MOI of a golf club, where did it go?

[Fade]

I = m * r^2 is the proper formula to use for calculating moment of inertia I, for a point mass m swinging at radius r. Of course the club-head is not a point mass, swinging at a fixed radius (as different portions of the club-head swing at different radii). As such, when a single radius estimate is plugged into the formula - as a shortcut- this introduces error in the calculation, which may explain why your measurements yield different results.

Area moment of inertia represents something different, it has different units, and it is not applicable here.

[Howard_Jones]

OK, then the formula ive been using is the right one. (Mass x distance squared).

For the club head its distance from the butt to COG

For the shaft its distance to the shafts BP from the butt

For the grip, its distance to the grips BP from the butt

The Summary of all 3 should then be the clubs total MOI, but my numbers DONT match the numbers the Auditor replies, i always get a return value a tad lower in excel.

ive been thinking it could be the distance from the shaft center and out to COG, so the actual distance from the butt to COG could be longer than in my calks of it. (the actual line is diagonal and a tad longer, could it be that simple?)

another possibility is the way we measure VCOG...its actually a bit lower than we locate it on the face, (its loft and RCOG depending) so it seems like here could be more than just one explanation for why my excel numbers dont match up, and becomes to low vs the Auditor.

 

[Fade]

Regarding your diagram: How does your machine swing the club? If it swings the club in the shaft-plane, then I think the horizontal (shorter) measurement is the more correct measurement, at least as far as comparing calculations and measurement results goes.

[Howard_Jones]

The Auditor MOI scale works almost like the classic method, the difference is the club dont hang down and swing forward and back again, its a horizontal movement a few rounds before you get a return value.https://www.youtube.com/watch?v=UrtmKOD6otY

[Fade]

Re. your calculations. I think your calculations for the grip and shaft may be off.

For a uniformly weighted shaft (that is, every inch of shaft has the same mass) the correct formula is:

MOI = (1/3) * m * L^2

m = mass of shaft

L = length of shaft

 

 

 

[Howard_Jones]

I think its my input values for COG thats off, i can see from my notes that ive been using the measurement we get from leading edge and UP to COG on the face, but that value is misleading, so i will have to measure RCOG and make the math for correction like the illustration of the head on the pen shows you. I should have known...from wedges and grinding where we have to take loft into account, i did not think of that when i made my sheets for MOI, so i think i have found the "error"....old rusty head :-.))))...il try to fix that and see if i can get to the same numbers

 

[cxx]

I guess I'll chime in here. There have been a number of posts about the MOI of objects made of parts with known mass and MOIs. The parallel axis theorem lets you combine the MOIs of components to get the MOI of the assembly. When translating the MOI around the center of mass to a parallel axis not through the center of mass you add the mass*distance^2 (between the parallel axes) to the MOI around the center of mass. This simplifying calculation only works when the known MOIs are around parallel axes. This is not the case with the complex assembly like a golf club. It is likely that the component MOIs are known only around convenient axes, like along the center of the shaft or around vertical or horizontal axes of the clubhead.

Unfortunately this makes calculating a clubs MOI around an arbitrary axis more difficult than measuring the MOI of the assembly directly.

[joostin]

I had to brush up on parallel axis theorem - been a long time since college when I probably didn't pay attention to it to begin with, haha. It seems it actually won't help in our case unfortunately. In the case of a golf club, it will be I = I (of whole club about it's CG, ie. balance point) + Md^2 (total mass * square of distance from CG axis to the parallel axis at the butt). If you hold your finger up vertically then balance a club horizontally on it, your finger represents that CG axis parallel to one at the butt. The parallel axis formula should result in the same number we already get by summing up the components MOIs.

I suspect Howard's calcs come out low compared to an Auditor because of a few things: head CG a little farther like he mentioned; the spreadsheet is probably using I = 1/3 m*L^2 for the shaft which assumes a constant weight distribution of a straight cylinder but may be off to reality; and not sure if grip & tape are assumed as a cylinder or point mass. Ferrule, epoxy, tip weights, etc. I'm guessing are point masses too which should be fine.

However, even if the absolute numbers are low, we should be able to "match" two clubs with a calculator like that, and they should still "match" pretty closely on an Auditor.

