Gear Effect in Irons? Diagrams and Calcs Using Tutelman, CAD Model CG/MOI, MPF Data. Vs Hybrids. Implications. 🦄

[joostin]

Gear effect in irons?  In short it depends on the iron, but in some cases possibly more than we would normally think, or even opposite.  This will be a loooong post, but there are pictures 😉

 

I wanted to take Dave Tutelman's equations and apply them to irons to see what we get.  He focused on drivers which of course have the most noticeable gear effect.  Also the only picture probably most of us have seen of gear effect, or lack of, in irons is the one on his site.

 

There's no detail there, so it can only paint a broad picture, and it makes it easy to give the blanket statement that "irons have no gear effect", which practically is probably a good enough statement for many cases.  Using a CAD model (credit to a guy named Winther) I wanted to make some diagrams with more detail.  I'll dig in to see what gear effect spin numbers we would get with that and also a few different Titleist irons using Maltby MPF data, even if it's negligible.  I've been wanting to dive into this and was also inspired by the thread @nkurz posted that pointed to research papers that had robot testing and interesting findings.

 

First let's take a look at the makings of gear effect (going to call it GE because this will be long...).  Basically if the clubhead's CG is anywhere behind the face, there is some kind of GE, as we look at the geometry of impact conditions.  Note that with everything below we're not looking at the total spin, delivery, path, AOA, etc. - just purely the GE factors.  Also, despite the complexity and length of Tutelman's analysis, he calculates GE in a view that's actually pretty simple in that it takes the ball without compression and a pure gear transmission from the clubhead to the ball.  To derive equations and calculate these things, that's pretty much a must for practicality (in light of actual variables of ball and club coefficients of friction, compression, environmental factors…), and I don't think we can be anything less than thankful to Tutelman for his body of work.

 

Horizontal Gear Effect

 

Here are diagrams of a ball being struck ½" towards the toe with an iron, changing the position of the CG in each.  Note, we have to look perpendicular to the face when analyzing these in a free body diagram, not a top view where you can see the face.

 

Diagram 1 below is when the head CG is directly on the face.  The red arrow is rotation around the head CG due to the force the ball imparts on the head.  The little pink arrow is the impact point movement from that rotation (tangent to the red rotation at the point of impact) - the instantaneous deflection direction of the head.  Notice it's pointing directly along the force vector of the impact.  This is pure backwards deflection, resulting in a loss of strike efficiency and zero GE:

(1)

 

Diagram 2 is when the head CG is behind the face.  This is the case with most irons these days by different amounts.  Notice the pink arrow again.  This time it's angled a little towards the toe.  Again, the deflection mostly results in a loss of strike efficiency, but this time it also creates a bit of a toe-ward movement along the face as the ball strikes.  The friction force in that direction creates GE:

(2)

 

Diagram 3 is if the CG is in front of the face.  If you look at Maltby MPF data, you will see clubheads with this when "basic VCOG" is lower than "actual VCOG", and more likely with blade designs that aren't pushing weight back.  Notice the pink arrow angled a little towards the heel this time.  This is interesting in that, in addition to loss of strike efficiency, it will create the opposite condition to the previous diagram - a "reverse gear effect".  To continue the mechanical analogies, I'll call it a "pulley effect".  Because the deflection of the face has a bit of a heelward component, this would impart a spin on the ball opposite to what we know from GE.  Not a good condition for slicers!

(3)

 

That's basically a hidden thing in real life because as you will see below, the GE (or negative GE) is pretty small, and due to the shape of clubs we don't see a CG in front of a face as much as designers can push it rearward.  And of course face angle vs path is a bigger factor that will dominate the spin.

 

Horizontal Gear Effect Spin Calculations

 

I'm using Tutelman's equation (which he derived from impulse and angular momentum equations) before he converted for mixed units:  GE Spin = 20.4 * Vb * C * x / I

 

Where Vb = ball speed.  C = CG distance from the face.  x = moment arm from CG to the impact point.  I = MOI of clubhead (need to take the relevant MOI).

 

For the iron CAD model pictured (33.5° 7 iron that is very light weight), the CG is .084" behind the face, and its MOI as shown below* is 2218 g-cm².  *This is the MOI needed in this case - around an axis through the CG vertically parallel to the face:

(4)

 

Maltby MPF and OEMs report MOI like below using a vertical axis through the CG, not parallel to the face.  This MOI would be close to the one above, but with collisions on a surface we have to analyze forces perpendicular and parallel to the surface.  So the way it's normally measured is more relevant to low lofts like with drivers.

(5)

 

Assuming delivery is at its static loft; strike 1/2" towards the toe; with a ball speed of 120 mph, the numbers are as follows:

 

GE spin = 20.4 * 53.6448m/s * .00213m * .0127m / .0002219kg-m²

= 134 RPM

 

As expected not much, but there theoretically.

 

Let's compare different irons taking Maltby MPF data for a few clubs - Titleist 620 MB, T100, T200, T300, T400.  Those nicely range from what we can call a blade to players CB to players distance to GI to SGI.  We can derive the CG distance behind the face (C) by trigonometry:

 

C = (Basic VCOG - Actual VCOG) / sin(loft)

 

Since we only have MOI as reported, those will be close enough for the calculations.  On the CAD model the MOI vertically parallel to the face is only 1.8% higher than what its MPF MOI (vertical axis) would be.

 

Using 120 mph ball speed and ½" toe strike again, here are the GE spin calcs for the Titleist irons:

(6)

 

Notice the C and GE spin are negative for the 620 MB.  This is because the CG is in front of the face according to the MPF numbers.  If basic VCOG and actual VCOG are the same, the CG would be directly on the face (almost the case with the T100 iron).

