Lessons from Progressive Launch Iron Sets
I get a lot of comments from readers of my golf shaft site, GolfShaftReviews, that they love the information but do not understand some of it. Much of this article will be a discussion of golf shaft EI profiles. If you are new to this term, my friend Dave Tutelman published an article explaining the basics many years ago. I wrote a more detailed discussion in these articles, Golf Shaft EI Profiling and Beyond Frequeny Matching on GolfShaftReviews. Other articles on this site further explain the background information you may need to understand this discussion.
I have been devoting a lot of time lately to completing the Fit2Score shaft profiling software that is now available through subscription. Many years ago I developed a spreadsheet for owners of my EI instrument that quickly profiles a set of shafts destined for use in a set. I call the process Iron Set Certification. The certification spreadsheet serves the club builder as a place to store not only the shaft data for a set, but most other aspects of the set; head brand, weights, balance, loft, lie, length, grip, etc. for future reference for that client. Using this software I have profiled a vast number of iron shaft sets. It became apparent that not all sets of shafts had the same bend profiles through out the set. In many sets there was some degree of flighting between the shortest shaft and the longest shaft in the set. I first heard the term flighting in reference to Project X shafts when they were made in Brunswick Connecticut by the Royal Precision. Flighted sets are designed to launch the long irons higher and the short irons lower. The objective is uniform ball flight height through out the set. The benefit is tighter distance gap control between clubs.
Be patient with me while I discuss a little more history. When I began as a hobby club builder 17 years ago I was introduced to shaft profiling using a frequency instrument. This is not simply measuring the butt frequency of a shaft. The shaft is measured at 5″ increments from tip to butt. The software that supported that system compared irons by looking at 6 irons only. When I developed my EI software I followed that model, writing my system to compare the bend profiles of 6 iron shafts. As I did numerous iron set certifications it was apparent how shortsighted only comparing 6 iron shafts was. An important aspect of iron shafts is the difference in bend profiles between the long and short iron shafts in the set. The complexity of converting 16 years of work to set profiles from 6 iron only profiles kept me from addressing this issue. About a year ago with the release of the True Temper Dynamic Gold Pro I decided it was critical to the understanding of irons shafts to incorporate set profiles. The view of irons as sets, that came from set certification profiles, needed to be brought into the Fit2Score shaft software system. It took a year to complete and debug the system software upgrade. I am still in the process of loading the data for the 300 iron shafts I have profiled in the past.
I have been looking at golf shaft EI profiles for 15 years. On this venture I continue to discover and understand nuances of shaft design and performance. This article is an attempt to explain an understanding of iron shaft sets that has developed over the last 5 years. If you get it on the first read, congratulations.
The amount of flighting in iron shaft sets varies from manufacturer to manufacturer, and from model to model. A good understanding of EI bend profiles can be seen in shafts sets that were intentionally designed for progressive launch. I wrote a detailed review of such a shaft, the Dynamic Gold Pro, last year. Read it as background information about flighted or progressive launch iron sets.
Look at the difference in the upper chart between the bend profiles of the wedge, 6 iron and 2 iron shafts in these sets. The vertical axis is the stiffness of a 10″ section of the shaft, centered at the position noted in the horizontal axis. The tip is to the left, the butt to the right. You can see that the butt of the shaft is stiffer than the tip. The tip is not always the softest section of the shaft. Very often the softest section is 10 to 12 inches up from the tip. If your measuring technology, for example frequency, does not allow accurate readings in this range, you are flying blind.
As you look at the R, S and X flex versions in the upper chart, you see that the entire curve moves upward as the shaft gets stiffer. And, in this model golf shaft, the shape of the profiles change as well. This is not true of all shafts. It is another reason that knowing both wedge and long iron profiles are important to the tour level fitter.
You can see how much flatter the wedge shaft profiles are than the 2 iron profiles. The steeper the change in stiffness from tip to butt, the higher the shaft will launch. The point where the bend profiles change the most is an indicator of shaft contribution to launch. The closer the maximum bend point is to the butt, the higher the shaft will launch.
The lower chart, shows the change in stiffness point to point on the shaft. It amplifies the understanding of the bend point of the shaft. You can see how the change in stiffness, especially in the R flex model, is steeper and moves significantly toward the butt in the 2 iron shafts. This method, looking at change of stiffness, is essential to understand shafts through their EI profiles.
