A practical simulation of a tennis serve trajectory

[jmnk]

Since we are still in that pandemic times, with a bit too much time on hand.... Between those famous frame-counting method of approximating serve speed, and various apps that measure such speed I got interested in physics and math behind it. Behind the tennis serve trajectory itself that is. So I created an interactive Mathematica notebook/presentation where one can control initial parameters of the serve: speed, spin, left/right angle, up/down angle, contact point and so on and see where such serve would actually land. Not that it has much of a practical value for a tennis player - since any good player knows where the ball will end up more/less based on years of experience - but a nice visual anyway.

I've submitted it to Wolfram Presentation, hopefully they will review and accept, after which it will be posted in a nice format on Wolfram Demonstration site. In the meantime anyone can see and play with it here: Tennis Serve Trajectory . It works on my browsers at least, with no need for any plugins or external programs - but I have not tested it extensively.

The demonstration format has a bit more details and what and how - but hopefully the controls are enough self explanatory. If you adjust any of the initial conditions the trajectory (the red line) will adjust accordingly. The green line represents the trajectory of the serve with the same exact initial parameters - but it shows what it would be if there was no air drag or Magnus Forces. I've spent fair amount of time researching the physics and math behind it - I'm quite confident it is pretty accurate. It takes into account air drag, Magnus forces due to a spinning sphere, various coefficients that were empirically proven/described in many scientific papers.

Initial defaults represent ATP level male flat serve.

Ask away if you have any questions. Or suggestions for improvement.

again, the link is: Tennis Serve Trajectory Presentation

 

[Chas Tennis]

One important principle is that the spin vector direction imparted to the ball at impact (or slightly after the ball distortions quiet down) remains in the same direction throughout the trajectory to the bounce. Is that true for your model? In other words, the ball acts like a gyroscope on the trajectory.

Where did you get ATP spin information?

If you have any links for that information, that I believe I've read in Rod Cross's writings, I'd appreciate any links.

There is a ball diagram that shows measured spin vectors right after impact for the kick, slice and flat serves. Did you use the ball diagram or the publication? It's the best information I've found on measured serve spins.

 

[jmnk]

One important principle is that the spin imparted to the ball at impact (or slightly after the ball distortions quiet down) remains the same throughout the trajectory to the bounce. Is that true for your model?

If you have any links for that information, that I believe I've seen in Rod Cross's writings, I'd appreciate any links.

There is a ball diagram that shows measured spin vectors right after impact for the kick, slice and flat serves. Did you use the ball diagram or the publication? It's the best information I've found on measured serve spins.

I've read many, many scientific papers on that topic, including the Cross's writing. Science is actually undecided 100% on the topic of spin vector. The general consensus is that both magnitude and the direction of the spin vector remains within 10% of the initial spin vector values throughout the entire trajectory. In my model the spin vector (magnitude and direction) is assumed constant. The model is pretty complicated as is, so I've taken the liberty to disregard that 10% discrepancy.

But yes, the model does assume that pretty much any serve, including the so-called flat one, is mainly the side spin - which is reflected in initial parameters where side spin is like 90% of the total spin. An astute reader may also notice that there's spiral spin component, i.e. the American football like - the one, according to laboratory measurements stays at ~200rpm level for _any_ type of spin.

 

[Keendog]

Since we are still in that pandemic times, with a bit too much time on hand.... Between those famous frame-counting method of approximating serve speed, and various apps that measure such speed I got interested in physics and math behind it. Behind the tennis serve trajectory itself that is. So I created a Mathematica notebook/presentation where one can control initial parameters of the serve: speed, spin, left/right angle, up/down angle, contact point and so on and see where such serve would actually land. Not that it has much of a practical value for a tennis player - since any good player knows where the ball will end up more/less based on years of experience - but a nice visual anyway.

I've submitted it to Wolfram Presentation, hopefully they will review and accept, after which it will be posted in a nice format on Wolfram Demonstration site. In the meantime anyone can see and play with it here: Tennis Serve Trajectory . It works on my browsers at least, with no need for any plugins or external programs - but I have not tested it extensively.

The demonstration format has a bit more details and what and how - but hopefully the controls are enough self explanatory. If you adjust any of the initial conditions the trajectory (the red line) will adjust accordingly. The green line represents the trajectory of the serve with the same exact initial parameters - but it shows what it would be if there was no air drag or Magnus Forces. I've spent fair amount of time researching the physics and math behind it - I'm quite confident it is pretty accurate. It takes into account air drag, Magnus forces due to a spinning sphere, various coefficients that were empirically proven/described in many scientific papers.