 

Vertical Gear Effect

 

Here are diagrams of a ball being struck by an iron bottoming on hard ground.  The point of impact is .37" vertically below the CG (.446" below CG when measured on the face).

 

Diagram 7 below is with the head CG directly on the face.  As before the deflection due to impact (pink arrow) is perpendicular to the face, inline with the force on the clubhead, resulting in a loss of strike efficiency and no GE.

(7)

 

Diagram 8 is with the CG behind the face.  The pink arrow is angled a bit downward.  This will impart a little GE:

(8)

 

Diagram 9 brings the CG farther behind the face, as if it's morphing into a hybrid.  The pink arrow angles downward even more:

(9)

 

Diagram 10 is zooming in showing the deflection arrow broken into components perpendicular to the face and parallel to the face.  The circled arrow is the deflection component causing a friction force imparting GE spin:

(10)

 

The farther the CG is behind the face, the more the deflection arrow angles toward the face, hence the reason drivers have the most GE.

 

Diagram 11 brings the CG in front of the face.  As before this will impart a reverse GE "pulley effect".

(11)

 

Vertical Gear Effect Spin Calculations

 

Same equation as before:

GE Spin = 20.4 * Vb * C * x / I

 

This time we need to use I (MOI) around a horizontal axis like this:

(12)

 

The CAD model shows this is only 557 g-cm², 25% of the other MOI taken before, or a quarter the resistance to rotate in this direction.

Assuming the strike pictured in the diagrams, and ball speed at 120 mph, here's the calculation:

 

GE spin = 20.4 * 53.6448m/s * 00213m * .01133m / .0000557kg-m²

= 475 RPM

 

Nothing huge again but more significant than the horizontal GE.

 

Let's look at the Titleist irons again, adjusting numbers for vertical GE.  Since we don't know MOI around a horizontal axis like we need for the calcs, I will assume 25% of the reported vertical MOIs, similar to the CAD model.  Assuming a strike ½" below the CG measured on the face, and 120 mph ball speed:

(13)

 

GE spin numbers are more significant here because of the low MOI as the clubhead deflects in this direction.  T100 again has almost no gear influence.  620 MB has a negative number again - reverse GE.  T200 and T300 are close.  T400 with the farthest back CG has much more GE spin.

 

Calculations vs Reality 

 

As mentioned Tutelman takes a true gear-to-gear approach:  In his calculations, the tangential velocity of the point of impact on the clubhead is the same tangential velocity the ball gets (ωC in the equations).  I have to believe there are losses in reality like anything else when dealing with conservation of energy and momentum in a collision (vibrations, inelastic deformation, heat, other).  Different balls and clubfaces will have different coefficients of friction.  Those would have to be applied in friction force calculations.  Actual GE spin numbers vs calculated is something I don't know exists because of lack of GE studies in controlled environments. 

 

It should be relatively easy to calculate theoretical ball spin due to clubhead speed, dynamic loft, and delivery in a similar way Tutelman calculates gear effect as a 1:1 transmission from club to ball.  It won't reflect reality because of all the real life factors, but as a comparison to GE spin mathematically as a ratio, it might shed some light to how much spin can be accounted for by GE given a certain iron head at a certain dynamic loft, strike location, and ball speed, knowing its actual total spin.  However you can probably deduce that already with launch monitor data esp. with robot testing.

 

Tutelman goes as far as estimating how much a shaft can restrict the head rotation and limit GE.  Analyzing that effectively would require computer simulation with FEA software.  However he can estimate that even a low torque shaft can only resist about 1% of what the clubhead's MOI can.  Vertically is another story, and he concluded that a shaft can limit up to 14% vertical GE, likely less, though he's not the most confident with the end calculations.  Again it would best be done with computer analysis with accurate models. 

 

Thoughts 

 

IMO vertical GE is probably more of a thing than many think when it comes to comparing irons of different builds.  Strike for strike, loft for loft, there are still differences in CG and MOIs of clubheads that will make the impact with the ball different when hit off different parts of the face (let alone the delivery of the club and the feel).  I think it's safe to say we are not striking directly on the CG a lot of times, creating some kind of torque and head rotation.  This might be the case even when we think we're puring it (sweetspot size/area and COR mapping is another topic). 

 

One thing that comes to mind is the flyer, and the much discussed/debated "hot spot" of GI irons.  What the diagrams above help to see is where on the face you actually have to hit that particular iron if you want impact to truly be inline with the CG, and it's pretty high up the face vs where the ball would impact the club on hardpan.  This is despite the CAD model having a relatively low CG (.746") that's below the ball's CG.  The force vectors, which are taken normal to the face, don't align with the head CG until that impact moves another .45" up the face.  And in slow mo videos, there's almost no movement of the ball up the face when fully compressed, only when it's decompressing.  If struck inline with the CG, there will be no rotational deflection, so a more efficient strike, and there would be no gear effect.  Tees, fluffy lies, hitting fat on forgiving range mats - those all help getting high strikes that can demonstrate these high smash lower gear spin conditions. 

 

As seen with the T400, the vertical GE can be significant according to the math.  So if you normally strike low (vs CG) on a GI iron, then all of a sudden hit it higher inline with the CG, it would have a higher smash and lower spin.  There's the flyer or hot spot.  Add in some wet grass to reduce friction, and spin drops even more.  Vertical strike variance on the face should have greater GE spin variance as a component of total spin for a GI vs blade, depending on CG location.  There would be more spin consistency when CG is close to the face, due to a lack of GE (by the math T100 would be more consistent spin-wise than even 620MB).  With better players interested in controlling spin, from a GE point of view alone, it's no surprise there's a general preference for shallow cavity or blade irons.

