Serve speed cage

[5263]

found it!

Velocity
The serve speeds you see on courtside digital displays are measured just as the ball leaves the racquet. Fortunately for returners, by the time the ball reaches them, air resistance and the friction of the court surface have diminished its speed by roughly 50 percent. Tennis instructor and analyst John Yandell has found that, on average, a 120-mph serve slows to 82 mph before the bounce, then to 65 mph after the bounce, and finally to 55 mph at the opponent’s racket.

published info

It had a pic showing 120 being only 82 near the net and 65 right after the bounce.

 

[J011yroger]

Close enough. he said about didn't he?
I think it's closer to 20% by the net anyway. I used to have a chart that broke it out. Was it in tennis mag?

Jolly, did you post the results yet?

Well if it is 10% then with a stiff back and an old ball out of my bag I just clocked 121mph with my wooden Pancho Gonzales racquet.

If it is 20% then it would be 136mph.

So we are gonna stick with the 10% figure lol.

J

 

[J011yroger]

Results to follow, going to start editing the video now. Just need another Miller Lite. A fella can work up a powerful thirst with this science project stuff.

J

 

[r2473]

Velocity
The serve speeds you see on courtside digital displays are measured just as the ball leaves the racquet. Fortunately for returners, by the time the ball reaches them, air resistance and the friction of the court surface have diminished its speed by roughly 50 percent. Tennis instructor and analyst John Yandell has found that, on average, a 120-mph serve slows to 82 mph before the bounce, then to 65 mph after the bounce, and finally to 55 mph at the opponent’s racket.

published info

It had a pic showing 120 being only 82 near the net and 65 right after the bounce.

Really?!?

Can you link to anything on this? Very interesting.

 

[J011yroger]

OK, *fine!*

Since I am resting my leg, I will go hit some serves tomorrow. I will measure the distance to the back fence and see if I can hit it on the second bounce. I will disregard placement, serve percentage, and I won't try for any spin. I will just serve as hard as I can.

If I hurt myself, you will all feel terrible.

You shouldn't try to serve as hard as you can. EVER.

My biggest serves come in the middle of a match when I am loose and rolling.

Not when I am in practice trying to serve hard for the radar gun for pee pee waving rights, and get all tight.

You should video your motion and go over it with your pro. Or someone whom you trust.

Hitting the fence should just happen naturally.

J

 

[J011yroger]

The Measuring.

http://vimeo.com/6042364

J

 

[J011yroger]

The experiment.

Answer to question #1.

No I am not really trying to get it in the opposite box, just trying to serve as slow as possible and hit the back fence exactly with a ball that bounces before the service line.

This was a LOT harder than I thought it would be. Even my lamest, slowest warmup type serves hit easily, so I had to resort to just putting the ball up and dinking it. It was more like playing beer pong or shuffleboard than serving.

Answer to question #2.

Yes, I paid for that haircut.

$13+$5 tip.

Answer to question #3.

If I approached the radar, and it saw anything move, it would pick up that speed, and kill the recall. So I had to sneak up on it, ninja style.

Please excuse the profanity when I set it off sneaking up.

I make a better European auto mechanic than ninja or tennis player.

http://vimeo.com/6042807

J

 

[J011yroger]

Bonus Footage:

Serving with my $2.99 Pancho Gonzales woodie, a stiff back, and an old ball from my bag.

Figure 109mph at the net is around 121 off the racquet face.

http://vimeo.com/6043100

J

 

[canadave]

lol....wow, you are one dedicated tennis scientist, JR!! Amazing setup, great videos, thanks for that.

But your video has left me confused. At the 1:35 mark of your video, unless I'm hearing you wrong on the video, you hit a 64mph serve pretty much down the middle (which would have the greatest chance to hit the backstop on one bounce, as opposed to serves out wide--nice job on that btw!), and it still took two bounces (as evidenced by the high arc it took off the backstop once it hit, and the backspin it had when it came down).

But then at the end of the video, you hit a 51mph serve that you said just barely hit the backstop on one bounce? How could 51 mph hit the backstop and 64mph not?

 

[J011yroger]

lol....wow, you are one dedicated tennis scientist, JR!! Amazing setup, great videos, thanks for that.

