Newton at Niagara Falls

[Jinx]

After a visit to Niagara Falls, I was puzzled by one observation. Shouldn't the path of the water make a significantly noticeable arch? Especially at the Canadian side, the water looks more like a hanging curtain. Maybe it's simply an illusion?

Considering that the river has significant velocity, I would expect the "arch" path to be more prominent. Of course, later in the free-fall, rocks interfere. But, just passed the brink, shouldn't significant arching be detected?

In short, I would expect the water to fall further out (away) from the brink. Even at lesser velocities, arching is observed. For example, using a simple garden hose placed horizontally against the top of the railing of a deck, with end aligned with edge of railing and pointed out to the yard, a noticeable arch is observed.

I've played with some numbers, guessing at reasonable river speeds, and the displacement in the y-direction should be substantial considering the distance of the fall.

I know...I'm standing on the brink myself, right? I should take a vacation when on vacation! :o

[tomndebb]

This may not answer your question, but have you considered that there may be an arching that you simply can't see? The river is between 3 and 7 feet deep at the edge of the precipice. Are you sure that when you look at what you perceive to be the edge, it isn't actually several feet behind and below the point where you're looking?

Another difference between the river and your analagous hose: the river is running purely on gravity, which means that the layer of water that is physically on the edge is being forced downward by all the water above the bottom layer. In a hose, the "shallow" depth of the hose stream means that there is insignifiant downward pressure on the stream as it exits the nozzle.

(I suspect that the very nature of the dynamics of water exiting a hose my also play a part, but I don't have any hydraulic theory to back that up.)

------------------
Tom~

[Jinx]

Tom, I have considered what you say, and I can only WAG that it must be an illusion of perception. I can only WAG that it is very hard to compare the arch against any reference behind the falls.

The second part of your answer addresses hydraulic pressure within the river due to its depth. But, once over the brink, the water is in free-fall and there would be no hydraulic pressure (static head) no matter how deep the river at the brink.

Strictly, the initial velocity in the x-direction governs. (I'm assuming all motion to be in the x-direction despite eddies, etc., etc. I think one would agree the motion is primarily in the x-direction up to the brink.) Also, from fluids, one would expect the top surface of the river to have a velocity vector of greatest magnitude.

Likewise, the garden hose pressure does not enter into a free-fall problem; water pressure simply grants some initial velocity in the x-direction.

[frolix8]

Jinx,
Your WAG is correct. The scale is large, and the arching takes place on a relatively small scale. The speed of the river isn't that great, the falling water quickly reaches a high veloctity in the Y direction

(Vy = -32ft*sec)), hence a steep angle (angle is ARCTAN(Vy/Vx)). We're used to seeing similar motion on a small scale, and we expect the path shape of the falling object to scale up, but it doesn't. The same faulty reasoning leads people to believe they can throw a ball incredible distances off the top of a building. The movies don't help because they will frequently film a scale model and try to pass it off as full size, after seeing enough of these scenes we think they're real.

[Jinx]

Thanks, Frolix8, but did you mean to say Vy is -32 ft/sec? Are you confusing velocity with acceleration due to gravity of 32 ft/sec^2? I believe you meant to mention that the water quickly reaches a terminal velocity, perhaps, in the y-direction? I haven't cranked the numbers real hard, but maybe it's just a coincidence? (Still, a terminal velocity in the "y" wouldn't impact motion in the "x" direction.)

You are correct, also, that it is hard to judge the speed other than "swift"! There are ways to find it, but the park authorities don't take too highly to that sort of thing!

[TBone2]

I'm afraid we're over-complicating the answer to the OP's question. References to movement in the x- and y-axes are on the right track, and the answer lies there.

For our purposes, the hydraulic properties of water are best ignored, since they're essentially irrelevant to the degree of a waterfall's arch. Instead, what we have is a pretty simple exterior ballistics problem.

First of all, what Jinx refers to as the river's "significant velocity" in the x-axis is less significant to the shape of the arch than one might think. Using average flows and depths, my calculator tells me that the water's average speed in the x-axis ranges between 2 and 6 fps at the brink. Given that, past the brink, the water accelerates in the y-axis in pretty much the same manner as any other falling body (i.e., at approximately 32 f/s/s), the x-axis speed loses its significance very quickly.