[Howard_Jones]

Seems like i have found the error. it seems to be 2 factors at once. I did not take the loft or RCOG into it, a 45* lofted club will lower COG by 50% vs the way we locate VCOG with 0* loft, so 1.0" becomes only 4/8"without RCOG correction who brings it further down., and the next was GRIP CAP, where the control club has grips on, pushing everything 2/8" forward, while my calcs is un-gripped where the grips moi value alone was added without me thinking of that we push both the shafts BP and the heads COG 2/8 further out when a grip is added. My calcs was meant to be used for dry fit (w/o grips), so they are not really wrong, but comes to short compared to the reference club, and this 2 factors seems to be why.

Im using actual BP for shafts, not the shortcut with a 50/50 BP who aint right, and would only be valid for old fashion bore trough design heads. Today the norm is a BBGM of 1.25" on iron heads, so even a 50/50 shaft would have its BP 1 inch higher up on a play ready club. (BBGM 1.25 moves it 1.25 up, a grip gap of 2/8 moves it 2/8" back, net = 1.0" shorter than 50% of play length for 50/50 shaft)

So the formula used by Tutleman - Play length squared x (head weight + 1/3 of shaft weight) is not the one im using because of variable shaft BP from model to model and BBGM.

Tutlemans formula will make a error from #3 to PW depending on head design (progression of VCOG), since he is using play length, not COG of the club head and those compares i did gave a difference of about 68 MOI points higher on Tutlemans numbers than mine for a #9 iron who is the reference club ive been using. I dont have enough components to try off, and have sold my Auditor, so i will have to push this project further out in time, it was just very annoying that i could not get to the numbers the reference club had, but it seems like i know why now.

The 2 reference clubs i have, a #3 and a #9 has a actual difference to MOI of 47 points down from #3 to PW (both SW matched as D2), and that got me thinking if the SW system actually is a mechanical short cut to the formula Tutleman has used since the numbers i did ended 68 points to high on the PW with that formula. If my numbers is precise (im not quite sure yet), then we talk a "error" of 20 MOI points from #3 to #9 using the 14" inch fulcrum, so again, it actually seems like that scale tried to MOI match clubs with the formula Tultleman has used in mind. The problem with THIS theory is that they did NOT have steels shafts with neutral balance points in the early 30s, it was Hickory and they must have had a BP higher than the middle, even for irons.

But the method will fail, simply because we cant use play length unless VCOG progression in the heads makes actual VCOG the same for all clubs as lofts changes, and i have no idea how COG looked like on clubs in the 20 and 30s

If we look into Monte Doretys MBI excel sheet, we get to see many small calculations done on the heads itself to get a actual COG for each head, so its a LARGE job to measure and calk this right, and that will make this method for hobbyists way more demanding to get right, compared to simply using the SW scale and a offset factor of 1.33 SWP pr. inch since most who does club making has a SW scale.

END NOTE:

What we know about the SW system for todays clubs is that it gives a actual progression in resistance as clubs goes longer, and that might have been the natural way to play irons. Cobra report the same from their Single length club users. If its because this players is grooved to play SW matched clubs, or if its simply "human nature" to add more power the longer club we use, i cant say for sure.

We ends up with that both MOI and flat SW has its problems, but we can avoid both if we simply forget all about them and tune up the longest and the shortest club in the set without thinking of them at all, and when done, we can measure both clubs on the SW scale and draw the slope between them to find the values to build the clubs in-between to. Then resistance will be fitted to the actual player, no matter how it looks like, be it flat MOI, flat SW or a SW or MOI with progression no matter direction it goes.

 

 

[Fade]

This formula ...

MOI = m * L^2

... where m is mass, and L is the measurement from butt to BP is not useful, nor correct, for estimating the MOI of a shaft.

For example: For a uniformly weighted shaft, using the formula as above would lead to an underestimate of MOI by 25%. Or, in other words, the formula yields a value that is only 75% of actual MOI.

The above formula is only for point masses, it is not applicable when mass is spread out in space.

[Howard_Jones]

hmmmm. is that a constant "error" or offset factor for a rod like a shaft?

 

[cxx]

In the special case where all of the parts have an MOI around parallel axes there is a formula that gives the combined MOI. My point is that there isn't a useful axis when combining the golf club components because the component MOI's are either unknown or available only around axes that are not useful. Using point masses and distance to an axis provides incorrect numbers because the MOI is the sum or integral of the square of the distance times the point masses.

Another way of looking at it is that using the COG as a point mass ignores the rotation of the part itself.

