Black Ariel engine balance factor

Singles, twins and fours.
User avatar
cmfalco
Holder of a Nylon Anorak
Holder of a Nylon Anorak
Posts: 174
Joined: Fri Apr 07, 2017 4:53 pm
Location: U.S.
Contact:

Black Ariel engine balance factor

Postby cmfalco » Sun Dec 17, 2017 5:56 pm

As background, 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 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.
Digital calipers.

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.[sup]3[/sup]. Using 0.29 lbs./in.[sup]3[/sup] 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

Piston weight:
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 g

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 grams
-- weight of aftermarket +60 Gandini piston assembly 516.5 g
-- weight of aftermarket +60 Omega piston assembly 435.0 g


Balance weight:
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 90[sup]o[/sup]. 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 90[sup]o[/sup] 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 grams
-- 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 Omega 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 grams
---------------------

User avatar
cmfalco
Holder of a Nylon Anorak
Holder of a Nylon Anorak
Posts: 174
Joined: Fri Apr 07, 2017 4:53 pm
Location: U.S.
Contact:

Re: Black Ariel engine balance factor

Postby cmfalco » Sat Jan 13, 2018 3:23 pm

I now have my crankshaft apart and am able to make additional measurements to substitute for estimates I previously made.

-- revised using new data and with a math error corrected ------

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 13/16" bushing to reduce it for a smaller gudgeon pin than the original 1" pin it weighs 267.5 +/-1 g. However, from this subtract 48.2 g for the "excess" weight of the bronze in this smaller ID bushing so it originally would have weighed 219.3 +/-1 g.

-- Current small end weight = 267.5 +/-1 g
-- Original small end weight = 219.3 +/-1 g

Piston weight:
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

Balance weight:
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 90 deg. 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 90 deg. 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, offset by the 48.2 g "excess" of the current bronze reducing bushing, to balance the crank originally, i.e. 196.6 + 5.5 - 48.2 = 153.9 g.

-- weight to balance crankshaft in its current form = 196.6 +/-0.1 g
-- weight to originally balance crankshaft = 154 +/-2 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 originally balance crankshaft without the four 5/16" holes =122 +/-3 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:

154 + 260.0 / 505.0 + 260.0 = 414 / 765 = 54.1 +/-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

115 + 260 / 505 + 260 = 375 / 765 = 49.0 +/-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%

If Gandini piston were used in it without any other changes:
196.6 + 267.5 / 516.5 + 267.5 = 464.1 / 784 = 59.2 +/-0.3%

If Omega piston were used in it without any other changes:
196.6 + 267.5 / 435.0 + 267.5 = 464.1 / 702.5 = 66.1 +/-0.3%

To reduce the balance factor to 55% if using the Gandini piston would require reducing the required balance weight by 33 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. 3/4" deep each. I would carefully and incrementally make any such changes only after assembling the flywheel and checking the balance.

If anyone wants to follow my progress in rebuilding this machine I'm describing it in a fair amount of detail at:

http://www.britbike.com/forums/ubbthrea ... s/721893/1

The web site for the Motorcycle Cannonball Run, for which I'm rebuilding this Ariel, is at:

http://www.motorcyclecannonball.com/
Last edited by cmfalco on Sun Jan 14, 2018 10:07 pm, edited 1 time in total.

jj.palmer
Holder of a Nylon Anorak
Holder of a Nylon Anorak
Posts: 185
Joined: Tue Oct 15, 2013 3:07 pm
Location: Denby Village, Derbyshire.
Contact:

Re: Black Ariel engine balance factor

Postby jj.palmer » Sun Jan 14, 2018 6:07 pm

Hello
Spent last evening reading and digesting your post on your balancing project, helped along with a whisky or two of coarse, found it very interesting.

I have now done some calculations of my own using your supplied weight data on the various components, see attached calculation sheets. I have come up with the following balance factors, BF for short.

1.0 Original BF including the 4 x 5/16 inch holes as if fitted at factory - 65 %
2.0 Original BF excluding 4 x 5/16 inch holes as if fitted at a later date - 60 %
3.0 Current BF - 63 %
4.0 BF if fitted with new Gandini piston - 59 %
5.0 BF if fitted with new Omega piston - 66 %

If I am correct, I am no expert, you could reduce the weight of the Gandini piston to bring the BF upto say 63 %, the Bf would be as you are now and in between the two original BF's.

I had to do a similar weight reduction on a Gandini piston some time ago, see attachments, it shows a home made sectional caliper guage to check section thickness.

Hope this helps,

John P.
Attachments
Balance calcs, page 1..pdf
(493.45 KiB) Downloaded 27 times
Balance calcs, page 2..pdf
(269.13 KiB) Downloaded 24 times
003.JPG
007.JPG

User avatar
cmfalco
Holder of a Nylon Anorak
Holder of a Nylon Anorak
Posts: 174
Joined: Fri Apr 07, 2017 4:53 pm
Location: U.S.
Contact:

Re: Black Ariel engine balance factor

Postby cmfalco » Sun Jan 14, 2018 8:33 pm

I posted the details of my measurements and calculations precisely in the hopes it would prompt someone to check them for possible errors, so thanks very much for posting your two pdfs. I've printed them and will look them over tonight.

