# Causes for different topspin bounces on the forehand

#### SystemicAnomaly

##### Talk Tennis Guru
How very Chas of you...
Ok, how so? I tend to read & understand my own posts a bit more often than I read or understand his. And I predate him on TT by some 5 years -- have been discussing physics & biomechanics in these here parts before his arrival. So, if anything, we might say that Chas is sometimes very SysAnom...

Actually, former contributor @charliefedererer was more SysAnom than Chas is.
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#### FiReFTW

##### Legend
You guys should go on the court and hit a very spinny loopy short forehand just over the net and you will see that the ball picks up horizontal speed after bounce compared to just before..

Heck I could do a video and prove it but im not playing much, maybe over the weekend.

Just prior the ball touches the ground before bounce its traveling almost completely downwards, specialy if its slow and loopy but with alot of spin... so I dont get how you cant see that it has almost no horizontal speed at that point.

#### Fintft

##### Legend
This is the dreaded WTA fh.
Nope, although my coach played WTA she teaches ATP FH, not only with lag but with a compact take back etc. Her brother and student is the best player in town (Futurities and tried also Challengers).

#### Kevo

##### Legend
Well, it is possible for a shot to gain horizontal speed after the bounce, but it has to have very little horizontal speed before the bounce. It's the same concept as spinning a basketball when you drop it. That's a bit different than the type of shots mentioned at the beginning of the thread.

#### Hmgraphite1

##### Hall of Fame
@FiReFTW @Hmgraphite1 @Kevo

The physics tells us that there is a very high rate of spin where a tennis ball, theoretically, can have a greater horizontal speed (horizontal component of velocity) after the bounce than prior to the bounce. However, I don't believe that these conditions have ever been met in the real world on the tennis court. According to the calculations, for a given set of conditions in the Scientific American article below, a topspin ball would need to exceed 7200 RPM (120 revs/second) in order to see an increase in horizontal speed. The fastest spin rates observed in tennis -- Nadal (topspin Fh), Sampras (2nd serve), Federer (Bh slice) -- have been around 5200 RPM, possibly 5400 RPM. I believe that @JohnYandell can confirm this observed spin rate.

I don't believe that there are any conditions where the total speed of the ball after a bounce will equal or exceed its speed prior to the bounce.

https://www.scientificamerican.com/article/experts-tennis-topspin-ball/
As FiReFTW pointed out a vertically dropped ball with heavy spin will gain a horizontal component where it had none. So in this case it increased. I would presume there is some range of horizontal components that with certain ball spin components would cause an increase also. Its kinetic energy both the horizontal velocity and the spin. Not sure where the boundary conditions are, and for "real world" conditions. I'll read the article.

#### SystemicAnomaly

##### Talk Tennis Guru
@FiReFTW
Well, it is possible for a shot to gain horizontal speed after the bounce, but it has to have very little horizontal speed before the bounce. It's the same concept as spinning a basketball when you drop it. That's a bit different than the type of shots mentioned at the beginning of the thread.
As FiReFTW pointed out a vertically dropped ball with heavy spin will gain a horizontal component where it had none. So in this case it increased. I would presume there is some range of horizontal components that with certain ball spin components would cause an increase also. Its kinetic energy both the horizontal velocity and the spin. Not sure where the boundary conditions are, and for "real world" conditions. I'll read the article.
Do those conditions ever happen in tennis? With tennis strokes, we are propelling the ball forward -- not dropping it vertically. So there is always some component of forward speed with a topspin ball, however small. Outgoing angle is often less than the incoming angle so it might appear that the horizontal speed increases in some situations. Are the articles I linked in posts #45 and #47 wrong about changes in forward (horizontal) speed? Can you plug in values for the equation (shown in post#45) that will show increases in horizontal speed for spin rates that are actually attainable in tennis? (Perhaps there are).