 

There's certainly a good case for lowering CGs especially for GI/SGI irons, as low strikes would be closer to the CG - more efficient more often, and likely tighter GE spin ranges as the distance from impact to CG reduces.  Even Ping, after many high CG designs, is advertising lower CGs with their latest irons for ball speeds.  It'll be interesting to see their MPF AVCOGs.

 

Hybrids would be interesting to analyze.  I know there are a few in the MPF charts that might be worth running through the GE calculations.  What I suspect is that some may display CGs that of course are farther back than GI irons, but also relatively low MOIs, creating GE situations that may rival those of fairway woods or possibly worse.  GE depends on CG distance from face (C) in the numerator of the equation and MOI in the denominator, so if you have a relatively large "C" with a relatively low MOI, GE spin can get pretty high... toe hooks 😞.  Designing some clubs in CAD other than putters is something I hope to get to this year, and that'll make it easy to analyze these things. 

 

I'll leave it there as this turned into a paper!  With this thread out in the ether, I hope when someone Googles gear effect with irons at least there will be some more info rather than simply "it doesn't exist".  Go Blue 🏉

Edited January 22, 2023 by joostin

[Therty]

Awesome content Joostin!!!

[Red4282]

Mighty impressive work. Thanks for putting that together!

[Cwebb]

Nice in depth analysis.  Something to make note of in the MPF, is the "rearward COG" measurement they list, is a measurement that is combined with the "basic VCOG" to arrive at the Actual Vertical COG.

 

From Ralph Maltby: "Rearward COG is measured from a point where the face plane intersects the ground line.  It is measured in this manner so that it is a relatively simple trigonometry function to find a clubhead's Actual Vertical COG....

When measuring the Rearward COG to be used as a separate and additional performance characteristic, it is measured from the center line of the hosel to the rearward COG."  (example: Dynamic Loft)

 

So if we draw a line down the face to where it intersects the ground line, we end up with the forward measuring point for the RCOG in the MPF.  This is the main reason why iron designs with more offset do not necessarily show a larger rearward COG in the MPF

[nkurz]

Beautiful graphics and great descriptions, and I think your analysis of "flyers" makes sense.  

 

One area I was wondering about is whether it's reasonable to assume that the club head always rotates about its COG, rather than about the combined COG of the ball and the head.  At least while they are firmly in contact, it seems like it would be reasonable to treat it as an inelastic collision.   If true, it might substantially move the COG forward, reducing gear effect, or potentially even inducing reverse gear effect.  Thoughts on why this isn't done, or reasons we should assume independence?  

 

That leads to the other place I thought you might want to explore, or at least mention.  The immediate effect of off center impact is the rotation of the golf club, which "induces" loft, which causes spin.   When Tutelman says "No gear effect", the charitable interpretation is that he means the spin from the new angle is greater than the spin from the gear effect.   I think it would be great to try to quantify this, so that the size of the effects can be compared.  I suspect we'll find that for a given swing speed there is some "sweet spot" for MOI and COG where the two effects mostly cancel.   What would be really cool (and probably make for a fun paper) is if these measurements correspond to the usual difference between "blades" and "cavities".  

 

20 hours ago, joostin said:

Since we don't know MOI around a horizontal axis like we need for the calcs, I will assume 25% of the reported vertical MOIs, similar to the CAD model.

 

It may not affect your conclusion much, but the Wallace et al paper might be a better start, as they measured MOI's for some modern clubs.  If I'm reading it right, they found the "blade" at 1.2 kg cm^2 vertical and 2.8 kg cm^2 horizontal.  Cavity is 1.6:3.6.  See Table 1, X_p vs Y_p.  

 

 

Edited January 22, 2023 by nkurz

[joostin]

Dug through MPF data and found some hybrids - highlighted yellow below.  The light yellow ones look like "thin" ones, not as wood-like as the others.  These are gear effect spin numbers for 1/2" toe or heel side strikes at 120 mph ball speed - same as before.  For comparison I'm leaving the Titleist irons on, and added a couple others I was curious to see.

 

Hybrid Comparison

 

 

The hybrids, as expected, result in higher GE spin numbers than all the irons.  The Nike had the farthest back CG ("C" column is along a line perpendicular to the face as needed, which is different than RCOG Maltby measures that @Cwebb mentioned).  It had a relatively high MOI, but not enough to offset it from having the highest GE.  **Btw, "C" here is not to be confused with the MPF C-dimension... Tutelman chose the same letter, but totally different measurement.**

 

All the hybrids here display what I mentioned in the OP:  Significantly deeper CGs behind the face vs irons (even SGI), but relatively low MOIs vs what we might think compared to irons.  The Pings shown have higher MOIs than all the hybrids.

 

The "thin" hybrids have GE numbers that are lower than the more wood-like ones, but mostly higher than the irons.  These could be considered iron-like (in a GE view), especially the Maltby.

 

Ping Irons

 

The 2 Pings I added display very high MOI but low GE, because look how close their CGs are behind the face.  It seems similar for many Ping irons as well just looking at MPF data (G series).  This supports people that might say "they just go straight".  In a GE view, there basically is none, so any significant side spin / tilted axis is not really from gear spin.

 

Driving Iron Implications

 

Theres only MPF data for usually 6 irons, but assuming lower lofted irons are similar, at least relative to other brands/models.... let's see.  I added a Nike Vapor Fly Pro because I believe it's still used as a driving iron by Finau and Koepka (others?).  Is it special?  It has a relatively high MOI, similar to T400, but low GE spin because the CG is very close to the face (.030" in front, giving a tiny bit of reverse GE).  In addition to them liking the looks, moderate offset, etc., there's basically no gear effect.  Like the Pings it would "just go straight" on mishits - no added gear spin.  What you hit is what you get kinda thing.  Nike VFP has a relatively high CG, but not a big deal off a tee finding a strike inline with the CG.  Plus they have plenty of speed to not worry hitting off the ground.