User avatar
cmfalco
Holder of a Nylon Anorak
Holder of a Nylon Anorak
Posts: 174
Joined: Fri Apr 07, 2017 4:53 pm
Location: U.S.
Contact:

Re: Black Ariel engine balance factor

Postby cmfalco » Mon Jan 15, 2018 2:20 am

jj.palmer wrote: ...see attached calculation sheets...
John,

Thank you very much for catching my mistake. What a difference a '-' sign in the wrong place makes. In the hopes that the third time's the charm:

-- revised a second time with another math error corrected ------

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 13/16" bushing to reduce it for a smaller gudgeon pin than the original 1" pin it weighs 267.5 +/-1 g. However, from this subtract 48.2 g for the "excess" weight of the bronze in this smaller ID bushing so it originally would have weighed 219.3 +/-1 g.

-- Current small end weight = 267.5 +/-1 g
-- Original small end weight = 219.3 +/-1 g

Piston weight:
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

Balance weight:
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 90 deg. 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 90 deg. 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, plus the 48.2 g that the current bronze reducing bush weighs more than the original 1" bush. So, to originally balance the crank it would have required 196.6 + 5.5 + 48.2 = 250.3 g.

-- weight to balance crankshaft in its current form = 196.6 +/-0.1 g
-- weight to originally balance crankshaft = 250.3 +/-2 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 originally balance crankshaft without the four 5/16" holes =211.4 +/-3 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:

250.3 + 219.3 / 505.0 + 219.3 = 469.6 / 724.3 = 64.8 +/-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

211.4 + 219.3 / 505 + 219.3 = 430.7 / 724.3 = 59.5 +/-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%

If Gandini piston were used in it without any other changes:
196.6 + 267.5 / 516.5 + 267.5 = 464.1 / 784 = 59.2 +/-0.3%

If Omega piston were used in it without any other changes:
196.6 + 267.5 / 435.0 + 267.5 = 464.1 / 702.5 = 66.1 +/-0.3%

To reduce the balance factor to 65% if using the Omega piston would require reducing the required balance weight by 7.5 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. 3/16" deep each. If I did this I would carefully and incrementally make any such changes only after assembling the flywheel and checking the balance.

Again, thank you very much for catching this mistake. I would like to think I would have caught it myself when I went through the calculation a final time, but I certainly might not have.

david.anderson
Holder of a Golden Anorak
Holder of a Golden Anorak
Posts: 1163
Joined: Mon Mar 28, 2011 4:52 am
Location: south coast NSW Australia
Contact:

Re: Black Ariel engine balance factor

Postby david.anderson » Mon Jan 15, 2018 2:58 am

A good pick up there.
While Ariel did not seem to publish balance factor figures, in the 1955 interview with Val Page, he stated that Ariel balanced Red Hunter singles to 65%. The Black Ariels now also have been 65%.
See the article below from the members library.
David
http://www.arielownersmcc.co.uk/members ... rview3.jpg

User avatar
cmfalco
Holder of a Nylon Anorak
Holder of a Nylon Anorak
Posts: 174
Joined: Fri Apr 07, 2017 4:53 pm
Location: U.S.
Contact:

Re: Black Ariel engine balance factor

Postby cmfalco » Mon Jan 15, 2018 3:28 am

david.anderson wrote: in the 1955 interview with Val Page, he stated that Ariel balanced Red Hunter singles to 65%.
I'm not sure I had read that but, even if I had, I'd forgotten. It's interesting that my measurements show they used the same balance factor for the rigid as well as the swinging arm frame.

jj.palmer
Holder of a Nylon Anorak
Holder of a Nylon Anorak
Posts: 185
Joined: Tue Oct 15, 2013 3:07 pm
Location: Denby Village, Derbyshire.
Contact:

Re: Black Ariel engine balance factor

Postby jj.palmer » Mon Jan 15, 2018 10:47 am

Happy to oblige, it brought back memories of some years ago when I was at work, during one period of time it was my role to check other peoples calculations associated with gear design and manufacture. At that time there was no computers or even calculators it was all done using six figure logarithm tables, each calculation took hours, happy times.

Back to reality, by my calculation you need to remove 48 grams from the Gandini piston to achieve 63% BF.
With my piston I needed to remove 55 grams, I managed to remove 40 grams from the piston and the remaining 15 grams I removed from the flywheel. This was on a twin cylinder engine, KH500.

Regards,
John P.

User avatar
Eero.Korhonen
Holder of a Waxed Cotton Anorak
Holder of a Waxed Cotton Anorak
Posts: 577
Joined: Tue Sep 04, 2012 10:02 am
Location: Oulu, Finland
Contact:

Re: Black Ariel engine balance factor

Postby Eero.Korhonen » Mon Jan 15, 2018 12:18 pm

How about dynamic balancing? Here is some theory:
https://tonyfoale.com/Articles/EngineBalance/EngineBalance.pdf
I did that to my VH in local experts and the change was huge.
Br, Eero
Ariel VH 1954, IZH 350 1962, H-D Sportster Hugger 1992, AOMCC Member 133

User avatar
simon.holyfield
Holder of a Golden Anorak
Holder of a Golden Anorak
Posts: 2605
Joined: Mon Oct 17, 2011 11:16 pm
Location: Norfolk
Contact:

Re: Black Ariel engine balance factor

Postby simon.holyfield » Mon Jan 15, 2018 1:29 pm

cmfalco wrote:... It's interesting that my measurements show they used the same balance factor for the rigid as well as the swinging arm frame.


Interesting point. Are you aware of any manufacturer using different BFs for different frame types, where springing is offered as an option within a model range?
cheers

Simes

'51 Square Four, Masquerading D3 Bantam, '58 Huntmaster, '42 W/NG, http://ariel-square-four.blogspot.com


Return to “Four stroke”

Who is online

Users browsing this forum: No registered users and 5 guests