Understanding the EI profiles is tricky. As you look at the actual profiles your eyes are drawn to the lowest point on the shaft, where it changes from losing stiffness to increasing in stiffness. But in the lower signature chart, the change of stiffness is not greatest at the lowest point of the EI curve. It is higher in the shaft, closer to the butt, where the shaft is rapidly losing stiffness. Doing a compression test on the R Flex 2 iron shaft, the point where the shaft bends is 17″ from the tip. This is exactly the spot that is the lowest in the profile signature chart of this shaft.
And that is a simple understanding of reading shaft launch propensity from 3 point EI data. This is not clearly shown in frequency or deflection profiling systems. But it is hard to miss in 3 point EI profiles. And that is why 3 point EI profiles are the language of shaft designers.
Lets take a quick look at the Dynamic Gold X100 and the Dynamic Gold Pro X100 wedge and 2 iron shafts. The Dynamic Gold X100 is a very flat profile as iron shafts go. There is little launch assistance and the wedge and 2 iron have the same profile. The wedge is stiffer, as indicated by being higher on the chart, but there is very little difference between it and the 2 iron shaft. Now look at the Dynamic Gold Pro X100. First you will notice a distinct zone in the 12″ to 22″ area where their is a noticable loss of stiffness. And, that loss of stiffness is more pronounced in the 2 iron than in the wedge. Then, with the profiles superimposed on each other, you can see the wedges are quite similar. The 2 iron shafts are noticeably different. This illustrates why a fitter needs to know set profiles, not just 6 irons.
A golf club fitter needs to know the properties of the shafts he is fitting you with. I first learned about shaft profiling from Tom Wishon. He assembled a database of linear shaft bend profiles using a strain gauge frequency instrument. It got my interest and I put a great deal of time into frequency profiling shafts on my own and developed a rudimentary database of my own.
During a visit to a shaft company R&D site I was introduced to the concept of EI profiling. That began my exploration of other methods of describing the properties of a golf shaft. I learned the term EI from engineers in the business of designing shafts. The instrument used was in the $10K+ range, not affordable to most. Not even all shaft companies had these instruments.
It took about 2 years to come up with an workable, affordable EI measuring design. After many years of use, I decided it was time to redesign and improve the original. I knew all the sources of error in the original design and fixed them. The machining was beyond the capacity of my mill and I had to outsource the cutting of the parts. The precision of the parts made by a machine shop further improved the instrument and made designs I could only imagine possible.
The new design far exceeded expectations. Most of the original instruments have been upgraded. A number of my instruments are now owned by shaft companies. The latest to acquire one has reported it is the fastest, easiest to use and most accurate instrument in the business. The first production run of the new instruments is nearly sold out and a second production run is commencing.
Recent promotion of hoop strength by a shaft company lead me to explore how hoop strength is measured. One method is compression testing. A tube is placed on a block and a weight is placed on it. The amount it bends under this load is a measure of hoop strength. After a few tests I designed a support and added hoop strength measurement to my instrument and database.
With a driver shaft database of 1200 shaft profiles that include stiffness, torque and hoop profiles, I and my affiliated fitters know the shaft you are being fit with. That knowledge makes us exceptional fitters. Six of the fitters using this system are on the recent Golf Digest Top 100 ClubFitters list. To learn more about the instrument and software look at the bottom of the Products page for links.
This year Matrix Shaft company has put together a fitting system. It combines the Red Tie, White Tie and Black Tie with the REIGN product line. I start with your current driver, then select the appropriate Red Tie weight and flex. From the launch and spin numbers gathered from good test swings, the shafts on the grid shown are tested to fine tune launch and spin. The system was developed by Matrix based on both robot and human testing. The idea got my attention and I brought in the entire system of 38 shafts.
I built the system with the UniFit driver tip system and can use this Matrix of shafts in most adjustable hosel driver heads. My fitting heads this year include the TaylorMade R15 and the Mizuno JPX850. Both can be used with this set of shafts.
To make certain you get the right grip fit, this fitting kit uses Pure grips. Pure grips can be easily blown on and off. I do fittings with the proper grip size and texture.
If your looking for a new driver or thinking you would get more distance from you current driver if it had the right shaft, book a fitting appointment and discover which shaft if right for you.
Custom Built Clubs – Golf Shaft Set Certification
I have been using the prototype of our new version shaft EI instrument for several months. The parts are now being machined and distribution of the upgrade and the new instrument will begin in July of 2014. Much of my software is being revised.
