Random Swells

This could probably use a little more finessing to get it to work just right, but I think it's close enough to publish, and to be honest, I'm kind of getting tired of messing with it.  I've got a backlog of more immediately entertaining ideas I want to post about, so I'm going to kill this particular monster and fling him to the public.

OK, you've got players adventuring on the ocean somewhere and want to randomly determine a swell.  There's no compelling in-game reason to pick a very large swell or a very small one, or even a very medium sized one.  You're letting the dice decide whether it's safe to land the boats on this shore, or how dangerous it is to go into the sea cave at this time, or whatever.  So, the first thing you do is figure out what kind of sea or shoreline your characters are working from.  Constricted areas like the Mediterranean Sea or the Gulf of Mexico get smaller swells on average than the Atlantic, with the Pacific getting bigger swells yet.  This system measures out the ocean in 1200 mile hexes.  Here's an icosahedral world map template; for an Earth-sized planet, each hex is 1200 miles. If your world isn't more or less Earth-sized, you'll need a different number of hexes per triangle to come out to 1200 miles per hex.

For reference, here's a map of the Earth in this template.

To describe the sea in any given area, we'll use two variables which I'll call exposure and fetch.  Exposure is the number of hexsides of ocean a given area is exposed to, not counting the hex in question.  For example, in the following diagram, the western end of Australia is exposed to four hexsides of ocean. (The fourth hex is split into two halves in the template; the two hex halves that the number sits on in the picture don't exist.  Only the two hex halves within the triangles of the grid.  This should be obvious from the full diagram, but gets a little less obvious zoomed in like this.)

Fetch is the straight line distance out from the starting hex until land is hit.  For these purposes, small islands count as ocean, but large, thickly seeded archipelagoes count as land.  If there are enough islands to break up and diffuse waves at this scale, it's land.  Just kind of eyeball it.

By "straight line distance" I don't necessarily mean just the six lines of direct contact radiating out from the six hexsides of the original hex.  Any hex that isn't already counted is one higher than the lowest number touching it, as shown here:

Note that for Western Australia, the mass of Australia itself blocks fetch into the Pacific, Africa shadows the fetch into the Atlantic, and South America and Antarctica shadow fetch into the Pacific to the west.  We could conceivably extend the fetch in this direction further than 9 hexes, but I'm going to go ahead and rule that Cape Horn and the Antarctic Peninsula block off wave propagation to Western Australia except for that very small window immediately past them.

Ideally, this would give us a nice, unambiguous number to use for fetch, but in most cases it will be something like this, with a fetch of 5 being the single most common number, followed by 6, with a small but distinct extreme of 9.  Let's call this 7 in this case.

Now, exposure and fetch won't change very often (unless you have a very chaotic world map).  These numbers can be noted down in your world descriptions for any important or commonly visited areas, and you won't need to go back and recount every time.

Once, you have these numbers, you can roll 4d6 with an additional d6 of another color (to be read as a d2, d3, or d6 as indicated) and consult the following table, taking fetch adjustments into account:

Exposure (hexsides) →	1	2	3	4	5	6
4	0	0	0	0	D2-1	D2-1
5	0	0	0	D2-1	D2	D2
6	0	0	D2-1	D2	D3	D2+1
7	0	D2-1	D2	D2+1	D2+1	D3+1
8	0	D3-1	D3	D2+1	D3+1	D3+1
9	0	D2	D2+1	D3+1	D2+2	D3+2
10	D2-1	D2+1	D2+2	D6+2	D3+2	D3+4
11	D3-1	D3+1	D3+2	D3+5	D3+6	D6+6
12	D3-1	D3+2	D3+5	D3+7	D6+8	D6+8
13	D2	D3+5	D6+6	D6+8	D6+11	D6+11
14	D2+1	D3+7	D6+9	D6+12	D6+14	D6+14
15	D3+3	D6+8	D6+14	D6+16	D6+20	D6+20
16	D6+5	D6+12	D6+17	D6+20	D6+25	D6+25
17	D6+8	D6+18	D6+20	D6+25	D6+25	D6+25
18	D6+12	D6+21	D6+25	D6+28	D6+28	D6+28
19	D6+18	D6+24	D6+28	D6+28	D6+28	D6+32
20	D6+24	D6+30	D6+32	D6+32	D6+32	D6+32
21	D6+30	D6+32	D6+32	D6+32	D6+32	D6+32
22	D6+32	D6+32	D6+32	D6+32	D6+32	D6+32
23	D6+32	D6+32	D6+32	D6+32	D6+32	D6+32
24	D6+32	D6+32	D6+32	D6+32	D6+32	D6+32