Initial defaults represent ATP level male flat serve.

Ask away if you have any questions. Or suggestions for improvement.

again, the link is: Tennis Serve Trajectory Presentation

One important principle is that the spin vector direction imparted to the ball at impact (or slightly after the ball distortions quiet down) remains in the same direction throughout the trajectory to the bounce. Is that true for your model? In other words, the ball acts like a gyroscope on the trajectory.

Where did you get ATP spin information?

If you have any links for that information, that I believe I've read in Rod Cross's writings, I'd appreciate any links.

There is a ball diagram that shows measured spin vectors right after impact for the kick, slice and flat serves. Did you use the ball diagram or the publication? It's the best information I've found on measured serve spins.

This is like when Sheldon met Amy

 

[Keendog]

 

[Chas Tennis]

I've read many, many scientific papers on that topic, including the Cross's writing. Science is actually undecided 100% on the topic of spin vector. The general consensus is that both magnitude and the direction of the spin vector remains within 10% of the initial spin vector values throughout the entire trajectory. In my model the spin vector (magnitude and direction) is assumed constant. The model is pretty complicated as is, so I've taken the liberty to disregard that 10% discrepancy.

But yes, the model does assume that pretty much any serve, including the so-called flat one, is mainly the side spin - which is reflected in initial parameters where side spin is like 90% of the total spin. An astute reader may also notice that there's spiral spin component, i.e. the American football like - the one, according to laboratory measurements stays at ~200rpm level for _any_ type of spin.

You can measure the percentages of components for each serve type off this diagram. See the publication for details and maybe the components in tables. Search Ball Spin Vector Elliott in Researchgate.

I would choose to assume that the magnitude of the spin vector decreases and that its direction stays the same.

My view of the bounce direction is - If the spin axis has a considerable tilt and remains the same from launch to bounce then we can see the speed and direction of the ball felt that first contacts the court. The effect of ball distortions on the court bounce are complicated for the kick serve but the direction of the felt velocity vs court surface is clear if our spin axis direction remains the same.

It helps to visualize the felt vs court to imagine the spin vectors extended out through the bottom of the ball in the drawing. The slice and flat serve axes exit very close to the spin axis, but the kick serve axis exits the ball a considerable distance away from the spin axis = the felt has much higher lateral speed to the court surface for the kick serve and bounce would seem to be to the right.

 

[Rubens]

^How can I think about this when I'm busy thinking about what my myosin, actin and titin are doing?

 

[jmnk]

You can measure the percentages of components for each serve type off this diagram. See the publication for details and maybe the components in tables. Search Ball Spin Vector Elliott in Researchgate.

I would choose to assume that the magnitude of the spin vector decreases and that its direction stays the same.

My view of the bounce direction is - If the spin axis has a considerable tilt and remains the same from launch to bounce then we can see the speed and direction of the ball felt that first contacts the court. The effect of ball distortions on the court bounce are complicated for the kick serve but the direction of the felt velocity vs court surface is clear if our spin axis direction remains the same.

It helps to visualize the felt vs court to imagine the spin vectors extended out through the bottom of the ball in the drawing. The slice and flat serve axes exit very close to the spin axis, but the kick serve axis exits the ball a considerable distance away from the spin axis = the felt has much higher lateral speed to the court surface for the kick serve and bounce would seem to be to the right.

@Chas Tennis - thx for the note but I'm unclear what your suggestion is. My model as is already allows a user to provide each the magnitude of each spin component (in rpm format). When you play with the demonstration the 'spiral spin = spinAroundX', 'topSpin=spinAroundY' and 'sideSpin=spinAroundZ'; where X axis is parallel to the sidelines, Y axis is parallel to the baseline, and Z axis is pointing up. The axis of rotation itself is then derived from that - because that axis vector in 3D is sqrt[spinAroundX^2+spinAroundY^2+spinAroundZ^2].

Originally I was thinking about making the controls ask the user to provide 'the percentage of each component (x, y, z) of total spin' - but because we are adding vectors and not scalar values here that is a hard concept to grasp. For example, for the default values we have: spinAroundX=210, spinAroundY=176, spinAroundZ=1117. If you were to do scalar additions you would end up with spinAroundZ=sideSpin=~75% of the total spin (1117/(1117+210+176)). But in fact spinAroundZ=sideSpin is over to 97% of the total spin 1117/sqrt(1117^2+210^2+176^2). That is why I simply ask the user to provide magnitude of each component.