Another physics source on the subject:
http://ffden-2.phys.uaf.edu/webproj/211_fall_2014/max_hesser-knoll/max_hesserknoll/Slide4.htm

"When a ball hit with topspin impacts the ground, the forward spin of the ball reduces the effect of the friction force of the court on the ball. If the tangential velocity of the top of the ball is less than the horizontal velocity of the ball, then while the ball is in contact with the court during the bounce, the force of friction increases the ball's forward angular velocity. Once the tangential velocity of the top of the ball is the same as the overall horizontal velocity of the ball, the ball begins to roll, which reduces the friction of the court on the ball dramatically. This causes a smaller net friction force to be applied to a ball with topspin during its bounce and results in a ball losing less horizontal speed. The smaller decrease in horizontal speed of the ball causes the ratio of vertical speed to horizontal speed to be lower after the bounce. This results in the ball to leaving the ground at an angle lower than its angle of incident. Further, since both the vertical and horizontal speeds of the ball are decreased during the bounce, the overall speed of the ball is also decreased... "

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#### FiReFTW

##### Legend
@SystemicAnomaly perhaps you are correct... but I somehow have an extremely hard time believing it, if you look at this pic:

To me it seems physically impossible and I can't comprehend how the ball could be possibly moving towards you faster at the RED spot, than it does on the BLUE spot.

At the blue spot its close to 0 degrees so its traveling almost completely horizontaly, while on the red spot its traveling almost completely vertically at 80 degrees or so?

Im not great at math but considering such a sharp angle downwards wouldn't the ball at the RED part need to have like 10 times greater speed than at the blue spot in order to be moving faster towards you at the red spot, considering what a big difference in angle of travel there is?

#### SystemicAnomaly

##### Talk Tennis Guru
@SystemicAnomaly perhaps you are correct... but I somehow have an extremely hard time believing it, if you look at this pic:

To me it seems physically impossible and I can't comprehend how the ball could be possibly moving towards you faster at the RED spot, than it does on the BLUE spot.

At the blue spot its close to 0 degrees so its traveling almost completely horizontaly, while on the red spot its traveling almost completely vertically at 80 degrees or so?

Im not great at math but considering such a sharp angle downwards wouldn't the ball at the RED part need to have like 10 times greater speed than at the blue spot in order to be moving faster towards you at the red spot, considering what a big difference in angle of travel there is?
Difficult for me to wrap my head around it as well. Perhaps someone out there can do the math for us with some actual data.

Disclaimer from @TimeSpiral for the image above:

#### user92626

##### G.O.A.T.
Again, this kind of picture is very misleading.

Shots do not clear the net that high and then bounce up less than half.

Look at this.

#### SystemicAnomaly

##### Talk Tennis Guru
Again, this kind of picture is very misleading.

Shots do not clear the net that high and then bounce up less than half.

Look at this.
Did you see the disclaimer linked in post #58?

Instead of making us watch 7.5 minutes of video, perhaps you could point to specific instances in the link you provided.
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#### SystemicAnomaly

##### Talk Tennis Guru
@SystemicAnomaly perhaps you are correct... but I somehow have an extremely hard time believing it, if you look at this pic:

To me it seems physically impossible and I can't comprehend how the ball could be possibly moving towards you faster at the RED spot, than it does on the BLUE spot.

At the blue spot its close to 0 degrees so its traveling almost completely horizontaly, while on the red spot its traveling almost completely vertically at 80 degrees or so?

Im not great at math but considering such a sharp angle downwards wouldn't the ball at the RED part need to have like 10 times greater speed than at the blue spot in order to be moving faster towards you at the red spot, considering what a big difference in angle of travel there is?
Don't have any numbers for this example. But I can refer to the 120 mph Sampras serve I mentioned previously. His 1st serves averages something like 2700-3000 RPM. A the blue location (top of the bounce) the forward speed equals the total (tangential) speed. For the Sampras serve that speed was about 54-60 mph. The total speed just prior to the bounce was about 90 mph. Sorry, don't know the horizontal speed at that point.
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#### Kevo

##### Legend
@SystemicAnomaly perhaps you are correct... but I somehow have an extremely hard time believing it, if you look at this pic:

To me it seems physically impossible and I can't comprehend how the ball could be possibly moving towards you faster at the RED spot, than it does on the BLUE spot.

At the blue spot its close to 0 degrees so its traveling almost completely horizontaly, while on the red spot its traveling almost completely vertically at 80 degrees or so?