Fetch adjustment	die roll	steps
	4-12	-3 if fetch=2; -2 if fetch=3; -1 if fetch=4
	13-16	-2 if fetch=2; -1 if fetch=3-4
	17	-2 if fetch=2; -1 if fetch=3
	18-19	-1 if fetch=2
	20-24	no adjustment

 So, continuing with our Western Australia example, if we rolled an 18 on our 4d6 and a 6 on the other d6, we'd check the fetch adjustment for fetch of 7 and a roll of 18 (no adjustment here), then check the table (d6 + 28 = 6 +28 = 34 foot swell). 

Most ocean hexes or ocean shores will not really get a fetch adjustment.  Enclosed areas like the Gulf of Mexico tend to have exposure of 1 and fetch of about 2, and much smaller swells because of this.  With the same rolls as the last example, we would get a fetch adjustment of -1 (making the die roll 17 instead of 18), then check the table to find a swell of d6 + 8, for a total swell of 14 feet. 

The last thing we need to do to get a complete swell description is period.  I'll admit this isn't all that elegant, but like I said earlier, I was starting to get tired of messing with it.  Basically, once you have your swell height, you cross-reference it on this table against your fetch to find a minimum and maximum period.  I'll leave it up to you how you pick the value in between.  If you'd like, you can use the maximum fetch on this table, instead of the fudged number we used above.  

		Maximum period
wave height	minimum period	Fetch=2	Fetch=3	Fetch=4	Fetch=5	Fetch=6	Fetch=7	Fetch=8	Fetch=9	Fetch=14
2	2	7	11	12	13			14		15
3	2	9	11	12	13			14	15
4	3	10	11	13		14			15
5	3	10	12	13		14		15
6	3	10	12	13		14		15
7	4	11	12	13	14		15
8	4	11	12	13	14		15
9	4	11	12	13	14	15
10	4	11	13	14		15
11	5	11	13	14		15
12	5	12	13	14		15
13	5	12	13	14	15
14	5	12	13	14	15
15	5	12	14		15
16	5	12	14		15
17	6	12	14		15
18	6	12	14		15
19	6	12	14		15
20	6	13	14	15
21	7	13	14	15
22	7	13	14	15
23	7	13	14	15
24	7	13	14	15
25	7	13	14	15
26	7	14		15
27	7	14	15
28	8	14	15
29	8	14	15
30	8	14	15
31	8	14	15
32	8	14	15
33	8	14	15
34	8	14	15
35	9	14	15
36	9	14	15

For the Western Australia example, in this case, with a fetch of 7 and a wave height of 34 feet, we'd have a period somewhere between 8 and 15 (d8 + 7 possibly).  If we wanted to use the maximum fetch for W. Australia, we'd use 9 instead, although for waves this high, it makes no difference (waves this high are generated pretty close by and haven't had time to degrade).  The 14 foot swell from the Gulf of Mexico would come in with a period somewhere between 5 and 12 (d8 + 4 most likely). 

And that's about that.  Random swells with not a whole lot of screwing around to get them.  I think they come out a little higher on average than real world swells, but I think wind speeds are higher in the 2d6 wind speed table used in B/X and RC D&D than in the real world, and that (more or less) is what I started from.  High winds and waves provide adventure material though, and give spell users a reason to learn more than magical artillery spells.  I have a few more small things on waves and wave related topics that I think I'll stick all together in one miscellaneous post, and then move on to some new project.  Or probably post a bunch of standalone, unrelated posts on various topics, like DCC patrons or adventure ideas or what have you.  Hopefully I'll post a little more often since I don't have tables and tables of math to do first anymore.

PS:  Thanks to Daniel "Theophage" Clark and his In a Dark Cell blog for the icosahedral hex grid I used for this post.  He didn't post much, and hasn't updated for years, but he didn't nuke the blog when he gave it up.  I wish more people would leave their thoughts out there.  You never can tell what someone will find immensely useful.

Also, thanks to whoever made the mp_IcoSnyder_s82.45(yadayada, etc...it's a long string of numbers after this and you can search for it without them) icosahedral Earth map.  I don't remember where I snagged it, and when I search it none of the hits seem to be the original source.  It, obviously, was also immensely useful.

