Goeff,

We have a question for you. I wondered if you know of any study/evidence regarding parallel vs perpendicular alignment aids on different putter heads.

What does the brain have the most success using from the over the ball position.

Clearly is parallel if your behind the club, like shooting a rifle.

I did a quick test 10 shots of each time and was better with perpendicular style but that is the style of putter that I use all the time now. I used the Pelz lazer trainer with a mirror on the face of each club for the 20 shots.

Walked around between each shot so I did not just adjust between each shot. (Pics of Quantum vs YES attached) The shots plotted are not in the order that I took them, they are in the order that I read them off the carbon imprint paper that I put at the target to record the miss distances.

Maybe need more shots than 10, to I get more practice with each style during the test. I did putt with a parallel line YES for years and switched to a perpendicular aim queue with Quantum a few months ago so its not like I dont have any experience with parallel line head aim lines. Would enjoy your comments and any evidence reference.

Bye the way, notice the Yes Hanna as a pretty strong perpendicular to the trajectory line in the silver top 1/2" of the club but your eyes get drawn to the long white alignment line. When I put a ball down with a black alignment line on it I clearly use the parallel line on the YES head more than the perpendicular face line. (At least that is my feeling). But this does for a nice T shape. Maybe I use the T.

With the Quantum I find, 1st look I use the front and back edge of the head and then focus on the 2 dots that are perpendicular... Would make for an interesting eye tracking experiment if I had the equipment. On Quantum there is not clear T shape.

I also did an experiment based on my old billiard days. Aim too far left, then too far right and narrow it down and get the feel with the laser reflection dead on.

I also notice that head/shaft symmetry seems to be key. (the look of the shaft, how it attaches to the head and its bends). A straight shaft, and a symmetrical left right eye view of the head seems to help. Same is true of the ball marker line, seems better in the plane of the eye line. In doing this I found that I am not careful enough with alignment of the ball mark. Does take much to setup the ball for a 1 deg miss unless you get very low behind the ball. Because of this I try to use your spot/blade of grass idea but there is not always something clear to see 5" away from the ball that is on the aim line.

Rick

Dear Rick,

You are extremely perceptive in noticing things! Great.

My view is:

Perpendicular is better than paralell because the DIFFERENCE of good vs bad is greater difference swing off perpendicular of toe and heel than the DIFFERENCE swing of the parallel line(s) at the end of the parallel line(s) at the putter face, since the greater separation of the toe and heel in the perpendicular orientation magnifies or amplifies the feedback greater than the movement out of good aim of the end of the parallel line(s) at the face. There is also an orienting process whereby the line across the pupils is matched up to the oputter head, either by seeing whether the pupil line is sqaure and perpendicular to the face as a whole from heel to toe or is matched up so the pupil line is the same as the parallel line mark on the putter head front to back. For me, getting the pupil line square to the putter face perpendicularly is better than the other, probably for the same reason, but also getting the pupil line matched up is not really about aiming the putter face on a line. The line that is compared to the putter face is usually an imaginary line or perceived direction that the putter face should aim down. Most golfers (nearly all) lack the skill required to match the putter face up to an imaginary line or direction, and instead fancy they are "aiming" the putter face "over there at some location", and even then they are terrible at defining the other location over there perceptually, knowing HOW to do this accurately, and monitoring their technique to KNOW whether they are getting accurate senses of locations in space in relation to the body at address and the putter face aim in space.

No specific studies to prove this, just general application of visual neuroscience. No one in academia is aware enough of the skills in putting to know this needs studying. And since no putting instructors have ever tried to undertsand and teach this at-address aiming skill (most don't even know it needs teaching), there are no golf studies either, except for the one noted below.

Putter companies don't know anything about this, don't test differences, and don't know visual neuroscience any at all, so I would regard anything they do for their design as just random guessing. Aiming aid / mark designs throughout golf history are just junk efforts by well-meaning enthusiasts lacking science.