 

[Chas Tennis]

@Chas Tennis - thx for the note but I'm unclear what your suggestion is. My model as is already allows a user to provide each the magnitude of each spin component (in rpm format). When you play with the demonstration the 'spiral spin = spinAroundX', 'topSpin=spinAroundY' and 'sideSpin=spinAroundZ'; where X axis is parallel to the sidelines, Y axis is parallel to the baseline, and Z axis is pointing up. The axis of rotation itself is then derived from that - because that axis vector in 3D is sqrt[spinAroundX^2+spinAroundY^2+spinAroundZ^2].

Originally I was thinking about making the controls ask the user to provide 'the percentage of each component (x, y, z) of total spin' - but because we are adding vectors and not scalar values here that is a hard concept to grasp. For example, for the default values we have: spinAroundX=210, spinAroundY=176, spinAroundZ=1117. If you were to do scalar additions you would end up with spinAroundZ=sideSpin=~75% of the total spin (1117/(1117+210+176)). But in fact spinAroundZ=sideSpin is over to 97% of the total spin 1117/sqrt(1117^2+210^2+176^2). That is why I simply ask the user to provide magnitude of each component.

I wanted to see what your calculator shows for some real measured values of pro kick serves or of the ball diagram spin rates. In other words, what do some real spin components show for the trajectory. Have you put in some real spin components?

 

[jmnk]

I wanted to see what your calculator shows for some real measured values of pro kick serves or of the ball diagram spin rates. In other words, what do some real spin components show for the trajectory. Have you put in some real spin components?

The default spin values as shown on the demonstration are for flat serves. For ATP level topspin serves you can adjust the sliders as follows:
spiralSpin~300rpm, topspin~1900rpm, sidespin~2600rpm (these are average spin rates as measured by authors of that research article "Ball spin in the tennis serve: spin rate and axis of rotation"). And to make it realistic you should also adjust speed, from the default of 185kmh down to about 150kmh

 

[Chas Tennis]

^How can I think about this when I'm busy thinking about what my myosin, actin and titin are doing?

During a tennis serve, don't ever "think about" whether using Titin & minimizing the moment of inertia of the arm is what the pros are doing.......never.

Click Youtube if no sound.

 

[Chas Tennis]

The default spin values as shown on the demonstration are for flat serves. For ATP level topspin serves you can adjust the sliders as follows:
spiralSpin~300rpm, topspin~1900rpm, sidespin~2600rpm (these are average spin rates as measured by authors of that research article "Ball spin in the tennis serve: spin rate and axis of rotation"). And to make it realistic you should also adjust speed, from the default of 185kmh down to about 150kmh

That brings up an issue. I believe a top spin serve is different than a kick serve. The kick serve will bounce to the right.

The top spin serve has top spin and side spin components but not much spiral spin component and the ball does not bounce to the right (for rightie). Racket face not tilted much at impact.

The kick serve has top spin and side spin components but more spiral spin component and bounces to the right. The racket face in more tilted closed just before impact for the kick serve.

These are estimates and need some careful high speed video observations to confirm.

 

[jmnk]

That brings up an issue. I believe a top spin serve is different than a kick serve. The kick serve will bounce to the right.

The top spin serve has top spin and side spin components but not much spiral spin component and the ball does not bounce to the right (for rightie). Racket face not tilted much at impact.

The kick serve has top spin and side spin components but more spiral spin component and bounces to the right. The racket face in more tilted closed just before impact for the kick serve.

These are estimates and need some careful high speed video observations to confirm.

That's cool too. If you want to simulate kick vs top just adjust the amount of spiral spin accordingly. Note however that it will not make much difference for the in-flight trajectory - my model is about in the air trajectory only. It does not simulate/show what happens after the ball bounces off the court.

 

[Chas Tennis]

The default spin values as shown on the demonstration are for flat serves. For ATP level topspin serves you can adjust the sliders as follows:
spiralSpin~300rpm, topspin~1900rpm, sidespin~2600rpm (these are average spin rates as measured by authors of that research article "Ball spin in the tennis serve: spin rate and axis of rotation"). And to make it realistic you should also adjust speed, from the default of 185kmh down to about 150kmh

How do your results compare to this display? I don't have hand on the original publication now. Will look.

"I believe that for all types of serves and average server heights the ball typically leaves the racket with downward projection angles including for high level kick serves. There are probably a few 1 degree upward projection angle serves according to the very informative graph below. The scale for "Projection Angle" ranges from +1 degree (up) to -8 degrees (down). "Ball Velocity" is listed. Server height & jump is taken into account by the "Impact Height".

