# (Updated) Why do vertical distances appear much larger than horizontal distances?

Note: I have reformulated this question and provided more concise examples to avoid confusion and allow for better discussion.

According to Google Earth, the distance from where the photo below was taken to the highlighted car is about 450 feet. Which, all things considered, is a short distance (for walking, driving, and flying).

Now, the images below were taken at 500 feet.

Corrected for the height of the flight deck. Credit.

It is difficult to grasp the idea that, if I could hypothetically walk downwards from those airplanes to the ground, I would travel the same distance as from where the first photo was taken to the car.

What causes the impression that vertical distances (such as the approach views above) appear much larger than horizontal distances (such as the street above)?

P.S. We find another great example of this illusion in the second photo, where the distance from the beginning of Runway 22 to the aiming point (two white rectangles) is 1000 feet. In other words, that distance is double the height of the airplane in the photo, while it appears to be way higher than that.

• For some reason I was staring at the second picture for a long time. It was when I realized where it is. I live in Campinas for almost 15 years now. :) Commented Oct 18, 2022 at 12:48
• How cool. I also used to live there. Commented Oct 18, 2022 at 14:47
• Can your question be paraphrased: Why does the runway look longer when viewed from a higher angle like the first photo, but look shorter viewed from a low angle like the second photo? Because the answer you accepted explains this perfectly, but that didn’t seem to be what you were asking. My interpretation was: Why does 500’ up feel higher than the 500’ markers look…” Commented Oct 19, 2022 at 14:56
• @Michael Hall: Not really. The runway is just an example. If you look down a 500-feet-long residential road, it doesn’t appear that long. However, if you are, for example, flying 500 feet above a neighborhood, it seems very high up, and not nearly the same distance as the aforementioned street. Commented Oct 19, 2022 at 16:24
• OK, but it's the angular effect you are asking about then, not the feeling of height being greater? For example, if I look at a 12" ruler from 90 degrees off it looks 12", but if I look at it end on, or nearly so, I can't perceive the full length correctly. Because if that's the case then I grossly misinterpreted your question and will delete my answer. Commented Oct 19, 2022 at 16:31

This is a psychological illusion, roughly similar to the one that makes the Moon look huge when it's close to the horizon, even though you can still cover it with a fingertip at arm's length.

Essentially, we're used to looking long distances along the ground (if you're standing on the ground, the horizon is around three miles/4.7 km away), and the way distances make objects look smaller -- but few if any of us grew up with enough flight experience to be equally used to looking down similar distances to the ground, or to seeing buildings, cars, runways, and farm fields shrunk by perspective the same way a skyscraper seen from the edge of a city is.

• Isn't the horizon more like ~3mi/5km for 1.7m eye height?
– Max
Commented Oct 18, 2022 at 13:49
• Ack, you're much closer to correct, formula says about 4.7 km over sea for a 1.7 m eye height. Commented Oct 18, 2022 at 14:00
• Refraction will do the last 300m ;)
– Max
Commented Oct 18, 2022 at 14:06
• Welcome new Max. ;) I decided to change my screen name to "Max R" today to disambiguate. Commented Oct 18, 2022 at 20:51

The problem is not the elevation; it's the angle you are looking at it. Looking from top down, you'll see the real proportions, while looking at 30° you'll see half the size (directed towards the line of sight). At 3° it's only a bit more than 5%. Technically it's the sinus function.

The size perpendicular to the line of sight is influenced by the distance only.

Here is a sketch illustrating the principle in 1D using a line instead of a 2D rectangle (note: I just used the center of the line; actually beginning and end have different angles and distances):

I used three sample points at the same height, but with varying distance, and a sample point at same distance (well: almost), but different altitude. You'll see that the line will be shorter when reducing the altitude much more than increasing the distance would. (I know: The sample should have been below the "Distance 92" point for better comparison)

Also not I used rather arbitrary scaling for reasonable numbers to compare: Viewing down at a distance of 100 would yield 100% virtual size.

## Alternative Illustration

The following illustration has a black element in the lower right that has equal horizontal (H) and vertical (V) size. Then there are three reference points:

• The blue starting point looking down at 45°
• The closer (but same height) red point looking mostly down
• The lower (but same horizontal distance) green point looking mostly forward

Colored lines illustrating the center (corner) of the black object, as well as the borders (front and top).

The rest is a bit complicated, so take the time to understand: The thicker more intensely colored lines attached to at least one corner of the black object are perpendicular on the corresponding view direction, thus a projection of the black object's sizes.

The colored letters H and V mark the corresponding proportions of the projected horizontal and vertical size, respectively.

So for the blue view H and V are equal size, while for the closer red view the vertical element seems much smaller than the horizontal one. Finally for the lower green view the vertical component of the black element seems much larger than the (projected) horizontal one.

## "3D" Illustration

Finally a "3D" illustration of the effect of lowering the altitude shortening the horizontal size (as explained above). The object looked at is a square with a "center cross", and the relative sizes should be correct (while the absolute size was "zoomed in a bit" to let you see some details):

I hope I got the mathematics right. The numbers right to each image are:

lateral offset (X),elevation (Y),distance (Z) (negative)@viewing angle (A)

The first three numbers are integers anyway, and the angle is rounded to whole degrees. The distance is constant the elevation increases (top to bottom, left to right).