Possibly onto something

Trying to streamline the determination of swell in a given area of the game world's ocean.  Every other part of this wave project so far was fairly straightforward, each piece following on the last naturally, and merely requiring hours of patient number crunching and typing out into tabular form to produce.  Turning a whole world's worth of weather into a table takes a little more thought, and a little effort into making it elegant and easy to use.  More so than just rounding off heights to whole numbers, anyway.

At first, I was thinking that I would simply use the icosahedral world map template that came with the AD&D 2nd Edition World Builder's Guidebook (now available on DrivethruRPG.com; I've never regretted buying the print version, and I highly recommend the PDF for anyone interested in world building). For an Earth-sized world, that comes out to 600 miles per hex.  I'm making the call that weather systems generally run about that size (Wikipedia says storms are in the vicinity of 60-1250 miles diameter, so not far off).  For my purposes here,  a weather check (determined through whatever method, but here mostly concerning wind speed), covers a 600 mile hex, at least over the ocean where terrain doesn't break it up.

Next, starting with the 2d6 wind speed roll used in the D&D Expert rules, I figured the probabilities of high winds across multiple 600 miles hexes.  Swell is produced by high winds, so when looking at multiple hexes, you really only need to worry about the highest wind among them.  I did the math by hand to figure out the new probability curves for a 2 hex region, but somehow couldn't get it to work out for more than that.  I still don't know what I was doing wrong.  Luckily, the Troll Dice Roller and Probability Calculator was there, and didn't take too long to figure out.  Thanks, Torben Mogensen; Troll was invaluable.

My idea at this point was to look at all the ocean in a straight line out from a given point in all directions and use that number of hexes to figure out what swell was hitting that point, thus taking into account every direction it could come from and the fetch in those directions.  This way, an island or a point on the tip of a peninsula is more likely to have a large swell than a point in a protected bay or inland sea. 

I decided to look at the Hawaiian Islands to see how well this system maps out to the real world.  The Hawaiian Island chain fits pretty much into a single 600 mile hex, at least the main islands do.  There are six hexes of ocean surrounding that, and 12 more surrounding those, so I worked out the probability curve for winds across 19 hexes.  And that's where the problem came in.  With 19 hexes, there's an 80% chance of winds of Beaufort number 11 or 12, and since it's only three hexes out, the waves have little time to dwindle down.  Hawaii is a surfer's paradise, but swells over 20 feet (growing higher as they start running inshore) are not an everyday thing.  I distinctly remember, when I was stationed there, going to the beach and not being swept away or pounded by massive plunging waves (I did see some some frighteningly large ones, though, on occasion).  And those 19 hexes aren't even all of the ocean hexes that could possibly be the source of a Hawaiian swell.

But, I think using a larger hex might work.  A 1200 mile hex would mean fewer chances of a really high wind result, and also double the average distance the swell would travel, giving it time to diminish to a more reasonable (from my perspective) level.  I'm going to work some numbers for a few different real-world areas at 1200 miles per hex and see where that takes me.

Last waves project (probably)

I've posted already about how swell is formed and propagates across the oceans, but it is based on swell created by local conditions.  But in an RPG, we're generally not concerned with the size of the swell created where the PCs are and how far it goes, we're more concerned with the size of the swell generated elsewhere and now arriving where the PCs are.  The system I posted earlier is fine for this, if you're willing as DM to generate weather for the entire world, work out the swell generated in dozens of separate weather systems, and then figure out how much it decays in the distance it has to cover to get to where the PCs are.  If you want to get really technical, you'd have to figure out how long it takes that swell to reach the PCs' area from its source weather system, not to mention all the lesser swells generated by that weather system (it stands to reason if it takes 50 hours to fully develop the waves, that there would be less developed waves created beforehand, which would also travel until they hit a shore). 

No, the best thing to do here, from a game feasibility standpoint, is to work out some sort of statistical stand-in that would take into account all the directions a swell could come from, the likelihood of strong winds somewhere in those directions, and how far the swell generated by those winds would have to come.  Roll some dice to see a generalized picture of the world's weather and go from there.  A simple table wouldn't meet my standards here; the Hawaiian Islands, surrounded by thousands of miles of ocean in all directions, should not get the same results as Galveston, Texas, which only has any kind of long fetch distance to the southeast, and even that gets buffered by Florida, Cuba, and Mexico.  I'll have to figure out some sort of equation, or a table complex enough to take everything into account, but not so complex that it can't be used on the fly if need be. 