When I custom build iron sets I document the measurements taken. Often the measurements include checking every shaft in the set. This is offered as an additional service. On occasion a shaft in a set is an outlier. It does not match the rest of the shafts in the set, or it has a weak or hard spot along its length. That shaft gets returned to the manufacturer and replaced. Without having each shaft checked, you will never know if your set is consistent. The following report is provided to document the certification and building specifications on custom built sets.
Hybrid Golf Club Shafts
After many years of fitting with old TaylorMade Hybrid heads I converted to the 2014 Adams XTD Ti head. I believe it is the pinnacle of hybrid golf head design technology. That conversion required me to change the tips on a huge accumulation of fitting shafts. In doing so, I took a hard look at what I was using and assembled a unique set of hybrid shafts. My primary objective was to assemble a diverse set of shafts that did not significantly overlap each other. Having the EI profiles of every shaft I have made this a manageable task.
I get asked a lot of questions by players in their process of deciding on a club fitter. Some to gauge my experience and expertise, other to understand what equipment I use in the fitting process. My golf shaft review site, GolfShaftReviews is the most comprehensive and detailed source of information about golf shafts on the internet. But there is no clear indication there about what shafts I have in my fitting system. This is a quick review of the shafts I have available for Hybrid fittings. My fitting system includes about 45 shafts. The selection is from different manufactures and include a wide range of designs and weights. Below is a quick overview of the shafts available for testing during a Fit2Score Hybrid Golf Club Fitting.
KBS Tour C-Taper Lite
I like fitting strong players with steel in their hybrids. They are easy to hit long irons that give a bit more launch and spin than a similar lofted iron. The C-Taper Lite is a lighter softer version of the KBS Tour C-Taper. The lighter weight makes low launch steel an option for more players that the original KBS Tour C-Taper. This is an excellent super low torque option offering superior control for a strong player.
KBS Tour C-Taper
If you are a strong swinger looking for long hybrid shots that do not balloon in the Texas wind this is the shaft. If you do not feel you can take a full swing with your hybrid and not completely turn the head over and create hooks that can get around a barn, this is your shaft. I have had numerous conversations with Kim Braly about hybrid shafts. We have the same opinion, if you are fitting a strong player that hits down through the ball, use steel in their hybrid.
KBS Tour Hybrid
The KBS Hybrid shaft is one of their first designs. By comparison to the current shafts it is soft. It is stepless, the first stepless shaft produced by Femco Steel bearing the KBS name. Like all the Kim Braly designs, it consistently looses stiffness from butt toward tip. The deflection curve shows it is significantly softer than the KBS shafts that followed. If you are looking for a mid weight hybrid, with outstanding torque properties at a reasonable price. you should try the KBS Tour Hybrid
Mitsubishi Diamana Thump
The Diamana Thump is no longer stocked in the US or shown in the Mitsubishi catalog. It is still available on special order from Japan. The torque numbers look like steel. It is a demonstration of what is possible with carbon fiber if cost is no object. The feel is in the name, thump. I play it, I love it. It is not for everyone, most find it too stiff. If you want to try it, its in the Fit2Score fitting system. Be prepared to wait a month to get the shaft from Japan.
Mitsubishi Diamana D+
Adams hybrids have over the years offered great shafts in their hybrids. In 2014 the Diamana D+ is the stock shaft in the classic design Adams Super 9031 hybrid, a 2013 model. Mitsubishi no longer labels shafts ‘made for’. Instead a line of shafts, the + models, fill that slot. Compare this shaft to the Thump and you will see the difference, about a half degree of torque. Does it matter? That is a question that can only be answered in a radar tracked fitting session. The Adams version of the Diamana D+ is 10 grams lighter that the catalog version. If you have not developed the strength to hold on for a late release, 10 grams lighter is a good thing.
Mitsubishi Fubuki Ax Hybrid Shaft
The Fubuki Ax Hybrid is the second generation shaft to bear the Fubuki name. The profile is similar to the Diamana Blue Board. In its weigh class, 70-80 grams is is among the best hybrid shafts on the market. A look at the tip torque numbers and radial consistency indicated why this shaft delivers consistent ball flight. It is a first class product. It is a mid launch design that works well for aggressive transition, fast tempo golfers in the moderate speed range. The 80X version is stout. It will not Thump on your wallet, but it will put your hybrid cost close to what the average retail is for a driver.
