MYTH: You can't hit a "flat" serve without being extremely tall. MATH: You can do it at just 5'0" even at 120mph due to gravity & drag. ADVICE: Don't

[Wurm]

Just out of curiosity... why the such a small integration step? Anything smaller than 0.1ms looks like overkill to me.

No particular reason other than it's Euler integration so the smaller the step the more accurate it'll be and I just put a load of zeros in until it looked convincingly small

Anyway, I've not had anyone verify the maths for me as my colleague is off work until next week so I've just plopped up my first version at https://github.com/Prognathous/TennisProjectiles/tree/main for people to check out.

Again, I'm not saying I've gotten the maths right for this as it took me about 5 minutes to implement that bit of it versus about 5 hours to do the rest I do program for a living but not web dev, and I've not done any proper physics programming for nearly 20 years so everything's very rusty in that area.

 

[Wurm]

Of course, at the beginner and social level, some players are hitting so slowly that they might need to hit the ball horizontal or slightly upwards to hit the back of the service box, while 120 mph is too fast for many amateurs, but I think hitting down on the ball 1 degree below the horizontal will require an achievable speeds for many amateurs even below 6 feet tall, and at the right speed it will definitely go in, and with a higher margin than the 120 mph case.

Well, it's there for you to try out. I expect to update it over the coming weeks as it's in a quite basic (and slightly hacky) form at the moment. I wouldn't put too much stock on its results as yet, though.

I think the biggest stumbling block to someone hitting 120mph serves if they're, say, sub 5'5" is the physicality required to get the racket moving quickly enough with shorter limbs and less muscle available than bigger people... All the biggest rec servers I've come across, so far, have been big, heavy set shouldered guys that move like steamrollers.

All 5'5/5'6" (I know they list him as 5'7" but that seems generous) of Diego Schwartzmann can/could hit first serves into the 110s on a regular basis, and I'm presuming he must've cracked 120mph occasionally - by mid-80s standards he has a pretty big serve! However, I guarantee you he's hitting those first serves with around 2000 RPM of spin on them, at least. He's not having to launch the ball within a sub-1° window, that changes with the exact speed it's hit at, to get the ball to go in.

I think the terminology of "flat" first serves for pros is where the problem starts.

 

[ppma]

I'd like to add here, that serve effectiveness in terms of power is not all about speed, but also on bite. Power is divided into rotational (spin) and linear (speed) mtion. A *completely* flat ball with no spin loses a lot of energy on the bounce since in the bounce it is made to take the needed spin from the friction, thus the resulting penetration and height that it reaches quite much goes down after. While, if the ball has a spin that accommodates to the ball speed (or higher) the energy would be mostly transferred to the bounce, therefore having a lesser impact on the speed after the bounce, plus getting higher which is difficult to return.

BTW this goes for all the shots.

 

[AlecG]

I think the biggest stumbling block to someone hitting 120mph serves if they're, say, sub 5'5" is the physicality required to get the racket moving quickly enough with shorter limbs and less muscle available than bigger people... All the biggest rec servers I've come across, so far, have been big, heavy set shouldered guys that move like steamrollers.

All 5'5/5'6" (I know they list him as 5'7" but that seems generous) of Diego Schwartzmann can/could hit first serves into the 110s on a regular basis, and I'm presuming he must've cracked 120mph occasionally - by mid-80s standards he has a pretty big serve! However, I guarantee you he's hitting those first serves with around 2000 RPM of spin on them, at least. He's not having to launch the ball within a sub-1° window, that changes with the exact speed it's hit at, to get the ball to go in.

Sure, but the only reason I used 120mph for my calculations is in order to be extremely generous to the myth, so that we can show more clearly that it's false.

The myth is that you need to be over six foot (a whole range of extreme heights are given, like 6'9") to hit a "flat" serve into the box, and they don't mean in some hypothetical scenario where there is no gravity. They mean a serve with minimal spin, at a normal amateur first serve speed. The myth doesn't say "you can't do it at 120mph if you're below 5'5" tall because you're too weak". The myth claims that even people who are 6 feet tall cannot hit a "flat" serve even at the amateur level. At it's a very common myth on Youtube etc, even among very respectable coaches.