I'll probably have to dredge up my old statistics textbooks, too.  If I can't figure out a decent way to math this problem out the smart way, I'm going to have to brute force it, and generate a world's worth of weather for several hundred days, and then figure out what kind of swells that produces in different places.  I'm not entirely sure I want to take on that kind of number crunching if I don't have to.

Breaking news

Okay, so these numbers could probably use a little better going-over than I've given them, but like I said, this whole process has been a grind.  I still have my raw numbers for each step of the way, and I have some ideas for how to go back and get better results, but I really need to step away from this for a little while before I attempt any of that.  Besides, I have other nitpicky projects of insane detail to torture myself with.

So, on to the beta version of my official waves-breaking-on-shore tables.  They are three separate tables, representing beach slopes of "steep", "moderate", and "mild".  To read the table, cross reference the wave period across the top and wave height down the left side.  The entry for any given height and period will give you the wave height at the point the wave breaks (waves tend to get higher as they approach shore and their energy is concentrated into a shallower column of water), the water depth at the point the wave breaks, and the form the wave breaks into.  The types of breakers are Spilling (Sp), Plunging (P), and Surging (Su).  Spilling breakers are the gentlest of the three, with the top of the wave literally spilling down the front with minimal turbulence.  Plunging breakers are the classic surfers' curl, and surging breakers are just a huge turbulent mess smashing into the shore.  This video has a decent example of each type.

Steep sloped beach (1 foot rise per 10 feet horizontal distance)

 