 

[Chas Tennis]

That's cool too. If you want to simulate kick vs top just adjust the amount of spiral spin accordingly. Note however that it will not make much difference for the in-flight trajectory - my model is about in the air trajectory only. It does not simulate/show what happens after the ball bounces off the court.

You can drill a hole through both sides of a tennis ball and put a pencil or long bolt through it. Make it snug. Spin it with the pencil aligned with the spin axis as shown in the ball diagram. Lower it down onto a surface. When the felt first touches the surface the ball tends to move in a direction. You can see why the kick serve has so much more side bounce, the felt touching the court is farther from the spin axis. The flat and slice serves have the felt meet the surface where the felt is closer to the spin axis and is not moving so fast. That is what your model assumes, correct?

I also read that the high bounce of a kick serve is due to the incidence angle to the court being more vertical than for a flat or slice serve.

The unknown effects of the spinning ball distortions from court impact could be examined with a protected high speed camera.

In any case, be aware of the felt that first touches the court, and its motion.

 

[jmnk]

How do your results compare to this display? I don't have hand on the original publication now. Will look.

"I believe that for all types of serves and average server heights the ball typically leaves the racket with downward projection angles including for high level kick serves. There are probably a few 1 degree upward projection angle serves according to the very informative graph below. The scale for "Projection Angle" ranges from +1 degree (up) to -8 degrees (down). "Ball Velocity" is listed. Server height & jump is taken into account by the "Impact Height".

The demonstration I've created is interactive. You can go to the link provided and adjust control sliders on the left to your liking The very initial parameters depicted on that graph of yours can indeed be set on that demonstration - and the path, as well as the text, will tell you if the serve was good or not. And yes, the results are fairly comparable to that graph you posted.

 

[jmnk]

You can drill a hole through both sides of a tennis ball and put a pencil or long bolt through it. Make it snug. Spin it with the pencil aligned with the spin axis as shown in the ball diagram. Lower it down onto a surface. When the felt first touches the surface the ball tends to move in a direction. You can see why the kick serve has so much more side bounce, the felt touching the court is farther from the spin axis. The flat and slice serves have the felt meet the surface where the felt is closer to the spin axis and is not moving so fast. That is what your model assumes, correct?

I also read that the high bounce of a kick serve is due to the incidence angle to the court being more vertical than for a flat or slice serve.

The unknown effects of the spinning ball distortions from court impact could be examined with a protected high speed camera.

In any case, be aware of the felt that first touches the court, and its motion.

I'm sorry, I do not understand what you are suggesting here. My demonstration does not simulate any bounce off the court.

 

[Chas Tennis]

I am interested in first checking out your calculator by seeing how it does with some known inputs that produce known results. When I go to the slider I don't know what input values to enter to check how the calculator works against some known results. I would have to research spins, type serve, projection angles, etc. and basically see if the calculator produces a reasonable result.

I guessed some inputs and the serves went out. I'd have to research each input to give it a fair check. I am worrying now about Covid 19 variants, vaccines and several other issues including a list of very interesting tennis issues.

When I use the slider it does not show the value until a few seconds after the sliding is finished. This makes playing with it both cumbersome and not very informative since I don't know enough real inputs.

Read the article by Rod Cross, The Physics of the Kick Serve. You could probably check your calculator vs his graphs.

Your trajectory gives the angle of the ball onto the court.

One of my main interests for a kick serve is to see high speed video of the ball bounce, ball impact distortions and to roughly understand how impact causes the bounce to the right for the kick serve. That is very easy to video once a high level kick serve is available. Point camera, get answer. Free advice.

 

[travlerajm]

Since we are still in that pandemic times, with a bit too much time on hand.... Between those famous frame-counting method of approximating serve speed, and various apps that measure such speed I got interested in physics and math behind it. Behind the tennis serve trajectory itself that is. So I created an interactive Mathematica notebook/presentation where one can control initial parameters of the serve: speed, spin, left/right angle, up/down angle, contact point and so on and see where such serve would actually land. Not that it has much of a practical value for a tennis player - since any good player knows where the ball will end up more/less based on years of experience - but a nice visual anyway.

I've submitted it to Wolfram Presentation, hopefully they will review and accept, after which it will be posted in a nice format on Wolfram Demonstration site. In the meantime anyone can see and play with it here: Tennis Serve Trajectory . It works on my browsers at least, with no need for any plugins or external programs - but I have not tested it extensively.