But your video has left me confused. At the 1:35 mark of your video, unless I'm hearing you wrong on the video, you hit a 64mph serve pretty much down the middle (which would have the greatest chance to hit the backstop on one bounce, as opposed to serves out wide--nice job on that btw!), and it still took two bounces (as evidenced by the high arc it took off the backstop once it hit).

But then at the end of the video, you hit a 51mph serve that you said just barely hit the backstop? How could 51 mph hit the backstop and 64mph not?

I hit a bunch in the 60somethings that didn't make it, 51 was the slowest that exactly hit the fence.

I had one good run of them that hit about 1' short of the fence, which would be about where the fence would be on a normal 20' from the baseline fence (The one at this school was nearly 22').

Pretty much anything in the 70's hit the fence, 60's could hit or fall short, but would probably hit a 20' fence.

51 was the slowest that hit the fence exactly. I think that one hit because it had a loopier trajectory. I guess that would be like just popping the serve in with a western FH grip.

J

 

[J011yroger]

All speeds were of course and obviously measured at the net, and so would register higher on pro radar which measures off the racquet face.

J

 

[canadave]

51 was the slowest that hit the fence exactly. I think that one hit because it had a loopier trajectory. I guess that would be like just popping the serve in with a western FH grip.

J

Ah yes, that's probably the reason....thanks, should've thought of that, since I suggested it in one of my earlier posts as a possible way a slow serve might hit

So, it appears a 55mph serve MIGHT hit a backstop, if it had the right trajectory. Just for closure, would you agree a 40mph serve has no chance of hitting a backstop on a single bounce unless the backstop is a fair bit closer?

 

[J011yroger]

lol....wow, you are one dedicated tennis scientist, JR!! Amazing setup, great videos, thanks for that.

But your video has left me confused. At the 1:35 mark of your video, unless I'm hearing you wrong on the video, you hit a 64mph serve pretty much down the middle (which would have the greatest chance to hit the backstop on one bounce, as opposed to serves out wide--nice job on that btw!), and it still took two bounces (as evidenced by the high arc it took off the backstop once it hit, and the backspin it had when it came down).

But then at the end of the video, you hit a 51mph serve that you said just barely hit the backstop on one bounce? How could 51 mph hit the backstop and 64mph not?

Just watched again, the 64mph one you are talking about hit the concrete step at the base of the fence and bounced straight up.

J

 

[canadave]

Just watched again, the 64mph one you are talking about hit the concrete step at the base of the fence and bounced straight up.

J

ah, okay, that makes more sense....it did seem to jump quite abnormally high Didn't see the step.

 

[J011yroger]

So, it appears a 55mph serve MIGHT hit a backstop, if it had the right trajectory. Just for closure, would you agree a 40mph serve has no chance of hitting a backstop on a single bounce unless the backstop is a fair bit closer?

Well, I could try, but it would have to be some kind of really loopy heavy kicking topspin serve.

I could try to hit a FH 40mph that might do it. . .

Or a slow ass spinny topspin moonball serve.

But semi flat, and 40mph, nah.

I think I hit ones nearly 70, so probably close to 80 on real radar that didn't hit on one bounce.

J

 

[J011yroger]

ah, okay, that makes more sense....it did seem to jump quite abnormally high Didn't see the step.

Ya, if you look in the still picture I posted, you can see the concrete step that the fence is set in.

Or the beginning of the measuring video.

That is what it hit.

J

 

[WildVolley]

So, Jolly, what's your estimate on ball speed just off the racket face on the 51mph one that hit the back fence? Was that serve less than 60mph off the racket face?

 

[canadave]

Thanks JR....I think that pretty much provides all the evidence anyone could want.

I think one thing coming out of this that was interesting to me, was the vast difference trajectory makes in the result of a serve. I mean, I know all about different trajectories and so on, but the difference in results based on trajectory was pretty dramatic. Also makes one think about how trajectory might influence *perceived* speed as a returner....goes to the "heavy serve" concept, and so on.

Fascinating stuff....again, thanks for taking the time to actually do the experiment and film it for us

 

[J011yroger]

So, Jolly, what's your estimate on ball speed just off the racket face on the 51mph one that hit the back fence? Was that serve less than 60mph off the racket face?

I would guess 56-57mph.

I really have no proof one way or the other, but that seems reasonably close to an accurate measure to me.

J

 

[J011yroger]

Thanks JR....I think that pretty much provides all the evidence anyone could want.