ht \period->

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

2

2/3/Sp

2/2/P

3/2/P

3/2/P

3/3/P

4/3/Su

4/3/Su

4/3/Su

4/4/Su

5/4/Su

5/4/Su

5/3/Su

5/4/Su

5/5/Su

5/5/Su

3

3/5/Sp

3/4/P

4/4/P

4/3/P

5/3/P

5/4/P

5/4/Su

6/4/Su

6/5/Su

6/5/Su

7/5/Su

7/5/Su

7/6/Su

7/6/Su

8/6/Su

4

4/5/Sp

5/5/P

5/5/P

6/5/P

6/5/P

7/5/P

7/5/Su

7/6/Su

8/6/Su

8/6/Su

8/7/Su

9/7/Su

10/7/Su

10/7/Su

5

6/6/P

6/6/P

7/6/P

7/6/P

8/6/P

9/6/P

9/7/Su

9/7/Su

10/7/Su

10/8/Su

11/8/Su

11/8/Su

11/9/Su

6

7/7/Sp

7/7/P

8/7/P

8/7/P

9/7/P

10/7/P

10/8/P

10/8/Su

11/8/Su

11/9/Su

12/9/Su

13/9/Su

13/10/Su

7

7/8/Sp

8/8/P

9/8/P

9/8/P

10/8/P

11/9/P

11/9/P

11/9/P

12/10/Su

13/10/Su

13/10/Su

14/10/Su

15/11/Su

8

9/11/Sp

9/9/P

10/9/P

10/9/P

11/9/P

12/11/P

12/10/P

12/10/P

14/11/P

14/11/Su

14/11/Su

15/11/Su

16/12/Su

9

9/12/Sp

10/11/Sp

10/11/P

11/10/P

12/11/P

13/12/P

13/11/P

14/11/P

15/12/P

15/12/P

16/13/Su

16/13/Su

17/13/Su

10

10/12/Sp

11/12/Sp

11/12/P

12/11/P

13/12/P

14/13/P

14/12/P

15/12/P

16/12/P

17/13/P

17/14/P

17/15/Su

18/15/Su

11

12/13/Sp

12/13/P

13/12/P

14/13/P

15/14/P

15/13/P

16/13/P

17/13/P

18/14/P

19/15/P

19/16/Su

20/16/Su

12

13/17/Sp

13/14/P

14/14/P

15/14/P

16/15/P

16/14/P

17/15/P

18/14/P

19/15/P

20/16/P

20/17/P

21/17/Su

13

13/18/Sp

14/16/Sp

15/16/P

16/15/P

17/16/P

17/16/P

19/16/P

19/16/P

20/16/P

21/17/P

22/17/P

22/18/P

14

14/19/Sp

15/18/Sp

16/17/P

17/16/P

18/17/P

18/17/P

20/17/P

20/18/P

22/18/P

22/18/P

23/18/P

24/19/P

15

15/19/Sp

16/19/Sp

17/18/P

18/18/P

18/18/P

19/18/P

21/18/P

22/19/P

23/19/P

23/18/P

24/19/P

25/20/P

16

16/20/Sp

17/22/Sp

18/19/P

19/20/P

19/19/P

20/19/P

22/19/P

23/20/P

24/20/P

25/20/P

25/20/P

26/20/P

17

18/25/Sp

19/20/P

20/21/P

20/19/P

21/20/P

23/20/P

25/21/P

25/22/P

26/21/P

26/21/P

27/21/P

18

19/26/Sp

20/21/Sp

21/22/P

21/20/P

22/21/P

24/21/P

25/22/P

26/23/P

27/23/P

28/23/P

28/22/P

19

20/27/Sp

20/23/Sp

22/23/P

22/21/P

23/22/P

25/22/P

26/23/P

27/24/P

28/24/P

29/24/P

29/23/P

20

20/28/Sp

21/25/Sp

23/23/P

23/23/P

24/23/P

26/23/P

26/24/P

28/24/P

29/25/P

30/25/P

31/24/P

21

21/31/Sp

22/27/Sp

24/24/P

24/24/P

25/24/P

26/24/P

27/25/P

29/25/P

30/26/P

31/26/P

33/25/P

22

22/34/Sp

23/29/Sp

24/26/P

25/25/P

26/26/P

27/25/P

29/26/P

30/26/P

31/27/P

32/27/P

34/27/P

23

23/37/Sp

23/31/Sp

25/28/Sp

26/26/P

27/28/P

28/26/P

30/27/P

31/27/P

32/28/P

33/29/P

35/28/P

24

24/40/Sp

24/32/Sp

26/30/Sp

27/27/P

28/29/P

29/27/P

31/28/P

32/28/P

33/29/P

35/30/P

36/30/P

25

25/43/Sp

25/35/Sp

26/31/Sp

28/28/P

29/30/P

30/28/P

31/28/P

33/29/P

34/30/P

36/31/P

37/31/P

26

26/46/Sp

26/37/Sp

27/33/Sp

29/29/P

30/31/P

31/30/P

32/29/P

34/30/P

35/31/P

38/32/P

38/33/P

27

27/46/Sp

27/39/Sp

28/35/Sp

30/31/P

31/32/P

32/31/P

33/30/P

35/31/P

36/32/P

38/33/P

39/34/P

28

28/46/Sp

29/37/Sp

31/33/P

32/33/P

32/32/P

34/31/P

36/32/P

37/33/P

39/34/P

41/35/P

29

29/47/Sp

30/39/Sp

32/35/Sp

33/34/P

33/33/P

35/32/P

37/33/P

38/34/P

39/35/P

42/36/P

30

30/47/Sp

30/41/Sp

33/35/Sp

34/35/P

34/35/P

36/33/P

38/34/P

39/35/P

40/36/P

43/37/P

31

31/47/Sp

31/43/Sp

33/38/Sp

35/36/P

36/37/P

37/35/P

38/35/P

40/36/P

41/37/P

43/38/P

32

32/48/Sp

32/46/Sp

34/40/Sp

36/37/P

37/37/P

38/37/P

39/36/P

41/37/P

42/38/P

44/39/P

33

33/48/Sp

33/48/Sp

35/42/Sp

37/39/P

38/38/P