The big problem even at below 120 mph, let's say whatever the average speed is for an amateur, is that the margin of error is small and it's just not worth the extra pace, especially given that spin has many advantages.

 

[Better_Call_Raul]

You haven't provided any evidence for this and have ignored all of the evidence against it. It's completely false. Try drawing a diagram with a curved path to account for the large effect of gravity, and with a very slightly downward trajectory at contact. You will see it's perfectly possible to hit down on it and still have it clear the net and land in the box with a curved path due to gravity.

Other posters have claoimed that projectile motion can be used to closely approximate the ball trajectory (I had my doubts since racquet face is interacting with the ball for 4 milliseconds with racquet face angle possibly changing during those milliseconds. And racquet face imparting topspin during those milliseconds).

But let's go with the assumption that path can be very closely approximated with projectile motion methods.

Let's assume a 6.0 foot player making contact at 8.0 feet.

And let's use a launch angle of minus 2 degrees from the horizontal, since that angle is a reasonable interpretation of " a giant hitting down and flat" on the ball.

Assumed values:

• Drag Coefficient (Cd): 0.5 (represents a realistic value for a tennis ball)
• Initial Velocity (v₀): 53.645 m/s (converted from 120 mph)
• Launch Angle (θ): -0.0349 radians (converted from -2 degrees)
• Launch Height (h): 2.4384 meters (converted from 8 feet)
• Mass of tennis ball (m): 0.056 kg
• Gravity (g): 9.8 m/s²
• Air Density (ρ): 1.2 kg/m³
• Surface Area of tennis ball (SA): 43.2 cm²

Have not yet been able to find a suitable simulator applet to test these values (the one below has a maximum input of 40 meters per second and won't allow a negative launch angle).

But it should be straightforward for you to show with projectile motion simulation (and your assumed values) that the serve will land in the box.

But so far the simulation does not seem to support your claim of a short player getting it into the box at 120 mph launch velocity.

 

[SystemicAnomaly]

Other posters have claoimed that projectile motion can be used to closely approximate the ball trajectory (I had my doubts since racquet face is interacting with the ball for 4 milliseconds with racquet face angle possibly changing during those milliseconds. And racquet face imparting topspin during those milliseconds).

But let's go with the assumption that path can be very closely approximated with projectile motion methods.

Let's assume a 6.0 foot player making contact at 8.0 feet.

And let's use a launch angle of minus 2 degrees from the horizontal, since that angle is a reasonable interpretation of " a giant hitting down and flat" on the ball.

Assumed values:

• Drag Coefficient (Cd): 0.5 (represents a realistic value for a tennis ball)
• Initial Velocity (v₀): 53.645 m/s (converted from 120 mph)
• Launch Angle (θ): -0.0349 radians (converted from -2 degrees)
• Launch Height (h): 2.4384 meters (converted from 8 feet)
• Mass of tennis ball (m): 0.056 kg
• Gravity (g): 9.8 m/s²
• Air Density (ρ): 1.2 kg/m³
• Surface Area of tennis ball (SA): 43.2 cm²

Have not yet been able to find a suitable simulator applet to test these values (the one below has a maximum input of 40 meters per second and won't allow a negative launch angle).

But it should be straightforward for you to show with projectile motion simulation (and your assumed values) that the serve will land in the box.

But so far the simulation does not seem to support your claim of a short player getting it into the box at 120 mph launch velocity.

A tennis ball, in flight, thrown or hit with a racket, is not similar to projectile motion, it IS projectile motion. It does not matter at all IF the racket face is changing its angle (wrt the Earth) while the ball is on the strings. Likewise, it doesn't matter that the hand/arm throwing a tennis is moving thru arc prior to release.

Consider a simple catapult throwing a stone (or a spear or some other projectile). The launching bucket, with it's payload, will move thru a fairly large arc before releasing the stone projectile. Once released, the stone experiences projectile motion. Its angular path, prior to release, does not disqualify this as projectile motion.

In the absence of air (drag), projectile motion, in a constant gravitational field (such as the Earth's gravity), will travel in a parabolic trajectory. However, in the presence of air, the projectile (ball, stone, etc) will deviate from a true parabolic trajectory. This deviation is readily apparent with a high, deep badminton serve -- since the shuttle experiences a considerable amount of air drag in its flight (but virtually no Magnus forces).