 

Just looking from a GE point of view, it would make sense for a driving iron to have little GE but high MOI for when you catch it off center.

 

Unicorn Irons

 

I know... whatever works best for you.

But from purely a strike efficiency, gearing, and MOI design point of view, I would say take the pic below.  Move CG (white dot) low somehow to get this theoretical strike inline with the force vector (a line perpendicular to the face inline with the ball CG).  Move CG on the face for zero gear effect.  High MOI and mid MOI designs.  Progressively move the CG along the face as loft changes.  Be able to tweak those CGs per iron based on a person's shaft lean and average strike height off their normal playing ground.  That's a lot to ask for, but hey... 🦄!

 

Edited January 22, 2023 by joostin

[joostin]

1 hour ago, nkurz said:

Beautiful graphics and great descriptions, and I think your analysis of "flyers" makes sense.  

 

One area I was wondering about is whether it's reasonable to assume that the club head always rotates about it's COG, rather than about the combined COG of the ball and the head.  At least while they are firmly in contact, it seems like it would be reasonable to treat it as an inelastic collision.   If true, it might substantially move the COG forward, reducing gear effect, or potentially even inducing reverse gear effect.  Thoughts on why this isn't done, or reasons we should assume independence?  

 

That leads to the other place I thought you might want to explore, or at least mention.  The immediate effect of off center impact is the rotation of the golf club, which "induces" loft, which causes spin.   When Tutelman says "No gear effect", the charitable interpretation is that he means the spin from the new angle is greater than the spin from the gear effect.   I think it would be great to try to quantify this, so that the size of the effects can be compared.  I suspect we'll find that for a given swing speed there is some "sweet spot" for MOI and COG where the two effects mostly cancel.   What would be really cool (and probably make for a fun paper) is if these measurements correspond to the usual difference between "blades" and "cavities".  

 

 

It may not affect your conclusion much, but the Wallace et al paper might be a better start, as they measured MOI's for some modern clubs.  If I'm reading it right, they found the "blade" at 1.2 kg cm^2 vertical and 2.8 kg cm^2 horizontal.  Cavity is 1.6:3.6.  See Table 1, X_p vs Y_p.  

 

 

Thanks for the info, and great thoughts!  I'll get back to you..

[Z1ggy16]

Cool info, thanks. Flyer aspect for me with a club like an i500 or p790 makes sense. I used to be afraid hitting the mid irons off the tee on par3 because I felt like I would randomly see an extra 10-15 yards but I didn't know why. Also makes sense now why my t100's feel so consistent and very neutral. It seems like no matter the lie, my clubs always go about the same distance.

[joostin]

On 1/22/2023 at 10:29 AM, nkurz said:

whether it's reasonable to assume that the club head always rotates about its COG, rather than about the combined COG of the ball and the head.  At least while they are firmly in contact, it seems like it would be reasonable to treat it as an inelastic collision.   If true, it might substantially move the COG forward, reducing gear effect, or potentially even inducing reverse gear effect.  Thoughts on why this isn't done, or reasons we should assume independence?  

I see what you're saying, but honestly don't remember treating a collision problem as something inelastic with a tiny dell time then releasing as an elastic one.  For our case of half a millisecond I guess it usually gets ignored because there's a clear exit condition of the ball at a faster velocity vs the head.  But say the ball sticks to the face and they did act as one body during compression.  The ball CG should follow as one with the club CG.  Does it happen?  Not sure, but I think it's more the case that the ball CG hasn't moved for the most part due to inertia while its deforming.  However during decompression they're definitely not one body as seen in slow mo videos where the ball starts rotating as it's releasing off the face.  In a sense, with gear effect on rigid bodies, the ball "rolls" to a slightly different spot on the face at the end of the impulse time.  In reality the ball will contact at an initial point on the face, compress, then decompress.  As it's compressing and decompressing, the clubhead is rotating, then the ball will release at a slightly different point.  Close enough to the rigid gearing?  I think mathematically that's the best we can do right now.  We know the effect is there with ball flights and launch monitors.  If we treated them as a combined body and inelastic for the whole contact time, a movement around a combined CG can tell us a deflection of initial ball path, but would leave us hanging for gear spin as it wouldn't explain an imparted friction force.

 

On 1/22/2023 at 10:29 AM, nkurz said:

The immediate effect of off center impact is the rotation of the golf club, which "induces" loft, which causes spin.   When Tutelman says "No gear effect", the charitable interpretation is that he means the spin from the new angle is greater than the spin from the gear effect.  

Yeah the GE spin is mostly small compared to spin due to loft and delivery conditions.  In the diagrams above looking at the toe, the impact point is below the clubhead CG.  This will torque the clubhead to a lower loft (and possibly induce GE because of the same movement), and also shift the club down a little due to the forces as seen in slow mo vids.  As loft decreases from initial contact to max compression and decompression, the induced loft should result in lower spin, but possibly gear some spin.  It's all small though.

The iron shots around 26 seconds and 35 seconds in this vid show this deflection:

http://www.youtube.com/watch?v=6dG9hb3_blo

 

On 1/22/2023 at 10:29 AM, nkurz said:

If I'm reading it right, they found the "blade" at 1.2 kg cm^2 vertical and 2.8 kg cm^2 horizontal.  Cavity is 1.6:3.6.  See Table 1, X_p vs Y_p.  

Their Zp is like my diagram (5), and Xp is like diagram (12).  Zp numbers are close to my CAD model but their Xp numbers look really high compared to the CAD.  I gotta trust the CAD here (applied 1020 steel properties to it), but great findings in the paper nonetheless.  I wish they used a real "blade" without a small cavity, but I'm picking.  Looks like a Bridgestone J's Profession Weapon iron!