[Howard_Jones]

Here is what i can find about formulas, but its a mix of Greek, Chinese and Russian to me, im not clever enough to figure out this and translate it to a useful formula for golf club components

Moment of Inertia - Distributed MassesPoint mass is the basis for all other moments of inertia since any object can be "built up" from a collection of point masses.I = ∑i mi ri2 = m1 r12 + m2 r22 + ..... + mn rn2  

https://www.engineeringtoolbox.com/moment-inertia-torque-d_913.html

 

This is the formula ive been using, and you who know this type of math better than i do, say we CANT use it.

Mass Moment of Inertia (Moment of Inertia) - I - is a measure of an object's resistance to change in rotation direction. Moment of Inertia has the same relationship to angular acceleration as mass has to linear acceleration.

Moment of Inertia of a body depends on the distribution of mass in the body with respect to the axis of rotationFor a point mass the Moment of Inertia is the mass times the square of perpendicular distance to the rotation reference axis and can be expressed asI = m r2                    (1)whereI = moment of inertia (kg m2, slug ft2, lbf fts2)m = mass (kg, slugs)r = distance between axis and rotation mass (m, ft)

[Stuart_G]

@Howard_Jones Those formula are just basically saying to calculate the MOI of a body, you have to break it up into a lot of small pieces, calculate the MOI of each piece as a point mass, and then add the results up from all the pieces to get the total MOI for the body. That's a mathematical integration. The smaller the pieces, the more accurate the answer. So in theory the exact MOI is when you break the body down to an infinitely small pieces. That form is only used in either theoretical work or computer programs that can handle a large number of individual calculations. It's not something that you would try to use by hand.
Since MOI is very dependent on the distance of the mass from the axis of rotation (L^2) and the mass is spread out over a wide range of L, that is why using the single point mass formula on a shaft c.g. does not work well.
You may have missed it but @Fade gave you a formula back in post #65 that can be used for the shaft. It's not perfect since it assumes the mass is evenly distributed across the length of the shaft - which may not be the case but it should still be close enough. Certainly significantly better than what you're using now.
MOI = (1/3) * m * L^2
where L is not the distance to the c.g. but rather the total length of the shaft and m is the total mass of the shaft.

[Howard_Jones]

Are you saying that we CAN use the formula for a point mass, and make the summary from the MOI of each part like i have done?

If so, my error is where i think it is...(actual COG due to loft vs how we locate VCOG and the extension made by the grip cap to both the heads COG and the shafts COG)

Yes im familiar with that formula, Tutleman uses it where he takes Play length squared x (head weight + 1/3 of shaft wgt), and that gives the same return value as when we do them part by part and make a summary. I tried it yesterday, but prefer the way im doing it since we have to use the shaft balance point if we like it or not.

[Stuart_G]

I'm saying the summing the results from different point mass calculations is only going to be useful if the indivual pieces you are doing the calculation on are very small or the length from the axis doesn't very much over the piece. That's why we can get away with using the point mass formula on the head and it's weight and c.g., but not on the shaft c.g.

Now if you want to break up the shaft into about 10 different pieces and do the calculation for each piece and add up the results, that wouldn't be too far off, but it's hardly practical.

 

[Howard_Jones]

OK, im clearly to stupid to understand why we cant use the shafts BP when we assume the butt end as point of rotation, and we cant really cut the shaft in 10 or 20 pieces to get the actual weight for each part, so i always though the shafts BP would solve that issue, but will have to accept that for this math we dont.
Anyway, the clubs im doing the math for is all using the classic DG shaft, and my numbers say the shaft is 243 for the #9 iron, and @Fade say we only get 75% of actual that way, so 243/75 x 100 = 324.
The "reference clubs" im using has standard specs, and a MOI value of 2667 for the #9 iron, so the shafts contribution is somewhere between 243/2667 = 0.91% or 324/2667 = 1.2%, so i dont think we can mess up "big time" by using the shafts BP, it will give a return value closer to actual than just using 50/50 BP, but Fades info about a return of only 75% causes some worries....
Its just to bad i no longer have the Auditor, or the component specs of the "reference club" when i am this close, but in the end, its only for academical interest, im comfortable building sets based on the SW values from the longest and the shortest and just draw the slope between them. That method will be "better" anyway, but i would still like to know how to set up the formulas for MOI "better" than ive done.
What i can see from a fast calc from lofts starting at 21 and up to 42 who is a typical #9 players iron, COG moves about 3 mm (lets say 1/8"), unless the design has a built in compensation for that (they should have). I have no notes from iron sets, but for wedges and grinding from blanks we want VCOG at 0* loft (pen method) to be 7/8" to 1.0" above the leading edge, and 0.15 mm for each degree of loft lower, or minimum 0.5 mm between a classic set 52-56-60 (1 to 1.2 mm higher COG on the 60* vs the 52* the way we locate VCOG with 0* loft)

[cxx]

Hey Howard,

 

You might consider using a MOI measuring device on a number of clubs that you know the component weights and COGs/balance points and fit them to a simplified model. That way you could adjust you point mass model to get a little closer to a MOI estimate.