Thus, I'd have to conclude that Jinx's observation is a matter of perception or appearance, rather than some physical peculiarity of Niagara Falls.

The example of the water hose can be reduced to the exact same principle. The big difference between the water exiting the hose and the water falling at Niagara is simply the initial horizontal (x-axis) velocity. The water from the hose is traveling a LOT faster.

Tom, the water beneath the surface is NOT "pushed down" by the water on top. Hydraulic pressure at any point in a relatively still fluid body is omnidirectional. At the brink of the falls, that pressure disappears, but neither the pressure nor its disappearance has a significant effect on the motion of the water and, thus, the shape of the arch.

------------------
I don't know why fortune smiles on some and lets the rest go free...

T

[Jinx]

TBone, some questions: (A) You said that motion in the x-direction is less significant to the shape of the arch than one might think? I don't follow!

First, in every projectile (ballistics) problem, it is the x-velocity that determines the range. Range is displacement in the x-direction. The "y" direction determines how long the event will last. In this case, the time of the event can be found by relating the "y" displacement to acceleration due to gravity taking Vy=0 at t=0.

The longer the event, the more displacement in the x-direction, and the more arc noticed. (Surely you can recall, in physics, doing academic lab experiments rolling balls off tables and predicting the landing point.) I'm sure you noticed how the parabolic arc will have greater range as the velocity in the x-direction increases. No matter how small the x-velocity, there is displacement in the x-direction which is a parabolic arc, or virtually parabolic, but let's not split hairs! (Next, someone'll throw in Coreolis!)

(B) I find it very hard to believe the water from my garden hose, without a nozzle, is moving faster than the Niagara River! How did you come up with 6 ft/s? (~4mph)

[AWB]

<font color="#900000">frolix8: Jinx,
Your WAG is correct. The scale is large, and the arching takes place on a relatively small scale. The speed of the river isn't that great, the falling water quickly reaches a high veloctity in the Y direction
(Vy = -32ft*sec)), hence a steep angle (angle is ARCTAN(Vy/Vx)). We're used to seeing similar motion on a small scale, and we expect the path shape of the falling object to scale up, but it doesn't. The same faulty reasoning leads people to believe they can throw a ball incredible distances off the top of a building. The movies don't help because they will frequently film a scale model and try to pass it off as full size, after seeing enough of these scenes we think they're real.</font>

<font color="#009000">Jinx:
Thanks, Frolix8, but did you mean to say Vy is -32 ft/sec? Are you confusing velocity with acceleration due to gravity of 32 ft/sec^2? I believe you meant to mention that the water quickly reaches a terminal velocity, perhaps, in the y-direction? I haven't cranked the numbers real hard, but maybe it's just a coincidence? (Still, a terminal velocity in the "y" wouldn't impact motion in the "x" direction.) </font>

No, Frolix8 said <code>Vy = -32ft*sec</code>. A little miswritten, but the jist is that velocity is linear to the time of freefall; notice the "*" symbol is in there, not the "/" as you misquoted.

To be more acurate, the velocity at a given time t is:
<code>V(t) = g * t</code>
g being the acceleration due to Earth's gravity, 32 ft./sec2. So, after 2 seconds:
<code>
V(2 sec) = 32 ft/sec2 * 2 sec = 64 ft/sec.
</code>

------------------
Judges 14:9 - So [Samson] scraped the honey into his hands and went on, eating as he went. When he came to his father and mother, he gave some to them and they ate it; but he did not tell them that he had scraped the honey out of the body of the lion.

[TBone2]

Jinx, when I said that the x-axis velocity is less significant than one might think, I was referring to the specific problem you presented -- the x-axis velocity of the water passing the brink at Niagara Falls. The calculations are quite simple. Using an average depth of 5' at both falls, an average flow of 150,000 cfs at the American/Bridal Veil Falls and 600,000 cfs at the Horseshoe Falls, and a width of 1060' for the American and 2200' for Horseshoe, it's a matter of pounding a few calculator buttons to find an average horizontal speed of between 2 and 6 fps. Depending on when you were at the falls, flow could have been greater or less, depending on a number of factors, not the least of which is the pair of hydroelectric generating stations that siphon water from American when they're online.