39/38/P

40/37/P

42/38/P

43/39/P

45/40/P

34

34/48/Sp

34/50/Sp

36/43/Sp

38/41/P

39/39/P

40/40/P

41/38/P

43/39/P

44/40/P

45/41/P

35

37/44/Sp

39/43/Sp

40/40/P

41/42/P

42/39/P

44/40/P

45/41/P

46/42/P

36

38/45/Sp

40/44/Sp

41/41/P

42/43/P

43/40/P

44/41/P

47/42/P

47/43/P

37

38/46/Sp

41/45/Sp

43/43/P

43/45/P

44/42/P

45/42/P

48/43/P

48/44/P

38

39/47/Sp

41/47/Sp

44/44/P

44/46/P

45/43/P

46/43/P

49/44/P

49/45/P

39

39/48/Sp

42/49/Sp

45/46/P

45/47/P

46/45/P

47/44/P

49/45/P

51/46/P

40

40/49/Sp

42/50/Sp

45/47/P

46/48/P

46/46/P

48/45/P

50/46/P

52/47/P

41

41/50/Sp

43/51/Sp

46/49/P

47/49/P

47/48/P

49/47/P

51/47/P

53/48/P

42

42/52/Sp

44/51/Sp

46/50/P

48/50/P

48/49/P

50/49/P

51/48/P

55/49/P

43

43/54/Sp

45/52/Sp

47/51/Sp

49/51/P

49/50/P

51/50/P

52/49/P

55/50/P

44

46/52/Sp

48/53/Sp

50/52/P

50/52/P

52/52/P

53/50/P

56/51/P

45

47/53/Sp

49/54/Sp

52/52/P

52/53/P

53/54/P

54/51/P

56/52/P

46

48/53/Sp

49/56/Sp

53/53/P

53/54/P

54/56/P

55/52/P

57/53/P

47

50/57/Sp

54/55/P

54/55/P

55/58/P

56/52/P

57/54/P

48

50/59/Sp

54/56/P

55/56/P

56/59/P

57/54/P

58/55/P

49

51/60/Sp

55/58/P

56/57/P

57/60/P

59/55/P

59/56/P

50

53/62/Sp

55/60/P

58/59/P

58/61/P

60/57/P

60/57/P

51

54/63/Sp

56/61/Sp

59/60/P

59/62/P

60/58/P

61/58/P

52

55/65/Sp

57/63/Sp

60/61/P

60/63/P

61/60/P

63/59/P

53

58/64/Sp

61/63/P

61/64/P

61/61/P

64/61/P

54

59/66/Sp

62/65/P

62/65/P

62/63/P

65/63/P

55

60/67/Sp

63/67/P

63/66/P

63/64/P

66/65/P

56

61/68/Sp

63/69/P

65/67/P

65/66/P

67/67/P

57

64/70/P

66/68/P

66/67/P

68/69/P

58

65/72/P

67/69/P

67/69/P

69/71/P

59

65/74/P

68/70/P

68/70/P

69/73/P

60

69/71/P

69/71/P

70/75/P

61

70/71/P

70/72/P

70/77/P

62

71/73/P

71/79/P

A few things to note here: First of all, there are entries in the table for waves with long periods and very small heights.  This is due to degradation of the wave height over long distances, as discussed in this post.  Also, there are fewer entries for waves of period 7 than for period 6.  This post on wave generation shows that winds strong enough to generate waves of this period tend to build rapidly on to higher periods rather than higher waves of period 7.  Weird, I know.  Lastly, if you look at waves of a given height and how they are affected by period, you'll see some places where the outcomes (mostly breaker height or depth) will go up as period increases, and then go down as it increases some more.  Sometimes it wavers wildly as you look across the table.  Part of this is due to natural weirdness of waves -- the complexity of the interaction between the wave and the ocean floor -- but most of it is due to rounding errors on my part, in many cases errors being carried forward and compounded from one step of the process to the next.  I did some eyeball quality control before posting these tables, and I think I can get better numbers after another go at it, but like I said, I need to step away from this for a bit.  These numbers are "close enough" numbers for gaming purposes, not so much to be referred to and treated as gospel as to provide a baseline for a more accurate ruling by a GM.  Even if, ultimately, you're just pulling numbers out of your ass in the heat of the moment, it comes out as more realistic if your numbers have some connection to reality...

Okay, next table...

Moderate sloped beach (1 foot rise per 20 feet horizontal distance)