I think one thing coming out of this that was interesting to me, was the vast difference trajectory makes in the result of a serve. I mean, I know all about different trajectories and so on, but the difference in results based on trajectory was pretty dramatic. Also makes one think about how trajectory might influence *perceived* speed as a returner....goes to the "heavy serve" concept, and so on.

Fascinating stuff....again, thanks for taking the time to actually do the experiment and film it for us

It is fun, I actually like doing stuff like this.

Hopefully on the next page of this thread Ultra2 will bet me $20 I can't break 100mph with a wooden racquet.

J

 

[WildVolley]

I would guess 56-57mph.

I really have no proof one way or the other, but that seems reasonably close to an accurate measure to me.

J

That's cool. I never have measured a ball moving that slow hit the back fence, but then I haven't been looking for it either.

At least you've permanently killed the claimed rule of thumb that a ball that hits the back fence is traveling close to 100mph.

 

[J011yroger]

That's cool. I never have measured a ball moving that slow hit the back fence, but then I haven't been looking for it either.

At least you've permanently killed the claimed rule of thumb that a ball that hits the back fence is traveling close to 100mph.

I have been disagreeing with that claim as long as I have been around these boards. About time I actually got off my ass and did something about it.

J

 

[canadave]

Hopefully on the next page of this thread Ultra2 will bet me $20 I can't break 100mph with a wooden racquet.

lol.....oh, another entertaining saga....can't wait.......

 

[Mike Cottrill]

Bonus Footage:

Serving with my $2.99 Pancho Gonzales woodie, a stiff back, and an old ball from my bag.

Figure 109mph at the net is around 121 off the racquet face.

http://vimeo.com/6043100

J

If you’re up for it, how about placing the camera on the other side, zoomed in close the service line using the high speed mode. Catch a serve that is on or close to the line down the tee. Measure with your radar and compare it to the serve calc. program. It would be interesting to see what the diff is.

If your really up for a challenge, use powder to see were the ball lands and place a string on your racquet and hold it close to were you make contact and measure distance to the landing mark. Up for it?

Mike

 

[raiden031]

I guess it shows how bad my return is if 60-70 mph serves seem fast to me.

 

[J011yroger]

If you’re up for it, how about placing the camera on the other side, zoomed in close the service line using the high speed mode. Catch a serve that is on or close to the line down the tee. Measure with your radar and compare it to the serve calc. program. It would be interesting to see what the diff is.

If your really up for a challenge, use powder to see were the ball lands and place a string on your racquet and hold it close to were you make contact and measure distance to the landing mark. Up for it?

Mike

Wait, so you are saying sprinkle powder by the T so when the ball hits it will leave a mark. (Or play on freshly brushed clay!)

And then I could put a weight with a string on it, in that spot, and tie the other end to my racquet, and hold my racquet up to get the right length?

I don't know if the high speed from the other end would be clear enough to determine contact, but it sounds like fun.

J

 

[J011yroger]

If you’re up for it, how about placing the camera on the other side, zoomed in close the service line using the high speed mode. Catch a serve that is on or close to the line down the tee. Measure with your radar and compare it to the serve calc. program. It would be interesting to see what the diff is.

If your really up for a challenge, use powder to see were the ball lands and place a string on your racquet and hold it close to were you make contact and measure distance to the landing mark. Up for it?

Mike

I took some high speed after I was done fooling around, but it was too dark and it came out bad.

Plus I wasn't really feelin it so poor day to use to analyze my serve.

But here are 3 frames from around contact on the sideline. I suppose near the opposite service box wouldn't be too much further away, so we should be able to judge well.

J

 

[J011yroger]

Above shot at 210fps.

J

 

[Mike Cottrill]

Wait, so you are saying sprinkle powder by the T so when the ball hits it will leave a mark. (Or play on freshly brushed clay!)

And then I could put a weight with a string on it, in that spot, and tie the other end to my racquet, and hold my racquet up to get the right length?

I don't know if the high speed from the other end would be clear enough to determine contact, but it sounds like fun.

J

Your camera is good enough. At 300fps, you can get real close.
Outdoors with bright sun will be the best.
If you have an outdoor clay court, but if not a little powder would do the trick.
To measure the distance, two people would help with the string measure, but your idea would work if you something to secure the other end.
My camera stinks compaired to yours, and I can get real close even at 240 feilds per second.