The demonstration format has a bit more details and what and how - but hopefully the controls are enough self explanatory. If you adjust any of the initial conditions the trajectory (the red line) will adjust accordingly. The green line represents the trajectory of the serve with the same exact initial parameters - but it shows what it would be if there was no air drag or Magnus Forces. I've spent fair amount of time researching the physics and math behind it - I'm quite confident it is pretty accurate. It takes into account air drag, Magnus forces due to a spinning sphere, various coefficients that were empirically proven/described in many scientific papers.

Initial defaults represent ATP level male flat serve.

Ask away if you have any questions. Or suggestions for improvement.

again, the link is: Tennis Serve Trajectory Presentation

Cool project!

The spiralspin though, doesn’t seem right. On any tennis serve, the spiralspin component of the spin starts out at almost zero, and then increases significantly during flight, because the angle between the direction of travel and the spin axis starts out at close to 90 degrees (i.e., close to the zero spiralspin condition) and then that angle gets smaller as gravity combines with drag to bend the direction of the velocity vector. As the angle decreases, the spin gets partly converted into spiralspin. But the model shows it staying constant, if I’m not mistaken?

Edit: I believe what you are referring to as spiralspin is simply the z-axis component of the spin in the court frame of reference? (This is different than spiralspin, but I recall seeing this get confused with spiralspin in some of Cross’s articles).

It is possible (with some fun vector calculus - probably in your applied engineering wheelhouse?) to transform the components of the spin at the bounce from the court frame of reference to the ball frame of reference, which would give you the magnitude of the spiralspin developed during flight.

 

[Chas Tennis]

.................
The spiralspin though, doesn’t seem right. On any tennis serve, the spiralspin component of the spin starts out at almost zero, and then increases significantly during flight, because the angle between the direction of travel and the spin axis starts out at close to 90 degrees (i.e., close to the zero spiralspin condition) and then that angle gets smaller as gravity combines with drag to bend the direction of the velocity vector. As the angle decreases, the spin gets partly converted into spiralspin. But the model shows it staying constant, if I’m not mistaken?
.....

Look for the components of each serve type in the direction "X (forward)".

What do you find?

(PDF) Ball spin in the tennis serve: Spin rate and axis of rotation

PDF | The purpose of this study was to describe three-dimensional ball kinematics including spin axis and spin rate for the flat, slice, and kick serves... | Find, read and cite all the research you need on ResearchGate

www.researchgate.net

 

[travlerajm]

Look for the components of each serve type in the direction "X (forward)".

What do you find?

That diagram is in the court frame of reference. Spiralspin can only exist in the ball frame of reference.

 

[Chas Tennis]

That diagram is in the court frame of reference. Spiralspin can only exist in the ball frame of reference.

Now I'm getting all mixed up with your comment. Is this a matter of the use of the term 'spiral spin'?
The term spiral spin needs to be used more carefully?

But tennis usage, often uses a sidespin component, a topspin component and a spiralspin component discussing ball spin. ?

The authors of the ball spin publication chose the court frame of reference. I believe that the serves measured were directed toward the T and hit near there, within 1 meter?. The ball's initial trajectory would have been close to the court coordinate system, X (forward). (I need to read the publication again..........) Are the court frame of reference and ball frame of reference very close just after impact?

Strictly, is the term 'spiral spin' limited to a coordinate system based on the instantaneous direction of the ball's trajectory and that coordinate system is therefore constantly changing? And would always apply to one location only? That would be cumbersome to use because you would always need to find and know the changing trajectory. Reference?

I believe that the ball spin acts like a gyroscope from after impact to just before the bounce. And in the court coordinate system, the ball's spin vector direction stays about the same from just after impact to the bounce. It is extremely simplifying and useful to know that the spin of the ball in 3D space has the about the same orientation to gravity and the court from after impact to just before the bounce. That spin vector direction and magnitude and the trajectory give you parameters that you need to study the bounce. There would be some loss of rotation rate due to air resistance. I have watched balls leaving the racket and could see over 3-4 ball rotations that they seem to retain the same spin vector direction in space. To settle the spin vector direction question once and for all, one video of the ball spin after impact together with another video of the bounce would answer it. Cross has probably done that since I believe that he has stated that the spin vector direction stays the same across the court ? His research? travelerajm, do you agree with this paragraph?

 

[bigservesofthands]

One important principle is that the spin vector direction imparted to the ball at impact (or slightly after the ball distortions quiet down) remains in the same direction throughout the trajectory to the bounce. Is that true for your model? In other words, the ball acts like a gyroscope on the trajectory.

Where did you get ATP spin information?

If you have any links for that information, that I believe I've read in Rod Cross's writings, I'd appreciate any links.