It does seem like quite a bit of work. You may need a different factor for driver, fw, hybrid, iron heads as they are very different shapes and weights.

 

[Stuart_G]

@Howard_Jones said im clearly to stupid to understand why we cant use the shafts BP when we assume the butt end as point of rotation
Maybe this will help.
If we use the total mass and distance of the c.g. from the axis. There are lots of pieces of mass on each side of that c.g. that is using the wrong distance from the axis. That can work in some cases but only when the wrong values on one side of the c.g. balance out with the wrong values on the other side of the c.g. A moment arm or balance type calculation is one of those cases where we can make that assumption. But that happens only when the the formula is linear. e.g. moment area = m*L. But since MOI is based on L^2. It's not linear and those errors from each side of the c.g. no longer balance out anymore. The part on the head side of the c.g. needs to add more to the MOI than the butt side takes away.
@Howard_Jones also said Yes im familiar with that formula, Tutleman uses it where he takes Play length squared x (head weight + 1/3 of shaft wgt), and that gives the same return value as when we do them part by part and make a summary
Tutelman's form is really just short hand (using algebra to simplify) for the sum of the shaft contribution (1/3 * shaft wt * Length^2) added to the head contribution (head wt * Length^2). So it's not the same as doing it individually the way you seem to be doing it.

[Howard_Jones]

Im fully aware of that, but have to travel 4.5 hours to find someone with a Auditor (the man i sold mine too), and this excel sheets was not really for my own use, so it want be a priority to finish that project. When i compensate for loft and the error ive done to grip cap, im off with about 30 Moi points from the reference club i have, but it could be as simple as my input for head weight, using 282 grams, and the reference club could have been a 285 grams head, or a head with slightly lower COG than my calcs is based on. (maybe a combination of the two)...so for now, i just let it be.

[Howard_Jones]

Thanks Stuart, i can see it now, so a shaft with higher BP would actually compensate for some of that error opposite of what i though, then i guess 1/3 of the mass for the shaft is used as a good offset factor for shafts with a 50/50 weight distribution. i makes sense now.

 

[Stuart_G]

Mathematically it simplifies as 1/3 of the mass. But I think of it more as a compensation of the length, not the mass.

So instead of mass * (0.5 * L)^2 which would be based on the the location of the c.g. in a 50-50 shaft, it works out to be more like mass * (0.57735 * L)^2

 

[Fade]

Nice explanation, and easily doable with Excel. I already had this available, so I thought I would expand on your post, for illustration.

Consider a 100 gram (0.1 kg) shaft, 100 cm long, uniformly weighted (every cm has the same mass).

C uses the correct formula for this situation ( MOI = (1/3) * m * L^2 ). L is total shaft length.

1,2,5,10 use the formula for point mass ( MOI = m * L^2 ). These numbers are the number of shaft-segments. L is the distance from shaft-butt to BP for each segment. Bolded numbers sum up the contributions of all segments. The resulting MOI calculation are highlighted in yellow.

Indeed, when breaking it up into 10 segments you are not too far off. : )

[Noodler]

I may have missed it, but how did we get into this discussion where the "wheel" is being reinvented? Monte already had all these discussions way back when on the Wishon forum and worked with quite a few people to vet the process he defines in the gcv2p5 spreadsheet. I own an MOI Auditor and using Monte's build process I am generally within 5 MOI points of the build plan for the completed club. Monte's spreadsheet does make a few assumptions to simplify the process, but his BP method to determine the CG of the most critical components just plain works. No need to get crazy when the work has already been done.