 

[canadave]

JR, I think I see a new calling for you. "Tennis Mythbusters"?

 

[J011yroger]

JR, I think I see a new calling for you. "Tennis Mythbusters"?

As long as it pays more than $5 per hour and doesn't involve nudity, I am in.

J

 

[Mike Cottrill]

J,
Increase the shutter speed when you do high frame rate. It will be more clear when the raq makes contact with the ball.

 

[pabletion]

All speeds were of course and obviously measured at the net, and so would register higher on pro radar which measures off the racquet face.

J

is this true???? I always thought they were measured near the service lines, but thats just my guess, not that Ive researched or anything.

What would be the point of measuring off the racquet face, since what really matters is how fast it goes by the receiver, at least until it bounces and one reacts?

 

[Mike Cottrill]

is this true???? I always thought they were measured near the service lines, but thats just my guess, not that Ive researched or anything.

What would be the point of measuring off the racquet face, since what really matters is how fast it goes by the receiver, at least until it bounces and one reacts?

~ 4ft off the raq face. J's readings are not really at the net, but where the ball crosses the radar's field. There might be some angle error as well.
Hence the compare test talked about above.

 

[raiden031]

is this true???? I always thought they were measured near the service lines, but thats just my guess, not that Ive researched or anything.

What would be the point of measuring off the racquet face, since what really matters is how fast it goes by the receiver, at least until it bounces and one reacts?

Well I think the contact point is important because that is in the midst of the returner's split step. So the reaction actually starts during the server's motion before contact.

 

[pabletion]

hmmm, to be a 'net' measurement, I guess the measuring device should be pointed upwards.....................

this is eerie territory im walking in now.

So, what would be the speed of a Roddicks 140 mph serve:
a. Over the net?
b. Just as it is about to hit the court?

 

[J011yroger]

J,
Increase the shutter speed when you do high frame rate. It will be more clear when the raq makes contact with the ball.

Ok, I will try to see how to do it.

Remember, you are dealing with an idiot here.

I just let the camera do what it wants, sometimes it comes out good, sometimes it comes out like crap.

I do however very much appreciate all the help you have given me.

J

 

[canadave]

hmmm, to be a 'net' measurement, I guess the measuring device should be pointed upwards.....................

You mean, in order to capture the ball's speed as it crosses over the net and camera? A radar gun has to be pointed roughly in the direction of the oncoming object, so as to measure the difference in bounce/return radio wave distance over time. It can't measure speed of an object going "across" its field of view.

You could, theoretically, set up a high-speed camera pointing at a "wall" showing measured alternating stripes, have an object like a ball go across the field of view, and then view the video afterward to calculate speed (such as is often done on the "Mythbusters" TV show). Although obviously you wouldn't be able to use this method if the camera is pointing skyward....

 

[5263]

Ah yes, that's probably the reason....thanks, should've thought of that, since I suggested it in one of my earlier posts as a possible way a slow serve might hit

So, it appears a 55mph serve MIGHT hit a backstop, if it had the right trajectory. Just for closure, would you agree a 40mph serve has no chance of hitting a backstop on a single bounce unless the backstop is a fair bit closer?

Not so fast on these speeds.
Yes he makes them look pretty easy, but those serves are coming off pretty good. Speed trac on the ground near the net is going to read far slower than what we are comparing when looking at off the face numbers of the pros considered the standard. The pick up angle is not good and the distance is very poor.

Given the article I posted earlier, which showed where a 120 serve is about 82 around the net, indicates about a 1/3 mph loss, and this doesn't even account for the poor pick up angle of the speed trac on the ground.
Using this 1/3 drop in speed would mean that a 65 mph serve would be about 95-99 off the racket. This is clearly in the 100 mph range discussed on the rule of thumb.

Common sense dictates that for a rule of thumb dealing with a normal flat first serve attempt,
you would be doing things standard, going down the middle of the box,
And going solidly into the fence.
Not special spins, or
just catching the T down the middle,
or having bounced 4-5 feet and dropping forever only to catch the bottom edge of the fence,
(a fence short of 22' is close to the standard of 21'.)