ht \period->

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

2

2/3/Sp

2/2/Sp

3/2/P

3/3/P

3/3/P

3/3/P

4/3/P

4/4/P

4/4/P

5/4/P

5/4/P

5/4/P

5/5/P

5/5/P

5/6/P

3

3/5/Sp

3/4/Sp

3/4/P

4/4/P

4/4/P

5/4/P

5/4/P

5/5/P

6/5/P

6/6/P

6/6/P

7/5/P

7/6/P

7/6/P

8/7/P

4

4/6/Sp

4/5/Sp

5/5/P

5/5/P

6/5/P

7/5/P

7/6/P

7/7/P

8/7/P

8/7/P

8/8/P

8/8/P

9/8/P

9/8/P

5

6/6/Sp

6/6/Sp

6/7/P

7/6/P

8/6/P

8/7/P

8/8/P

9/8/P

9/8/P

10/9/P

10/9/P

11/9/P

11/10/P

6

7/7/Sp

7/7/Sp

7/8/P

8/7/P

8/7/P

9/8/P

10/9/P

10/9/P

10/9/P

11/10/P

11/10/P

12/10/P

12/11/P

7

8/9/Sp

8/8/Sp

8/9/P

9/9/P

9/8/P

10/9/P

11/10/P

11/10/P

12/10/P

12/11/P

13/12/P

13/12/P

14/12/P

8

8/11/Sp

9/10/Sp

9/10/Sp

10/10/P

11/8/P

11/10/P

12/11/P

12/11/P

13/11/P

14/12/P

14/13/P

14/14/P

15/13/P

9

9/12/Sp

10/11/Sp

10/11/Sp

10/11/P

12/10/P

12/12/P

13/12/P

14/13/P

15/14/P

15/13/P

15/14/P

15/15/P

16/15/P

10

9/12/Sp

11/13/Sp

11/13/Sp

11/13/Sp

13/13/P

13/13/P

14/13/P

15/14/P

16/17/P

16/15/P

17/15/P

17/16/P

17/16/P

11

12/14/Sp

12/14/Sp

12/14/Sp

14/15/P

14/14/P

15/15/P

16/15/P

17/17/P

17/17/P

18/17/P

18/16/P

19/17/P

12

12/15/Sp

13/15/Sp

13/15/Sp

14/16/P

15/15/P

16/16/P

17/17/P

18/18/P

19/19/P

19/18/P

20/17/P

20/18/P

13

13/16/Sp

14/16/Sp

14/16/Sp

15/17/Sp

16/16/P

17/17/P

18/18/P

19/18/P

20/20/P

20/20/P

21/19/P

21/19/P

14

13/17/Sp

14/18/Sp

15/17/Sp

16/17/Sp

17/17/P

18/18/P

19/19/P

20/19/P

21/20/P

22/21/P

22/21/P

23/20/P

15

14/18/Sp

15/19/Sp

17/19/Sp

17/18/Sp

17/18/P

19/20/P

20/20/P

21/20/P

22/21/P

23/23/P

23/23/P

25/22/P

16

14/19/Sp

17/21/Sp

18/20/Sp

18/20/Sp

18/20/P

20/21/P

21/21/P

22/21/P

23/21/P

24/23/P

25/25/P

26/24/P

17

18/24/Sp

19/21/Sp

19/20/Sp

19/21/Sp

21/22/P

22/22/P

23/22/P

24/22/P

25/24/P

26/27/P

27/25/P

18

18/25/Sp

19/21/Sp

20/21/Sp

20/22/Sp

21/23/P

23/23/P

24/23/P

25/23/P

26/24/P

27/27/P

28/27/P

19

19/26/Sp

20/23/Sp

21/23/Sp

21/23/Sp

22/24/P

24/24/P

25/24/P

26/24/P

27/25/P

28/28/P

28/28/P

20

20/27/Sp

20/25/Sp

22/25/Sp

22/24/Sp

23/26/Sp

25/25/P

26/25/P

27/25/P

28/25/P

29/28/P

29/30/P

21

21/28/Sp

21/27/Sp

23/26/Sp

23/25/Sp

24/27/Sp

26/26/P

27/26/P

28/26/P

29/26/P

30/29/P

30/30/P

22

22/30/Sp

22/30/Sp

24/27/Sp

24/26/Sp

25/28/Sp

26/27/P

29/28/P

29/27/P

30/28/P

31/29/P

31/31/P

23

23/32/Sp

23/33/Sp

25/28/Sp

25/28/Sp

26/29/Sp

27/28/P

30/29/P

30/28/P

31/29/P

32/29/P

32/31/P

24

24/34/Sp

24/34/Sp

26/30/Sp

26/29/Sp

27/30/Sp

28/29/P

30/30/P

31/30/P

32/31/P

33/31/P

33/32/P

25

25/36/Sp

25/36/Sp

26/31/Sp

28/31/Sp

28/32/Sp

29/31/Sp

31/31/P