Mitsubishi KuroKage Black Hybrid
Mitsubishi has always offered a lower price range shaft selection for those that wanted to experience the Mitsubishi feel but did not want to invest in a Diamana. The KuroKage is currently that product. This shaft was last years stock Adams hybrid shaft. These budget priced models are now made with High Density Prepreg strategically placed in the shaft. Not as much as will be found in the signature Diamana line, but enough to make this an above average shaft at a below average price. The profile is similar to the Diamana Blue, soft mid in relation to tip and butt. It tends to launch a little higher than average and is a good fit for a quick tempo swing.
Mitsubishi Bassara Ultra Light Hybrid Shaft
If you’re still reading, you realize by now Fit2Score is a full line Mitsubishi distributor. The 45 to 60 gram Bassara is the lightest hybrid golf shaft I use. It has enough torque to transmit feel to the slower swinger, yet not so much that it compromises dispersion to deliver launch. Look at how the tip stiffness tightens on the EI profile. Launch is accomplished back away from the tip, a further indication that this design does not create dispersion that comes with a soft tip strategy to delivering launch. If your strength requires light, the Bassara UltraLight shafts are as good as it gets in the 50 gram weight class.
Matrix Ozik Altus hX3White Tie
The Matrix Ozik Altus hX3 White Tie is the stock shaft in the 2014 Adams DHY hybrid driving iron. That particular model is at the moment the #1 hybrid on the PGA tour. The low spin balls designed for driver distance are not spinning enough with long irons to create drop and stop flight. The Adams DHy addresses that problem with a lower center of club head that retains the look and playability of a long iron. The EI profile is a common driver shape, not often seen in hybrid shaft designs. The Mitsubishi Fubuki Ax has the same design. That upturn at the tip does a lot for bringing the overall deflection of this shaft into line with shafts that are heavier and stiffer overall. In my first fitting with this shaft in the bag it was the winner for a truly talented ball striker that was best fit with light weight shafts. Early success with any addition to my fitting system always gets my attention.
Matrix Ozik Altus hQ3 Red Tie
Another stock shaft in the 2014 Adams hybrids, the Matrix Ozik Altus hQ3 Red Tie comes with the XTD Ti hybrid. The Adams XTD Ti like many of the 2014 designs merge the patents of the new Adams parent, TaylorMade, with the Adams patents, creating what I think are the best heads in the business. There must be some other believers as well, Ernie Els just joined the Adams team. This design reminds me of the Graphite Design YS Hybrid. The YS was one of those shafts my customers loved. I would send people to the range, I worked indoors at the time, with the shafts that tested well, and they kept coming back with the YS as their pick. The long tip section makes this shaft easy to trim to the proper stiffness for the range of hybrid lofts now available. I had found the YS to be a mid launch mid spin shaft suitable for a wide range of golfers. The Matrix Ozik hQ3 is like having an old friend back in the fitting bag. The overall torque is a little higher, but the tip torque is very close. Radial consistency, the ’roundness’ of the shaft is exceptional making the shaft well suited for the rotating hosel of the new Adams XTD Ti hybrid head. Spine aligning this shaft is a waste of time, it is spineless, and in a golf shaft that is a good thing.
UST Mamiya Proforce AXIV Black Hybrid Shaft
I have been fitting with the UST AXIV Black for a very long time. It is still available and the expression, if it’s not broken don’t fix it comes to mind. Compared to the current Elements Wind, there is very little difference. Some profiles are proven by success over time. This is one of those designs. Marketing demands that companies deliver new products every year of so. It is nice to know that this design is going to stay with us in the UST Mamiya Elements line. I have a lot of success fitting mid to mid high launch shafts with low tip torque. They are great in fairways and hybrids. The Proforce AXIV Black is such a shaft.
UST Mamiya ProForce VTS TourSPX Hybrid Shaft
A few years ago UST Mamiya launch the VTS line of shafts. VTS stands for variable torque system. Their research ranked the importance of shaft parameters to performance in order of importance as tip, mid, torque, butt. That was contrary to the belief in butt frequency matching espoused by many club makers. Adding three torque models to the matrix of weights and stiffness creates a massive fiting system. I added only the 85 gram models to my hybrid fitting system. The EI profiles of the different torque designs were not exact matches. But they were not too far from one another to translate into significant performance differences. The design, gradual loss of stiffness from butt to mid, followed by a stiffness ‘lump’ in around 15″ from the tip is very common. More common among most shaft companies than those designs that lose stiffness uniformly down the shaft. Having these shafts in my fitting system gives me one more option in our search for your perfect fit. Some golfers like the feel of higher torque shafts. And good feel generally translates into better consistency.
