GSA Advanced Golf Simulators
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The Theory of Golf Simulators
The ideal golf simulator would need to capture the following 9 parameters in real time:
1. Club speed
2. Club path
3. Clubface angle at impact to the ball
4. Club attack angle
5. Ball speed
6. Ball path
7. Ball vertical launch angle
8. Ball spin rate
9. Ball spin axis tilt.
Methods of measuring and calculating ball spin and spin axis tilt
Most simulators don't actually measure ball spin and axis tilt, they calculate them from the relative club face angle to club path.
There being a direct relationship between club head data and ball spin. ie a relative to path open or closed club face will cause the ball's spin axis to tilt one way or the other and the trajectory will curve to give fades, draws, hooks and slices.
For most players this method works well enough but it is basically only estimated based on this club data. Ideally your system would actually measure the ball spin and spin axis tilt.
Of all the 9 parameters, ball spin and - more importantly - spin axis tilt is the most difficult to measure.
There are two basic ways of accomplishing this:
1. You capture photographic images of the ball in flight and use sophisticated image processing to determine the movement of either markings on the ball or the dimples themselves.
2. You fire a signal - such as light (laser or IR light) or a microwave (radar) - at the ball and measure the amplitude modulation of signals reflected back from the ball to a sensor.
Radar methods include using a ball with a metal chip in it or (apparently) measuring and analyzing the air turbulence around the ball.
The air turbulence method seems a tad ( to say the least ) far fetched to me but this is what I've heard that one manufacturer is claiming.
Because radar based launch monitors used outdoors have the ability to measure the curve in the flight I rather suspect that they back engineer the ball flight trajectory to obtain ball spin and spin axis tilt.
As with calculating ball spin from club data, the reverse is also possible. i.e. club data can be determined from ball spin data and ball spin data can be calculated from ball flight.
In the space confines of a golf simulator however, there is no measurable side curve in the ball flight in the 15 feet or so from the tee to the impact screen so this method wouldn't work.
Photographic method.
The main challenge here is to freeze frame capture clear multiple images of the ball while it is travelling at speeds of up to 200 mph.
In order to accomplish this the camera's shutter speed has to be very fast. ie arround 1 micro second or 0.000001 seconds.
At that very fast shutter speed the amount of light reaching the camera's sensors will - under normal lighting conditions - be too low and the captured images will not be usable.
If using markings on the ball (either a line or a pattern) we could get away with using a constant light source but if attempting to capture a lot of detail then a strong close-up strobe or flash light would be required.
The above image shows a series of images of a ball captured by a camera during flight. The ball has one line and image processing could easily detect the motion of the line and thus the spin rate.
The above shows two ways of marking the ball. The disadvantage with using a single line on the ball is that the ball must be placed on the tee or mat so that the line is centered and visble to the camera before taking the shot.
The ball on the left has pattern markings all around the ball so can be placed in any position on the tee or ground.
Using really sophisticated camera image or signal processing it is conceivable to measure ball spin by detecting the dimples on the ball.
For this method to work though you'd need to know the dimple spacing on the ball which - as shown in the above image of two balls - is not quite so easy.
As can be seen, the ball on the right has uniform dimple spacing but the ball on the left does not.
Spin axis tilt
Although spin rate itself is an important aspect in calculating the trajectory of the ball's flight, it will only affect the carry distance by a relatively small amount when compared to initial ball speed.
For most players, the axis tilt of the ball's spin will be more noticeable in the flight of the ball as this is what causes the ball to curve i.e. fades, draws, hooks and slices.
As mentioned above, most simulators don't actually measure ball spin and axis tilt, they calculate them from the relative club face angle to club path.
To measure - not calculate - spin axis tilt (otherwise known as side spin) the only proven method (at least known to me) is to capture images of the ball in flight and use
sophisticated image processing to measure the movement of markings or dimples on the ball.
The above image shows our method of measuring ball spin and axis tilt using a single line mark on the ball. Click on above image to learn more about our ball spin camera.
The following math explains how the spin rate is determined.in our system
The above image of the ball shortly after impact shows that the spin line has shifted back 10.47 mm from it's original position.
The ball is already in flight and spinning at this stage.
The camera detects a pixel shift of 44 pixels which equates to10.47 mm when the pixel shift is multiplied by the scale factor.
In the above case the scale is 0.238 so 44 * 0.238 = 10.47 mm.
