How fast is a football going as it leaves the punter's foot?

[sj-roc]

Ever wonder how many miles an hour a football is travelling when it leaves the punter's foot?

So have I, so I just did some quick calculations to figure this out. (Just skip to the big font below if you want :P)

Let's assume the punt travels 60yds (say, 45 from LOS plus another 15 behind where the punter stands) with a hang time of 4 seconds, and let's neglect the effects of wind and air resistance.

The ball travels in two dimensions at once: horizontally (parallel to the plane of the field), and vertically (perpendicular to the field) as it rises and then falls in each half of its trajectory.

So let's consider the horizontal motion first. It turns out that under our assumptions, the ball travels at constant speed along the horizontal direction, and this constant horizontal speed is just the 60yd distance divided by the 4 second hang time. If you convert all the units it comes out to about 31 mph.

But this isn't the full story — because as I mentioned, the ball doesn't travel horizontally as it begins its flight but rather at an angle, perhaps somewhere in the 30-60 degree range. So you need to consider the vertical motion, too. So, what's the vertical velocity?

There's a well-known physics equation that gives the vertical height h of the ball above the field at some time t after launch, a relatively simple one: h = v.t - (1/2).g.t^2

... where the dots just mean multiplication, v is the initial vertical velocity of the ball and g is just a well-known constant number that governs how strongly gravity attracts an object back to the earth's surface as it travels through the air. It doesn't matter whether the object is a football or a feather or a battleship — the number g is still the same, it's basically a fundamental property of our planet Earth and only depends on what units you're working in. If you want to measure things in miles and hours then this value turns out to be around 78973.

Now we know that h = 0 when the ball comes back down so we can use that with the 4 second hang time for t and determine from the equation above that in this case v = 44 mph at the moment it leaves the punter's foot. Obviously it doesn't stay at the same 44 mph indefinitely — unlike in the horizontal part of the motion — or the ball would leave the earth's atmosphere and eventually even the solar system, our galaxy and beyond! Nope, the effect of gravity is always present so that the 44mph speed gradually drops to zero as the ball rises to its apex. Then the ball starts picking up downward speed and drops vertically at 44 mph once again as the punt returner catches it. This actually neglects the slight height difference of the ball when it's kicked and caught; in reality the ball being slightly higher at its catch point means that at this latter instant, it will be dropping vertically at somewhat less than 44 mph.

So at the start of its flight, the ball is going 31 mph along the horizontal and 44 mph along the vertical. But what's the speed along the line of its initial launch, along that 30-60 range angle I mentioned?

That's actually simpler to determine than you might think. Remember that old pythagoras formula for finding the long side of a right-angle triangle when you know the two sides that form the 90 deg angle? Turns out you can use that one for speeds, too.

So the answer is just the square root of 31*31 + 44*44.

Do the math and you get:

About 54 mph.

Bonus question: How high in the air does the ball go?

Easy. We already found that it starts at 44 mph along the vertical, so we just go back to that h formula with v = 44 and use t = 2 seconds (i.e., ball height maxes out halfway through the hang time). So the answer is:

About 64 feet.

Anyone have any idea how high above the field the BC Place scoreboard is? Lions4ever posted a Sun article Wednesday about WB wanting a single all-purpose kicker, with a quote from Paul McCallum that he saw Richie Leone — our latest kicking prospect pending whatever NFL opportunities come his way — hit the scoreboard in practice this year.

Obviously both of the above figures are only approximate values that neglect the effects of wind and air resistance as I said at the outset. Taking wind into account, the ball will obviously launch faster (or slower) if the wind is blowing on the punter's back (or in his face). The presence of air resistance on the other hand means (with all else equal) that the ball will always launch faster than 54 mph to overcome these counter-acting effects while still travelling the full 60yds from the punter's foot in 4 seconds. For equal launch velocities in a vacuum versus calm terrestrial conditions it will also reach a lower apex in the latter case, less than 64 feet as air resistance will oppose the ball's motion at all points along its trajectory.

It of course depends on the exact distance and hang time of the punt, with the hang time being a more sensitive factor than the distance. As most football fans know, kickers who can put a long hang time on the ball are valued for giving the cover team plenty of time to get downfield to help avoid surrendering a long return. In the CFL, it might also be a factor on surrendering a long MFGR. Not only are the on-field personnel for FGAs generally not the same adept cover group used on punts and kickoffs, but there's also no premium on long hang time to get the three points.

I don't know if anyone has ever bothered comparing hang time data for FGAs with those for punts and kickoffs — you'd obviously have to control for kick distance, and perhaps preferably examine numbers within the stats of individual all-purpose kickers and then look for trends among such kickers — or if kickers consciously try to alter the hang time in specific ways under different scenarios, but it would be interesting to see how the numbers compare.

[Toppy Vann]

I'm not a physics sort but 54 mph sounds reasonable but I can imagine a very hard kicker can hit a ball that is moving faster than up and then coming down would be upwards of that too.

Soccer kicks are 40 -60 and some have hit just over 100.

[WestCoastJoe]

I'm not a physics sort but 54 mph sounds reasonable but I can imagine a very hard kicker can hit a ball that is moving faster than up and then coming down would be upwards of that too.