There is a ball diagram that shows measured spin vectors right after impact for the kick, slice and flat serves. Did you use the ball diagram or the publication? It's the best information I've found on measured serve spins.

I've read many, many scientific papers on that topic, including the Cross's writing. Science is actually undecided 100% on the topic of spin vector. The general consensus is that both magnitude and the direction of the spin vector remains within 10% of the initial spin vector values throughout the entire trajectory. In my model the spin vector (magnitude and direction) is assumed constant. The model is pretty complicated as is, so I've taken the liberty to disregard that 10% discrepancy.

But yes, the model does assume that pretty much any serve, including the so-called flat one, is mainly the side spin - which is reflected in initial parameters where side spin is like 90% of the total spin. An astute reader may also notice that there's spiral spin component, i.e. the American football like - the one, according to laboratory measurements stays at ~200rpm level for _any_ type of spin.

I may be close to proving (through empirical and slow motion footage) that I have come up with likely a new set of shot making mechanics that is able to control spin vector in a way that it trends to pure topspin during the terminal phase of the trajectory starting when the ball crosses the net. This PoPoPoMo technique allows me to hit at or down on the ball and still get the ball to land in the box at very high speeds.

Sadly my body is aging as I make these breakthroughs. Race against time to gather data at as high a fidelity as I am able as a hobbyist. The progress in smart phone slow motion imaging has been extraordinary. A few more years and I will have the 1000fps at 4K.

 

[travlerajm]

Now I'm getting all mixed up with your comment. Is this a matter of the use of the term 'spiral spin'?
The term spiral spin needs to be used more carefully?

But tennis usage, often uses a sidespin component, a topspin component and a spiralspin component discussing ball spin. ?

The authors of the ball spin publication chose the court frame of reference. I believe that the serves measured were directed toward the T and hit near there, within 1 meter?. The ball's initial trajectory would have been close to the court coordinate system, X (forward). (I need to read the publication again..........) Are the court frame of reference and ball frame of reference very close just after impact?

Strictly, is the term 'spiral spin' limited to a coordinate system based on the instantaneous direction of the ball's trajectory and that coordinate system is therefore constantly changing? And would always apply to one location only? That would be cumbersome to use because you would always need to find and know the changing trajectory. Reference?

I believe that the ball spin acts like a gyroscope from after impact to just before the bounce. And in the court coordinate system, the ball's spin vector direction stays about the same from just after impact to the bounce. It is extremely simplifying and useful to know that the spin of the ball in 3D space has the about the same orientation to gravity and the court from after impact to just before the bounce. That spin vector direction and magnitude and the trajectory give you parameters that you need to study the bounce. There would be some loss of rotation rate due to air resistance. I have watched balls leaving the racket and could see over 3-4 ball rotations that they seem to retain the same spin vector direction in space. To settle the spin vector direction question once and for all, one video of the ball spin after impact together with another video of the bounce would answer it. Cross has probably done that since I believe that he has stated that the spin vector direction stays the same across the court ? His research? travelerajm, do you agree with this paragraph?

Yes. Cross used the court (or “lab”) frame of reference to describe the components of the spin. None of these components are spiralspin. They just tell you the angle of the spin axis in the xyz.

In general, a tennis racquet cannot apply spiralspin at contact because it only contacts one side of the ball. (Yes technically there is a tiny amount of initial spiralspin because the stringbed is traveling faster at the upper edge of the contact area on a serve than at the bottom edge of the contact area, but for all practical purposes, spiralspin can be neglected). Spiralspin only becomes significant as the ball’s velocity vector bends relative to the spin axis due to gravity.

This is in contrast to throwing a football, where the thumb and fingers can apply moments to opposites of the ball at once to generate spiralspin.

 

[Chas Tennis]

Yes. Cross used the court (or “lab”) frame of reference to describe the components of the spin. None of these components are spiralspin. They just tell you the angle of the spin axis in the xyz.

In general, a tennis racquet cannot apply spiralspin at contact because it only contacts one side of the ball. (Yes technically there is a tiny amount of initial spiralspin because the stringbed is traveling faster at the upper edge of the contact area on a serve than at the bottom edge of the contact area, but for all practical purposes, spiralspin can be neglected). Spiralspin only becomes significant as the ball’s velocity vector bends relative to the spin axis due to gravity.

This is in contrast to throwing a football, where the thumb and fingers can apply moments to opposites of the ball at once to generate spiralspin.

