Tiger bends the shaft --
but that much?!?Over the past few years, the camera has
become an integral part of golf instrumentation. We find them in launch
monitors, feedback systems for swing training, and shaft behavior
recorders (for instance, see the Fujikura Enso).
Digital cameras have the advantage of cost, integration with computers
(to number-crunch the photographic data), no moving parts and the
inherent speed of electronics. So you can trust the camera readings.
Right? Not necessarily.
Photographic studies of shaft bend may be influenced by distortion in
the photos themselves. In particular, shaft bend itself is often
exaggerated in photos due to the way digital cameras and camcorders
scan their pixels. But this is not new. Film cameras with focal plane
shutters do the same thing, and that distortion has been known for a
century.
An SLR camera with the back open. #18 is the focal-plane shutter.Single-lens
reflex cameras were the basic tool of photojournalists and action
photographers for the last half of the 20th
century. And an essential part of the SLR was the focal-plane shutter.
Unlike the older leaf shutter, which sat just behind the lens (or even
between elements of the lens) the SLR's shutter was a pair of curtains
that covered the film, then briefly exposed it, then covered it again.
It is called "focal plane" because it is almost against the film, the
plane in which the image is in focus.
The picture at the left shows how a focal-plane shutter works. The
green-shaded rectangles are a pair of metal curtains, with an opening
between them. Before the picture is snapped, the upper curtain obscures
the film; that is, it lies fully across the large rectangular opening,
preventing any light from reaching the film. When you snap the picture,
this upper curtain starts traveling upwards, exposing the film as its
lower edge ascends.
Moments after the upper curtain exposes the film, the lower curtain
follows it up, once again covering the film. So the shutter works by
exposing the film between the upper curtain withdrawing and the lower
curtain advancing. The "speed" of the shutter -- the time it is open
and exposing the film -- is proportional to the width of the opening
between the curtains (the yellow dimension in the picture) divided by
the speed of travel of the two curtains.
Focal plane shutters control the exposure by setting the width of the
opening. Then a precise mechanism drags both curtains at the same
precise speed, so the width of the opening completely determines how
long the film is exposed to light.1
It works really well. Just one hitch. Not
all parts of the image are exposed at the same time.
True, all parts of the image
are exposed for the same amount
of time. But the bottom of the film is exposed before the top is. That
is fine, as long as the subject is stationary or moving
slowly. 'Slowly' is not too literal. The difference between
bottom
exposure and top exposure is seldom much more than 1/50 of a second.
But in sports photography in general -- and golf instumentation in
particular -- 1/50 of a second, or 20 milliseconds, is a significant
interval. And, as we shall see, it can make a big difference.
Car Trip -- Papa at 80 kilometers an hour
Jacques-Henri Lartigue, 1913
Let's try some numbers here. Suppose I set my focal-plane shutter to
take a picture at 1/1000 of a second. (That's 1 millisecond.) My camera
moves the curtains so they cover the whole frame in 20msec. So the
mechanism sets the width of the slit between the curtains to 1/20 of
the whole frame height, then lets the two curtains move in sync. Each
grain of film is exposed for 1/20 of 20msec, or one millisecond.
Exactly correct! But the bottom of the film "sees" its portion of the
image 20msec earlier than the top portion does.
This effect -- and the distortion it can cause -- was not freshly
discovered in 2010 with digital camcorders making distorted frames of
shaft bending. It was well-known as soon as focal-plane shutters were
used for action photos. For instance, look at this picture of a
speeding automobile taken almost 100 years ago. The camera was
"panning" with the moving car, at a speed between the speed of the
car and the stationary spectators in the background.
Remember, it
was exposed with a sliding slit. The top of the picture was exposed
milliseconds after the bottom. So the car appears tilted to the right,
and the stationary items appear tilted to the left. That is an obvious
result of the top being exposed measurably after the bottom.
If you want to see how a focal-plane shutter works in full-motion video, Gavin
Free of The Slo Mo Guys has done such a
video.
Worth watching, a lot of fun.
This
Distortion Exaggerates Shaft Bend
If you apply the same technology to a releasing golf shaft, the result
is a distortion-induced shaft bend. The diagram at the right shows how
it happens. Here are the words to go with the picture:
We have a camera whose focal-plane shutter takes
20msec to go from the top of the shaft to the bottom.2
We have a perfectly straight shaft near its top
speed. It is turning about 2º per millisecond, or 40º over the duration
of the shutter movement. Once again, the shaft is not bent at any
point in this scenario.
The horizontal dotted lines are the position of the
shutter opening at 0 milliseconds, 5msec, 10msec, 15msec, and 20msec.
The shaft position at each of these times is given by the
corresponding-color solid line.
I have put a circle at the intersection of the
corresponding-color lines. The circle is the position of the shaft seen by
the film
at the moment the slit focuses on it. If you connect these circles by a
smooth curve, you will see all the fractional images of the shaft that
the film sees.
I have "connected the dots" in exactly that way. The
fat gray curve is the image of the shaft captured on film.