[Stuart_G]

17 hours ago, joostin said:

I see what you're saying, but honestly don't remember treating a collision problem as something inelastic with a tiny dell time then releasing as an elastic one.  For our case of half a millisecond I guess it usually gets ignored because there's a clear exit condition of the ball at a faster velocity vs the head. 

 

A better reason is that gear effect is really the result of a dynamic interaction between the two bodies.   Any assumption that the two act as a single body would potentially be contrary to their being any dynamic interaction existing.

 

Also, regardless if whether they do "act as one" body for any period of time, the results of treating them as independent bodies would still give the correct results and therefore be a valid approach.  It is obviously an elastic interaction.  The only reason to treat it as a inelastic would be to gain some simplification in the equations.  But unfortunately in this case, such simplifications could be detrimental to the results we're specifically looking for.

 

 

17 hours ago, joostin said:

 

In a sense, with gear effect on rigid bodies, the ball "rolls" to a slightly different spot on the face at the end of the impulse time. 

 

Actually, IMO, it's better to look at it as an imparted velocity - then it is to think of it as a relative motion Largely due to the extremely short contact time and extremely small magnitude of relative motion (as can be seen in high speed videos).  But then, maybe that's just me and the way my brain works.

 

17 hours ago, joostin said:

Yeah the GE spin is mostly small compared to spin due to loft and delivery conditions.  In the diagrams above looking at the toe, the impact point is below the clubhead CG.  This will torque the clubhead to a lower loft (and possibly induce GE because of the same movement), and also shift the club down a little due to the forces as seen in slow mo vids.  As loft decreases from initial contact to max compression and decompression, the induced loft should result in lower spin, but possibly gear some spin.

 

I've come to suspect that the downward motion of the head from impact with a lofted head (e.g. Tutelman's "Newton and the divot") plays a significant roll in the backspin imparted on the ball.  Not exactly the same thing as gear effect since it's a linear motion of the head and not rotational - but definitely related in the way forces are transmitted to the ball.   That might explain why hitting off a hard mat (with the downward motion of the head restricted) can reduce the back spin we see when hitting of those mats.   But I've never gotten to the point of trying to work through the equations to see how much basis there might be for that.

Edited January 24, 2023 by Stuart_G

[BarfordGolf]

Joostin, this is really good stuff - the kind of content people (like me) love to see on the forum!  

 

Just a note on your optimized CG location, under "Unicorn Irons" - don't forget that iron strike is a descending blow, so the impact is always oblique (cg misalignment). The idealized vectors you have drawn are over-constraining compared to the actual dynamics of the impact, I think, where the force vector of the club head is roughly -45 degrees  to the green vector (dark red in my image here). The condition you have drawn there might be more applicable with a Driver, however. 

 

[Cwebb]

50 minutes ago, Stuart_G said:

I've come to suspect that the downward motion of the head from impact with a lofted head (e.g. Tutelman's "Newton and the divot") plays a significant roll in the backspin imparted on the ball.  Not exactly the same thing as gear effect since it's a linear motion of the head and not rotational - but definitely related in the way forces are transmitted to the ball.   That might explain why hitting off a hard mat (with the downward motion of the head restricted) can reduce the back spin we see when hitting of those mats.   But I've never gotten to the point of trying to work through the equations to see how much basis there might be for that.

 

The mat situation is also likely the result of totally clean contact being more difficult from a tight lie, that is not elevated at all on turf.  A good fairway lie is up somewhat above the "ground line".  The slight "drop kick" contact from a mat that may still feel solid, is not totally clean contact and results in less spin

 

 

[joostin]

6 hours ago, Stuart_G said:

I've come to suspect that the downward motion of the head from impact with a lofted head (e.g. Tutelman's "Newton and the divot") plays a significant roll in the backspin imparted on the ball.  Not exactly the same thing as gear effect since it's a linear motion of the head and not rotational - but definitely related in the way forces are transmitted to the ball

That's interesting.  I could definitely see that adding to the friction force imparted to the ball, similar to gear effect.  I didn't see Tutelman making that connection, though it's a pretty significant deflection.

[joostin]

6 hours ago, BarfordGolf said:

Joostin, this is really good stuff - the kind of content people (like me) love to see on the forum!  

 

Just a note on your optimized CG location, under "Unicorn Irons" - don't forget that iron strike is a descending blow, so the impact is always oblique (cg misalignment). The idealized vectors you have drawn are over-constraining compared to the actual dynamics of the impact, I think, where the force vector of the club head is roughly -45 degrees  to the green vector (dark red in my image here). The condition you have drawn there might be more applicable with a Driver, however. 

 

/cdn-cgi/mirage/cbd6c01271048efd0541935dc7ed3ac1d2d79f1a574a1ed018d17f8873efe2e4/1280/cdn-cgi/mirage/cbd6c01271048efd0541935dc7ed3ac1d2d79f1a574a1ed018d17f8873efe2e4/1280/https://wrxcdn.golfwrx.com/uploads/monthly_2023_01/image.png.7d657f0515839079bae3c260c93c4481.png

Thanks!  I figure most people roll their eyes with technical stuff, or if math is involved, and it doesn't do anything to help their game 🤷‍♂️

 

My take is that, yes, the club path will determine the velocity vector at impact, but for collision conditions against a surface we have to break those into components normal to and parallel to the surface.  So the dark red line would be broken into normal velocity and parallel velocity.  The normal component will result in my green arrow force for projectile motion.  The parallel component will result in the friction force (would be an arrow pointing down along the face) for the ball's main spin.

