Saturday, August 3, 2013

The Toy Boat Problem

Here's a rule for you: When you're drawing boats on flat water, the horizon passes over every boat at the same height above its waterline.


The photo above shows several kayakers in a harbor. Each kayaker is overlaid with a graphic of a kayaker's silhouette multiplied three times to reach the horizon. Each of their boats is sitting about eight feet below the horizon. That's because the viewer is standing with the camera about eight feet above the water.

If you were drawing this scene, and wanted to add another kayak, whether close or far, you would have to make sure its waterline was also a little over three sitting man-heights below the horizon.
A boat placed at a given distance below the horizon must be of a certain size, and a boat of a certain size must be a certain distance below the horizon.

If you get this wrong, the harbor will be filled with toy boats. A lot of artists have made this mistake, even a lot of famous artists, such as Frank W. Benson (1862-1951). Mr. Benson has established that observer is about four feet above the water, because the horizon crosses about one head higher than the standing boy.


But if we apply that measure to the rowboat to the left, we have a problem. That rowboat now looks four feet long. If you stand it on end from bow to stern, it would just reach from the waterline to the horizon. The rower would have to be just one foot tall. And the figure in the the sailboat at right would have to be the size of a GI Joe.

Will you forgive my effrontery in revising Mr. Benson's perspective? Here's a corrected version. I raised the sailboat and also raised the rowboat and made it bigger. If you prefer that rowboat to be smaller for compositional reasons, that's OK, as long as it intersects the horizon in the right place.


Edit: Since so many people asked about the Loomis explanation of this principle using figures on land, I have added them here. Thanks, Ben!

Related post: Tiny Train

32 comments:

Joshua Hendry said...

Ok, visually I understand that this looks better, but I am confused about the three silhouettes for each kayaker and your use of the term horizon. I think of the horizon line, but don't think that is what you're talking about.

Nick Russell said...

Joshua, I believe he refers to the horizon line not only as a line off in the distance but also a plane that extends from the viewers eyes to the far off distance. In the case of the Kayakers photo, this plane would always be eight feet above the water. So stacking the kayakers three times at any distance will always yield eight feet in height. I hope that makes sense, and correct me if I'm wrong James.

James Gurney said...

Joshua, yes, Nick has it right. "Horizon" and "eye level" are the same thing here. I have redone the first visual to add a horizon line in red.

Rubysboy said...

I'm confused. Firstly, the horizon line (or plane) visibly does NOT intersect (cross, come in contact with) any of the kayaks in the picture. So I guess the meaning is "the distance between the boat's waterline and the horizon plane." So this distance is the same in space, but in the picture further boats will be closer to the horizon plane, adjusted for perspective, so it's not clear how this principle helps the artist to position and size the boat. And I completely miss the point of the 3X magnification. I must be obtuse, but I'm not getting the message.

Ted Renteria said...

The horizon is defined as where the sky meets the ground, assuming we are describing a seemingly endless ground plane. Typically, the "horizon line" is associated with "eye level", assuming that the viewer is standing on the flat plane, looking straight toward the horizon, as we make the assumption that the line of sight is parallel to the ground plane.

This is a convenient method to explain the basic theories of perspective and principles of applying the basic technical methods in drawing, so that it (object or scene) "appears" to look "realistic".

Ted Renteria said...

BTW, this is a great analysis of Frank Benson's work.

James Gurney said...

Rubysboy, you're right: the horizon doesn't intersect the kayaks in this case, and perhaps I didn't define it clearly enough. I guess I meant to say that the distance from the waterline to the horizon (or eye level) is constant for every boat. I like to think of the horizon eye level as a 3D plane that runs parallel to the water surface, slicing through boats, or flying above them at that constant distance.

Thanks, Ted

Joshua said...

Rubysboy, part of the point is that the position and size are interrelated. If you know how big you want it to be on the canvas or paper, that determines how far below the horizon it has to be placed in order to appear to scale; if you know how far below the horizon line you want to put it, that determines how big it has to be drawn. That works because the waterline for every boat is on the same plane in calm water.

If you only know how far back (in depth) you want it to be from another boat, I believe you need to draw some receding lines and use them to scale it.

Please correct me if I'm wrong; I am still trying to learn perspective myself.

Gail Sauter said...

Thanks, James. Could you please do a post on inventing people on a flat plane (like a beach). If you draw/paint the first one, how do you position others standing and sitting so they are in the correct relationships to the first?

James Gurney said...

Joshua, you explained that better than I did. Gail, yes, I'll make a point of addressing your question in a future post.

Marvin said...

James,
Perhaps you could explain this better with figures on a flat ground plane?

bill said...

You've misunderstood Benson's work. The little boy has a radio control in his pocket and controls the toy boat.

Karen Robinson said...

Yes, please would you do a post about people e.g. on a beach, ASAP, because I don't "get" this at all, despite others' explaining it in different words. I know I don't "get" it because if I was to paint some boats on the sea right now I would feel anxious and have no idea how I would right-size them. I would mentally triple them up to the horizon, confuse myself, not know what this proved and end up just painting them so they 'look right'. Trouble is, I expect that's what Benson did and as you say, it wasn't right. Sigh.

Erik Bongers said...

I was confused as well. It took me quite a while to understand the graphic.
I think it might be better to fade the underlying photo to almost white as the graphic overlay blends too much with it.
The basic idea is to show that for every boat you have 3 man-heights to the horizon.
Other option might be to place the graphic next to the photo.