No, this rule of thumb won't work for every bast**dized exception one can come up with. We can argue this forever I guess, but till more folks get to hit on a quality measurement system on an ATP setup and see how easy it is to hit 100.
People only think it is sooo hard cause of these little speed trac machines that are so hard to set up even to get with 10% accuracy.
I still think that the rule of thumb is very useful if used with common sense and in the circumstance it is intended.
Jolly, thanks for your effort to clear it up some, but I think in the end, few see things different than they did to start with.
Maybe steady eddy now sees that his speed trac placed at the back fence gives him a number to double to get close to what the speed off the face was.
You did a nice job of collecting data and presenting it for us and I guess there will be quite a lot of interpretation on what it means.
At least maybe you proved how silly the 40 mph number is.

 

[raiden031]

Not so fast on these speeds.
Yes he makes them look pretty easy, but those serves are coming off pretty good. Speed trac on the ground near the net is going to read far slower than what we are comparing when looking at off the face numbers of the pros considered the standard. The pick up angle is not good and the distance is very poor.

Given the article I posted earlier, which showed where a 120 serve is about 82 around the net, indicates about a 1/3 mph loss, and this doesn't even account for the poor pick up angle of the speed trac on the ground.
Using this 1/3 drop in speed would mean that a 65 mph serve would be about 95-99 off the racket. This is clearly in the 100 mph range discussed on the rule of thumb.

Common sense dictates that for a rule of thumb dealing with a normal flat first serve attempt,
you would be doing things standard, going down the middle of the box,
And going solidly into the fence.
Not special spins, or
just catching the T down the middle,
or having bounced 4-5 feet and dropping for ever only to catch the bottom edge of the fence,

No, this rule of thumb won't work for every bast**dized exception one can come up with. We can argue this forever I guess, but till more folks get to hit on a quality measurement system on an ATP setup and see how easy it is to hit 100.
People only think it is sooo hard cause of these little speed trac machines that are so hard to set up even to get with 10% accuracy.
I still think that the rule of thumb is very useful if used with common sense and in the circumstance it is intended.
Jolly, thanks for your effort to clear it up some, but I think in the end, few see things different than they did to start with.
Maybe steady eddy now sees that his speed trac placed at the back fence gives him a number to double to get close to what the speed off the face was.
You did a nice job of collecting data and presenting it for us and I guess there will be quite a lot of interpretation on what it means.
At least maybe you proved how silly the 40 mph number is.

What jolly should do is create his own speed cage where he hits the ball into a net that is just a couple of feet in front of him, where the speedtrac is right behind the net so that it gets a better reading. Then he should see how fast the ball goes on his normal relaxed motion and see how it compares to when he's hitting on a court with the exact same motion. There's a problem in that you can't see where the ball would land in the cage, but it might help demonstrate how much speed loss occurs between baseline and the net.

 

[5263]

hmmm, to be a 'net' measurement, I guess the measuring device should be pointed upwards.....................

this is eerie territory im walking in now.

So, what would be the speed of a Roddicks 140 mph serve:
a. Over the net?
b. Just as it is about to hit the court?

It would cross the net in the 100-105 range and
be in the 8o range just after the bounce.

just guess in around 90 just before the bounce, as that is a short distance from the net.

 

[Mike Cottrill]

Using this 1/3 drop in speed would mean that a 65 mph serve would be about 95-99 off the racket. This is clearly in the 100 mph range discussed on the rule of thumb. .

This is so ironic. J flicks a serve across the net and someone says he hit 100mph serve.

 

[5263]

What jolly should do is create his own speed cage where he hits the ball into a net that is just a couple of feet in front of him, where the speedtrac is right behind the net so that it gets a better reading. Then he should see how fast the ball goes on his normal relaxed motion and see how it compares to when he's hitting on a court with the exact same motion. There's a problem in that you can't see where the ball would land in the cage, but it might help demonstrate how much speed loss occurs between baseline and the net.

It's a good idea, no doubt,

but I can tell you that getting a speed trac within 10% of the off the face mph, is quite a challenge whatever you try.

We did a bunch of things, like mounting on a pole to get them closer to level with the contact pt, along with several methods of improving the alignment without getting the machine hit and all of these things helped to an extent,
but we cold only get to about 8-10% of a good off the face number.
They are great machines for under $200, but do have some limitations that are hard to get around. Or you could just say that the ATP stuff is really quite Awesome!

