Golf Shaft Deflection

Modeling Static Load Deflection

By Russ Ryden, A Golf Digest America’s 100 Best Clubfitter
Fit2Score, Dallas Fort Worth, Texas

Understanding the differences in golf shafts has never been easy. Bending is the 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.

Working with my friend and technical mentor, Dave Tutelman, I added deflection modeling to my shaft knowledge base. Deflection can be calculated from EI. Knowing the EI of 36 sections of a driver shaft, a composite bend can be modeled with weight as a variable. This illustrations shows the EI profile of two shafts on the left. On the right the shafts are loaded with different weights to model their deflection when loaded.

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 club makers 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 which many software systems translate into 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. This lets shaft engineers translate the matrix of material properties used in the shaft, wall thickness, wall diameter and taper rate into computer simulated bend properties of a golf shaft. All major shaft design companies have created software to model their ideas before they develop prototype shafts.

My EI instrument brings the shafts we play with back into modeling. The club fitter, equipped with EI measurements, understands the bend properties of the shafts he fit with. That understanding is why it was necessary to invent my own instrument and system for measuring golf shafts. The fitters that are authors on this site understand the golf shafts they fit with from this perspective.

The load applied during a golf swing is transformed into shaft deflection. That deflection is what you feel as stiffness when you swing. Feel feedback helps you time your swing. 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/shaft interaction presents the club head to the ball at impact.

Soft Stepping and Hard Stepping Iron Shaft Sets

Adjusting Shaft Stiffness with Soft and Hard Stepping

By Russ Ryden, A Golf Digest America’s 100 Best Clubfitter
Fit2Score, Dallas Fort Worth, Texas

Soft stepping is the term used to indicate changing flex of a taper tip shaft by adjusting the stiffness of a set of irons by putting the lower numbered iron shaft throughout the set.  For example, the 8 iron shaft is put in the 9 iron, the 7 iron shaft in the 8 iron and so on through the set. Hard stepping is just the opposite, putting the 9 iron shaft in the 8 iron, the 8 iron shaft in the 7 iron.  This practice applies to sets of shafts that are produced with specific designs and lengths for each iron in the set.

KBS_Tour_ETT_XP95_EiWhen we look at shaft sets we see two design philosophies. The consistent EI weight/flex designs and the True Temper Dynamics design . This is best explained by looking at some EI stiffness charts.The first chart shows the KBS Tour X, S and R flex shafts. The profiles and consistent, simply getting overall stiffer as they get heavier. Most True Temper shafts have different profiles. The tips are not only softer, but longer up the shaft in the R flex model. The tips get both progressively stiffer and shorter in the S and X flex models. In a shaft like the KBS, the difference between and R and an S is simply a little heavier and a little stiffer overall. In the Dynamics design, the profile of the S is significantly different from the R.

Now lets take a look at what happens when these different designs are hard or soft stepped to change stiffness. And, compare hard and soft stepping to changing flex.

KBS_Tour_SteppedHere again is the KBS Tour. Soft stepping, putting the 5 iron shaft in the 6 iron, moves the flex of the shaft about 1/3 of the way toward the R flex shaft.  A double soft step, 4 iron in the 6 iron will move the flex another 1/3 toward the R flex. The weight of the shaft changes very little with stepping. The 120 gram S flex is still 120 grams while having a stiffness similar to the 110 gram R flex model.

TT_XP105_SteppedNow lets look at the same EI chart of the True Temper XP105. We see the same change of profile from hard or soft stepping. A slight change of overall stiffness of the shaft. However, when we look at the R flex shaft we see that it has a significantly different Ei bend profile.

Fitting the True Temper Dynamic Designs

From a club fitting perspective EI Bend Profiles give us a new understanding of fitting the True Temper designs. Adjustment made with hard and soft stepping have a small effect on stiffness and flighting. Adjustment made with flex changes have a significant effect on both stiffness and flighting. To get a precision fitting it is important to work with a fitter that offers the options to hard and soft step the different flex offerings.

Shaft Alignment

GOLF SHAFT ALIGNMENT

By Tom Wishon, Tom Wishon Golf Technology

This was copied from a discussion on another forum. It is the same as a private conversation I have had with Tom while researching the history of SST alignment.

“I was the guy that Dick Weiss came to back in 1996 after he had been doing his initial research into the effects of shaft asymmetry, when he wanted someone to verify what he was seeing in his initial work. Dick insisted that the result of testing we did for him was to be kept confidential. We honored that request.

But I can tell you that back then, while shaft makers were aware that their shafts did not have the same exact bending properties in all directions about the circumference of their shafts, they did not have any awareness of how asymmetrical many of their shafts were, and what this could do to shot performance for certain swing types.