I don't understand the limitation of the racket to apply certain spin axis directions, including spiral spin components. Impact is 3D with the ball flattening and cupping into the string bed. Cross & Lindsay show a contact area on the top half-left side of the ball. For a kick serve, I believe that the racket face is being tilted closed about 14 degrees to first contact the top half of the ball because I have seen it in a few observations. But the racket head might be rotating at 2000-3000 degrees per second, impact lasts 4 milliseconds, racket head rising ......string cupping.......ball distorting....off racket centerline effects that vary...........too compilcated..... Translating that into 'no spiral spin' seems very difficult. Do you have a reference?

ISR causes the string bed to travel forward faster on the left side of the ball (from the right handed server's viewpoint). At the same time, forward swings around axes below the contact area cause the upper edge of contact area to have a higher velocity. And the upward path of the racket head for the kick serve causes strings to rise around axis in wrist area. These word descriptions are based on overall gross rack motions and are muddled by the complications of impact. See high speed videos. See Stosur serves in thread Junior Twist Serve. Try describing racket on ball by words.

 

[Chas Tennis]

..............................................
The authors of the ball spin publication chose the court frame of reference. I believe that the serves measured were directed toward the T and hit near there, within 1 meter?. The ball's initial trajectory would have been close to the court coordinate system, X (forward). (I need to read the publication again..........) Are the court frame of reference and ball frame of reference very close just after impact?
.............................................................................................................

This is what the authors of the ball spin publication had to say. It links their court reference frame's (X) component to the ball reference frame with spiral spin component after impact. It states that the "(X) component" is "indicative" of the magnitude of the "spiral spin" component.

"The lateral (Y) and vertical (Z) components of the angular velocity of the ball represent the
magnitude of topspin (or backspin) and sidespin, respectively. The horizontal (X)
component, on the other hand, is indicative of the magnitude of ‘spiral spin’, which has no
Magnus or lift effect (Cross & Lindsey, 2005)."

(a) Testing environment and (b) a ball with three reflective markers. Global and local coordinate systems are also illustrated.

(PDF) Ball spin in the tennis serve: Spin rate and axis of rotation

PDF | The purpose of this study was to describe three-dimensional ball kinematics including spin axis and spin rate for the flat, slice, and kick serves... | Find, read and cite all the research you need on ResearchGate

www.researchgate.net

But I guess that as the ball travels, as travelerajm says, the spiral spin would change. I am going to stop using the term 'spiral spin' or 'gyrospin' for the ball when the ball moves away from impact through the court.

I believe that the spin direction in 3D space stays about the same as the ball moves in the court frame of reference. We would still like to confirm that the direction of the spin axis remains about the same as it was just after impact.

 

[bigservesofthands]

This is what the authors of the ball spin publication had to say. It links their court reference frame's (X) component to the ball reference frame with spiral spin component after impact. I believe that there they are close, "indicative", and about the same.

"The lateral (Y) and vertical (Z) components of the angular velocity of the ball represent the
magnitude of topspin (or backspin) and sidespin, respectively. The horizontal (X)
component, on the other hand, is indicative of the magnitude of ‘spiral spin’, which has no
Magnus or lift effect (Cross & Lindsey, 2005)."

But I guess that later, as travelajm says, the spiral spin would change. I am going to stop using the term spiral spin or gyrospin for the ball when the ball moves away from impact.

I believe that the spin direction stays the same as the ball moves in the reference frame of the court. We would still like to confirm that the direction of the spin axis remains about the same as its direction shortly after impact.

Your statement about spin direction might be true for traditional stroke mechanics.

I am able to hit traditional strokes where the spin direction stays fairly constant.

But to me the more interesting strokes are those that have not been explored the Po*Mo ones. I believe I am able to generate strokes where the direction rapidly changes and stabilizes to one that we are interested in which is top spin heavy by the time the ball is just past the net. So the change in direction is much more than the 10% that current literature that travlerajm is referring to. This opens up very interesting possibilities both for how we generate the stroke and also changes in equipment to amplify this effect.