David Edel (www.edelgolf.com) and David Orr (www.davidorrgolf.com) have been studying influence of hosel design, putter head shape, and alignment marks on accuracy of aiming, without benefit of visual neuroscience; so their data basically depends on reasonable sorting of sample subjects according to where the subjects start -- left-aimers seem to benefit from this or that; right-aimers seem to benefit from that or the other, etc. This is a good beginning on a scientific approach, but it is very rudimentary without the top-down science guiding and informing the interpretation of their data-gathering.

Yes indeed the hoseling influences aiming.

Regardless of the "influences", there is REAL VISUAL NEUROSCIENCE that needs understanding and applying in the design AND the training of skill. For example, vision usually scans for salient features, not just everything, so corners and planes and connections and marks and areas of sharp contrast matter much more to the "usual" looking at something without the golfer applying purposeful skill and controlled visual routine. Lines and borders and contrast and corners matter much more than interior areas and transitional features. So, bottom line, a designer who designs an alignment mark or putter head shape or hoseling pattern in order to "influence" unskilled, untrained golfers simply "looking at" a putter while attempting to aim it will just be floundering around without guiding their training with visual neuroscience. Nike hired an "optometrist" (i.e., prescriber of lenses for improving visual accuity, and NO visual neuroscience) to design the putter for Nike to have good aiming, and what he designed was crap that had parallel lines in white and the rest of the ugly shape of the putter in green to blend with the grass (sort of a stealth hiding of the ugliness) but also ruined by having dark contrasting "holes" in the putter head that distracted usual vision from the parallel lines, so the whole was just crap. Nike doesn't know the difference between optoimetry and visual science, and so wasted their money. OF COURSE, the optometrist hired pretended to know visual science!

This all means that a) there is a value for good visual neuroiscience in the design, but b) good training essentially gets rid of most of the crap if not all of the crap. You can study what makes a "better" design in general for badly trained golfers in general, or you can learn the skillful viusal routine based upon actual visual neuroscience and then the bad designs are not especially hurtful but are almost entirely rendered uninfluential in the aiming and the good designs don't really help musch at all and are certainly not required for effective aiming. The design ends up being only a backstop of a sort against lapses in skill. For the untrained golfer without a sound visual routine, the design cannot really help all that much. Some golfers get more help from this, some from that, some from the other, depending upon how messed up they are for visual aiming skills by their everyday haphazard visual processes. A designer trying to help this population cannot really design for a fattest demographic without first surveying the population for their bad tendencies and sorting them into general categories of badness and then applying real visual neuroscience to address in general the CAUSES that cover the golfers in each category of flawed visual processes. One thing you would doubtless discover in this surveying and categorizing of the CAUSES of poor aiming is that not all causes are visual, and many are simply the manner in which one stands and moves when employing the senses -- i.e., posture, distance, turning face, angle of regard, relation between lines of vision and aim of face, etc. I would say that nearly ALL golfers, pros included, have BOTH really poor visual routines and really poor postures and movements in aiming. The alignment marks and other aiming-directed design features won't do anything about the postural and movement causes of poor spatial sensing of location of hole in relation to posture and body location (and indeed stroke action). That's a whole other kettle of fish.

Cheers!

Geoff Mangum
Putting Coach anmd Theorist
Golfclub Weisenthal, Schopfheim Germany
www.puttingzone.com

Geoff .... this may be slightly off topic, but the discussion makes me wonder how putting alignment and putting results were in the pre-ping days when most pros putted with a Wilson 8802 or Reuter Bullseye putter designs with nothing more than a dot on the topline, if that.

You have stated there is 'instinct' involve in the speed of the stroking to get the ball to the hole, but in the old days was 'instinct' also at play for alignment of putts? Is putting alignment really a 'best guess' effort regardless of any science? Are humans snookered by their inherent physiology and psychology to aim dead on when standing at address?

When standing at address to a level 10 foot putt, is it humanly possible to align oneself within say +/- 5/4/3/2 degrees of the hole after trudging on a golf course?

Nowadays we are using lasers and a variety of markings that are parallel, perpendicular, angled, curved sectors, differential color slots and even two-balls on the top of putters to aid in static alignment. Do they really work or are they superfluous since the stroke path and face alignment at impact is what produces the desired putting results?