 

[AlecG]

Let's assume a 6.0 foot player making contact at 8.0 feet.

A six foot tall player will contact at 8.5 feet, which is about 2.6 metres, but lets go with 8 feet and 2.4 metres instead for margin of error, which would be a player who is about 5'7".

And let's use a launch angle of minus 2 degrees from the horizontal, since that angle is a reasonable interpretation of " a giant hitting down and flat" on the ball.

1 degree would be adequate to disprove the myth, but OK let's go with 2,

Assumed values:

• Initial Velocity (v₀): 53.645 m/s (converted from 120 mph)
• Launch Angle (θ): -0.0349 radians (converted from -2 degrees)
• Surface Area of tennis ball (SA): 43.2 cm²

Loads of problems here.

Firstly, you can't assume both the launch angle AND the velocity in your assumptions, because then you might pick the wrong angle for the velocity, as you have done here. At 2 degrees, a 120 mph mile serve with minimal spin will sail very long and far over the net at any normal height.

Secondly, you don't actually need a speed of 120 mph to disprove the myth since that's not part of the myth. The myth is that it's impossible at any decent first serve pace, including at amateur level, but I used 120 mph to be generous and my calculations show that it is possible without drag. Drag only increases the margin further, but not to the extent that you would have to hit up on the ball at 120 mph. The calculator in your screen shot goes up to 40 m/s which is 89 mph, and doesn't allow negative angles, so we can work out what is the correct speed at that angle, but it will be much slower because of the high launch angle.

Thirdly, your tennis ball surface area is wrong, and your conversion to square metres is also wrong.

Surface area of a sphere = 4π(r-squared) = 4*3.14*(3.4*3.4) = 145 square centimetres = 0.0145 square metres (There are 10 thousand square centimetres in a square metre)

Using your simulator with the correct numbers and a launch angle of zero which is the minimum allowed, using the maximum speed allowed of 89 mph, the ball sails long by 8 metres. The distance to the back of the service box is 18.3 metres.

All this tells you is that you need to hit down on the ball if you are hitting that hard or harder. But it's going way over the net here. You can test that by reducing the launch height by the height of the net to 1.5 metres (Launch height relative to the top of the net).
The ball travels 21 metres before it drops to the height of the net.

Now reduce the launch speed until the ball is dropping to the height of the net after 12 metres, just after passing the net, and you will find the minimum speed to get the ball over the net is around 50 mph at a 0 degree launch angle.

Now increase the launch height again back to 2.4 metres (8 feet) and find that the ball is landing more than 3 metres inside the service box.
So the window for hitting harder and still getting it in is about three metres (horizontally).

Now increase the launch speed until the the ball reaches the back of the service box at 18.3 metres to find the maximum launch speed at this angle, which is around 60 mph.

Now reduce the launch height again to 1.5 metres to see how far it's travelling before dropping to the top of the net, about 14.5 metres, so we've still got almost 3 metres of margin for error horizontally to hit down on the ball a little bit, even at 60 mph.

So with horizontal strike, anything between 50 mph and 60 mph will land in the service box, with about 3 metres of margin for error horizontally.

Obviously that is plenty of margin to hit at higher speeds and reduce the launch angle to compensate, while still going over the net, but you can't tell what the maximum speed is from this simulator. That's what the calculations are for.

At this point there is overwhelming evidence against you, and you have provided nothing rational in opposition, and yet you still seem to think it's my responsibility to show you a simulation. If you can find a simulation tool that allows a negative launch angle and put the correct numbers in this time (you're going to need a launch angle below 2 degrees at 120 mph), let me know. Until then, maybe respect the time and effort and higher quality reasoning that has been presented against the myth and stop making false assumptions.

 

[ppma]

THis thread made me have some quick fun, so I leave here this resource. It's all rusty and the interface needs improvement, but still seems to work. Did not review the physics twice to be honest.

Tennis shot calculator

 

[AlecG]

THis thread made me have some quick fun, so I leave here this resource. It's all rusty and the interface needs improvement, but still seems to work. Did not review the physics twice to be honest.

Tennis shot calculator

Nice, thanks. This tool suggests you can get it in at 120 mph with launch angle of 3.1-3.6 degrees downwards, hitting height of 7 feet, friction of 0.53 and everything else set to zero.

