8125"
From this, the excess weight of the small end over that with the stock bush = 7.4 g