 

[5263]

This is so ironic. J flicks a serve across the net and someone says he hit 100mph serve.

So you don't think 65 on a speed trac set on the ground near the net would be about 95?
I do realize you have a lot of experience with this as well from the vid perspective and respect that.
I'm not just someone, but have traveled quite a bit with my son,
who won several fast serve contests,
(every one he was in)
who was known for having one of the fastest serve in his conference
as a freshman (div I)
So I too have quite a bit of experience in dealing with various radars, speed trac, jugs and a couple others.
Of course I should be used to the skepticism as we met quite a bit of it prior to leaving with the trophys.
At that point all the questions switched to how we trained, set, etc...

(i haven't worked with the newer ones, so maybe they have improved in the last 5 years- do we know how old Jolly's is?)

 

[Mike Cottrill]

So you don't think 65 on a speed trac set on the ground near the net would be about 95?

No doubt there is error with the speed track. No doubt the radar gun is not picking up the max velocity with the radar gun at that location. However, it is not picking up the speed at the net either. Also, keep in mind that the loss of speed as the ball travels through the air is not linear. Also, the faster the initial velocity the faster the ball loses speed.

BTW, those “ATP” readings go off the map sometimes too, just not as often.
Good luck to your son, sounds like he has got a real weapon.

 

[rfprse]

All this talk made me wonder. Which one is more accurate, the speed gun type or the one Jolly used? Is there any technique to get more accurate reading (closer to the speed of the ball right after its leaving the racquet)?

 

[5263]

No doubt there is error with the speed track. No doubt the radar gun is not picking up the max velocity with the radar gun at that location. However, it is not picking up the speed at the net either. Also, keep in mind that the loss of speed as the ball travels through the air is not linear. Also, the faster the initial velocity the faster the ball loses speed.

BTW, those “ATP” readings go off the map sometimes too, just not as often.
Good luck to your son, sounds like he has got a real weapon.

You have good points.
I had mentioned that I sort of figured that while the speed trac set at the net can pick up 7-10' out, that this is more than offset by the very poor angle it gets on the ground up there. We found placing it on a table to raise it when used at the net was significant.

I also made a post earlier about how much bigger the air resistance is at higher speeds and related it to bike racing. This would seem to support how one of the biggest losses in mph takes place in the first 10 feet off the racket, further supporting the toughness of getting a good number by placing the speed trac near the net. Moving it near the svc line was a big improvement for us.

Thanks about my son. He has lived many of the ups and downs of a big server in college tennis. While they have refs in college, there are rare over rules on 135 mph serves near the line.

 

[5263]

All this talk made me wonder. Which one is more accurate, the speed gun type or the one Jolly used? Is there any technique to get more accurate reading (closer to the speed of the ball right after its leaving the racquet)?

Some of the gun types tend to better but not all. Our bushnell worked pretty good.

The trick is getting in good position close to the contact point, without getting hit, LoL

Not to pick on Jolly, but the speed trac, on the ground near the net, is just not that useful really.
It would be ok for a % adjustment, but the angle is off so bad there, that it just gives quite a variation.
Dang sure beats nothing, assuming that you realize how much adjustment is required from there. If not
you become just another guy who thinks serving 100 is almost impossible for the club player. Jolly is one of the
rare ones who can clock a 109 with that set up.

 

[rfprse]

Some of the gun types tend to better but not all. Our bushnell worked pretty good.

The trick is getting in good position close to the contact point, without getting hit, LoL

Is it good to measure the speed at the diagonal position of the hitting point (obviously, the easiest way to avoid getting hit ), or does it have to be in line with the hitting point/ball trajectory (if so, is it ok to measure the speed from the back of the player or should it be in front of the player)?

 

[5263]

Is it good to measure the speed at the diagonal position of the hitting point (obviously, the easiest way to avoid getting hit ), or does it have to be in line with the hitting point/ball trajectory (if so, is it ok to measure the speed from the back of the player or should it be in front of the player)?

more in line the better unless there have some big improvements in equipment.

remember how even on the atp, the T serves always were the fastest. That was mainly due to angle error. Now with hawk-eye, the tracking systems can give more accurate numbers on the wider serves too, but they used to be off around 5% or so. Now you can see some 130 out wide, which almost never happened before.

It's just hard to do well.
That's why Mike C's video method is really quite good as it removes many of the problems.