[joostin]

@Noodler Since Monte D's spreadsheet is nowhere to be downloaded anymore, does it break down how he works out shaft MOI? Even integral calculus would be different for each shaft due to differences in wall thicknesses, tapers and densities, so maybe he is estimating with segments like @Fade is showing (?).
I worked up a few examples in CAD to show how different the numbers can be vs. the I = 1/3*m*L^2 equation for a uniformly distributed cylinder.
1) Here's a graphite shaft, with variable wall thickness from 0.04" to 0.125", straight grip section, then tapers from 0.600" to 0.355". I just threw these numbers in, but luckily it came out to a nice 125g. CG is 53.4cm (21.03") from the butt. MOI about the butt is pointed to below, 454 kg-cm^2:
[img]https://s3.amazonaws.com/golfwrxforums/uploads/LJSLYNAF05Z7/shaft-ig1-png.png[/img]
[img]https://s3.amazonaws.com/golfwrxforums/uploads/KNZYA1LO4V7F/shaft-ig2-png.png[/img]Compare that to the straight cylinder calc: I = 1/3*m*L^2 = 1/3 * 0.125kg * 99.06cm^2 = 409 kg-cm^2
Also compare to a point mass calc: I = m*r (butt to BP[CG])^2 = 0.125kg * 53.408cm^2 = 357 kg-cm^2
2) Here's a steel shaft, no taper, uniform wall thickness, 0.4775" (halfway between 0.600" and 0.355"), 122g. CG is dead center, 49.53cm (19.5"). Our equation here works out perfect of course: 1/3 * 0.12218kg * 99.06cm^2 = 399.6 kg-cm^2, same as the CAD:
[img]https://s3.amazonaws.com/golfwrxforums/uploads/A6J6D1804CUX/shaft-is1-png.png[/img]
[img]https://s3.amazonaws.com/golfwrxforums/uploads/DKQ2N4VO1SN4/shaft-is2-png.png[/img]3) Here's a steel shaft, same weight, same wall thickness, but just with a straight taper from 0.600" to 0.355". CG moved closer to butt, 45.14cm (17.8"). MOI at butt is now 346.6 kg-cm^2:
[img]https://s3.amazonaws.com/golfwrxforums/uploads/C9D6E8FAE61F/shaft-is3-png.png[/img]
[img]https://s3.amazonaws.com/golfwrxforums/uploads/ZOLBG82Y3D4L/shaft-is4-png.png[/img]@cxx Incidentally if you take any of those examples, you can use parallel axis theorem to verify MOI at the butt from the MOI at the CG. For ex 1, MOI at the butt is I = I (at CG) + m*d (shifted distance)^2 = 96.937 (Lyy value above red arrow) + 0.125kg * (53.408cm)^2 = 454 kg-cm^2 which matches the CAD.
If anyone can measure thickness along the length of shafts (cut in half, Magna Mike, ...) I'd try it out in CAD.

[Noodler]

gcv2p5.xlsHere is a copy of Monte's original spreadsheet (and last known available version). I didn't realize the original links had all died.

[Stuart_G]

@joostin said If anyone can measure thickness along the length of shafts (cut in half, Magna Mike, ...) I'd try it out in CAD.
I wouldn't assume a constant density for composite shafts like you can with steel. The ratio between graphite and epoxy can vary. So you'd really need the weight of the cut up pieces. I have a shaft I could cut up but I don't have an accurate enough scale for weighing the small parts.
BTW, just curious which cad package are you using?

[Howard_Jones]

I cant find the Wishon forum with the debates you reference too, and i should have contacted Monty years ago, but dont even know if he is still around?
The reason i never used his Excel files for building, is both because i had a auditor, and that his file has hidden sheets and write protection on a few parts that made it useless for me.
I have a shaft database with...god knows, more than 4000 shaft models at least, but since the sheet for the shaft database is hidden, and the fields for input is write protected, i cant merge my DB of shafts to this file, or use input fields for each shaft if that was needed. My file contains the shafts balance point, but only for 1 club in the set, but its easy to calculate the others when needed, except for shafts like AMT who has a build in progression from shaft to shaft. A good reason to merge it all would be to get the option to see changes in both MOI or SW when we change shaft models like from DG to Modus or KBS.

I would also like to modify the SW return values, (i know most of you dont care but i do), so we can see SW values like D2.1 or D3.8 etc...Montys file only have full numbers like D1 or D2
In sum, his work is more than impressive, (understatement), but there is still room for a few improvements as i see it, so if you know if Monty is still around, i should probably reach out to him with this.
PS! the file you shared here is newer version than the one i had, and tanks a lot for that.