That would be a player height of around 5'0" or below.

At 2 degrees downwards, the more realistic speeds of 80 to 95 mph are needed.

 

[Better_Call_Raul]

A tennis ball, in flight, thrown or hit with a racket, is not similar to projectile motion, it IS projectile motion. It does not matter at all IF the racket face is changing its angle (wrt the Earth) while the ball is on the strings.

Vic Braden said, something along the lines of "Only a giant 6 foot 9 playet can hit down on the serve..". I take that to mean that the launch angle is slightly closed. Think that a very slightly closed launch angle of minus 2 degrees is reasonable for determining if only a giant player can hit it "flat and down" into the box,
Also assume that the player contacts at apex of toss so that dropping toss makes zero contribution to topspin.
This will closely simulate the type of "flat" serve being discussed here, i.e. "Only a giant player can hit down on a serve".

 

[SystemicAnomaly]

Nice, thanks. This tool suggests you can get it in at 120 mph with launch angle of 3.1-3.6 degrees downwards, hitting height of 7 feet, friction of 0.53 and everything else set to zero.

That would be a player height of around 5'0" or below.

At 2 degrees downwards, the more realistic speeds of 80 to 95 mph are needed.

@Better_Call_Raul

I do not dispute that shorter players can hit "flat" serves. (Have we defined what we mean by a "flat" serve?). And I can accept that one does not need to be a "giant" to hit a serve with a "launch angle" that is downward by a few degrees.

However, I do not believe that this slightly downward "launch angle" means that most of us are actually hitting (swinging) down on the ball for our flat serves. By "launch angle" I assume this refers to the angle (wrt horizontal) that the ball exits the stringbed.

That exit angle can be very closely related to racket face angles. While it may or may not be perpendicular to the plane of the stringbed, it Might be somewhat close to that.

Many players will hit the flat serve with a slightly closed racket face or with a racket face that is close to vertical. But a (slightly) closed racket face and a (slightly) downward launch angle is not an indication that the racket face is moving in a downward direction.

The high speed data and video that I've seen has not shown servers swinging down on the ball. The 6000 fps video of Adam Kennedy (192+ cm) hitting a 143 mph "flat" serve shows him hitting with a slightly closed racket face. However, the racket head appears to be moving in a direction that is nearly horizontal during the 4 ms or so of contact. It might even be moving in a slightly upward direction, perhaps a degree or so, during contact and for a short time after contact.

I've also seen data & graphics, gleaned from very high speed cameras, of Pete Sampras' serves in a Racquet Head Serve Speed project from the late 1990s. This project was headed by Dr. Jani Macari Pallis and included Dr Paul Roetert (biomechanics), Dr Duane Knudson (biomechanics), Dr Howard Brody (physics) and others PhD's involved in fluid dynamics and tennis science. John Yandell was also involved with this project team.

The project graphics showed data for nearly a dozen different Sampras serves, both 1st and 2nd serves. For the 2nd serves, it is obvious that contact occured while the racket head was moving upward. For the 1st data, contact was made closer to the apex of the swing -- either right at the apex or just prior to the apex.

None of the data / graphics showed contact after the apex -- racket head moving downward. Yet the launch angle appeared to be downward in all cases. The racket head is moving horizontally or slightly upward for all serves

Our Research Project - Serve Racquet Head Speed

 

[SystemicAnomaly]

The following article refers to the same project that I linked above. More info:

www.tennisserver.com/set/set_03_09.html

 

[AlecG]

Have we defined what we mean by a "flat" serve?

I have tried to, yes, but it's a myth regardless of which definition you use, so it doesn't really matter. The myth is in the practical context of giving advice to a general audience not to hit flat serves (and not to try to hit them), which is generally good advice, but they justify the advice with the claim that it's not possible to get it in at a high speed when it's flat, which is false.

In a practical context, a "flat" serve means one that you are trying to hit with as little spin as possible.

In a theoretical context, we can discuss a hypothetically "flat" ball with zero spin, and if we have proven that the myth is false with this definition (we have), it follows that it is also false with the practical definition which only increases margin further when there is some topspin, and only decreases the margin in the case of under-spin, which is rare.