 

[jmnk]

I am interested in first checking out your calculator by seeing how it does with some known inputs that produce known results. When I go to the slider I don't know what input values to enter to check how the calculator works against some known results. I would have to research spins, type serve, projection angles, etc. and basically see if the calculator produces a reasonable result.

most of the data you are looking for is directly in front of you, in that diagram you posted. From there you can see that:

• up/down angle is in the range +1 to -8 degrees
• impact height is in the range 200cm to 270cm (There's a lot of empirical data that shows that contact point for ATP male player is as high as 300cm)
• ball speed 90kmh to 190kmh (flat serve ~190kmh, slice ~165kmh, kick ~145kmh)

some rudimentary google search will give you spin rates too: flat ~1200rpm, slice ~2200rpm kick ~3200rpm. These roughly translate to spin rates about respective axis as follows:

• flat: spiral spin component ~210rpm, side spin component ~1120rpm, top spin component ~175rpm
• slice: spiral spin component ~280rpm, side spin component ~2050rpm, top spin component ~700rpm
• kick: spiral spin component ~300rpm, side spin component ~2600rpm, top spin component ~1900rpm

I guessed some inputs and the serves went out. I'd have to research each input to give it a fair check. I am worrying now about Covid 19 variants, vaccines and several other issues including a list of very interesting tennis issues.

??

When I use the slider it does not show the value until a few seconds after the sliding is finished. This makes playing with it both cumbersome and not very informative since I don't know enough real inputs.

if you click on '+' by the slider it will open input field, you can type in the number.

Read the article by Rod Cross, The Physics of the Kick Serve. You could probably check your calculator vs his graphs.

you are clearly a big fan of Rod Cross, and he does have good papers, but there are plenty others too. I've read quite a few.

Your trajectory gives the angle of the ball onto the court.

One of my main interests for a kick serve is to see high speed video of the ball bounce, ball impact distortions and to roughly understand how impact causes the bounce to the right for the kick serve. That is very easy to video once a high level kick serve is available. Point camera, get answer. Free advice.

??

 

[Chas Tennis]

Your statement about spin direction might be true for traditional stroke mechanics.

I am able to hit traditional strokes where the spin direction stays fairly constant.

But to me the more interesting strokes are those that have not been explored the Po*Mo ones. I believe I am able to generate strokes where the direction rapidly changes and stabilizes to one that we are interested in which is top spin heavy by the time the ball is just past the net. So the change in direction is much more than the 10% that current literature that travlerajm is referring to. This opens up very interesting possibilities both for how we generate the stroke and also changes in equipment to amplify this effect.

You should document and post some spin observations. I once saw some discussion somewhere of how to mark a ball to improve your chances of observing the spin axis. Cross?

 

[jmnk]

I'm mighty impressed with your understanding. I'm not kidding. you are almost correct.

Cool project!

The spiralspin though, doesn’t seem right. On any tennis serve, the spiralspin component of the spin starts out at almost zero,

scientific experiments show that this is not entirely so. In fact any serve has some component of spin around X axis (where X is parallel to the sidelines) from the beginning. Since most of the forward speed vector is in X direction as well that means that there's spiral spin in the ball frame of reference too.

and then increases significantly during flight, because the angle between the direction of travel and the spin axis starts out at close to 90 degrees (i.e., close to the zero spiralspin condition)
and then that angle gets smaller as gravity combines with drag to bend the direction of the velocity vector. As the angle decreases, the spin gets partly converted into spiralspin. But the model shows it staying constant, if I’m not mistaken?

I think you might be mistaken here. If you draw up the vectors you will see that as the ball's speed vector 'bends' downward, the component of the spin that would be considered 'spiral', in the ball frame of reference, actually becomes smaller. (Assuming that the spin vector in court frame of reference remains constant). I need to think a bit more about it - but I think the spiral spin (in ball frame of reference) is actually the biggest at the start of the serve, and then gets (marginally) smaller.

Edit: I believe what you are referring to as spiralspin is simply the z-axis component of the spin in the court frame of reference? (This is different than spiralspin, but I recall seeing this get confused with spiralspin in some of Cross’s articles).

yes indeed, the spin vector, and its X, Y, Z components are in the court frame of reference. I agree that having that vector in ball frame of reference would be perhaps a bit easier to conceptually visualize - but I've never seen it done that way in any scientific paper. I suspect it is because it becomes more unwieldy to figure out the equations as in the ball frame of reference the vectors would be constantly changing due to ball direction changing. I wouldn't however label such court frame of reference approach 'different' or 'confusing'. As long as the model is consistent and clearly described either approach should yield the same results. Although you are correct that in many papers the authors do not clearly, or consistently, define whether 'spiral spin' (or side or topspin for that matter) is in court or in ball frame of reference.

It is possible (with some fun vector calculus - probably in your applied engineering wheelhouse?) to transform the components of the spin at the bounce from the court frame of reference to the ball frame of reference, which would give you the magnitude of the spiralspin developed during flight.

definitely yes. Actually that is not a bad suggestion, let me try to do just that. The model is already based on a set of six first-order differential equations, how much more difficult could it be to do some more calculus .