[nkurz]

10 hours ago, Stuart_G said:

I've come to suspect that the downward motion of the head from impact with a lofted head (e.g. Tutelman's "Newton and the divot") plays a significant roll in the backspin imparted on the ball.  Not exactly the same thing as gear effect since it's a linear motion of the head and not rotational - but definitely related in the way forces are transmitted to the ball.

 

It's definitely related, but I'm not sure whether it's better to view the downward motion of a lofted club head as a cause of spin or an effect.  I think the "effect" interpretation might be more intuitive:  the loft causes spin, and the force opposing the spin causes the club to deflect downward.  

 

In defense of that view, here's a page from Peter Dewhurst's "Science of the Perfect Swing" that (if I'm interpreting him correctly) makes this argument.  Or maybe that's not what's he's saying?  In any case, he's definitely addressing the relation between the downward jump of the club and the loft-induced spin.  

 

 

 

This does raise the question:  have you (collectively) checked out this book: https://www.amazon.com/Science-Perfect-Swing-Peter-Dewhurst/dp/0199382190?   I definitely need to read it more closely, but my impression was that it's by far the best of the recent "science of golf" books.  It's a great update to Jorgensen, which was in turn a great update to Cochran and Stobbs.  

 

 

 

 

[Stuart_G]

9 hours ago, joostin said:

That's interesting.  I could definitely see that adding to the friction force imparted to the ball, similar to gear effect.  I didn't see Tutelman making that connection, though it's a pretty significant deflection.

 

No, he didn't.   But then, as far as I know, Tutelman has not tried to look at the "mat effect" on spin.

 

15 hours ago, Cwebb said:

 The slight "drop kick" contact from a mat that may still feel solid, is not totally clean contact and results in less spin

 

Yes, that's certainly another potential contributor if the mat changes the velocity vector (direction) of the head prior to impact with he ball.     Personally I would think that would result in greater inconsistencies in the spin difference between mat and turf for any one single mat session than what I've seen - but then what I've seen is hardly a statistically significant sample size.

 

5 hours ago, nkurz said:

 

It's definitely related, but I'm not sure whether it's better to view the downward motion of a lofted club head as a cause of spin or an effect.  I think the "effect" interpretation might be more intuitive:  the loft causes spin, and the force opposing the spin causes the club to deflect downward.  

 

Anything that happens during impact or after it is technically an effect.   And if any effect, in turn causes some other subsequent effect - then it can be a cause as well as an effect.   But in most cases the distinction is not going to be all that important when dealing with such an small impact time.

 

The downward deflection of the head is really about the conservation of linear momentum  and energy, not spin or angular momentum/energy.    It's better to think of it as -  the club is going down to compensate for the ball going up  (assuming the club's motion is unrestricted).

 

 

5 hours ago, nkurz said:

In defense of that view, here's a page from Peter Dewhurst's "Science of the Perfect Swing" that (if I'm interpreting him correctly) makes this argument.  Or maybe that's not what's he's saying?  In any case, he's definitely addressing the relation between the downward jump of the club and the loft-induced spin.  

 

He's produced an equation for spin of the ball that is a function of the tangential component of the force vector from impact.   That's definitely a valid contributor to the ball spin and is believed to be the dominant factor - but it isn't the same as what I was saying.    That would potentially be an additional component of the spin that is related to the downward velocity of the head and the friction forces that occur between the ball and face.   He mentions friction a little but is basically ignoring it's effects - likely due to the complexity involved.

 

[BarfordGolf]

12 hours ago, joostin said:

Thanks!  I figure most people roll their eyes with technical stuff, or if math is involved, and it doesn't do anything to help their game 🤷‍♂️

 

My take is that, yes, the club path will determine the velocity vector at impact, but for collision conditions against a surface we have to break those into components normal to and parallel to the surface.  So the dark red line would be broken into normal velocity and parallel velocity.  The normal component will result in my green arrow force for projectile motion.  The parallel component will result in the friction force (would be an arrow pointing down along the face) for the ball's main spin.

It will depend on the reference frame you choose to define to do the collision physics, but yes you will for sure take the component vectors. That makes sense. 

[nkurz]

On 1/25/2023 at 5:20 AM, Stuart_G said:

He's produced an equation for spin of the ball that is a function of the tangential component of the force vector from impact.   That's definitely a valid contributor to the ball spin and is believed to be the dominant factor - but it isn't the same as what I was saying.   

 

Maybe you could explain more how what you are saying is different?  I was concentrating more on his sentence "Neglecting any center of mass offset, the tangential force integrated over the contact time, which causes the tangential velocity of the ball, must also be solely responsible for the ball angular velocity."  I think he's right about this, although the converse is not true: while tangential force is the only thing that produces spin, this does not mean that all the tangential force goes into producing spin.  As you said elsewhere, most of it goes into making the ball go up. 

 

On 1/25/2023 at 5:20 AM, Stuart_G said:

 

That would potentially be an additional component of the spin that is related to the downward velocity of the head and the friction forces that occur between the ball and face.   He mentions friction a little but is basically ignoring it's effects - likely due to the complexity involved.

 

 

Dewhurst mostly ignores spin in the part I quoted, but Chapter 4 on "The generation of ball spin" is one of the more complete treatments of friction that I've seen.  It's got a lot of interesting analysis looking at what the tangential forces must be during the impact, based on how the spin rate changes during the (very brief) impact.   He describes with a model of the ball that separates Normal COR from Tangential COR, and then tries to explain what we actually see based on that and frictional forces.   Unfortunately for me, I don't feel like I fully understand what he's saying yet.  