We could also discuss a theoretical case of a "flat" serve with no gravity AND no spin, but this is so theoretical that it's irrelevant to any practical advice, and therefore irrelevant to the myth, but as I showed in the first half of my calculations, the myth is false even under this pointlessly theoretical definition where there is no gravity.

While it may or may not be perpendicular to the plane of the stringbed, it Might be somewhat close to that.

Many players will hit the flat serve with a slightly closed racket face or with a racket face that is close to vertical. But a (slightly) closed racket face and a (slightly) downward launch angle is not an indication that the racket face is moving in a downward direction.

Sure, but this is irrelevant to disproving the myth, which claims that you physically can't do it because the ball will go long or into the net. The myth has nothing to do with whether the racquet is generally moving downwards at contact.

Personally, I think it is basically impossible if you are leaning over the baseline with your body and your arm and your racquet for the racquet to be moving exactly horizontally or upwards, even if it looks basically horizontal because the angle is very small, but I think this is too far off the topic of the myth. It doesn't relate to the claims in the myth, or disproving them, at all.

 

[SystemicAnomaly]

I have tried to, yes, but it's a myth regardless of which definition you use, so it doesn't really matter. The myth is in the practical context of giving advice to a general audience not to hit flat serves (and not to try to hit them), which is generally good advice, but they justify the advice with the claim that it's not possible to get it in at a high speed when it's flat, which is false.

In a practical context, a "flat" serve means one that you are trying to hit with as little spin as possible.

In a theoretical context, we can discuss a hypothetically "flat" ball with zero spin, and if we have proven that the myth is false with this definition (we have), it follows that it is also false with the practical definition which only increases margin further when there is some topspin, and only decreases the margin in the case of under-spin, which is rare.

We could also discuss a theoretical case of a "flat" serve with no gravity AND no spin, but this is so theoretical that it's irrelevant to any practical advice, and therefore irrelevant to the myth, but as I showed in the first half of my calculations, the myth is false even under this pointlessly theoretical definition where there is no gravity.



Sure, but this is irrelevant to disproving the myth, which claims that you physically can't do it because the ball will go long or into the net. The myth has nothing to do with whether the racquet is generally moving downwards at contact.

Personally, I think it is basically impossible if you are leaning over the baseline with your body and your arm and your racquet for the racquet to be moving exactly horizontally or upwards, even if it looks basically horizontal because the angle is very small, but I think this is too far off the topic of the myth. It doesn't relate to the claims in the myth, or disproving them, at all.

Seems that you did not fully understand my intent. There appears to be a partial disconnect between what you are saying and what others, such as Raul, are saying. In part, there is a difference in what the MYTH entails. What I suggested is not off-topic.

As I see it, there is more than one aspect to the so-called myth. The subject has been brought up numerous times before and is not as narrowly defined as you now seem to be suggesting.

One part of the myth is that shorter players cannot hit flat serves? Is that not your primary concern? I am not discounting that part of the myth.

The other part of the myth is that most players are can hit down on the serve. This has always been part of this myth in discussions. For most readers, this implies that most server are swinging down on the serve. I've provided some compelling evidence here that this is probably not true for most servers. Even those who are 6'1" to 6'4".

Raul, in several of his posts, has talked about hitting down on the ball. In post #90, you also refer to being able to hit down on the ball. Many, if not most, readers would take this to mean moving the racket head in a downward direction (before &) during contact. For this reason, this is a valid part of the myth / discussion. You might be saying that it is theoretically possible to swing down very slightly on the serve for most servers. But not certain that this is really happening IRL (except for the very tallest players).

 

[AlecG]

The other part of the myth is that most players are can hit down on the serve. This has always been part of this myth in discussions. For most readers, this implies that most server are swinging down on the serve. I've provided some compelling evidence here that this is probably not true for most servers. Even those who are 6'1" to 6'4".

"Servers usually aren't hitting down" and "servers can't hit down" are two completely different claims. Nobody ever denied the former so why bring it up. It's irrelevant to the myth I'm discussing.

Raul explicitly claimed that you can't hit down in terms of the initial launch angle of the ball. He wasn't just claiming that the racquet head isn't usually travelling downwards.

You might be saying that it is theoretically possible to swing down very slightly on the serve for most servers. But not certain that this is really happening IRL.