The significance of the x-axis speed -- which remains relatively constant -- and its effect on the apparent "sharpness" of the arc is inversely proportional to the y-axis speed, which increases constantly over time. After only one second, for instance, the y-axis speed exceeds the x-axis speed by a factor of between 5 and 16.

I don't know what sort of projectiles you may have experimented with, but in any ballistics example I've ever seen, the "sharpness" of the parabolic arc is greatest close to the apogee. In the case of a waterfall, we may assume that the brink IS the apogee of the parabolic curve.

As to the speed of the water exiting your garden hose, consider a hose of 5/8" diameter (that's a big one) discharging just 10 gpm (pretty weak). Approximate speed of the water exiting the hose: 10 fps. Drop the hose diameter to 1/2" (more likely) and the same 10 gpm leaves the hose at nearly 16 fps. Even so, I think if you stood, hose in hand, on the top of an 18-story building (a rough equivalent to the height of Niagara), you'd be flat amazed at how quickly the sream assumes a nearly-vertical orientation.

------------------
I don't know why fortune smiles on some and lets the rest go free...

T

[TheDude]

I just performed the exact same experiment with a graphing calculator. If you have access to one I suggest you do the same. Graph y=-x2. This is a good enought approximation to the fall of an object. Focus on the range from y=0 to y=-4. You see a significant arc. Now zoom out to the range y=0 to y=-200. The arc is now almost completely gone. So it's simply a matter of scale.

TheDude

[Jinx]

Tbone, I see what you are saying, but using your data and the formula Q=vA, for the Horseshoe Falls, I get the river moving at 54 ft/s or about 37 mph which is a bit more believeable. Is this the formula you applied? Just curious. (I assumed the water was moving through an imaginary area with cross section of 5' x 2200'.) Did you lose a decimal place, perhaps, in your calc?

Overall, I can see where the acceleration downward quickly "outranks" the horizontal motion thus giving an almost plumb-vertical appearance. Mystery solved!

--------
They had me over a barrel on this one!

[TBone2]

Jinx:

OK, ya nailed me! I didn't exactly "lose a decimal place." What I did was quote the wrong units. The numbers -- 150,000 and 600,000 -- were correct, but the unit should have been gallons per second, NOT cubic feet per second. I apologize!

The conversion factor from cfs to gps is seven-point-something, I believe. (My hydraulics textbooks are in a box somewhere...) Since our calculations aren't likely to rearrange the world of physics, I think I just rounded it to 8. Dividing your result by eight yields 6.8 fps, a bit higher than the range I quoted. Using the American Falls data, I get about 3.5 fps at average flow -- 150,000 gps -- but that can be reduced by as much as two-thirds by the hydropower plants I mentioned before.

Incidentally, you're right there with most people in calling water moving at those speeds -- 2-5 mph -- as having "significant velocity." Water seems to be a substance we tend to think of as relatively static -- just sitting in a bucket or a puddle or a pond or a lake. Water moving at a walking speed is considered "fast-moving," simply because we don't often see water in such a hurry.

And TheDude, BINGO! It is, after all, a matter of scale. In the case of Niagara, if one were able to capture an image of the first, say, 10 feet of the fall, one would see a recognizable section of the beloved parabolic curve that Jinx longs for. But the other 17 stories of fall are going to look an awful lot like a straight, vertical line.

------------------
I don't know why fortune smiles on some and lets the rest go free...

T

[funneefarmer]

I'd say scale but I also want to chuck another variable in. While watching one of those home repair shoes on TV install some of the newest drip edging they show how the curve at the edge will direct the water down into the gutters while shooting the debris over the top of the gutters. Basically the water sticks to the metal drip edge and is thus directed down and back under to fall neatly in the gutter thus keeping debris out. Granted we're talking a much deeper stream and frankly I don't know whether there is any type of overhang to Niagara but couldn't the actual shape of the edge of the falls greatly effect the amount of arc ?

[TBone2]

Originally posted by funneefarmer:
While watching one of those home repair shoes on TV install some of the newest drip edging they show how the curve at the edge will direct the water down into the gutters while shooting the debris over the top of the gutters. Basically the water sticks to the metal drip edge and is thus directed down and back under to fall neatly in the gutter thus keeping debris out.