Are we tying ourselves in knots over something that is not significant and looking for technological crutches? Sorry for sounding a tad cynical, but in the golden olden days, the putters were basic and the greens were lumpy and grassy ... and today greens must be like pool table tops and putters must be hi-tech toys to compensate for lack of practice and still attempt to gain a technological advantage over opponents on the battlefield. Opps, there I go again ... the luddite that I am ...LOL

There are just so many crappy putters out there. I expect the major OEMs to start utilizing visual neuroscience in their putter designs at about the same time Megan Fox and I get married on the 11th green at Augusta.

I can tell for the most part what isn't a good putter design. Geoff mentioned Nike, and I could spend all day picking apart putters that look like things I used to make out of Legos. There's just too much going on. I tend to gravitate toward the most neutral, conservative putter I can find. This usually means a center-shafted blade with few alignment marks. All I want to see is a sliver of the face and the ball. I'm not saying I'm right and everyone else is wrong, but I just want to aim the face. I don't spend any time staring at the topline of my pitching wedge. I don't really care about the back of the putter, or the top, or about any garnishes that manufacturer wants to put on there. That's all these alignment "aids" are: garnishes. No basis in science, just in the hope that the average consumer thinks Golf Digest is an informed source of knowledge. I've never heard any type of substantial, scientific explanation from an OEM on why its particular alignment aid is effective.

Geoff, do you know what a "neutral" design would be? By this, I mean one that doesn't in any way disrupt the golfer's instinctual aiming process. What is the closest thing you've ever seen to whatever your idea of optimal putter design is in regards to alignment features?

Dear Giancarlo,

Before responding to sammy's great questions above, I wanted just to spread out some photos of pretty simple putter designs that strike me as nicely uncomplicated:


Ben Sayers 1920


Bogee Aluminum 1915


Brown Vardon


Cafferty Topspin Putter


Tommy Armour Ironmaster and Spalding Cash-In


Arnold Palmer Original


Australian Pendulum Putter


Otey Crisman Putters


Wilson Ferrier 1947


George Low Putter


Go Classic Scorpion Mallet


Go Classic Scorpion Flange


Nicket ISSO


Plop Putter


Q-Roll Classic IV


TaylorMade TPi 27


Tour Edge Equator


Wilson Harmonized 746

There are other similarly simple designs.

Cheers!

Geoff Mangum
Putting Coach and Theorist

Offering Free Podcast Tips for Putting Every Friday on GolfSmarterTips.com.

The best putting instruction book in golf history is now available for purchase in hardback or as an immediate ebook download: Optimal Putting: Brain Science, Instincts, and the Four Skills of Putting (2008, 282-pages)

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Hi Geoff
There are some golden oldies here. Could you please tell me if The Symple Putter would be sutable to be used with a standard putting stroke or is it only sutable to be used with their suggested Symple Putting Method. I am concerned that the lie angle on them may set my hands to low in a std putting stroke and may cause other problems. I have only seen them on the internet and have never had the oppertunity of trying one on a putting green and make a decision on how they preform, are you able to reveal what you like about them and what makes them work so well if you rate them a good product.
Thanks for your assistance
Luvabirdie.

Dear sammy,

Your question is a very important one to get right, and this response can only be a beginning, due to the complexity of the topic -- how precisely and accurately can we expect an adult golfer to be able to aim the putter face, setup, and stroke and what can be done to assist in the proper training and coaching for optimal performance, and what sort of testing is required for assessment, monitoring, and training?