OK. I've already explained why it almost certainly is happening IRL in the serves with the least amount of topspin and you didn't address that, and again it's not a topic I care about discussing. I came here to debunk a specific myth and Raul was restating the myth. If you want to make some other unlikely claim based on literally one video of one serve that wouldn't support the myth even if it were true., I don't really care. I've already explained why it's not relevant and don't really want to keep going back and forth.

"The myth is in the practical context of giving advice to a general audience not to hit flat serves (and not to try to hit them), which is generally good advice, but they justify the advice with the claim that it's not possible to get it in at a high speed with that type of serve, which is false."

Your claims are also irrelevant to height. If Adam Kennedy is that tall and doing it, and if you think one video is good evidence of general tendencies, then it has nothing in particular to do with height, so there is just no way it can be relevant to the myth, except for the fact that it makes the myth even sillier, because if everyone is hitting at tiny bit of topspin even when they are trying to hit "flat", then that just further increases the margin over the net when trying to hit flat, which further debunks the myth that you can't get that type of serve into the service box at speed. But in reality, you are basing this one one video of one serve. If you hit the ball at the peak with a straight racquet, it will be moving downwards from that point onwards. If it isn't, it's because the racquet wasn't straight yet, and that straightening up is compensating for the downwards angle of the arm.

The myth I'm talking about doesn't say "you can't hit a ball flat because the there is always a little bit of spin". That would be a completely separate and irrelevant myth. I'm also not discussing the claim that "people usually aren't hitting down". That claim is quite likely to be true but would require empirical evidence (with a large sample size) and is a completely separately claim that I'm not interested in trying to debunk. It's not the claim that I have been debunking (that Raul kept repeating) which is the claim that you *can't'* get it in with a negative launch angle unless you're a giant, not just that most people aren't hitting down.

 

[AlecG]

The amount of my life I've wasted because of some jerks too disrespectful to respect the work of the original post or to take the time to understand it is really hard to forgive myself for.

 

[Dragy]

“Hitting down on the ball” most likely refers to feel you get hitting an OH well inside the court. Unless you are a 6’9 giant, you don’t hit your serve this way. Hitting 2 or 3 degrees downward is still swinging up at the ball, hitting forward.

 

[TennisCJC]

“Hitting down on the ball” most likely refers to feel you get hitting an OH well inside the court. Unless you are a 6’9 giant, you don’t hit your serve this way. Hitting 2 or 3 degrees downward is still swinging up at the ball, hitting forward.

Also, you can hit upward and the ball trajectory off the strings can be downward. Think about it and you'll see it's possible. I can slightly close the racket face on a forehand, hit slightly upward while making contact above the equator of the ball and the ball will go downward. If your racket face is slightly tilted forward, the racket face can be moving upward and the ball will go ever so slightly downward. You can also envision, "hitting up on the top half of the ball" when serving and get topspin and a downward trajectory. Think of hitting a short shoulder high forehand where you swing slightly upward for topspin but the face is slightly closed, the ball trajectory will be downward but the racket path will be upward. It's amazing isn't it?

 

[Dragy]

Also, you can hit upward and the ball trajectory off the strings can be downward. Think about it and you'll see it's possible. I can slightly close the racket face on a forehand, hit slightly upward while making contact above the equator of the ball and the ball will go downward. If your racket face is slightly tilted forward, the racket face can be moving upward and the ball will go ever so slightly downward. You can also envision, "hitting up on the top half of the ball" when serving and get topspin and a downward trajectory. Think of hitting a short shoulder high forehand where you swing slightly upward for topspin but the face is slightly closed, the ball trajectory will be downward but the racket path will be upward. It's amazing isn't it?

You can also swing downward on the ball and send your serve up with backspin!

 

[SystemicAnomaly]

The amount of my life I've wasted because of some jerks too disrespectful to respect the work of the original post or to take the time to understand it is really hard to forgive myself for.

Discussions evolve.

 

[SystemicAnomaly]

You can also swing downward on the ball and send your serve up with backspin!

Yeah, the upward Magnus force can offset the drop due to gravity.

 

[TennisCJC]

You can also swing downward on the ball and send your serve up with backspin!

Yes, but I don't and I bet you don't either.