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I know how hyper focal distance works in theory and I got the PhotoPills app. My question is though, let's say you're overlooking Grand Canyon. You want to capture everything from the bottom of the canyon to infinity. With 24mm f11.0 you know you need to focus at 5'8'' according to the app. However...there is nothing within your vicinity to focus on. The closest object in your shot is the bottom of the canyon floor which could be 5000 feet down.
So where do you focus in this scenario?
You could focus at infinity and still get everything from a few dozen feet to the horizon within DOF; in this situation, that's what I'd suggest. Your horizon and everything a mile or more away will be (very slightly) sharper than it would be at hyperfocal, and there's nothing closer in frame to be concerned about.
Hyperfocal is about maximizing the range of things that are in focus. If everything is far away, it doesn't really apply, so just focus on these far away things.
The focused distance is the point of maximum sharpness in your image. Anything else is out of focus to some degree.
The purpose of hyperfocal focus is to have depth of field from infinity back to half of hyperfocal. Which can be wonderful if there is purpose for that. But if no purpose, then of course, instead focus on your subject.
If the closest point is 5000 feet, and there is nothing closer, it would be foolish to focus at 6 feet. Focus at 5000 feet (which is infinity). Focusing on your subject would be greatly better for that subject.
But if using hyperfocal, then step back a bit and include someting on the near rim on which you are standing.
If you focus at ∞, the size of your blurring will be 24mm/F11=2.2mm at whatever distance an object is at. You say the closest may be 5000ft down which is 1524m. Those 2.2mm will, at 24mm focal width, map to a distance of 35nm on the sensor. Diffraction will do a much worse job than defocusing here. Actually, a wagonload of other issues will do a worse job than defocusing. It would be actually quite wondrous if the focus could be anywhere near as precise as that.
If you maintain aperture number while increasing focal length, the blur disk will grow in proportion with the focal length, and its depiction on the sensor will also grow by a similar scale, so at 240mm focal length, you are already at 3.5µm of disk size. If you have a sensor that is 36mm across (namely full-frame), we are still talking about 1/10000 of the sensor width. So unless you have a 60MP sensor, this would still be not realistic to detect. And if you have a 60MP sensor, again diffraction at F11 should be a larger problem.
At any rate, the hyperfocal distance gives you a worst case scenario, a distance where focus at infinity will still be acceptable. If you focus farther than the hyperfocal distance (but not farther than infinity, something which optics could easily do), the blurring will become less, not more. And your hyperfocal distance calculation more likely than not is not based on a 60MP full-frame sensor...
Hyper-Focal Distance, Depth-of-Field (DoF) and Manual Focus
The idea of the hyper-focal distance is that it is meant to maximize the area that is within generally acceptable focus (not perfect focus... just pretty good).
With older cameras and lenses, it was much easier to find hyper-focal distance -- no applications or charts needed because everything you needed to know was printed on the lens.
Here's a camera focused to "infinity":
Notice also that the aperture ring is set to f/22. But also notice that the lens barrel as DoF marks between the aperture ring and focus ring. The circled area has the values
22 16 11 8 4 | 4 8 11 16 22
That's the built-in DoF table... since the aperture ring is set to f/22 it means we'll use the "22" marks on the DoF scale ... and match those up agains the distances on the focus ring.
Trivia: There's a tiny red dot next to the number "4" to the right of the focus mark. That's the "IR" mark... when shooting IR file, focus the camera for visible light, then rotate the focus distance to the red dot.
The focus is set to "infinity". Looking to the "22" to the left, you find that it matches up between the 10' and 15' marks on the imperial distance scale -- or between the 3 and 5 meter marks on the metric scale. This indicates that everything from roughly 12' or 4 meters ... or farther ... will be in acceptable focus.
But ALSO notice that there's a "22" to the far right... well-beyond the infinity mark. That's all the stuff that will be in focus "beyond infinity" and since nothing is "beyond infinity" ... that's just wasted range.
So here's another image:
This time, notice that I've circled the fact that the aperture ring is set to f/22 ... so I have adjusted the focus ring such that the "infinity" mark is aligned with the "22" on the far end of the focus.
Using this setting nothing "beyond infinity" is in focus... just everything up TO infinity is in-focus.
But now look at the "22" DoF mark on the left and you'll see it's between the 5' and 7' marks (we'll call it 6') and between the 1.5 and 2 on the metric scale (we'll call it 1.75 meters).
This improves upon how close something can be and still be in acceptable focus. This means we have maximized the range of distances for which things will be in acceptable focus without wasting focus on things that are "beyond infinity".
No nearby subjects
If you don't have any subjects nearby where you care about focus... then you don't need all of the DoF offered by focusing to the Hyper-Focal Distance. So... just focus on the nearest subject you can find beyond the Hyper-Focal Distance. You wont maximize your range, but you wont care because nothing closer is in the frame.
Auto Focus Lenses
The camera lens in the image that I used was a manual focus lens. Auto-Focus lenses present a new challenge. Since they are auto focus lenses, few photographers use them in manual mode. And since few photographers use them in manual focus mode, many of these new lenses no longer include DoF marks. Some lenses don't even put a focus ring that includes distance marks. This means that for some lenses manual focus is a wild guess.