Human Factors

The precision and accuracy attainable in aiming a putter at a specific target some distance across a green surface involves a number of variables, including visual acuity in several functions; the ability to judge parallel and perpendicular relationships of edges, lines, and object shapes; the accuracy and precision of spatial perception of the relationship between the putter face and the target in light of the intended stroke movement and body posture; the haptic sensitivity and ability to judge the relationship of the handle shape to the body and the direction of aim; the relationship n the event of the aim of the putter face and the ability to stroke the ball where aimed or in some other consistent direction relative to the initial aim; the disciplined visual skills of the player in responding to the stimuli of the putter design for purposes of assessment of aim; the ability to sight a straight line from behind the ball; the ability to retain the perception of the straight start line thru the ball at the target or to anchor the transitory and imaginary geometric relations to real locations and objects in the scene; the ability to select an interim spot target on the line and to accurately and precisely aim the putter face thru the ball at this interim target; the ability to assess the aiming of a planar slab of the putter head thru the center of the sphere of the ball in terms of perpendicularity to the intended line; and a few others.

Human Visual Acuity

According to established optometric science, the normal adult human vision is 20/20 as measured by the Snellen Eye Chart. This means that at 20 feet, the subject is able to discriminate and resolve the same small distances between marks that people with normal vision can see from the same distance. The "resolution" of two points in space means they are sufficiently separated in distance that the eye can see two different points as just separated, not two points overlapping each other appearing as one point. Poor vision such as 20/40 means that what discriminations the normal person can resolve from 40 feet from the chart, the subject must walk to within 20 feet before he is able to see the same degree of resolution. Superior vision such as 20/10 means the subject can see from 20 feet away what the normal person cannot see without walking to within 10 feet of the chart.



But in fact, the 20/20 standard is actually a measure of "good enough" vision so that medical or optometric intervention is not warranted, and REAL normal adult human vision is closer to 20/16 or 20/12. So someone who is exceptionally proud of their specialness for having "keen eyesight" because they were able to read the 20/15 size letters actually has average eyesight. Tiger Woods had 20/15 vision wearing contacts but didn't like the dryness and changing and discomfort, so he opted for Lasik surgery, with the result that his cornea was reshaped so he had 20/15 vision without contacts.

The letters of the Snellen chart and the distance of 20 feet from the chart for measurement are basically a compromise for using the chart in an office setting where larger distances are not usually available, but actually the proper use of the chart in relation to normal vision would distance the chart perhaps 25-30 feet away. This is the real distance where almost all human eyes as a pair become parallel, and short of this distance there may well be some inward converging of the aims of the two eyeballs. At any rate, the 20-foot distance was decided upon, so from this distance the letters of the 20/20 line such as a capital E stand 5 minutes of arc tall from bottom edge of letter to top edge, with the width of each of the three horizontal flag features of the letter 1/5th this angular size or 1 minute of arc from bottom edge to top edge of each flag, and the two gaps between the three flags also the same 1/5th or 1 minute of arc. Each "minute" of arc is 1/60th of a degree, so the apparent angular size of the letter E from 20 feet on the 20/20 line of the chart is 5/60th of a degree tall from top to bottom and each flag or gap is 1/60th degree from top to bottom wide.

Using trigonometry, a right triangle represents half the height of the E letter at 20 feet, with the long adjacent leg of the triangle being 20 feet (6.1 meters or 610 cm in Europe) directed halfway up the letter (middle of the middle flag), half the height of the letter being the opposite base of the triangle from this point to the top of the letter, and the angle subtended at the eye up from the adjacent line to the top edge of the letter being 1/2 of the 5/60th degree, or 5/120th of a degree. The distance 20 feet is equivalent to 240 inches or 610 cm. The trigonometry is then tangent(5/120) = h / 610 cm, with h being 1/2 the letter's height H. Rearranging the formula to give the full letter height at 20 feet or 6 meters, H = 2 x h = 2 x 610 cm x tan(5/120), and H = 0.88721 cm. The Snellen chart "normal 20/20" vision is able to discriminate or resolve the difference of the flags and gaps or 1/5th this size, so that is 0.17744 cm.

In putting, the distance is not 20 feet or 240 inches from the eye to the putter head and ball, but usually something like 56-60 inches from height of eyeball at address bending slightly forward and downward above the ball. Roughly, this is about 1/4th the distance (60 inches or 5 feet), so the eye can discriminate 4 times more detail or 4 times a smaller gap, or a gap 0.04436 cm wide.