In any case, a very usefull rule!

Meg Lyman said...

I think this assumes any kayaker, at the top of their head, is ~2.5 feet above the water. That's where Mr. Gurney got the 8 feet.

James Gurney said...

Erik, thanks, you're right. I have redone the graphic to ghost the BG, so hopefully it's clearer.

JonInFrance said...

I seem to remember Loomis covers size of people on a beach, etc? can't remember which book tho', I'm afraid.

Michael said...

This is much clearer, especially with the Loomis diagrams. Thanks!

Mara Mattia said...

I get it! I get it!!! Thanks, Mr. Gurney!

Simone said...

Makes perfect sense...now I have to go look at a whole bunch of paintings to see had much I screwed things up....

scruffy said...

It's a lovely principle as long as the surface is flat and everyone is the same height...

Tom Hart said...

This is a really helpful rule, and especially because when creating a scene that isn't actually observed, the need for the rule might not even be realized - at first.

For me, the Loomis explanation is particularly helpful, as is Joshua's point that "If you only know how far back (in depth) you want it to be from another boat, I believe you need to draw some receding lines and use them to scale it." Even when the distant boats aren't directly in line with the closer, reference boat, you can use this rule by mentally (or temporarily) moving the distant boat over. I find that a little more intuitive than the height rule, personally. Also, I assume it's crucial that the boats are relatively the same size, or the rule requires some significant adjustment.

This reminds me of the rule for placing evenly spaced fenceposts or telephone poles receding into the distance. That's another very helpful rule.

Karen Robinson said...

I've got it now, I've got it now!! Hooray and many thanks x

Steve Shamburger said...

As Scruffy pointed out, you must assume that everyone in the Loomis graphic is the same height (i.e 6ft. men, 5 ft. women, 4 ft. child, etc.) for the horizon line to intersect them ALL through the same points (mouth for men, eyes for women, etc.). But, it's a great general rule to establish correct placement.

Melissa Shelly said...

I'm completely and utterly confused! If I were on a hilltop (thinking Santa Barbara) looking out over the pacific, my eye level would be above the waterline so the horizon line would be at my eye level, right? then what?

2) why would this line always be 8 feet above the water? Always?

3) And why, in the figure with people, is the line always going thru the men's lips and the women's eye?

Now that I'm in the comment section I can't go back to the blog post so I'm going on memory (which is almost as abysmal as my understanding of perspective).

I feel so confused, I'm ready to give up making art! Can you please please clarify (aren't you glad you decided to share all your wisdom in this blog?)

And I am grateful, Jim....truly. If you wrote another book, I'd be the first in line to buy it...same with a DVD.

I sure hope there are others out there stumbling around like this......

Wouter Tulp said...

Good advice, thanks!

57d76b80-fda8-11e2-814f-000bcdcb471e said...

OK. I get it but with the enlarged boat the figure feels squeezed, almost claustrophobic within the space. In addition with the correction the figures do not dominate the space as in the original. I would think he felt the figures and their relationship to one another was the focus of the painting. Maybe he should of filled the space with a buoy instead.

James Gurney said...

Melissa, don't worry. If you didn't get it, it was because I didn't explain it clearly enough. To answer your first question, no, the eye level line is not always 8 feet above the water.

It might help to think of a person standing on a completely flat earth. As they look ahead, the flat plane they're standing on goes way back to the horizon.

Now imagine a second plane at the eye height of that viewer, extending out parallel to the ground plane. It would be about five feet above the ground, or however high their eyes are. If they got up on a ladder, that eye-plane would be 10 feet off the ground. The "eye-plane" is really the eye level, and it extends to the horizon, too.

So if the observer looked off at a giraffe standing on the same ground plane, the viewer's eye-plane would intersect the giraffe at the height of the viewer's eyes—5 feet or 10 feet above the ground, depending on where the viewer was standing.

So Loomis's line is sort of a rough guideline, based on ideal heights of observer and subjects, but the basic principle applies to all situations.

Scruffy, I used the example of still water because it's essentially flat. And I used kayakers because their height is reasonably constant. Getting the perspective right on kayakers going over waterfalls is something for another post.

mp said...

It seems perspective is more confusing when water is involved, though it shouldn't be. Maybe the plane that creates the water lines lends to a sense of being ungrounded.

Beautiful painting, inaccuracies aside.

Melissa Shelly said...

I still am having trouble. I need to reformulate my questions but since this came up again, I thought I'd repeat my mantra: Huuuuuuuuuuh?
Like a few come to mind if you even feel like addressing:
1) in Parag 1, how do you know how far above the water the viewer's camera is based on the photo you provied?
2) I'm assuming that the 8 feet figure (camera height) is also eye level and somehow determines the distance each boat is sitting below the horizon.
3) In the Bensom example, how do you get that the observer is standing 4 feet above the water based on where the boys' head is in relation to the horizon?
I wish you could do another bunch of blog entries just breaking this one down for simpletons like me.
Thanks, Jim

James Gurney said...

Melissa, these are great questions, and don't worry: This idea can be difficult to grasp. You're not alone! You have reminded me of the need for a good, thorough explanation of this point, maybe a demonstration on video. That would be fun to do, but forgive me, I can't tackle it right now because of deadlines, but I promise you I'll get to it eventually.

Melissa Shelly said...

Thank you, Jim. I would buy that video in a heart beat. I'm actually printing out this string of comments so I can muse over it when I want to give myself another headache :)
Thanks again and I'll look forward to that video demonstration.
Melissa