So yes, shafts back then exhibited a very wide range of asymmetry. And in our testing for Dick, we most certainly saw that finding the most stable plane of bending in these asymmetrical shafts and then orienting that plane at the target line most certainly improved the consistency of the impact and ball flight. We even were able to orient certain shafts in a way in which it virtually made it impossible to hit a draw or fade.

This was a point that the USGA also discovered when Dick came to them to appeal for a conformity ruling for his process. The USGA did actually write into their rule concerining shaft orientation that it was only to be done to allow shafts to play as they were intended to be designed to play, and not to be done for the purpose of purposely influencing the flight of the ball.

Once Dick’s SST PURE process became more and more known, the shaft makers began to look more closely into this. Today, most of the better shaft makers do institute a test or tests on all of their shafts as a normal step in production. From this they position the shafts’ logo/name such that what they find under their test as a stable plane of bending is then oriented at the target when the shaft is installed logo up or logo down.

So today you won’t see as wide of a variation in asymmetry in shafts made by quality shaft makers as there was back when Dick discovered this and invented his process. But because every shaft maker has a “flyer shaft” here and there, there are times purely at random when a golfer might have a shaft checked and re oriented and see a difference in impact consistency on the face and a change in ball flight.”

TOM

Golf Shaft EI Profiling

EI SHAFT PROFILING

By Russ Ryden, Fit2Score, A Dallas Fort Worth Club Fitter & Club Maker
The Golf Center at the Highlands, Carrollton Texas

If you want to understand golf shafts the way a golf shaft engineer understands the, you need to see the three point EI profiles of the linear strength of the golf shaft. The term, EI is engineering short hand for E= Modulus of Elasticity and I = Area Moment of Inertia. Or, more simply, the elasticity of the shaft material and the thickness of the cross section of the shaft. The combination of these combine into the stiffness of the shaft at any point on the shaft. If the walls are thicker that section the shaft is stiffer.  If the graphite strands are running from butt to tip the stiffness they give to the shaft is more than if they are angled to control torque.

EIv7_Overview_640

Simple marketing terms, high mid or low kick point are just that.  The marketing department of the shaft companies attempt to give the golfing public easy terms to understand. In today’s world of elaborate shaft design and fabrication, only three point EI profiling can reveal the linear bend character of the golf shaft. Detailed EI profiles, like the ones seen here can show how the shaft bends under load. That information, simply stated, is the functional knowledge of the golf shaft needed for golf club fitting.

A few years ago, when I was introduced to the concept of three point EI measurement, there was no generally available instrument.  Mark Timmes had had one designed and built at Hot Stix.  I believe that instrument is now owned by Mizuno.  Don Johnson a fellow club builder designed a home made instrument and my friend and mentor Dave Tutelman also made a simple version.  A laboratory quality computer controlled hydraulic instrument starts around $10K.

EI_InstrumentI set out to build an instrument that used gravity in the form of a stack of weights, and some form of powered assistance to raise and lower them.  Along the way, I had a long and expensive encounter with friction.  About a year after I started, fifteen of these were made. The original owners were mostly club fitters, many of my instruments are have now been purchased by golf shaft companies. Because it was designed specifically for the golf shaft, It does a better job of measuring a golf shaft than the computer controlled hydraulic instruments.

A few weeks before the C-Taper Lite released, I caught up with Kim Braly at the PGA Tour Crowne Plaza Invitational at Colonial tournament.  This is an outtake from that interview. We talk about EI profiling.

The engineering principal is not new.  A beam has two properties that affect deflection. The stiffness of the material and the cross sectional area of the beam.  EI charts for building components are available to help building engineers know how much a support beam will bend under the weight of the building place on it. Golf shafts are not much different to a shaft design engineer.  The material, steel or carbon fiber, has known load bearing properties. The cross sectional area is the walls of the shaft.  In carbon fiber design, the beam stiffness is affected by the direction of the fiber. When the fiber runs from tip to butt, all if its strength is applied to the stiffness of the shaft.  When the fiber is oriented at an angle to control radial stiffness which we call torque, some percentage of the tip to butt strength is lost. Knowing these material properties, a bend design is translated from material strength into wall thickness and a shaft layup is forecast by design software.

A three point EI instrument validates the prototype shaft design.  In the hands of a club fitter, it decodes the design into bend profiles.  A golf shaft, in its simplest terms is weight, EI profile and GJ profile.  We can add another property, feel, which is affected by material. And perhaps yet another, elasticity, again a material property.  But at the top of the list for understand the modern golf shaft is EI and GJ.