Soccer kicks are 40 -60 and some have hit just over 100.

My first thought was the 100 mile per hour fastball, and that a punt would be considerably less than that.

Without looking it up, I recall vaguely the scoreboard in the SuperDome. Ray Guy hit it a few times pre game. He was apparently the first punter able to do that.

Ray Guy was an astute draft pick back in the day when Al Davis was still a sharp operator. It was considered an out of the box decision to draft a punter in the first round. All the way to the Hall of Fame.

Edit. 1976 Pro Bowl. Video screen raised as a result. (Wik)

And from the Wik, Guy was a Safety in college, and he replaced George Blanda as the Emergency QB for the Raiders.

Anyone have any idea how high above the field the BC Place scoreboard is? Lions4ever posted a Sun article Wednesday about WB wanting a single all-purpose kicker, with a quote from Paul McCallum that he saw Richie Leone — our latest kicking prospect pending whatever NFL opportunities come his way — hit the scoreboard in practice this year.

At the 1976 Pro Bowl, Guy became the first punter to hit the Louisiana Superdome video screen. Officials raised the screen from 90 feet to 200 feet. The NFC team pulled the ball and had it tested for helium; it was filled with regular air. -- Wik

[Tighthead]

It was always a pretty good test of bravery in rugby to try to block a kick from hand.

50-60 mph sounds about right. There has to be something on the web about it.

[South Pender]

Very interesting thread. It got me to thinking about the typical speed of a pro forward pass that is being gunned into a tight window. (Not my intention to take this thread off-topic, but thought that since the topic was velocity, this might fit here.)

Anyway, I ran across the following article, detailing the clocked speeds of a number of college and NFL quarterbacks at the NFL combine (where they have a radar gun for this purpose).

It appears that these fast balls go close to 60 mph. Not surprising that most receivers these days wear gloves! I recall discussions of Brett Favre's fastball and bruised hands of his receivers. I also recall talk many years ago of the Bombers' "Indian" Jack Jacobs (I guess today it would be "First Nations Person" Jack Jacobs!) throwing so hard, guys tried to get out of the way!

This article gives the 10 fastest clocked speeds of players at the combine. Interestingly, two of the guys on the list--tied at 8th with a 58 mph pass--are now in the CFL: Mike Reilly and Drew Willy.

http://www.cbssports.com/nfl/eye-on-foo ... stest-pass

[TheLionKing]

Must be a slow day sj-roc While you're at it, what effect does cold weather and frozen football have on the speed ?

[sj-roc]

Very interesting thread. It got me to thinking about the typical speed of a pro forward pass that is being gunned into a tight window. (Not my intention to take this thread off-topic, but thought that since the topic was velocity, this might fit here.)

Anyway, I ran across the following article, detailing the clocked speeds of a number of college and NFL quarterbacks at the NFL combine (where they have a radar gun for this purpose).

It appears that these fast balls go close to 60 mph. Not surprising that most receivers these days wear gloves! I recall discussions of Brett Favre's fastball and bruised hands of his receivers. I also recall talk many years ago of the Bombers' "Indian" Jack Jacobs (I guess today it would be "First Nations Person" Jack Jacobs!) throwing so hard, guys tried to get out of the way!

This article gives the 10 fastest clocked speeds of players at the combine. Interestingly, two of the guys on the list--tied at 8th with a 58 mph pass--are now in the CFL: Mike Reilly and Drew Willy.

http://www.cbssports.com/nfl/eye-on-foo ... stest-pass

Nah, not OT at all. I just discussed punting specifically, because two of the main parameters of a punt — hang time and distance — naturally lend themselves to a kinematic analysis where the launch speed can be estimated. For me, that's more fun than just reading a number from an instrument panel If it seems they don't measure the speed of punts in this fashion, it's probably because the trajectory of a punted ball is tougher to control than that of a ball thrown presumably at a target, where the radar gun is aligned more or less right along the (short and relatively straight line) flight path of the ball. This is probably more difficult/less practical to arrange for punts.

[notahomer]

There is a book I've had my eye on that may interest some of you. Can't vouch for it because I haven't gotten around to reading it (YET )but the title alone caught me eye.... came out in 2013 and its called "Newton's Football" and is supposed to explore some of the science behind the game (probably from an NFL/NCAA point of view of course...)

[Hambone]

Must be a slow day sj-roc While you're at it, what effect does cold weather and frozen football have on the speed ?

Not to mention humidity, elevation and gravitational pull.

[Coast Mountain Lion]

Must be a slow day sj-roc While you're at it, what effect does cold weather and frozen football have on the speed ?

Not to mention humidity, elevation and gravitational pull.

You forgot salinity, Captain.

[aklawitter]

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anybody want to make the claim that punters aren't athletes now?

[Hambone]

Must be a slow day sj-roc While you're at it, what effect does cold weather and frozen football have on the speed ?

Not to mention humidity, elevation and gravitational pull.

You forgot salinity, Captain.

Doh!

[sj-roc]

anybody want to make the claim that punters aren't athletes now?

Nice vids. I redid the calculations from my OP on a couple of the better punts in the 2nd vid and found they were launching around 67 mph and getting to heights of about 130 ft or so. Putting plenty of air under them!