If your lens has a marked focus scale or focus window, you can switch to manual focus mode and focus to any distance at or slightly farther than the Hyper-Focal distance.
If your lens does not have a marked focus scale, you're going to have to take an educated guess.
In taking that guess, if you pick a point and use auto-focus ... make sure your camera is not in continuous focus mode (e.g. not using Nikon AF-C or Canon AI-Servo mode) ... use Nikon AF-S or Canon One-Shot mode (or equivalent depending on your camera vendor) so that once you lock focus on the focus point you can re-point the camera without it re-focusing.
Short answer:
When the foreground of the scene is further away than the hyperfocal (as in the case presented in the question), focus on the foreground, as a result the whole scene will be in focus.
In fact, any focusing distance greater than the hyperfocal will get, in this case, the whole scene in focus. Focus on the foreground, as proposed above, is simply practical. And it seems to me that this is what a camera does in autofocus auto mode (i.e. when you let it choose where to focus) at least for the less sophisticated camera.
Long answer:
The explanations that follow are a little long but allow to come back to certain points that must be perfectly assimilated. The most important of these point is the two definitions of sharpness.
I. Shapness / Sharpness Range - Depth of Field / Hyperfocal
a. Shapness
There are two possible approaches to the sharpness in digital photography:
The first approach (hereinafter referred to as "digital") leads to take into account the size of the sensor sites.
The second is the legacy approach (hereinafter referred a bit misleadingly to as "film") , but it is still relevant for digital photography, as the view of humans has not evolved. Indeed, this definition of sharpness is based on the human visual acuity. As the eye has a limited power of resolution, any spot on the reproduced image (printout or screen) whose size is smaller than what the visual acuity can distinguish is interpreted as a point. The size of this spot on the reproduced image corresponds to the diameter of a circle on the sensor (or film), this diameter is what is called "circle of confusion". Obviously when, as can be done on a screen (pixel peeping), the image is enlarged, the assumption taken for the calculation of the circle of confusion is no longer valid.
It is therefore very important to determine what the objective is in terms of sharpness digital or film.
b. Sharpness Range - Depth of Field
When my focus is made at a distance D, some of the points located in front will result on the sensor by a spot whose size is smaller than the confuge circle, these points will appear sharp. The smallest distance for which these points appear sharp corresponds to the first sharpness plane. In the following, the distance to this plane is noted FSP.
Reciprocally, the last sharpness plane (LSP) corresponds to the distance beyond which the points will start to appear unsharp.In the following, the distance to this plane is noted LSP.
The space between these two planes (or the range of distances between these two planes) is the sharpness range also called "depth of field".
But remember, there are two notions of sharpness, therefore two notions of depth of field.
When a lens has depth-of-field markers, these markers are positioned taking into account "film sharpness".
By the way, some camera that indicate a depth of field scale in the viewfinder allow to choose on which of the two sharpness (digital ou film) notions the scale should be based.
There are formulas to determine FSP and LSP but the simplest call for the hyperfocal distance.
c. Hyperfocal distance
Note: the following is applicable to the common case (i.e. outside of macro photography) when the distance of the scene is much greater than the focal length.
The hyperfocal distance (H) is defined as the shortest focusing distance for which points at infinity remain sharp.
This distance is given by the formula H = f² / (N c) in which f si the focal length, N the f stop number, c the value of the circle of confusion.
With the hyperfocal, the formulas for FSP et LSP are FSP = D H / (H + D) and LSP = D H / (H - D) in which D is the focus distance.
Applying thess formulas, we find that for D = H then LSP = infinity, which is reassuring since this is how the hyperfocal; and also that FSP = H/2. Thus, by focusing at the distance of the hyperfocal, all the points whose distance is between half the hyperfocal and infinity are sharp. We can also see that for an focus at infinity, FSP = H which is just as interesting. It is also the second definition for the hyperfocal.
But again, remember that there are two notions of sharpness, therefore two notions of hyperfocal.
Reformulation the question
From the above, it is obvious that if the foreground of the scene is at a distance greater than the hyperfocal, any focusing distance between the hyperfocal and infinity will ensure sharpness at any point of the scene.
It is however interesting to reformulate the question as follows "For an aperture N, a focal length f, a scene in which the first plane is at the distance d1 and the last plane at the distance d2 (possibly infinity), at what distance D must the focus be made to ensure the best sharpness?"
To keep it short, D = 2 (d1 d2) / (d1 + d2), which gives for d2 = infinity, D = 2 d1.
II. Diffraction
However, the above does not take into account defects of the lens, nor especially the nature of the light which introduces diffraction. Simply put, when light passes through a hole, it spreads beyond this hole, the more as the hole is smaller.
Given the data provided (24mm, f/11, H:5'8''), we can deduce that you are using a full format camera. With an aperture of f/11, your image will be affected by diffraction if your sensor has more than 24M pixels.
As a rule of thumb , the "sweet pot" of sullframe lenses is around f/8.
Summary
So what I would suggest in the case described in the original question is:
Focus manually. Usually if you are using a wide lens you focus 1/3 of the way into the scene. If there is no foreround subject you have no reason to focus that close. Watch your angle.