Aldila RIP Alpha Hybrid Shaft
One of the things I strive for in my fitting cart is a diversity of designs. As I was making the decision of what I would focus on in 2014 I came across the profiles of the Aldila RIP hybrid. A few review samples were in the fitting bag but did not get much use. This past fall I received prerelease review samples of the new KBS Tour V iron shafts. When I looked that the profiles of the Aldila RIP Hybrid, I saw the KBS Tour V and the Nippon Modus3 Tour 130 . This is not a profile I have any significant experience with. It will be getting a lot of attention this year, the KBS Tour V2, the lighter weight version of the KBS Tour V, is the stock shaft in the Callaway Apex Pro irons. I added all weights and stiffness to my hybrid fitting system to explore this new design that Phil Mickelson used in his irons when he won the British Open this past year.
Understanding the differences in golf shafts has never been easy. There are a lot of terms used to define a shaft, too many to review in this article. Without any industry standard, they have little value to anyone trying to understand the differences between two shafts. Over the time I have been involved in club fitting, I have tried several systems. Each had limitations and finally, I gave up and invented my own. Yes, I added one more system to the plethora of systems already in use.
That system is based on text book mechanical engineering beam theory. Bending is he product of the elastic modulus E and the area moment of inertia I of the beam cross section at a point on the beam. The formula looks like this:
w is the bending of the beam, x is the location and k is the curvature. This is the fundamental science used by all golf shaft designers of significance. It makes simple sense to use the same system to understand their designs.
What this formula means is that if you know the EI along the shaft it can be transformed into the bend profile of the shaft as shown in this illustration.
I picked these two shafts to illustrate the value of knowing the EI profile of golf shafts. These two shafts are both rated by their respective manufacturers as S flex. The EI profile shows the butt and tip stiffness to be about the same. And yet, they show very different bend patterns when loaded as shown on the right.
The loading illustration is what you would see if you used a deflection board. I borrowed this image of a deflection board from GolfWorks. This is a classic tool used by clubmakers to understand shaft bending properties and to rate stiffness. Frequency instruments have replaced this instrument in most club makers shops. Frequency gauges give the club maker a number from which many systems translate frequency of oscillation to stiffness. What is not seen on frequency instruments is the bend profile seen on a deflection board. The shortcoming of deflection boards is that they do not quantify the bend profile, leaving the club maker to compare bend properties with tracings.
Using EI values along the shaft, the deflection profile can be calculated and quantified as shown. And this lets a shaft engineer translate material properties, shaft wall thickness, shaft wall diameter and shaft taper into computer simulated bend properties of a golf shaft.
The club fitter, equipped with EI measurements, understands the bend properties of the shafts he fit with.
And that understanding is why I felt it was necessary to invent my own instrument and system for measuring golf shafts. The amount of load applied during a golf swing is transformed into shaft deflection. The amount of deflection is what you feel as stiffness when you swing. Feel feedback helps you time your swing. Too much deflection creates dispersion, too little, bad timing. The EI bend profile determines not only the amount of deflection but also the shape of the deflection. And that shape influences how your swing presents the club head to the ball at impact. EI profiles guide me in fitting my clients into the best shaft for their golf swing.
Adams Speedline Super LS Fairway
THIS HEAD IS HOT!
In fitting after fitting, the smash factor of this head is showing up as 1.5. Smash is the ratio of ball speed to head speed. 1.5 is the maximum for driver heads with a maximum USGA CT Characteristic Time. The older term is COR, Coefficient of Restitution, a measurement of the spring effect of a club face. This is it, the driver legal limit on a fairway head. Marketing departments can make whatever claims they want, but this head is simply the best I have ever tested.
The interchangeable hosel insert of the 2013 Adams Super LS Fairway and the speed slot technology was an incentive to invest the time and money into converting my fairway fitting system. This new design from Adams is the third generation of slotted fairway heads. It uses a Titanium Face and Crown with a Stainless Sole. The combination of titanium face, brazing and compression slots puts the CT of the face as close to the USGA limits as manufacturing tolerances allow. There is a weight port on the bottom, making it easy to customize the weight of the head for your swing dynamics.