Another way of thinking about this is: "At 12 inches, the normal visual acuity of the human eye is 0.00349 inch." If the eyes are at 60 inches (5 feet) above the ball, this sees a gap 5 times fatter than it sees from 1 foot high, which is 5 x 0.00349 inches, or 0.01745 inches or 0.044323 cm. So these approaches closely agree -- at address with the eyes standing 60 inches above the ball, the "normal Snellen" vision can see two points on the top of the putter head as separate points when the two points are a mere 0.044 cm or 0.01745 inches apart.

But this is 20/20 vision, and human "normal" vision is really better than that, about 20/15 or so. From 15 feet away from a Snellen chart, the ability is closer to seeing gaps no larger than 0.8 minutes of arc or so. This results in a 20/15 letter seen from 20 feet or 600 cm with a gap or flag width of H = 2 x h = 2 x 610 cm x tan(0.8/120), or 0.141953 cm or 0.055887 in (about 5/100th of an inch). Compared to the width of the 20/20 flag or gap (0.17744 cm), this is about 20% smaller discrimination -- quite a difference!

A typical putter head on the top planar surface is roughly 1" (2.54 cm) left to right and 4" (10 cm) heel-toe. Two thin lines running left-right in the middle of the top of the putter face need to be at least 0.055 inches or 0.14 cm apart in order for a normal sighted 20/15 golfer to tell there are two separate lines.

Okay, that's a small achievement! But at least it's a start. Much more later.

Cheers!

Geoff Mangum
Putting Coach and Theorist

Offering Free Podcast Tips for Putting Every Friday on GolfSmarterTips.com.

The best putting instruction book in golf history is now available for purchase in hardback or as an immediate ebook download: Optimal Putting: Brain Science, Instincts, and the Four Skills of Putting (2008, 282-pages)

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Dear sammy,

Please allow me to collate some pertinent human factors data for human aiming tasks. Then we can make sense of things better, once this information is laid out in the open.

A major source of this information comes from Human Factors Engineering in the military, especially the Air Force. The "EDC" is the Engineering Data Compendium compiled by Wright-Patterson Air Force Base, Boff, D. R., & Lincoln, J. E. Engineering Data Compendium: Human Perception and Performance. AAMRL, Wright-Patterson AFB, OH, 1988, and K. R. Boff, L. Kaufman, & J. P. Thomas (Eds.), Handbook of perception and human performance: Volume I. Sensory processes and perception. John Wiley & Sons, Inc., 1986.

The "tasks" in aiming and assessing the aim of a putter face, putter, body in address setup for stroke, and stroke action are numerous, complex, and subtle to describe with clarity. And there is a large role for training and education to simplify efficient and effective aiming tasks into a routine for accuracy, precision, and consistency in a manner that causes minimal cognitive load and resistance to degradation under varying conditions physically and psychologically. The human factors data is generally compiled without respect to any specific task, so whether the tasks of aiming are addressed at all and whether there is meaningful and useful data depends rather critically upon whether one truly comprehends and understands the tasks involved. So, one expects numerous gaps in coverage of the data for the tasks, and first simply collects and organizes whatever data might be available.

Visual Acuity

We have already discussed the data that applies to vision of the putter face itself under normal viewing conditions (average daylight, normal eyesight, etc.). The limit of visual resolution for normal vision of a putter head about 60 inches below the eyes is a minimum separation of two points or two parallel lines of about 0.055 inches or 0.14 cm apart in order for a normal sighted 20/15 golfer to tell there are two separate points or lines. But this limit increases substantially under less intense contrast and lower illumination conditions, meaning the limit is probably larger. Other factors affecting the size of the lowest discrimination are health of eyes, moisture of eyes, glare and eye strain, aging of eyes, and other factors, all of which hurt and none of which help improve the threshold of discrimination.