The point is that the image on the film shows a very curved shaft,
but we know that the shaft was perfectly straight throughout this
exercise. The apparent shaft bend is completely an artifact of the way
the focal plane shutter exposes the film.
Digital
to the Rescue -- Not
Today's
camera is digital. All electronic. No film. No moving parts. That means
no moving parts in the shutter.3 So we
shouldn't have those problems any
more.
Well, maybe we shouldn't, but we do. The reason is in the numbers.
The
picture to the left is formed as a collection of pixels, picture
elements. Every digital picture is made up of individual pixels. The
smaller and the more the pixels, the sharper the picture. We call that
"resolution". And of course you knew that. So let's get back to the way
the camera works.
The camera's "retina" is an array of
photosensors, one per pixel. At the moment of snapping the picture, all
those photosensors are sampled at once. Well, not exactly.
The picture here is made up of a 40x40 array of pixels, for a total of
1600 pixels. If the camera had enough electronics to sample
1600 pixels simultaneously, it would be bigger and more expensive
than the digital cameras we are used to. Instead, the camera
electronics scans the pixels, sampling them one at a time
(or perhaps a few at a time).
That means it takes some time to for the photosensor to
gather the entire picture. Suppose we can sample
one pixel per microsecond; that's a million pixels per second. So we
can completely scan this picture in 1.6 milliseconds. That's fast. No
problem scanning at all. We just start at the upper right of the
picture (pixel 1), scan across the row (to pixel 40), then start on the
next row (starting at pixel 41 and sweeping across to pixel 80).
Eventually -- less than 2msec later -- we have scanned pixel 1600 and
the entire picture is saved.
But wait! 1600 pixels is 0.016 megapixels. The cameras you buy today
typically have 10
megapixels
and more. If you scan 10 megapixels at one per microsecond, it will
take ten seconds to save the whole picture. Think of the distortion
that could build up in ten seconds. Obviously, digital cameras do
better than that.
As it turns out, fast
photosensors and multi-pixel scanners reduce this time. In the typical
digital camera, it winds up at
about the same 20msec that a mechanical focal-plane shutter takes. (Not
coincidence; the digital designers needed to compete with
top-of-the-line film SLRs. They didn't need to far exceed them, so they
spent what was necessary to compete.) And they scan row by row, as in
the picture above. The numbers that result from this are:
A 10 megapixel photosensor has about 2800 rows of
3600 pixels each.
If the array is scanned in 20msec, then each row
takes 7 microseconds.
So
a whole row is scanned in less than 1/100 of a millisecond. That's
instantaneous compared with any motion we're trying to capture. But
the rows are scanned in sequence, so it takes 20 milliseconds to scan
in the whole picture.
That
is exactly what we saw with a focal plane shutter!
The row being scanned corresponds to the slit between the curtains, and
the row-by-row scan corresponds to the motion of the slit across the
frame of the film. The distortion is going to be exactly the same as it
was with the focal plane shutter. Digital cameras have not rescued us
from that.
How
to minimize distortion
How
do we minimize this distortion? The obvious answer is to scan faster.
Grab all the pixels quickly, so the shaft does not have a chance to
move very far during the scan. This can certainly be done. For
instance, we could get a high-frame-rate camera. A video camera that
runs at 1200 frames per second has less than a millisecond to record an
entire image. So we know it will scan fast enough to keep distortion
very low. Such cameras exist, but are much more expensive that what you
are
likely to have on hand. If you can spend enough money on
instrumentation, then the solution is out there.4 But can it
be done with conventional cameras?
Rick Malm has
suggested a way to minimize distortion in pictures taken
with conventional digital cameras and camcorders. Well, it's not the
first time I've heard the suggestion. But Rick is the first guy I've
seen to actually go out and do something about it. He has used his Casio EX-F1 camera to demonstrate
the technique.
Rick
(and many others) observed that a horizontal shaft is not distorted
much. That is because it is parallel to the scanning rows of pixels. So
the scan catches and passes the shaft in just a few rows -- a very
short time. There isn't much chance for the shaft to move during that
time. Since the distortion is due to an object moving while it is being
scanned, we can minimize distortion by scanning more or less parallel
to the shaft.
For
example, look at the picture on the right. This is analogous to the
picture above, but with the scan lines nearly parallel to the shaft at
T=10msec. So the only scan lines that actually intersect the shaft are
those just around 10msec. (Remember that the shaft positions and scan
lines are color-coded; intersection only counts for like colors. So the
only intersection is just before the green positions.) In other words,
the duration of actual views of the shaft is right around a
millisecond, instead of 20 milliseconds. The shaft only has a fraction
of the movement during exposure, and there is far less opportunity for
distortion.
Unfortunately, our cameras are what they are. Not many of us
are in a position to modify the scan of our digital cameras. I
have two degrees in electronics engineering, and I wouldn't dream of
attempting it on an existing camera that I own.
