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Discussion Starter #1 (Edited)
NOTE: For the enhanced new camera angle footage about ball hitting line judge check this post here:

[Analysis] How Fast Novak Djokovic Hit Ball In...

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I have tried to calculate ball speed at the moment of arrival (fish eye cam) and at the border (baseline) of the court (bird eye cam). It is not precise, with limited 1920x1080 FHD resolution (click to open bigger size). Animation has 6 images in total (28 seconds duration):

updated more accurate version
(thanks to @Martin12 and @masterclass for additional info): [right click to open a full original size]

356450



old less accurate version:
[Analysis] How Fast Novak Djokovic Hit Ball In 'Line Judge Incident' US Open 2020.gif
 

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Discussion Starter #2 (Edited)
In fish eye view, ball travels for approx. 0.600 seconds (0.567 seconds if you omit the initial contact) and the distance it travels is somewhere between 8 and 9 meters (actually, after looking at the bird eye cam, it is more likely 10 - 11 meters).

In bird eye view cam, we have a much cleaner almost distortion-free court view, and it is much easier to calculate initial ball speed, but we don't see the entire scene, and speed at the time of arrival. Unfortunately, I can't do the approximations for that now.
 

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I don't think the ball loses more than 10 to 20% of its initial speed within that time and distance. I compared with another footage, and this confirms a time of around 0.55 s from the moment when Djokovic hits the ball until the women is hit. The estimate of ~9 m distance looks reasonable as well, so something around 60 km/h should be a good guess.
 

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I have tried to calculate ball speed at the moment of arrival (fish eye cam) and at the border of the court (bird eye cam). It is not precise, with limited 1920x1080 FHD resolution (click to open bigger size). Animation has 6 images in total (28 seconds duration):

View attachment 356440
Thanks for the calc. attempt. However, you need the correct distance and time. The correct distance is not too difficult to be fairly precise.
On every court, It is ~ 5.5 meters from the service line to the baseline. Novak is about a meter outside the service line, maybe 1.5 meters. So sure, let's give it 4 meters to the baseline from racquet impact point.
Now the standard court distance from baseline to the fence is 21 ft or 6.4 meters. But this is a stadium court and there is more room behind the baseline Iin Arthur Ashe stadium, the distance from the baseline to the wall is 28 ft. or 8.5 meters. But the woman is not quite against the wall, let's say .5 meters from the wall. Still that is 8 meters from her to the baseline.
So a pretty close approximation of the total distance is at least 12 meters. from racquet impact to throat impact.

Time appears to be about 1/2 a second from impact of ball by racquet to impact on the woman's throat, but of course it would help to have a real time video and frame by frame measurement to get a fairly precise result..

Anyway, 12 meters/.5 seconds is of course 24 m/s or an average speed of about 86 kph (54 mph).
12 m/.6s is 20 m/s or about 72 kph (45 mph).
12 m/.4s is 30 m/s or 108 kph (67 mph).
12 m/.3s is 40 m/s or 144 kph (89 mph).
So the precise time is of course critical for a precise final result.

Whatever the result, she unluckily took the impact on the throat where there is little protection.

Is it time for line umpires to wear baseball umpire masks, throat and chest protectors for the "foul balls" in tennis???

Unfortunately,
masterclass
 

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Too fast to be hit to a lunes woman, next
 

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Looked 30-ish mph to me, indeed. Certainly fast enough to cause genuine shock if it hits a vulnerable spot. No acting here, just an unfortunate incident. Thanks for your effort discerning actual data on this, much appreciated.
 

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Speed doesn't matter. Accidental doesn't matter. He shouldn't do that. Period. Total disdain for the integrity of others. Move on
 
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Discussion Starter #8
Now the standard court distance from baseline to the fence is 21 ft or 6.4 meters. But this is a stadium court and there is more room behind the baseline Iin Arthur Ashe stadium, the distance from the baseline to the wall is 28 ft. or 8.5 meters.
That was my main point of concern - distance from the base line to the back wall. I used 21' for calculation, as I do not know exact AA measurements. In any case, even 50-60 km/h is not a 'light' speed given the unfortunate impact area.

Time appears to be about 1/2 a second from impact of ball by racquet to impact on the woman's throat, but of course it would help to have a real time video and frame by frame measurement to get a fairly precise result..
Yes, I used official footage and frame-by-frame analysis in VirtualDub. Around 0.55 seconds seems like a 'sweet spot', but could be wrong... High speed recording would greatly help in this case (or at least 60 fps).

Thanks
 

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Discussion Starter #10
But this is a stadium court and there is more room behind the baseline Iin Arthur Ashe stadium, the distance from the baseline to the wall is 28 ft. or 8.5 meters.
After doing some manual measurements of HQ photos I could find on the net (since Google didn't really understand what I was asking - answer was "8 miles" lol), geometric measurements were between 8 and 8.8 meters, so it supports your 8.5 m value (optical distortion, limited resolution and accuracy of manual measurements all contribute).

So, in effect, yes, the ball was going even faster than my most optimistic calculation at first. Thanks!
 

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After doing some manual measurements of HQ photos I could find on the net (since Google didn't really understand what I was asking - answer was "8 miles" lol), geometric measurements were between 8 and 8.8 meters, so it supports your 8.5 m value (optical distortion, limited resolution and accuracy of manual measurements all contribute).

So, in effect, yes, the ball was going even faster than my most optimistic calculation at first. Thanks!
Nice analysis. :) If you have a link to a fairly clear real time video of the racquet-ball impact and ball to throat impact, I would appreciate it. Almost all I have seen are in slow motion. :( A side angle or perpendicular view to the ball's flight path would be preferable, of course. Thanks.

Respectfully,
masterclass
 

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Thanks for this. The final analysis is the average ball speed seems to be around 80 kmph, gives us a good idea what the speed on impact was - probably somewhere around 70 kmph, give or take.

Edit: on second thought, the whole thing lasted less than a second, might barely have had any deceleration, if any.
 

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Replay the video at 25% speed, it shows clearly enough that the ball squarely hits the neck.

Shoulder, my ass.
I agree - it clearly hits the neck
 

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Replay the video at 25% speed, it shows clearly enough that the ball squarely hits the neck.

Shoulder, my ass.
Still doesn't change the fact that the dumb, nonchalantly hit ball was coming right in the direction of her eyesight. Instead of paying even remotely attention to her surroundings and by reflex make some movement she was simply daydreaming, completely unaware of what is happening around her. Not to mention that she was so much in need of air that she didn't even take off her mask and consequently came back to the court couple minutes later
 

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Discussion Starter #18
Wait... hold your breath. I am just finishing enhanced version. It looks very interesting.
 

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in this video with the best quality and angle that I have seen so far, it looks like the ball hits the referee in the shoulder. and this is also seen in the body's reaction, rotation, etc. after the hit.

Huh it’s clear her throat...

Still doesn't change the fact that the dumb, nonchalantly hit ball was coming right in the direction of her eyesight. Instead of paying even remotely attention to her surroundings and by reflex make some movement she was simply daydreaming, completely unaware of what is happening around her. Not to mention that she was so much in need of air that she didn't even take off her mask and consequently came back to the court couple minutes later
So now it’s her fault for not having quick reflexes lol?

She’s 60 yo and wasn’t expecting the hit, it came by surprise. It can happen to anybody, yes some people are quick to dodge it, some aren’t. You can’t blame her at all.
 

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It’s kind of lame that an over the hill, slow woman is in the back like it’s no big deal that balls are struck.
 
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