The adjustable hosel makes it possible to change the loft and lie of the Adams Super LS Fairway head. Titanium heads are generally unbend-able. The adjustable hosel insert makes lie/loft adjustment of a titanium crown fairway possible.
The Fit2Score fairway fitting system includes over 40 shafts experience has proved to be great fairway designs. They are generally low torque, active tip shafts that deliver great control and tight dispersion patterns.
Aldila NV 44 Magnum Golf Shaft 2012
Profile of the R & S Aldila NV 44 Magnum vs the Aldila RIP Phenom
This is a early look at the Aldila NV 44 Magnum, due to release to dealers in November. At the time of this post only the R and S Flex versions were available. I compared them to the similiar weight Phenom R & S shafts. The raw shafts are about 5 grams lighter than the Phenom at 44 and 46 grams respectively for the R & S models.
It looks like the 44 Magnum will play similiar to the Phenom with a slightly higher launch. Like all shafts in this weight range, the torques of 6.5 and 5.8 are typical.
My view of shaft alignment has matured since my last video and an update is in the works. The Aldila 44 Magnum shafts, with only 2 CPM points between the strong an weak planes are exceptional in this weight range. These shafts can confidently be used in a driver with a rotating hosel and will play the same in any orientation. 2 or less CPM differences are considered tour quality shafts. To see that number in a 44.3 gram R flex shaft is rare. Nice work guys.
Bob Vokey, Titleist Interview at the PGA Merchandise Show, Orlando, Florida 2012
The Devoted Golfer video team attends the PGA Merchandise annually. Mark Maness, PGA Class A Pro and Director of instruction at The Golf Center at the Highlands in Carrollton Texas got to discuss wedges with Bob Vokey. This and many other videos from the annual gathering of the golf business can be seen on YouTube at my DevotedGolfer channel.
This is a study of the radial properties of 6 shafts. It is a supplement to the golf shaft alignment video. I discussed bow vs spine in that video, and mentioned that the two did not necessarily align with each other. But the example used in the video very closely aligned with one of the FLO’s. In this larger study of 6 shafts, there are examples showing more clearly the point that was made in the video.
The charts below show the effectiveness of the Three Point bearing tool, often referred to as a spine tool and a tip weight laser tool in locating the radial stiffness high and low points of a driver shaft. The tip laser device, often refered to as Flat Line Oscillation FLO or Vertical Oscillation Plane VOP was an effective tool for finding the stiff and weak planes of the shaft. This can be accomplished by the club maker by FLOing the shaft in a CPM device and noting the CPM of the shaft at each of the two FLO planes. The stiff and weak planes are easily identified.
The bearing based Spine tool is not a reliable device for identifing the stiff and weak planes of a shaft.
This study was inspried by the writing of my friend, Dave Tutelman. This link is his article on the subject, http://www.tutelman.com/golf/shafts/allAboutSpines.php
Four properties were measured as follows:
The stiffnes of the shaft as measured every 10 degrees. The shaft was clamped at the butt end, the tip was deflected 1″, the load cell was set to zero. The shaft was then deflected 5″. This method measures the stiffness of the material without any affect from any bowing or curvature in the shaft. The readings are shown as the blue line. The readings were smoothed to eliminate measurement ‘noise’.
A weighted laser tip was attached to the shaft. The shaft was deflected 3″ and released. The laser trace was recorded in a 5 second timed exposure. The shaft was rotated until a stable plane of oscillation was found. The photo of the trace is shown to the right of the shaft. The shaft was then turned 90 degrees and the second stable plane was located. The solid red line shows the stable plane of the shaft closest to the stiff side of the shaft. The dashed red line, the stable plane that was on the softer side of the shaft.
Using a three point bending tool the bow of the shaft was located. This tool is a pair of bearings in a tube. The shaft is inserted into the ID of the bearings and a third bearing is used to deflect the shaft. The shaft turns to the bowed side to minimize the stress of the loading force. The Bow is shown as a Yellow line.
The shaft was inserted into a machining chuck which can be rotated. Two pieces of card stock were bent 90 degrees and set against each side of the tip. The shaft was rotated. The cardstock was pushed away from the shaft as the tip moved during the rotation. The points of maximum deflection to the right and left were noted and indicated by the black line.