The total circumference of a golf ball is 134 mm so 10.47mm is 7.81 % ( 10.47/134 * 100) of the circumference.
The time it took the line to get from it's original position to the one captured by the camera is determined by the ball speed and the distance the ball travelled from it's original position.
In this case the ball speed is 61 meters per second (measured by the Vcam ball tracking camera)
and the distance the ball travelled (calculated by the launch angle and the distance the trigger sensor is from the ball launch position ) is 50 mm or 0.05 meters.
Time is calculated by the formula t = d/v where d is the distance travelled and v the velocity (speed) of the ball.
So time taken for the shift in this case is 61 / 0.05 = 0.00081425 seconds.
To determine the spin rate of the ball we need to calculate the total time required for a complete revolution.
As we know the time the ball took to shift 7.81% of it's circumference - which equates to a 28 degree turn (360 * 7.81) - , we can calculate the time for a complete revolution
by dividing the time by the percent (to give 1% of the time) and multiplying by 100 to get the complete time.
In this case it would be 0.00081425/7.81 * 100 = 0.01041916 seconds.
This would then equate to 1/ 0.01041916 = 95.9 revolutions per second.
Multipy this by 60 to get revolutions per minute = 5758 rpm
With our overhead mounted camera we can detect up to around 85 degrees of turn which - with a Sand Wedge - will equate to over 10,000 rpm
Drivers will be in the 2000 to 4000 rpm range.
For simplicity we have omitted - in the above description - the fact that the camera sees the ball as a flat image and not as a sphere
and that the actual line shift has to be adjusted to compensate for this.
The actual line shift is the segment length of the ball given the line start and end positions.
However, due to the complexities of adding the varying camera perspectives of the line into the equation we can't just use the above formula to calculate the segment length.
A table look-up method was therefore choosen to convert the flat line shift into a spherical line shift.
Spin Axis and Side Spin
Spin axis is determined by calculating the side spin and using this to obtain a ratio of side spin to back spin which is then used to calculate the spin axis shift from it's norm of zero degrees.
Although some "experts in this field" would say there is no such thing as side spin we could just as equally say there is also no such thing as back spin either:
i.e. there is only spin and spin axis.
Our cameras see side spin as a shift in line angle from it's norm of zero degrees.
In the above image the line Tilt is 7.72 degrees which - when divided by 360 degrees - equates to 2.144 % of the total 360 degrees.
Knowing the time it took to get to this tilt we can calculate a theoretical side spin speed value. In this case that would be 1112 rpm.
From the previous calculations we know that the ball's back spin is 6584 rpm.
This then gives us a ratio of 1112 : 6584 which can be used to weight the degree shift from the ball's norm of zero degrees back spin axis to the norm of 90 degrees side spin axis.
In this case the spin axis is 7.6 degrees right.
If both the side spin and back spin where equal then the ratio would be 1:1 and the spin axis would be half way between 0 and 90 degrees i.e. 45 degrees.
To clarify: Back spin without side spin has a spin axis of zero degrees. Side spin without back spin has a spin axis of 90 degrees.
So if you hit a ball perfectly square with a lofted club then the spin axis will be zero degrees.
If you hit a ball with a club that has zero degrees loft but the club head is open or closed then you will have only side spin with a spin axis of 90 degrees.
Another - rather novel - method of calculating ball spin axis tilt is to detect the direction of the ball's rebound off the impact screen.
If the ball has any spin axis tilt then it will tend to spin off the screen in the direction of the spin. If the ball has no spin tilt then it will bounce and roll back to the player in a straight line.
The term "Calculating" is probably a little over the top here though. Gestimation would be a more suitable term but the method can give some indication of the ball's side spin.
The main problem being that the screen has to be quite taught in order that the rebound be detectable and this will cause the impact sound level too increase.
Warning: We know of at least two golf simulator companies that use this method - which is just fine - but at least one of them is claiming to measure ball spin and to capture club data - ie path, face angle and speed - from it.
This is total nonsense of course and is an example of extreme marketing hype and very misleading advertising. Buyer beware!
Methods of measuring ball vertical launch angle, ball path and speed
Sonic
A sonic system (sonic meaning sound) is a system that employs strategically placed microphones around the impact screen.
The system simply measures and compares the intensity of sound that is produced by the ball hitting the screen.