And NO, non of us is trying to reinvent the wheel, but have a academical interest in the math behind, so even if i made many sets thats MOI matched using my auditor, i never knew the details of the math behind it all, and often came up short, so i was left to trial and error with "half good" experiments who dont have the "scientific value" those experiments should have. We often see hobbyist who dont really know what end we should start it all from when building a set, and many turns out disappointed of the numbers they finally ends up with when they measure the clubs. For some clubs specs aint really important, but for those who tries to build sets to the tightest possible tolerances it is.
One task i could do on Montys file was to see the actual difference in MOI values due to both loft and lie, and both of them has been hard to measure accurately even with the Auditor since precision using the measure equipment most of us got, a regular bending machine can make the values to be a tad inaccurate when we wants to use them as education for others.
Example, ive tried my best to tell everyone, a quality build starts with LOFT AND LIE. Even new heads is off specs, so we ruin a good dry fit job if some heads need a adjustment later. By using Montys excel sheet i could finally see the precise numbers, without the error source from a bending machine and the operator. For short, Loft dont mean anything really, plus minus 2* want mess it up, while lie angles move a #5 irons MOI value by 3.8 points pr degree of lie angle, and many heads can be 2* off, and thats 7.6 Moi points so we get close to 1 gram head weight as "error", so a dry fit job where we grind down tip weights to 1/10 of a gram is destroyed if we dont start with loft and lie check of the heads. i know most will say...does it really matter? yes it does if you use more than one hour a club to build to the tightest tolerances possible, so its all this small details from correct measurement and cutting of shafts to loft and lie and constant amount of epoxy used. Some of us what it to be as good as we can make it if matters in play or not.
Thanks to ALL who have participated in this tread, keep it up, its treads like this one who makes this forum worth to spend time on.

The shaft DB is not marked with a owner, so i have no idea who made it, so even if it might violate someones rights (copyrights), im taking the chance to share it here for personal use like i think it was made for.
Like all other DBs this large, there is some errors found, but i cant and wont correct them since i dont have access to the actual shafts to measure them again and correct the values (some deflection values seems off) Its a few years old, and thats the reason for why "the latest models" cant be found in it, but since i dont know who made it, i cant ask for a update either. its been very useful for me.
Profile Testing (1).xlsx

[joostin]

That is true regarding densities. Things will change for sure. I use SolidWorks, and it would be able to capture MOI of multiple bodies of different densities.@Noodler Thank you much for sharing the spreadsheet.
So Monte uses our normal cylinder equation but adds a correction equation that works out pretty darn well. His correction equation relates the center of the shaft vs the measured balance point minus the grip cap. Haven't figured out how it was derived:
[img]https://s3.amazonaws.com/golfwrxforums/uploads/1TKI8ZA7ZVQZ/screenshot-20200723-005352-excel.jpg[/img]
[img]https://s3.amazonaws.com/golfwrxforums/uploads/JAHHB6DCFH3X/screenshot-20200723-002410-excel.jpg[/img]I tried a few examples. Below "test 1" is my previous post's example #1. "Test 2" was my example #3. And "test 3" is one not shown in graphite with wall thickness going from 0.030" to 0.150", a pretty extreme case. You can see Monte's numbers vs what the CAD or actual would come out to. Again pretty good - 3.5 points off, 0 points off (nice), and 10.7 points off. I also tried to point out what his formula is doing:
[img]https://s3.amazonaws.com/golfwrxforums/uploads/O8VB13MODPNM/20200723-080227.jpg[/img]It seems it would be most off in the case of variable wall thickness and densities as stated above. I'll have to dig deeper to understand Monte's work. Smart guy that Monte. I enjoy looking at the technical stuff even though I just fiddle with my clubs by feel.
Good stuff guys. OP opened up a can of worms!

[cxx]

This is interesting. MOI as a "swing weight" measurement is from the butt end of the club perpendicular to the shaft with the axis in the direction of the clubface. In order to use the parallel axis theorem you would need the club head MOI around the axis perpendicular to the shaft and parallel to the club face through the club head center of gravity. Not sure how you get that.

Even worse would be if the MOI as a swing weight was from the butt end to the COG, which with the clubhead attached might be in free space at some small angle to the shaft messing up all the convenient angles. That's how a pendulum behaves.

 

It may be that the club head contribution is dominated by the m*L^2 rather than the club heads center of gravity MOI.