• From the first photo, it does seem like the shrinking phenomenon is restricted to the dimension parallel to the line of sight, since both perpendicular dimensions (up-down and side-to-side) won't experience this angle-dependent shift. The runway in the photo is 150ft wide, about 1/3 the distance between touchdown markings, but it sure looks like a lot more than that. This explanation accounts for the observation that front-to-back distances shrink, but not side-to-side distances. Commented Oct 18, 2022 at 16:27
• @NuclearHoagie That's foreshortening -- you're looking at the runway at an angle, so the "vertical" dimension in your field of view is compressed by geometry, while the horizontal is shrunk only by distance. Commented Oct 18, 2022 at 18:58

Overestimating vertical scale isn’t limited to aviation, people often misjudge height above the ground. The reason you “feel” higher than you are is the effect of gravity. It is not a visual illusion, it is a psychological phenomenon - We are used to being anchored to the surface, and being elevated is an unnatural state so our eyes and brain process this information differently.

Although it is characterized as a “weak force” compared to magnetic and other forces, gravity exerts tremendous influence on our lives. It severely limits our travel in the vertical and imposes severe consequences for any misstep. Respect for its effects are ingrained in our DNA - A rational fear of heights is a good survival instinct, but it causes us to subconsciously overestimate actual vertical distance.

Consider the following examples: We think nothing whatsoever of walking 10’ across a small room. It takes little physical effort, and exposes us to minimal risk. However, 10’ up a ladder (not to the top of a 10’ ladder, but your feet 10’ off the ground!) is an entirely different story.

There’s not a lot of effort or risk as long as you are steady, but if you slip and fall gravity will accelerate you to bone shattering speed in the blink of an eye. You risk significant injury if you don’t land just right. Some people even fear jumping from 10’ into a soft medium like water, all rational people should fear stepping off their roof to land on their driveway.

Bump the example up tenfold: 100’ is roughly the length of supermarket aisle, while 100’ up is a significant climb up a very tall tree and risks probable death, or at least permanent physical disability as a result of severe injury if you fall.

Another tenfold: 1000’ is short walk down a rural road, a couple blocks of city streets, or the length or a mall. But 1000’ of vertical is an arduous hike for most, or an extreme climb to get to the top of a major Yosemite sized cliff. Falling is certain death.

The additional time and effort required to achieve displacement in the vertical, plus the danger element, skews our perception of this axis. There are no visual illusions causing us to be unable to accurately estimate vertical distance - Consciously we are just as capable of estimating dimensions in the Z axis as any other direction. Subconsciously, however, our brains perceive vertical distance differently because of the ingrained instinct to avoid falling.

• This doesn't really explain the visual difference between looking down 70+ floors to a street and looking three blocks along that same street -- but it's a good answer to the psychological side of the perceived difference. Commented Oct 18, 2022 at 19:01
• My point is that there is no actual visual difference, it's a subconscious perception. (unless you are referring to a horizontal layer of haze or other phenomenon...) Commented Oct 18, 2022 at 19:02
• We're saying the same thing, I think. We're not used to seeing the tops of cars or roofs of houses, but if you chopped down a tree to lie horizontally, or turned a car on its side, it would look very out of place from above, when you're seeing the tops of everything else. The "everything is smaller than it would be the same horizontal distance away" is a variation of the Moon Illusion, as in my answer. Commented Oct 18, 2022 at 19:06
• I agree things look different, but I'm not totally sure we are talking about the same thing... Our perception of something further away looking smaller is a function of the reduced angles causing the image projected on the retina to be smaller. It works the same way in all directions. Consider railroad tracks and a "vanishing point". Yeah, it would look out of place looking straight up or down a set of tracks, but the geometry is identical to horizontal tracks. Or am I missing your point? Commented Oct 18, 2022 at 19:12
• When you can see the perspective lines (like in a city looking along a street, or looking along a railroad track), your mind compensates for objects looking smaller at a distance. This is why the Moon looks huge on the horizon -- it's silhouetted behind several treetops, for instance, which you know to be large objects. When it's high in the sky, it's just a half degree circle with some texture inside -- unless a jetliner crosses its disk. Similarly, a car three blocks away doesn't look "tiny" because you can see the pespective, but from 500 feet up you can't compensate. Commented Oct 18, 2022 at 19:14

The perception of human vision is angular rather than linear. What our eye physically sees is an object that is 3 degrees wide. Our brains then use an assumption about the object's size to to estimate how far away it is, OR uses an assumption about how far away the object is in order to estimate its size.

A 747 10 miles away takes up as many nerve endings on your retina as a Cessna 172 that is 1 mile away. You look at the shape of the 747, you recognize it, and your brain is able to "reverse engineer" that it's a long ways away.

If you are standing a mile away from a runway, that runway still only "subtends" or "spans" a few degrees across your retina. That sends a powerful signal to your brain, "that's small."

If you are standing a mile away from an antenna tower the same length, it will literally subtend 45 degrees or more of your retina and sends a powerful signal to your brain, "that's big."

• This explains why things look smaller at a distance, but doesn't address any difference in perceiving distance vertically vs horizontally. Commented Oct 18, 2022 at 22:09
• This also explains why large planes seem to fly slower than small planes. Our brains can reverse engineer the size, but the angular speed is just too much to compute correctly. Commented Oct 20, 2022 at 16:09

A large psychological factor here is foreshadowed by Zeiss Ikon. Our perception of distance using focus or parallax is only effective up to about 10m from our eyes. A round dot 50m away looks pretty much like a larger round dot 50km away.

The moon looks larger on the horizon because there's reference points...maybe a city skyline, or some trees, but enough to see that, compared with these familiar references of known size, the moon is both larger and more distant. When well up in the sky, there's no visceral evidence to indicate definitively that it's much more than 10m away.

Similarly, your first picture shows sub-markings, access roads, other aircraft, scenery, and (I think) a train to provide size and distance references both beyond and between the marks. In the second, however, there is nothing between the plane window and the ground (which is in fact over 500ft distant, since the camera is not perfectly vertical). The mind registers that as >10m, and doesn't try too hard to improve the estimate, since height information is interpreted with heavy weight on "how bad would it be if I fell from here" and 10m isn't much different than 1km in that equation.