Funnee, it sounds an awful lot like bullshit to me.

H2O is both cohesive and adhesive, when it comes to flow and the ability to carry "debris." In other words, where the water goes, there goes the debris.

Harking back to my house-building days, I hasten to point out that "drip-edge" -- actually a molding (usually aluminum) that is fastened to the outside edges of roof sheeting -- is designed to (A) be covered by other roofing materials and (B) be exposed to only minute proportions of roof runoff. Its purpose is to protect the edge of the sheeting material (sometimes boards, sometimes plywood, but these days, usually "flakeboard," "aspenboard," or some such) from direct exposure to runoff water.

Since "drip-edge" is, by design and application, shielded from direct runoff, I suspect you saw something else. My imagination tells me that there could be some sort of screening or slotted affair that could segregate the water and the crud.

------------------
I don't know why fortune smiles on some and lets the rest go free...

T

[funneefarmer]

You're right it wasn't drip edge but here is what it looks like...
http://cgi.pbs.org/cgi-registry/wgbh/thisoldhouse/big_img.pl?is_id=9000235

[Billdo]

There may be another factor at work here. All of the calculations here have assumed the underlying rock structure at the edge of the falls is a perfect right-angle ledge. Even if it started out that way, I would think that that centuries of water passing over the edge has eroded it so that it now has an arch shape (or something else more hydrodynamic than a sharp ledge). Though it may look like a sharp ledge from the distance we view the falls at, the region of worn-away rock is probably at least as wide as the 10-foot or so maximum arc length of water from a garden hose.

[Jinx]

Billdo, I don't quite follow. The brink to the NY Falls, for example, is easily observed as being very uneven. No matter how far a piece of uneven "edge" would protrude, the act of falling does not commence until the water has no more support from the riverbed. The brink, regardless of profile, is the very end of the riverbed.

[Billdo]

Although the edge, on a macro scale is uneven, I imagine (and this is just imagination -- I haven't been to Niagra Falls in a looooong time) that ends of the edges over which the water falls have been eroded by time, rounding them out. This is in contrast to the sharp metal edge of a garden hose.

Imagine that you have water running off a shelf with a rectangular edge like a bookshelf. That water would arch off of the edge, standing off for a little bit like the water running out of the hose.

However, if the edge of the bookshelf had quater-round molding on the edge (in other words the edge were rounded down) path of the water would be a lot closer to the rounded edge of the shelf. The "support" that the shelf was giving the water would be gradually diminishing over the width of the curve. Therefore the water drop would start not at the "edge" that you perceive, but rather somewhere back where the rounding begins. Another way of looking at this is that the quarter-round molding attached to the edge of the shelf is just filling in with wood the air space under the "arching" water. (Note that I'm using quarter-round molding as a crude approximation of a parabolic arch.)

From a distance, it can be hard to see whether a shelf has a perfectly rectangular edge or a rounded edge, particularly if there is water rushing over that edge. Similarly, I don't think distance observation of Niagra Falls can clearly identify what the underwater edge looks like, and you're not getting me out there to dive down and see.

[Jinx]

Originally posted by TBone2:
Hydraulic pressure at any point in a relatively still fluid body is omnidirectional.

Hmm...this gives a false impression. Take a tank of liquid or the ocean. The hydrostatic pressure increases with depth basically due to the weight of the fluid from above. Hydrostatic pressure will increase in small increments with depth. Hence, it is not equal in all directions.

[Zor]

Jinx, there's nothing wrong with TBone2's statement alone. Notice that TBone2 had specifically referred to a given point in water, and it is corerct to say that point of water exerts the same amount of pressure in all directions.

I think it's clear that you can't find out how far the warter lands because you're lacking a variable altogether. You know the flow rate, height of the fall, by you have no idea of it's speed/depth at the top of the fall. An estimate of 5 feet might sound right, but I wouldn't bet on it myself.

If you take 55 meters to be the height of the fall (general estimates are between 52 and 57), then the water will reach the bottom in 3.35 seconds. A current of 5 miles per hour would result in the water falling 7.4 meters away from the base. If the actualy current were 30 miles per hour (which isn't unlikely), the distance would increase to 44.7 meters. Comparing those figures with the height of the falls, I doubt the difference can be neglected.