To measure EI a shaft is supported at two points.  A weight is placed in the center and the deflection is measured.  This deflection is transformed into EI by factoring the weight of the load, length of the beam and the amount of the deflection.  We measure every inch from 6″ from the tip to 6″ from the butt.  The charts show the first reading at 6″, but this point includes 5″ below and 5″ above this point. The flex on the graphs shows the stiffness all the way to the tip of the shaft. The numbers are smoothed to remove measurement ‘noise’.

EI Profile Comparsions

I like to tell the story about my first meeting with Tim Gillis, who was then the Director of Sales at Miyazaki Golf Shafts. I stated that I had close to 1000 shafts profiled.  He smiled and said, ‘We have been doing this for years, our database is over 5000’. Three point EI is the measuring standard used by all of the major shaft companies to design and validate golf shafts.

This site is about shafts from the point of view of the shaft designer, all measured with a consistent and uniform methodology.  The group of fitters that writes the reviews here are among the first to fit with a completer EI/GJ understanding of the shafts they use.

When I started the project of designing an EI instrument, I looked at the work of Dave Tutelman.  Dave documented the design of a simple device, EI Machine to Profile Golf Shafts. Through Dave I became friends with Don Johnson,  Don also created an EI measuring instrument years ago. The exchange of ideas with Dave and Don guided the development of the three point EI instrument illustrated here. After several years of experience I designed and manufactured an improved design. The measurements are so good, the software no longer needs to smooth out the data.

When questions about shaft ovaling and overhanging weight affecting the readings on my instrument arose, Dave studied the issue. He concluded in Errors in EI Measurement due to Shaft Weight that it was not a significant source of error because I applied a preload to the shaft. I have measured ovaling at the butt of the shafts and found what little could be measured was within the measurement error seen in repeat readings.  The numbers being discussed here are ten thousands of an inch.

Golf Shaft Bend Profile Signature

EI BEND PROFILE SIGNATURE

By Russ Ryden, A Golf Digest America’s 100 Best Clubfitter
Fit2Score, Dallas Fort Worth, Texas

This term is the best I could come up with for a way to look at shafts that Kim Braly taught me several years ago.  You will often see him making presentations about the change of stiffness from point to point on the KBS steel iron shafts.  Kim describes his shaft designs as a perfect whip, uniformly loosing stiffness from point to point, butt to tip.

FlexuralSignature

In this illustration of the KBS C Tour shaft the EI profile is shown next to the Bend Profile Signature of the shafts.  You can see how the bend profile signature graphic magnifies the bend profile of the shaft. My math savvy friends looked at this and said, oh, you plotted the first derivative, the change in Y with respect to X, or in this case, how much stiffness changes inch by inch, down the shaft.

Don’t assume I understood the math when I created this chart, the idea for this came to me from Kim Braly. He told me in our first meeting, EI is not new, it has been around since the 30’s. He built his first EI instrument by cutting a hole in a desk. Ok, I can see where that would work. He said what you need to focus on is change of stiffness down the shaft.

My signature chart, the first derivative, is just that, how much does the shaft stiffness change from point to point down the shaft. It is actually the inch by inch slope down the shaft. Stiffness is removed, only the change of stiffness is shown. This is, perhaps, the most important metric for shaft fitting. However, I have never seen it outside of my software. But when you look at charts like the one below, you know some shaft designers are looking at it.

The graph on the left shows the EI profiles of the 2013 Mitusbishi Diamana B, the third generation of the Blue Board design.  Each shaft has a different stiffness.  The illustration on the right charts each of these shafts by showing change of stiffness from point to point.  The absolute stiffness is removed and what is left is an understanding of how the model bends.  Each of the shafts has essentially the same bend profile despite the fact that they are different weights and flexes.

FlexuralSignature2

By comparing shafts with this graphic a club fitter can easily understand the differences between shafts that would otherwise be clouded by weight and flex differences.  And by looking at the uniformity of all of the weights and flexes of a model, can quickly see if and when the designer changed the bend profile.  This often happens with different weights of a model.

Throughout this site you will see EI bend profile signatures used to highlight and explain differences in designs.  Having spent years looking at shafts from this perspective terms like kick point or bend point have come to have little meaning. In fact while doing research for a question I was asked, I found this quote in Total Clubfitting in the 21st Century. My copy was published by Dynacraft in 2007. “Additionally, the effect of bend point and kick point on ball flight now is considered marginal.”  Chapter 7, page 92.

We often see shafts with multiple hinges or knees for want of a better word.  By knowing the bemd signature of a shaft and getting feedback about feel from the golfer, a good fitter understands how a shaft will feel as well as how it will shape ball flight.