Im not great at math but considering such a sharp angle downwards wouldn't the ball at the RED part need to have like 10 times greater speed than at the blue spot in order to be moving faster towards you at the red spot, considering what a big difference in angle of travel there is?
You have to gather and sum all the speeds and forces and see what's what. But I can see a trajectory like that happening. I don't think it's too far off reality. A tennis ball is about 50% efficient on bouncing. So if you drop it on the ground it will bounce about half way back up. Maybe slightly more. So in this pic the height of the bounce is close to half, so that's reasonable. Topspin makes the ball bounce forward so the trajectory out of the bounce is lower than into the bounce, and that's also reasonable.

The thing you have to remember about the speed in and out of the bounce is the ball is slowing down continuously all the way to you, and hitting the ground slows it down since the ground has more friction than the air. The only way the ball could gain speed coming out of the bounce is if the amount of spin energy in the ball is enough to overcome the inertia of the ball and the friction of the ground. That is going to be difficult since as stated above the ball is built so that it loses about half its energy when it bounces.

Have you ever taken a toy car, rc or windup, and spun it's wheels up super fast and then dropped it onto the ground. They tend to barely go anywhere. The energy in the spinning wheels is not enough to overcome the inertia of the car.

We could probably do some simple tests with a ball machine and a good cell phone camera with a good slo mo frame rate. Set up a target zone, dial in the feed on the ball machine so it bounced in roughly the same place every time, and then film a handful of shots with no spin and with heavy spin. The ball machine can easily out spin anyone I've ever played so if the ball machine can't make the ball come out faster then no one can. And if it can make it come out faster it would be good to see if it's significant or just a little bit.

In my time with the ball machine I haven't noticed that it seems like the balls comes out faster. It just seems to throw a really heavy ball when you put a lot of spin on it.

#### user92626

##### G.O.A.T.
Instead of making us watch 7.5 minutes of video, perhaps you could point to specific instances in the link you provided.
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That's virtually all the shots in the clip, per physics.

If They go high over the net, their rise after the bounce is nearly as high. Definitely not less than half.

#### Kevo

##### Legend
That's virtually all the shots in the clip, per physics.

If They go high over the net, their rise after the bounce is nearly as high. Definitely not less than half.
Can you give a specific time of such a shot. I don't think that Nadal Cuevas video is the best for judging shots like this, but from what I saw of shots that you could see high over the net, several of them appeared to be over head high crossing the net yet were hit about waist high by the other player.

#### user92626

##### G.O.A.T.
Can you give a specific time of such a shot. I don't think that Nadal Cuevas video is the best for judging shots like this, but from what I saw of shots that you could see high over the net, several of them appeared to be over head high crossing the net yet were hit about waist high by the other player.
Go to 0:40, there's a long rally with many shots. Do you see any shot that crosses the net at X feet high but bounces up less than X/2? The answer is NO

#### Morch Us

##### Professional
The simple answer is the "spiral" and multi-dimensional spin. The topspin can have multiple axis rotation components. I remember having this talk with you very long ago (while discussing cross stings importance on some specific spins). But specific kind of spins can have cumulative effect, and some of these spins also can convert the "gravitation acceleration" into a bit more "horizontal speed" on bounce. (vs pure topspin loop will convert the spin into a more downward force before bounce, thereby creating a higher bounce, or more vertical speed). It is kind of pointless for most folks trying to apply this into game, since even at 5.0 level folks get these spins only as a "natural hit" rather than trying on purpose.

Also a more loopier ball stays longer in the air, and creates a feel that it is coming slower, there by cheating the mind to be a bit lazy, and then on bounce get a bit hurried, if it does not bounce exactly the way you were assuming. So it may actually be slower than you feel like after bounce.

The most odd one is from player A as I dont get how come he has such a high arc and as the ball bounces it picks up like 5x speed into you (jusr appears so obviously it doesnt work like that) from alot of spin, but yet the bounce is not particulary high, its very odd and I dont know what to make of that.