Using 3 or more directional microphones and an interface that can measure the sound amplitude of the impact from each microphone, an XY impact position can be determined.
If you then know the XY co-ordinates of the impact position on the screen and know where the ball launch position was, then it is a simple matter to determine the launch angle.
Ball speed can be calculated by measuring the time between the ball being struck (the microphones will pick this up too) and the ball hitting the screen.
In theory all this should work and is in actual fact used by a number of golf simulator manufacturers but I couldn't say how accurate the method is.
The main disadvantage is that the ball must always hit the screen with a fast shot so that there is no downward curve in the ball's trajectory before hitting the screen.
So chipping and other small shots like putting don't work with a system like this.
You are also forced to play the shot from the exact same position so hitting from other surfaces like simulated rough and sand and greens do not work with this method.
Optical Sensor arrays
This method uses two banks of IR sensors and emitters to capture two XY co-ordinates of the ball as if travels through them.
The two co-ordinates are then compared to determine the vertical launch angle, ball path and speed.
The system is very accurate but ludicrously expensive to construct as you need hundreds (if not thousands) of optical sensors and emitters.
Because the light from the emitters will reach not only the sensor it is aimed at but also many neighboring sensors - which will cause false readings -
the system has to be multiplexed (scanned). ie Individual sensors are activated only for a short period of time and to see if the ball is in the cross fire of the particular light emitter and sensor.
As with the sonic system, the main disadvantage is that the ball must always hit the screen ( or at least pass through both array banks) with a fast shot so that there is no downward curve in the ball's trajectory before hitting the screen.
So chipping and other small shots don't work very well with a system like this.
However, you can play the shot from other surfaces like simulated rough and sand and greens.
Camera ball tracking
Cameras are becoming the first choice of engineers designing ball tracking systems these days. They offer many advantages, are flexible, relatively inexpensive and reliable.
There are a number of configuration and setup choices with cameras including, XY or Stereophonic positioning, free running cameras or triggered methods, on-board or external image processing.
To capture the basic 3D ball flight parameters (speed, path and vertical launch angle or XYZ) you need at least two cameras.
Free running cameras
If the cameras are to run in free running continuous mode (ie they are continuously capturing and sending frames) then they must be cabable of frame rates in excess of 100 frames per second.
Using two cameras then means that the image processing must be able to handle at least 200 frames per second.
This would normally require a dedicated processing unit as the host PC would be too busy rendering complex graphics to handle this.
The processing unit could be a separate PC or the camera itself has on-board processing capabilities.
The big advantage of having on-board camera processing is that the image data does not have to be transmitted along slower lines to the PC.
This line (either USB or FireWire) is usually the bottle neck when attempting to capture high frame rates.
Triggered cameras
An alternative to the free running camera method is to trigger the cameras with a signal as and when the ball has been hit.
The trigger can be an optical sensor or array of sensors that picks up the ball as it passes by and generates a trigger signal to the camera so capturing
the ball in flight at an exact, precise and known moment. This is the method we are currently using.
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The trigger source can also be a line scan camera that detects the intensity of light reflected back.
As the ball is usually white the intensity of light reflected will be higher when a golf ball is in the camera's FOV.
Camera on-board image processing can be designed to fire a trigger signal to the cameras when the reflected light reaches a certain level.
Line scan cameras don't deliver frames, only lines but are therefore very fast. Usually in the 3000 lines per second range.
Using on-board processing, the line scan camera could detect if a ball is in it's field of view and generate a trigger signal to the other camera or cameras.
The line scan camera's disadvantage is that they are still quite expensive and if the image processing is not done on board then it will again require a separate dedicated additional PC .
The "High Speed Camera" hype
You'll notice that most golf simulator manufacturers that use camera ball tracking always quote: High Speed Cameras!
with statements like with over 2000 frames per second, you've never seen anything like this before! or the ball is tracked from stike point to the screen at 1000 fps giving unparalleled accuracy!
Unless the manufacturer is measuring ball spin - and to the best of our knowledge there is only golf simulator manufacturer that can do this using marked balls - then this is pure marketing hype and can be completly ignored.
The following images explain:
Camera ball tracking at !0,000 fps --------------------------------------------------------------- Camera ball tracking at 1000 fps
Camera ball tracking at !00 fps -------------------------------------------------------------------- Camera ball tracking at 0 fps (triggered)
The object of camera ball tracking is to measure ball path, ball launch angle and ball speed.