Focus Timing and Distance

The age factor affects the ability of the lenses of the eyes to focus at different distances by changing shape, as the protein structure of the lenses harden with age in the sun and respond less flexibly to the accommodative ring of muscles around the edges of the lenses that stretch the lenses flatter and thinner for far objects and then relax to allow the lenses to fatten back up for short distances, with the aging making the return to the original fatter shape upon relaxation less able to achieve near focus. A diopter (D) is a unit of focus at distances, with there being 1 diopter for each meter of distance, so correct focusing at 1 meter indicates 1 diopter, where focusing at 1/4th meter is 1 D/m / 0.25 m = 4 D. A diopter is the inverse of the distance in meters (small distance, big diopter). A change in the diopter is a measure of the change in focus for a given distance. Around age 10, the clinical norm for accommodative focusing is around 13 D, so that young eyes see close up very well (1/13th meter). Around age 40, however, many aging eyes can focus clearly only at a near distance of 6 D (1/6th meter), and this decline called Presbyopia continues to about 1 D by age 60 (with usual deviations in individual cases of about +/- 2D either way). EDC 1.222. This means that many older golfers cannot see the ground at their feet very clearly without corrective lenses.

The change in focus distance by looking from one object to another object (for example, by looking from the hole 20 feet away to looking at the ball and putter 5 feet away) causes the accommodative change in the focal shape of the lenses, and this changing from one shape to another usually takes about 1 second. If you suddenly look from far to near, the near object is not immediately in focus but requires about 1 second for the lenses to bring the near target clearly into maximum focus. And fixating on a specific target object at one distance causes fluctuations in accommodation of from 0.2 D up to 0.5 D, or changes in focus distance of up to 1/2 a meter while "looking at" a distance. The fluctuations typically occur in cycles of about 1/2 second each swing from lowest to highest D. So focusing steadily comes and goes in this range. EDC 1.224.

Another source of influence on target focus and acuity of vision is fluctuation of the target-eye distance, either from motion of the target near and far or motion of the head and eyes near and far. Obviously, failing to hold the head still while "looking at" the putter head will cause focus problems. A moving head can cause under-focus by roughly 1/2 to 1/3 the distance of head motion near-far (e.g., shifting the target-eye distance over a peak-valley range of 10 D (1/10th meter, 4") can affect the focus of the image as much as 3-5 D. EDC 1.229.

Point and Line Spread

Points and lines are not clearly points and lines when they register on the nerve pattern at the back of the eyeball on the retinal sheet. Instead, dues to physical and geometrical reasons, points and lines spread out. This spread gets broader with degradation of focus. The best illustration of points and lines (a linear series of closely spaced points) s the small letter "i" in newsprint or the telephone book or catalogs with small type sizes. If one holds the letter "i" at a close distance to the eyes and then extend the arms to move the "i" farther from the eyes, there comes a distance where the gap between the stem and the dot disappears and the "i" (eye) morphs into a small-letter "l" (el). This is the distance where the spread of the points gets too distant from the eyes for the ability of the eyes to discriminate between the two locations -- the spreads of two adjacent points overlap too much, and so the points blur together. This is a rough and ready way to learn about visual acuity for any person's current state of vision, as for older people this merging of the "i" points into a continuous series of points in an "l" happens closer than it does for younger eyes. EDC 1.215.

Visual Acuity off to the Periphery of Straight-Ahead

Visual acuity off to the side of the Primary Line of Sight (line straight ahead connecting fovea, center of lens and pupil and target center) degrades after about 12-15 degrees off the optical axis. By 25-30 degree off axis, the peripherally-viewed line spreads out about 2 D as if viewed from 1/2 meter further away. The line gets up to about 3 times fatter in the periphery. (" As the peripheral angle increases, line-spread function halfwidths gradually widen from ~11.5 to ~30 min arc of visual angle.") EDC 1.216.