#### travlerajm

##### G.O.A.T.
I notice this effect when I practice hard spin serves. If I hit a really hard flat serve, the ball bounces off the court at a shallow angle. If I hit a really hard serve with moderate topspin, the ball dives more downward into the court and bounces up a lot higher than the flat serve, and ends up hitting the fence higher up than the flat serve. And if a hit a really hard serve using a max-spin style stringbed (like kevlar/zx on a open pattern frame) that allows vicious spin, the ball dives down even more sharply, but in this case the spin rate is high enough to grab the ground and accelerate the ball forward off the bounce with a relatively shallow bounce angle compared to the downward path before it hits the court; and then after the bounce, the topspin is still significant enough to pull the ball downward as it moves forward, accentuating the lower bounce, and hitting the fence lower than the flat serve.

In other words, given a certain racquethead speed and a serve that starts out with downward initial trajectory, maxing out the topspin does not produce the highest bouncing hard spin serve. The maximum bounce height occurs by applying an intermediate amount of spin.

#### travlerajm

##### G.O.A.T.
I also believe I noticed this effect when I attended the 2008 French Open and watched a few games of the Nadal-Bellucci match, with a viewing angle from the sideline. From the side, Nadal's forehands seemed to bounce a lot lower than I was expecting.

#### Hmgraphite1

##### Hall of Fame
Its definitely complicated. As the ball can have differing top spin rates, the air pressure will build above the ball and drive it down. There are coefficients of friction when the ball rolls on the ground, a different one for skidding, both, trajectories etc... I think it would be difficult to predict the after bounce rpms using equations and numbers. Probably best measured using controlled experiments.

I think its fair to say experienced players expect the ball to reach them at a specific time after the bounce. Some times it can get there way earlier and therefore its going faster than expected. This is maybe more expected with driven flat/ backspin shots but also now with certain heavy topspin shots

#### FiReFTW

##### Legend
Did some tests today, ball definetely gains forward momentum after bounce compared to prior on certain shots, but I forgot to make video... will make video this weekend.

#### Kevo

##### Legend
Go to 0:40, there's a long rally with many shots. Do you see any shot that crosses the net at X feet high but bounces up less than X/2? The answer is NO
Well in general it shouldn't be LESS than x/2 unless the ball is flat. A standard ball is designed to bounce half or slightly more of the height from which it is dropped. I think a 54" or 58" bounce from a drop height of 100" is the standard. Might be a range of that sort. Also in a tennis rally the ball could potentially have more speed than just the acceleration due to gravity when it bounces off the court, plus the effects of spin. So while the bounce might be more than half, it would be quite rare for it to be nearly as high as the apex of the shot.

In the rally at :40 I think there might have been 2 shots that got close to the same height, but most didn't. Several of the shots were hit before the apex so we can't really judge based on those. The highest shots certainly did not get close to their original height.

#### BallBag

##### Semi-Pro
Chart of required topspin for roll at contact. For example, at 45 mph tangential speed and 45 deg angle, you would need to hit with more than 3961 RPM to make the ball have more ground speed. For a faster ball you need more spin. For a higher angle you need less spin.

I would say anything in the bottom right is a lob, anything in the bottom left is a drop shot, anything in the top left doesn't exist and anything in the top left requires more spin than I can hit.

#### FiReFTW

##### Legend
Chart of required topspin for roll at contact. For example, at 45 mph tangential speed and 45 deg angle, you would need to hit with more than 3961 RPM to make the ball have more ground speed. For a faster ball you need more spin. For a higher angle you need less spin.

I would say anything in the bottom right is a lob, anything in the bottom left is a drop shot, anything in the top left doesn't exist and anything in the top left requires more spin than I can hit.
Awesome!

So basically this chart shows how much spin you need for the ball to pick up speed on a horizontal plane towards you?

Proves my point then.

Very loopy balls probably fall down at like 80 degrees so you need like 1000 rpm at 50mph, which is more than doable.

Makes perfect sense and what you see in reality also, tnx for posting!

#### IowaGuy

##### Hall of Fame
Awesome!

So basically this chart shows how much spin you need for the ball to pick up speed on a horizontal plane towards you?

Proves my point then.

Very loopy balls probably fall down at like 80 degrees so you need like 1000 rpm at 50mph, which is more than doable.