The above images show that this can just as easily be accomplished using any frame rate as you only need two points to measure these parameters.
As there will be no detectable ball curve or deviation in it's flight to the screen in a normal shot, capturing more than just two frames is of no value.
For a free running camera 100 fps will be sufficient to capture two images of the ball flight within the 10 ft or so distance to the screen.
In fact, the ball trace left by a triggered camera is just as good - if not better - than that of a camera running at 10,000 fps.
In the very competitive golf simulator market, manufacturers like to try and blind unsuspecting customers with science in order to impress.
It works too. We've had many customers ask us what our camera's frame rates are and use this data to compare with the competition.
It's like "the higher the camera frame rate is the better simulator it is".
Hope the above images and explanation will shed some light on the matter for you.
IR light reflex method of measuring vertical launch angle
This method uses an embedded IR lightt emitter and sensor in the hitting mat. The sensor is hooked up to a high speed and high resolution Analog Digital Converter
which is capable of capturing at least 800 samples of a ball travelling at 170 mph. This in turn is interfaced to the host PC which processes the triggered light intensity samples.
The amplitude of the reflected light that bounces back to the optical sensor as the ball passes is directly proportional to the height of the ball so
if you know the launch position of the ball then it is an easy matter to determine the launch angle.
This method is used in our VX and ADX products.
(Note: The above image just shows a single emitter and sensor pair but for all practical purposes you'd use an array of sensors and emitters to allow for the ball to deviate left or right.)
Radar
Radar works by emitting micro-waves and processing the reflected signal back. The Doppler effect is used to measure ball speed and positions of the moving ball.
Radar ball tracking is very good when used outdoors because they can track the ball over long distances.
In the confines of a golf simulator enclosure the system has a number of drawbacks though. These include not being able to track the ball while rolling (ie putting) and small chips.
Ball spin and axis tilt is measured using special balls that have a metalic dot insert.
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Optical sensor or cameras
A case in point is the average sensor pad you can buy these days in the $300 to $3000 price range.
The problem with all optical sensor pad club track systems is twofold:
1. The ball path accuracy is dependent on the number of sensors used in the system, the sensor spacing and the distance the two rows are apart.
Seldom does a sensor club track pad achieve better than 1.5 degree resolution and most not even 2 degrees.
Cameras, on the other hand, feature millions of sensors (pixels) and can thus attain a club path accuracy to within one hundredths of a degree.
Golf simulator sensor pads detect club path with two rows of sensors.
The usual minimum sensor spacing is 3.84 mm (this being a standard circuit board component hole pitch) which is difficult to improve on due to the physical size of the sensors (usually >3mm).
The club path resolution is then dependent on the row spacing. The further the rows are apart, the better the resolution but if set too far apart the swing arc will distort the measurement.
With a sensor pad that has poor club path resolution (as most do) even 1.5 degree club path won't be detected.
2. Club face angle detection at impact to the ball. The inherent problem is that the club face is often curved and not straight and optical sensors just can't see that.
The above images show what typically occurs. If the player does not strike the ball dead on the sweet spot then the optical sensors will read a false club face angle.
Even though the club face is square, optical sensors can - and often do - read open or closed.
This can cause you to work on an apparent swing fault that is probably not even there.
The image on the right shows that increasing the sensor spacing doesn't help either.
If a sensor pad features multiple club face sensors then this will help but then the true club path would have to be known in order to determine the club face angle.
And as measuring club path with optical sensor pads is prone to large errors this method will also not be accurate.
As ball side spin (spin axis tilt) is a product of club face angle and club path - ie relative face angle - any errors in either of these measurements will lead to false ball trajectory calculations.
Because it's the relative club face angle that determines how the ball will curve, accurate club path measurement is just as important as face angle measurement accuracy.
One without the other can cause the ball flight to fade instead of draw, slice instead of fade, hook instead of draw etc. etc...
Inherent problem with Reflex optical sensor pads.
In addition to the problems inherent in shadow based club tracking pads (ie those requiring an overhead lamp)
reflex optical sensor pads (ie those that feature built-in IR LEDs that measure the reflection off the underside of the club) are subject to further inaccuracies
due to the fact that the underside of a club is also curved and thus the reflection strength is not uniform throughout the width of the club-head.