Illumination Changes and Depth of Field and Image Blur

The size of the pupil affects the "circle of confusion" or blur of the image of objects nearer and farther than the focal object distance, so changing the pupil size changes the "depth of field" of focus near and far at the target distance. Reducing the pupil diameter in half doubles the depth of field. Sudden increases in illumination causes the pupil to constrict, so taking sunglasses off on the green helps increase the depth of field, as does walking out of shadow into full sun. The response of the eye to sudden illumination increases is to over-constrict in the first 5-10 seconds and then settle down and re-dilate to a new, smaller diameter over the next several minutes. Sudden decreases in illumination causes immediate over-dilation followed by settling down to a new, wider pupil over several minutes. The pupil size under the same illumination of different people varies quite a bit, up to 2-3 mm over a total range of pupil sizes from 2-10 mm. EDC 1.233.

Some General Dimensions

Diameter of moon, 0.6 degree or 36 min arc

2-inch diameter circle at 20 in, 5.7 degrees or 342 min arc

Thumb width of 0.75" at 20 in, 2.14 degree or 128.9 min arc

Diameter of fovea , 0.5 degree or 30 min arc
Diameter of foveal retinal receptor, 1/120th or 0.0083 degree or 0.5 min arc

Width of Horizontal Bar on E on 20/20 Snellen Line, 0.0167 degree (1 min arc or 0.1774 cm or 0.0698")
Height of Letter E on 20/20 Snellen Line, 0.083 degree (5 min arc or 0.8872 cm or 0.349")
Height of Snellen 20/20 E but seen from 40 cm away on computer screen, 0.0579 cm or 0.0228"
Size of Snellen 20/20 E Flag or Gap seen from 60" (154.2 cm), 0.0449 cm or 0.0177"

Width of Bent Grass blade 1/16th in. (0.15875 cm or 0.0625") wide viewed at 5 feet (60 inches, 152.4 cm), 0.0597 degree or 3.58 min arc
Number of Separate Points or Gaps Visible left-right across Grass Blade, 3.58

Thickness of US Dime (10 cent coin), 1.135 mm or 0.053"
Diameter of US Dime (10 cent coin), 0.705 in. or 17.91 mm
Number of Reeds around Dime Circumference, 118
Dime Reed-Reed Separation (Circumference / 118), 0.21 mm
Dime Reed Gap seen from 60" (154.2 cm), 0.0078 degree or 0.468 min arc (too far to see gaps, gaps too small to discriminate)
Angular Width of Dime seen from 60" (154.2 cm), 0.665 degree or 39.93 min arc
Number of Separate Points or Gaps Visible left-right across Dime from 60" (154.2 cm), 39.93

Thickness of US Quarter (25 cent coin), 1.75 mm or 0.069"
Diameter of US Quarter (25 cent coin), 0.955 in. or 24.26 mm
Number of Reeds around Quarter Circumference, 119
Quarter Reed-Reed Separation (Circumference / 119), 0.640 mm
Quarter Reed Gap seen from 60" (154.2 cm), 0.02378 degree or 1.426 min arc
Angular Width of Quarter seen from 60" (154.2 cm), 0.901 degree or 54.08 min arc
Number of Separate Points or Gaps Visible left-right across Quarter from 60" (154.2 cm), 54.08

Angular Width of Golf Ball (1.68" or 4.2672 cm) seen from 60" (154.2 cm), 1.5852 degree or 95.11 min arc
Number of Separate Points or Gaps Visible left-right across Golf Ball seen from 60" (154.2 cm), 95.11
Number of Dimples visible left-right across Typical Golf Ball, 12
Number of Separate Features of Each Dimple Visible seen from 60" (154.2 cm), 7.9

Angular Width of Blade Putter Head left-right (0.5" or 1.27 cm) seen from 60" (154.2 cm), 0.4774 degree or 28.65 min arc
Number of Separate Points or Gaps Visible left-right across Top of Blade Putter seen from 60" (154.2 cm), 28.65

Angular Width of Golf Ball 1.68" wide seen by Eyes 66" high above spot 9' or 108" behind ball and 126.6" from ball, 0.76028 degree or 45.62 min arc
Number of Separate Points or Gaps Visible left-right across Back of Golf Ball seen from 126.6", 45.62

Angular Width of Grass Blade 1/16th in. wide seen from Eyes 66" high above spot 9.5' or 114" behind spot and 131.7" from spot, 0.0272 degree or 1.63 min arc
Number of Separate Points or Gaps Visible left-right across Grass Blade seen from 131.7", 1.63