But there is a simple,
pragmatic way to do it. We can tilt the camera, so it is scanning
parallel to the shaft at the shaft position of interest. (If you need
to measure shaft bend throughout
the swing, you will need the expensive, higher-speed
camera.)
Of particular interest is the case of the vertical shaft. One of the
most interesting and contentious details of shaft bend is the bend just
before impact, where the shaft is essentially vertical. A few of the
more
important things we get from bend in the vertical shaft are:
The loft added to that built into the head. We all
know that shaft bend changes the loft at impact.
Whether the hands are accelerating or decelerating
the clubhead at impact. If the shaft is bent forward (clubhead leading
the grip) more than about ½", then the hands cannot be providing any
clubhead acceleration. And almost every good swing does meet this
criterion. (See my article on ShaftLab
for
why this is, and the article on hitting
with the hands for why it matters.)
To get a rather distortion-free picture of the shaft at impact, just
turn the camera on its side. In fact, almost every camera and
camcorder has a horizontal picture format, so turning it 90º gives a
better fit to the frame anyway. (Of course, video formats don't
typically support that; you will watch the video turned on its side.)
Examples
Rick
has shared with me several pairs of pictures that he took to
demonstrate this. In each pair, one picture is taken normally, and
shows distortion that exaggerates
the bend of the shaft. The other is taken with the camera tilted 90º,
so the shaft is roughly parallel to the scan rows -- and, as a result,
is not distorted. Rick and I have added red lines to the pictures, as a
reference for where an absolutely straight shaft would be.
In
each of the picture pairs below, the left picture is taken normally and
the right picture with the camera vertical. Click on the sample
pictures to see the full-size raw picture as Rick sent it to
me.
Let's
start with an example that is identical with the diagram we used above
to explain the distortion. Here Rick is swinging a section of aluminum
tubing. It is fat and very rigid; it does not bend at all. (Well, not
enough to see, anyway.)
There is a lot of bend evident in the
first picture. But it is all illusion, due to the distortion. The
actual bend, seen in the second picture, is invisible.
Rick
attended the 2009 Long Drive World Championships in Mesquite, NV. At
the practice range, he had an opportunity to photograph Jamie
Sadlowski, the world champion. This pair of pictures shows that, while
Jamie's shaft is certainly bent forward at impact, it is not by nearly
as much as a conventional photo would show. (The left picture is taken
normally, the right picture with the scan lines vertical.)
This picture pair
and the next (the one of Dewald Gouws) are frames taken from video,
which was shot at 300 frames per second. Instead of a total scan time
in the order of 10-20 milliseconds -- as with a conventional camera or
camcorder -- it is only 2-3 milliseconds.
Therefore, even the
distorted picture does not exaggerate the bend as much as a
conventional photo. Even so, the bend in the first picture is
substantial -- and an exaggeration, as the second picture tells us.
The
same is true for long-driver Dewald Gouws, who came in second to Jamie.
His shaft is also bent forward just before impact, but a lot less than
the photo on the left suggests. The picture on the right is
distortion-free.
Some folks may be surprised that
the shafts do actually bend forward coming into impact, even for these
big hitters. But experienced clubfitters and golf engineers are not
surprised at all. They might even wonder at how small the forward bend
is. But remember, these guys use much stiffer shafts than you or I
would. While the bending forces might be a lot larger than the average
golfer, the XXX-flex shaft resists that bend fairly effectively.
Acknowledgement
My thanks to Rick Malm of SSC
Golf Swing and TourGolfVideos.com
for demonstrating a way to photograph shaft bend with greatly reduced
distortion, and providing some excellent photos as examples.
Notes:
This is an
accurate description of how it works for fast shutter speeds. The
operation is a little different for slower speeds. But a camera's use
as a golf instrument is high-speed only. We won't bother discussing the
low-speed operation.
But we said
that the travel was upwards, and this explanation calls for downward
movement of the opening. Well, not really. If you get into the optics
of cameras at all, you know that the lens inverts the image projected
on the film. An upward travel of the shutter across the film is
downward as far as the image is concerned. If this explanation doesn't
jibe with you, just imagine the shutter curtains moving downward
instead of upward. Some cameras are indeed built like that.
Some
digital cameras do have
moving parts. In particular, the expensive dSLR cameras still have
mechanical shutters for various reasons. (Written in 2012. I suspect in
5 or 10 years, this will no longer be true; the reasons will have been
trumped by technology.) But that doesn't solve the problem; it just
puts them in the same boat as a film camera with a focal plane shutter.
A bit more on
the higher-speed video cameras on the market. A 20msec scan time works
for the standard 30 frames per second (fps), but you need much faster
scans for 300fps (3msec) or 1200fps (0.8msec). Many camera
manufacturers (e.g.- Casio for the EX-F1 that took the pictures in
this article) handle this by cutting the resolution. If you cut the
resolution, there are fewer pixels in a frame, so you don't have to
throw technology at it to scan more pixels per second.
Last
modified - July 5, 2016
Copyright Dave Tutelman
2024 -- All rights reserved