Makes perfect sense and what you see in reality also, tnx for posting!
A topspin groundie at 50mph and 1000rpm will not fall down at 80 degrees, unless it's basically an overhead hit very close to the net. A baseline rally would never produce an 80 degree descending shot unless it's a super high topspin lob...

#### BallBag

##### Semi-Pro
A topspin groundie at 50mph and 1000rpm will not fall down at 80 degrees, unless it's basically an overhead hit very close to the net. A baseline rally would never produce an 80 degree descending shot unless it's a super high topspin lob...
Yeah, 50 mph is close to the terminal velocity of a tennis ball. Im guessing like a 250 ft lob would do that. He's point is that it is possible, just not regular play situation.

#### Hmgraphite1

##### Hall of Fame
I think a 60mph ball at 3000 rpm is reasonable

#### xFullCourtTenniSx

##### Hall of Fame
Only shot spot could answer this debate. But have to doubt horizontial speed increases--whatever that means...
You're probably right. It's the same phenomenon as the "rising" fastball in baseball. It's impossible given the recorded numbers, but pro batters still swear that some pitchers can throw a rising fastball and say you need to be on the receiving end of it to understand. Physicists demystified the phenomenon by recording the path the ball took, it wasn't even close to rising (or even horizontal). But compared to a normal ball's trajectory, it was slightly higher than normal. Basically, due to the lack of time when receiving a pitch, the brain does a lot of subconscious calculations to predict the flight path of the ball. These calculations are modeled on normal pitches, the stuff they saw for 99% of their life (the number is even larger when comparing to the motion of all objects they've seen in their lifetime). When the "rising" fastball is thrown at them, they perceive it as rising because it is higher than their brain has calculated, giving them the perception or idea that the ball must be rising to accomplish that, when simply just wasn't falling as quickly.

The same thing happens in tennis, but off the bounce. It's just the ball behaving differently than the brain predicted.

As for the bounce, many things affect the bounce of the ball. Velocity, RPM, height. Then there's the fact that the ball slows down on the bounce (reduced based on how much topspin it had), and gains topspin on the bounce (based on how fast it was going). The larger the vertical velocity going into the bounce, and the less vertical acceleration (downwards - gravity and topspin), the greater the maximum height of the bounce. More topspin generally means a greater downward velocity on impact, but it also means the bounce will be lower due to the topspin constantly pushing the ball down. More total velocity (overall ball speed, not horizontal or vertical components) also means the force of topspin on the ball is greater. Also, topspin doesn't act straight down. It acts perpendicular to the direction of motion. This means you actually get more downward work out of topspin if you have a more horizontal (a flatter) trajectory. But a higher (and therefore loopier) trajectory gets more work out of gravity. Nobody has done the research to figure out the optimal combination for height or velocity off the bounce. We know that the launch angle for the more distance in a vacuum is 45 degrees. With air resistance, it's something around 30 degrees iirc. But these are basic projectile problems, and the motion of a tennis ball is anything but that. Crawford Lindsey of TWU has found that the aerodynamic profile of the tennis ball is actually highly variable during its flight and changes with each impact (both with the court and the racket).

#### Bender

##### G.O.A.T.

This is how it looks so you can visualize.
So basically what you're saying is A is Rafa, and you are Federer?

With Fedal, the bounce height has more to do with pace more than anything else. Topspin shots with high pace reduces bounce height, so Rafa compensates by increasing the height of his groundstrokes. Fed hits a lot softer so the ball kicks up more. I suspect something similar is going on with you since you say A brushes up furiously.

#### BallBag

##### Semi-Pro
Chart of required topspin for roll at contact. For example, at 45 mph tangential speed and 45 deg angle, you would need to hit with more than 3961 RPM to make the ball have more ground speed. For a faster ball you need more spin. For a higher angle you need less spin.

I would say anything in the bottom right is a lob, anything in the bottom left is a drop shot, anything in the top left doesn't exist and anything in the top left requires more spin than I can hit.
I wanted to emphasize that the above chart is only for the horizontal component of velocity. For the speed of the ball to increase after the bounce, the spin would have to be double or triple what in the chart. The rotational energy of the ball would have to compensate for the energy loss during a bounce and a tennis ball doesn't hold much rotational energy.