The rock formation factor can probably be ignored in these calculations though. It's pretty well known that the edge of the fall looks roughly like a "T", with the water flowing across the top. The edge is of coruse rounded at the corner of the "T", but it doesn't go so far as to become a "D" shaped fall.

Now if one of you could just hike over and stick a yardstick on the top of the falls....

[Jinx]

Originally posted by Zor:
The rock formation factor can probably be ignored in these calculations though. It's pretty well known that the edge of the fall looks roughly like a "T", with the water flowing across the top. The edge is of coruse rounded at the corner of the "T", but it doesn't go so far as to become a "D" shaped fall.

Now if one of you could just hike over and stick a yardstick on the top of the falls....

I'll hold your ankles...but, seriously: I agree the formation can probably be ignored, but the brink of the American Falls is quite jagged with some places protruding out a little further than others...as opposed to the "T" profile. Of course, despite the jagged edge, the "curtain" of water appears rather uniform overall.

Also, the Horseshoe Falls carries the bulk of the load - so to speak. Due to erosion, the brink has a profile in keeping with the name. It could be said to somewhat resemble the "D" shape, or perhaps a backwards "C" shape.

[funneefarmer]

Niagara river -212,000 cubic feet/second.

Check out the site... http://www.iaw.on.ca/~falls/origins.html

Check out the sections on Erosion and Power of Niagara for all the info on the underlying rock, rate of flow, and the rate of erosion etc.

Wow! What a great thread! And not a single flame! I'm going to nominate you guys as the, er, poster-boys for the SDMB! ;)

Seriously, thanks for an interesting discussion. Just wanted to let you know there are lurkers out there (who wouldn't DARE try to get involved discussing the math!) who appreciate you!

-Melin

[Billdo]

Thanks for the link funnee. I was particularly interested by the first photo "The jagged edge of the American Falls," which can be expanded by clicking on it.
In looking at the drops seen in the center of the photo it seems clear that the water is falling in some sort of arch pattern, but that the lower part of the arch quickly approaches the nearly vertical. This would be logical because the horizontal velocity of the water would eventually overwhelmed by the exponential effects of gravity on the vertical velocity. (How quickly, however, remains an important question at the heart of the OP.)

However, looking at the top portion of a drop pictured in the foreground, it appears that the underlying rock does have a curved aspect leading into the edge of the drop. This would be a logical pattern of erosion. (I was actually surprised at the relatively rapid rates of erosion and geological change described in the website.)

Thinking of the garden hose sitting on the top railing of the deck example in the OP, after you ran enough water out of it, the bottom of the metal or plastic hose fitting would become eroded away, and then the wood (or whatever) railing of the deck until rather quickly (in a geological sense) you would have a nice channel shaped like a parabolic arch at "deck edge falls," and the water would run down the channel without any visible arching (i.e. there would be no air space between the arch of the water and the arch of the channel. In other words, given enough time, the underlying structure should erode to conform to the water's "natural" parabolic arch (subject, of course to variations in materials, etc.).

Another potential impact is the reduced flow over the falls due to upstream dams and hydroelectric plants. This would reduce the horizontal velocity of the water in the falls. If the prior rock channels or arches had been cut (eroded) during a period of higher flow, they would be "wider" for any given vertical distance because of the greater horizontal distance. If the flow rate decreases, the horizontal velocity over the falls will consequently decrease (assuming a constant cross-sectional area). In the century or so that the river has been artificially impeded (an eyeblink or so in geological time), the water would most likely gently roll off the "too wide" channel, rather than go spurting off the edge of the "too narrow" drop in your garden hose example.

Another factor raised by the website is the seasonal variation in river flows. Perhaps you saw the falls at a time of relatively low flows, and there might be some noticable arching at a time of high water flow?

[TBone2]

My natural inclination is to get radically offensive and denounce the lot of you as being imbeciles. My natural inclination is not FAR off that mark, but patience is a virtue, and mine with you must be a virtue worthy of the gods.....

All that has been said about the wearing down or 'rounding' of the brink at Niagara may or may not be true. Likewise, speculation as to the depth of the water at the brink at any given point is just that -- the true average depth is not accurately known. (I made the mistake of accepting the average of a poster's estimates -- 5'.)