 

He bases a some of this on work by Rod Cross at the University of Sydney.  Cross has a recent paper and seemingly relevant paper that I haven't been able to access: 

Experimental study of the gear effect

Rod Cross

Published 8 October 2021 • © 2021 European Physical Society
European Journal of Physics, Volume 42, Number 6

Citation Rod Cross 2021 Eur. J. Phys. 42 065013

DOI 10.1088/1361-6404/ac2938

 

Abstract:

The gear effect arises during the collision of a ball and an extended object due to rotation of the object across the surface of the ball. The effect is well known in golf, drivers being designed with a convex face to help reduce the problem of a mishit. An experiment is described to examine the gear effect for two different balls, one with a high tangential coefficient of restitution and one with a low coefficient. The outgoing ball spins were different, indicating that a driver designed for one type of golf ball is unlikely to work well with a different type of golf ball.

 

Any chance any of you have academic access to this article and could pass on a copy? 

[Stuart_G]

24 minutes ago, nkurz said:

 

Maybe you could explain more how what you are saying is different?  

 

I'll try.  Not sure I can say it any better than I already have but you never know until you try.

 

 

24 minutes ago, nkurz said:

I was concentrating more on his sentence "Neglecting any center of mass offset, the tangential force integrated over the contact time, which causes the tangential velocity of the ball, must also be solely responsible for the ball angular velocity."

 

He's only looking at the force acting on the ball from the club's pre-impact velocity and how (just) that force imparts spin on the ball.

 

You'll also note that none of those equations or force diagrams even begin to deal with gear effect.

 

But impact with the ball causes the motion of the head to change (just as it does with gear effect).   And thanks to the friction that exists between the face and ball while they are in contact,  that change in motion of the head can impart additional forces on the ball (just like gear effect) during the time they stay in contact.    The only difference between this and gear effect is that gear effect comes from a rotation of the head,  this is from a linear deflection.

 

He's looking at just the more theoretical ideal - no real compression of the ball and only instantaneous contact between the two bodies (think of impact with a steel or titanium ball).

 

24 minutes ago, nkurz said:

Any chance any of you have academic access to this article and could pass on a copy? 

 

Sorry, No.  I'm in industry, not academics - and it's not related to any of my current work (which is really fluid dynamics).

 

But looks like you might be able to get it through a (free) 15 day trial membership on deepdyve.com.   I'm not familiar with the site but it did come up as being available there.

 

Edited January 26, 2023 by Stuart_G

[BarfordGolf]

I couldn't fin the 2021 paper you linked, but I did find a previous published paper from the same author, Rod Cross: Experimental study of the gear effect in ball collisions

gear-effect.pdf

[ChaosTheory]

I'm not a physics major but I understand the basics if not the math.  Re vertical GE:  On the iron diagrams, in all cases the red arc of the iron's rotation at impact is clockwise.  And the ball is impacting the lower section of the face, so the ball should pick up CCW spin, always, even if the COG is in front of the face.   But your conclusion is that in that case the ball picks up clockwise spin.  The only condition in which I can see that is if the red rotation at impact is CCW.  Which would require a higher impact position.

 

Please help me on this.

 

@joostin

[ChaosTheory]

Regarding the unicorn idea, Maltby had the Glider models, some of which had the COG at or below 0.500".  They went high and short.  Not sure about spin.  I think I recall them being pretty straight, though.  They had a huge horizontal MOI.

Edited January 26, 2023 by Snowman9000

[Stuart_G]

34 minutes ago, Snowman9000 said:

Re vertical GE:  On the iron diagrams, in all cases the red arc of the iron's rotation at impact is clockwise. 

 

Yes - because they are all examples of toe side misses.

 

34 minutes ago, Snowman9000 said:

And the ball is impacting the lower section of the face, so the ball should pick up CCW spin, always

 

No.  Look at the small pink arrows.   That is the direction of motion of the face relative to the ball where the two are in contact with each other.   That's (sort-of) the "force" that the motion of the head imparts on the ball.   So the (potential) force creating gear effect comes from that pink arrow.   So technically what gives the gear effect is the component of that pink arrow that's tangent to the face plane.  

 

In simpler terms, when that pink line is completely inline with the  yellow and green arrows - then the force is inline with the ball c.g. and does not contribute to the spin.    If the pink arrow points down a little off of the green/yellow arrows, then it does impart some CCW spin to the ball.   If the pink arrow points up a little off of the yellow/green arrow, it is imparting CW spin the the ball.

 

Edited January 26, 2023 by Stuart_G

[ChaosTheory]

5 hours ago, Stuart_G said:

 

Yes - because they are all examples of toe side misses.

 

 

No.  Look at the small pink arrows.   That is the direction of motion of the face relative to the ball where the two are in contact with each other.   That's (sort-of) the "force" that the motion of the head imparts on the ball.   So the (potential) force creating gear effect comes from that pink arrow.   So technically what gives the gear effect is the component of that pink arrow that's tangent to the face plane.  

 

In simpler terms, when that pink line is completely inline with the  yellow and green arrows - then the force is inline with the ball c.g. and does not contribute to the spin.    If the pink arrow points down a little off of the green/yellow arrows, then it does impart some CCW spin to the ball.   If the pink arrow points up a little off of the yellow/green arrow, it is imparting CW spin the the ball.

 

I’m talking about the illustrations under the Vertical Gear Effect heading.

 

I see the relationship of the pink line to the COG, but still, if the head is rotating CW (forward), how can it not have CCW influence on the ball?

Edited January 27, 2023 by Snowman9000

[joostin]

36 minutes ago, Snowman9000 said:

I’m talking about the illustrations under the Vertical Gear Effect heading.

 

I see the relationship of the pink line to the COG, but still, if the head is rotating CW (forward), how can it not have CCW influence on the ball?

@Stuart_G explained correctly, but here's a diagram with pink component arrows again.  The face's deflection velocity component at impact along the face is upward.  So not a gear in this case, which is why I called it a "pulley effect":

[joostin]

12 hours ago, Stuart_G said:

The only difference between this and gear effect is that gear effect comes from a rotation of the head,  this is from a linear deflection.