Optical sensors and their associated latch logic switch at certain and constant light level thresholds so if the reflection strength is not uniform then the switching times of the sensors will vary.
While this may not be important for detecting ball path, it is imperative for measuring club face angle and club speed as the associated timers would be set at incorrect times which will lead to false readings.
In addition, the under side of the club would need to be quite reflective in order for a reflex pad to work at all. With woods and drivers this is often not the case.
The reflective tape nightmare
A part solution to these problems is to stick a straight length of reflective tape to the underside of the club.
It's only a part solution because many moden woods and drivers have highly reflective chrome areas under the club which will reflect the light back to the sensors
before the intended strip so you'd have to actually mask off these chrome areas with even more tape!
And then, after you've carefully and precisely taped up most of the underside of all your clubs it all starts to move and come off when the club makes contact with the grass fibers of the pad. (assuming the pad actually has a grass fiber top of course).
And to top that off you'd have to remove the tape again when playing golf in the real world and stick them all on again to play the simulator.
Optical sensor switching tolerances
Addditionally the optical sensors themselves have varying switching levels due to manufacturing and element tolerances so when two or more optical sensors are used to calculate timed parameters
such as club face angle and club speed, the sensors have to be matched or calibrated in order to produce accurate results.
As this is very time consuming process it is unlikely that any manufacturers of sensor pads would make the effort to do this.
The above image is from our Ccam club tracking camera. Notice how the ball path deviates from the club path.
The club path in this shot was 3.8 degrees out to in while club face angle was 11.89 open. The relative to path face and is thus 15.69 degrees open.
Up until recently, it was commonly thought that the ball path would follow the club path.
The above image however shows that the ball path is more following the face angle. i.e. it's going right and not left as the club path is.
In addition, the ball impact position on the curved club face will also influence the ball's path.
This shot shows that the impact position was more towards the toe of the club so the effective club face angle would be even more open.
Most (if not all) club tracking optical sensor pads on the market today will either use the club path, the club face ange or some combination of the two to determine the ball path.
None of which will be particularly accurate.
The bottom line is that if you want true and very accurate ball and club data detection then the only way is to use cameras.
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Measuring ball speed with Optical sensors
In order to measure ball speed you need to know the distance the ball travelled within a known time frame.
As opposed to measuring club head speed - which is travelling relatively flat over the sensor pad sensors - a ball is usually travelling at a specific launch angle (unless rolling).
Without knowing the launch angle it is not then possible to measure or calculate the distance the ball has travelled so any ball speed calculations will be inaccurate.
The distance the ball travelled is along the hypotenuse but optical sensors only measure distance along the the adjacent.
When considering a system from a certain manufacturer that claims to measure ball speed with optical sensors but not vertical launch angle then
you should be aware that this claim is flawed and probably nothing more than marketing hype.
Photographic evidence
Other manufacturers of optical sensor club and ball tracking systems make all sorts of wonderful claims about the accuracy of their systems
but at the end of the day you - the potential buyer - just has to take their word for it.
The purchaser of these systems has no way of actually confirming their claims so you are basically left blind.
Camera systems - on the other hand - show actual photographic evidence of the manufacturer's claims.
A camera doesn't lie.
Optical sensor pad reliability.
"Optical sensors are very reliable and will last a life time"
Unfortunately a prerequisite for the above statement to be more than just a hopeful wish is that they are not subject to massive shock vibrations caused by 4000 lb force club head impacts.
Which, in the case of a golf simulator sensor pad, is routine rather than the exception.
While sensor pads have realtively long life spans for home users, all electronic systems that are routinely subject to these types of forces will eventually fail.
The reasons for this is usually one of the following:
1. Over time, hair line cracks will start to appear in the solder joints which then grow in size until there is intermittent or no electrical contact.
2. Elements in the chips and sensors themselves start to break down
3. Static electricity - caused by the club sweeping through synthetic grass fibers - can burn-out and blow sensitive ICs and sensors.
4. Heat and humidity - and thus eventually mould - can build up in the pad causing short circuits.
These faults usually rear their heads outside of the manufacturer's warranty period (usually 6 months) so we advise that you check with the product manufacturer for the price of repairs and/or replacement parts.
If it's just a $300 pad then you can just buy a new one. That's usually not an option with a $3000 pad though.
Once again, if you want true reliability then the only way is to use cameras.