Angular Width of Golf Hole 4.25" diameter seen from 5' or 60" (154.2 cm), 4.056 degree or 243.4 min arc
Angular Width of Golf Hole 4.25" diameter seen by Eyes 66" high above hole 10' or 120" away along ground and 136.9" from hole, 1.778 degree or 106.7 min arc
Angular Width of Golf Hole 4.25" diameter seen by Eyes 66" high above hole 20' or 240" away along ground and 248.9" from hole, 0.978 degree or 58.69 min arc

Angular Width of Putter Shaft 0.37" diameter held at 20" from eyes, 1.06 degrees or 63.59 min arc

Angular Width of Sharpie Line 0.07" or 0.1778 cm thick on Golf Ball seen from 60" (154.2 cm), 0.0661 degree or 3.964

These calculations suggest that normal visual acuity can detect as separate up to 60 target widths across an object or location for each 1 degree in visual width. This also means that if a target size and distance results in an image's angular width being below 1 minute of arc (1/60th of a degree), then the normal vision will have difficulty seeing the target as separate from its surroundings. The following features of the putting environment as seen from the noted distances and positions present the stated number of separate target widths from side to side to a person of normal visual acuity under usual viewing conditions, with target-widths less than 1 being generally too small:

Object Position Distance Target-Widths

Grass Blade at address from 60" 3.5
Top of Putter at address from 60" 28
Golf ball at address from 60" 95
Line on Ball at address from 60" 4
Hole from directly above in address position at 60" 243
Dime at address from 60" 40
Dime Reeds at address from 60" 0.4 (too small)
Quarter at address from 60" 54
Quarter Reeds at address from 60" 1.4
Back of Ball from behind Ball 9' 45
Grass Spot 6" in front of Ball from behind Ball 9' 1.6
Hole at address from 10' 106
Hole at address from 20' 58

The width of the thumb extended 20" covers the hole at 10', as the thumb has 129 targets and the hole at 10' has only 106. The usual thickness of a shaft held at 20" (64 target widths) from 9' behind the ball will just cover the ball (45 target widths).

Aiming Precision Required

The required aiming precision for a dead straight 10-foot putt is determined by how much angle error in the face will change the line of the putt from the center of the putter face to the center of the hole to a line from the center of the putter face to the outside edge of the hole. The maximum allowable margin for error in aiming at a hole 10 feet away is half the width of the hole or 2.125" over 120 inches, which is an angle of 1.015 degrees. If the 4-inch long putter head in the heel-toe length swings 1 degree open, the tip of the toe end will move back a mere 0.035" or 0.09 cm or 0.9 mm. In other words, if the toe end swings off line "open" by about half the thickness of a grass blade or about the thickness of a dime, the putter aims outside the hole on a 10-foot putt. The allowable margin of error for a 20-foot putt is half this.

The above is based on the geometry of pivoting the putter face about the sweetspot midway between the heel and toe, as happens when the shaft enters the putter head on a line thru the middle of the putter head in the heel-toe direction. However, just as food for thought, consider that a heel-shafted blade putter is swiveled about the heel, where the shaft enters the putter head. As such, a 1-degree swinging open of the shaft at the heel moves the toe about twice as far along the arc in the "open" direction. Assuming the heel-toe length has the toe end 4 inches away from where the shaft enters the heel, a swing "open" of the shaft 1.015 degrees moves the toe end "open" on an arc that swings 0.077", or twice as far as the center-shafted putter moves a toe end that s 2 inches away from the shaft axis thru the putter head. So, paradoxically, perhaps a heel-shafted putter design offers an advantage in aiming due to this.

So these are the visual details typically available for aiming.

Next we can survey "vernier acuity" or the ability to assess the sameness of alignment of two short lines separated by a gap.

Cheers!

Geoff Mangum
Putting Coach and Theorist

Offering Free Podcast Tips for Putting Every Friday on GolfSmarterTips.com.

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