In keeping with the mechanical device names - gear effect, "pulley effect" - probably "rack and pinion effect" makes sense for this linear deflection induced spin.  Just coining names now 🤷‍♂️

[Stuart_G]

 

11 hours ago, joostin said:

  So not a gear in this case, which is why I called it a "pulley effect":

 

It's still a gear.   Just one where the teeth on one gear is on the inside of the circumference, not both on the outside.  (Internal gear vs external gear).   Like the ring gear of a planetary gear system.

 

12 hours ago, Snowman9000 said:

if the head is rotating CW (forward), how can it not have CCW influence on the ball?

 

It's like the relationship of the planet gear and ring gear in the motion that they call "reverse" - that you can see at time 0:48.  Both the ring gear and planets are rotating in the same direction - either both CW or both CCW.

 

 

Edited January 27, 2023 by Stuart_G

[nkurz]

22 hours ago, Stuart_G said:

He's only looking at the force acting on the ball from the club's pre-impact velocity and how (just) that force imparts spin on the ball.

 

Hmm, I think you might be misinterpreting what he's doing, perhaps because I showed just this page without the set up.  I think he's actually working from the club's post-impact tangential velocity (left as an unknown).  He's then saying that this velocity creates some unknown tangential force on the ball  which has two effects:  spin and deviation from normal direction.   There's no presumption of an ideal collision here, and no assumptions made either way about friction, although he is assuming impact at COG.

 

Breaking apart the final formula I included:

ω=mv1sin(δ−αvb)rb /Ib.     (3.10)

 

BallSpin = BallMass * BallVelocity * sin(DynamicLoft-LaunchAngle) * BallRadius / BallMOI

 

He's claiming an invariant relationship between final ball spin and the amount that launch angle is less than the loft angle, regardless of the how the tangential force manifests during impact.  The actual values will depend on friction and ball deformation.  For example, if friction is zero, launch angle will be exactly equal to loft angle, and the ball will have zero spin.  The next chapter is about extending this to include gear effect, trying to figure out the actual tangential forces, and showing the how changes to the surface (like grass) cause different effects at different lofts.  

 

One cool result, which I hadn't been aware of is, is that backspin for low lofted clubs is actually higher with a "grassy lie", with the crossover point being about a 7 iron, which is neutral to face friction conditions.  I'm tempted to start a thread trying to go through this chapter page-by-page.  While there is a lot of very interesting stuff, and while I trust his derivations more than most sources,  I could definitely use help in places to understand his reasoning.  

 

Edit: The other option, of course, is that you are way ahead of me, already taking this into account, and none of this is new info.  Or that I'm just completely wrong.  It's always hard to tell!

Edited January 27, 2023 by nkurz

[Stuart_G]

On 1/27/2023 at 10:15 AM, nkurz said:

 

Hmm, I think you might be misinterpreting what he's doing, perhaps because I showed just this page without the set up.

 

That's certainly possible.

 

 

On 1/27/2023 at 10:15 AM, nkurz said:

There's no presumption of an ideal collision here, and no assumptions made either way about friction, although he is assuming impact at COG.

 

Yes, he is assuming an ideal elastic collision.   The fact that he's using conservation of momentum equations is enough to show that.

 

He also explicitely states he's ignoring the potential rolling of the ball and the effects of any rolling friction that result.  Not to mention the energy lost in the deformation of the ball.    So really the equations show are generated with the assumption that the ball does not deform - which is really the same as assuming perfect elasticity.

 

That's not really a knock.   Most impact analysis start out that way because it's easier - then the imperfections can be accounted for a later stage of the analysis.

 

 

On 1/27/2023 at 10:15 AM, nkurz said:

BallSpin = BallMass * BallVelocity * sin(DynamicLoft-LaunchAngle) * BallRadius / BallMOI

 

Very minor point - "dynamic loft" and "launch angle" are angles defined against the horizon.   His work is independent of any horizon and those angles are defined relative to the head, not the horizon.

 

 

 

On 1/27/2023 at 10:15 AM, nkurz said:

He's claiming an invariant relationship between final ball spin and the amount that launch angle is less than the loft angle, regardless of the how the tangential force manifests during impact.

 

Yes - assuming that the normal force is aligned with the head c.g. and that the tangential force and change in linear momentum is the only source that contributes to generating spin in the ball.  And that force is applied to a ball with no deformation.   

 

 

On 1/27/2023 at 10:15 AM, nkurz said:

 The actual values will depend on friction and ball deformation.  For example, if friction is zero, launch angle will be exactly equal to loft angle, and the ball will have zero spin.  

 

Yes friction is required to allow that tangential force to be transmitted between the two bodies, but he doesn't really cover that in the page you showed.

 

 

On 1/27/2023 at 10:15 AM, nkurz said:

Edit: The other option, of course, is that you are way ahead of me, already taking this into account, and none of this is new info.

 

 

No don't worry about that.  I dont' have the time to work through any of the equations myself.   🙂

 

 

[Z1ggy16]

I just got my simulator up and running in my garage and noticed very low spin... This thread got me thinking, is it almost or entirely due to vertical gearing from my iron? 

 

With the very firm and very tight like from the mat, the ball sits ever so higher. Using some face spray, even my best hits are 6 grooves high and scruffy ones I've seen at 7. I haven't noticed launch going up much but spin is dropping 1-2k or more. Only time my spin seems to go up is on slightly fat hits, which I assume happens because the club bounces up slightly, lowering contact on the face. 

 

There's a whole thread with the gurus like Stu and Howard going on about why, people trying to think of code to try and simulate this phenomenon, but I think it's possibly as simple as this.