But the flows I mentioned are verifiable, as are the lengths of the falls. Even if we were to assume a 1' depth, the maximum x-axis velocity would be increased by a proportional value of 5, to 35 fps at most. (I strongly doubt that this sort of speed ever happens.) The water falling from the 'brink' would very quickly match that speed in the y-axis, and AGAIN the expected 'arch' would suffer.

Billdo and Jinx could very well be on to something, although I haven't the slightest idea what that might be..... ;)

Yes, regardless of depth, regardless of flow, one could expect that the brink at Niagara would be somewhat more rounded than the right-angle precipice we all may have imagined. Theoretically, that rounding could/should/would make a difference in the configuration of the the arch. In fact, it most certainly does.

To the extent that the bedrock underlying the brink is rounded, that is to the extent that the riverbed drops in the last few feet, the apparent arch of the falls is reduced. With its own fall, the riverbed reduces what apparent arch there may have been, by accomodating a certain amount of vertical acceleration.

But in any case, I can't abandon my position that the primary reason for the near-vertical appearance of a waterfall is the fact that the water is falling near-vertically!

------------------
I don't know why fortune smiles on some and lets the rest go free...

T

[Zor]

Perhaps my "T" isn't a good example. Maybe a "C" would be better, where the water is flowing across the top from left to right. This phenomenon is in fact very common for waterfalls across the globe. To explain this formation, you have to start from the beginning. I'm going to make an attempt with some crude ASCII drawing, so please don't laugh. If you aren't using fixed width font, this is going to look terrible. I suggest you copy and paste the whole thing to a small text editor like Notepad in that case.


Legend:
@ Water
- Softer Rock
# Harder Rock


Phase 1: River forms and begins to fall off an edge of rock formation.

@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
------------------------------@@@
------------------------------@@@
##############################@@@
##############################@@@
##############################@@@
------------------------------@@@
------------------------------@@@
------------------------------@@@
##############################@@@
##############################@@@


Phase 2: The Soft rock is easily eroded...

@@@@@@@
@@@@@@@@@@@@@@@
@@@@@@@@@@@@@@@@@@@@@
--@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
-------------@@@@@@@@@@@@@@@@@@@@
##############################@@@
##############################@@@
##############################@@@
----------------------------- @@@
---------------------------- @@@
----------------------------- @@@
##############################@@@
##############################@@@


Phase 3: Finally the riverbed is depleted of the soft rock and now consists mainly of hard rock, and the rock formation below the fall turns into a "C".

@@@@@@@@@@@@@@@@@@@@@
@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
##############################@@@
############################# @@@
############################ @@@
------------------------- @@@
------------------------ @@@
------------------------- @@@
############################ @@@
############################# @@@


So there... If there were more layers below, the softer rock will still be eroded faster, leaving the harder layers sticking out.

I hope that wasn't too ugly...

[Zor]

Ewe... get your Notepad out I suppose...

[Billdo]

Originally posted by TBone2:
But in any case, I can't abandon my position that the primary reason for the near-vertical appearance of a waterfall is the fact that the water is falling near-vertically!


TBone, I agree with you that the water falling off the waterfall quickly goes to a near-vertical drop for any reasonable value of horizontal velocity. However, my understanding of the part of the the question that I am answering (your conclusion about what I'm trying to say and whether it makes any sense may vary) is "why doesn't the water cascade off of the falls with a large air pocket behind it?" I think that the roundedness of the cliff edge makes a big difference in the way the water behaves, changing it from a problem in pure ballistics into one involving some combination of ballistics, geology and hydrodynamics.

Which brings to Zor's illustrations (which are much improved by putting them in a fixed width font). I hadn't thought about a stratified geology of the river bank. My assumption was that the river was some theoretical homogeneous rock, though of course it isn't. I'm not sure how this would affect the ballistics/hydrodynamics of of the waterfall. As I understand your illustration the rapid erosion of the soft rock and the adhesion of the water to the cliff face would actually draw the water back in for a bit to a more than vertical position, totally screwing up anything like an arch. Interesting.

I realize that I am hopelessly out of my depth in here in this combined discipline problem, and the only way to resolve the issue is to actually go over Niagra Falls in a barrel. You first.