33/32/P

33/32/P

34/32/P

34/32/P

26

26/38/Sp

26/37/Sp

27/33/Sp

29/32/Sp

29/33/Sp

30/32/Sp

31/32/P

34/33/P

34/33/P

35/33/P

35/33/P

27

27/40/Sp

28/38/Sp

28/36/Sp

30/33/Sp

30/34/Sp

31/33/Sp

32/33/P

35/35/P

35/34/P

36/34/P

36/33/P

28

28/42/Sp

31/39/Sp

31/34/Sp

31/35/Sp

31/34/Sp

33/34/P

36/36/P

36/35/P

37/35/P

38/35/P

29

29/44/Sp

32/41/Sp

32/35/Sp

32/36/Sp

32/35/Sp

34/35/Sp

36/37/P

38/37/P

38/36/P

39/36/P

30

30/46/Sp

33/43/Sp

32/37/Sp

33/37/Sp

33/36/Sp

35/37/Sp

37/38/P

39/38/P

39/37/P

40/37/P

31

31/47/Sp

33/43/Sp

33/38/Sp

34/39/Sp

34/37/Sp

36/39/Sp

37/39/P

40/40/P

40/39/P

41/39/P

32

32/48/Sp

34/45/Sp

33/40/Sp

35/40/Sp

35/38/Sp

37/40/Sp

38/40/P

40/41/P

42/41/P

42/40/P

33

33/49/Sp

34/47/Sp

34/42/Sp

36/41/Sp

36/40/Sp

37/41/Sp

38/41/P

41/42/P

43/42/P

43/41/P

34

34/50/Sp

35/50/Sp

35/44/Sp

37/42/Sp

37/42/Sp

38/42/Sp

39/42/Sp

42/43/P

44/43/P

44/43/P

35

36/46/Sp

38/43/Sp

38/44/Sp

39/43/Sp

40/44/Sp

43/44/P

45/44/P

45/44/P

36

40/52/Sp

39/44/Sp

40/45/Sp

40/44/Sp

41/45/Sp

43/45/P

46/46/P

47/46/P

37

41/54/Sp

40/46/Sp

41/46/Sp

41/45/Sp

43/46/Sp

44/46/P

47/48/P

48/47/P

38

42/56/Sp

40/47/Sp

42/47/Sp

42/47/Sp

43/47/Sp

44/47/P

48/49/P

49/48/P

39

43/58/Sp

41/48/Sp

43/48/Sp

43/48/Sp

44/48/Sp

45/48/P

48/50/P

51/50/P

40

44/60/Sp

41/49/Sp

44/49/Sp

44/49/Sp

44/48/Sp

46/50/Sp

49/51/P

52/52/P

41

44/60/Sp

42/51/Sp

45/50/Sp

45/51/Sp

45/49/Sp

47/51/Sp

49/52/P

53/53/P

42

45/62/Sp

43/53/Sp

46/51/Sp

46/52/Sp

46/50/Sp

48/52/Sp

50/53/P

53/54/P

43

45/62/Sp

44/55/Sp

47/52/Sp

47/53/Sp

47/51/Sp

49/53/Sp

50/54/P

54/56/P

44

48/60/Sp

48/53/Sp

48/54/Sp

48/52/Sp

50/54/Sp

51/55/P

55/57/P

45

49/63/Sp

48/54/Sp

49/56/Sp

49/53/Sp

51/55/Sp

52/56/Sp

56/58/P

46

50/67/Sp

49/56/Sp

50/57/Sp

50/54/Sp

52/56/Sp

53/58/Sp

56/59/P

47

49/58/Sp

52/58/Sp

52/56/Sp

52/57/Sp

54/59/Sp

57/60/P

48

50/60/Sp

53/59/Sp

53/57/Sp

53/58/Sp

55/60/Sp

57/61/P

49

50/61/Sp

54/60/Sp

54/58/Sp

54/59/Sp

56/61/Sp

58/62/P

50

51/62/Sp

55/61/Sp

55/60/Sp

55/61/Sp

57/62/Sp

58/63/P

51

52/63/Sp

56/62/Sp

56/61/Sp

56/63/Sp

58/63/Sp

59/64/P

52

53/64/Sp

57/63/Sp

57/62/Sp

57/64/Sp

58/63/Sp

60/66/Sp

53

58/66/Sp

58/63/Sp

58/65/Sp

59/64/Sp

61/67/Sp

54

60/69/Sp

60/65/Sp

60/67/Sp

60/65/Sp

62/69/Sp

55

61/72/Sp

61/67/Sp

61/68/Sp

61/66/Sp

63/70/Sp

56

62/74/Sp

62/68/Sp

62/69/Sp

62/67/Sp

64/71/Sp

57

63/70/Sp

63/70/Sp

63/68/Sp

65/73/Sp

58

64/72/Sp

64/72/Sp

64/69/Sp

66/74/Sp

59

65/74/Sp

65/73/Sp

65/69/Sp

66/75/Sp

60

66/74/Sp

66/70/Sp

67/76/Sp

61

67/76/Sp

67/70/Sp

67/77/Sp

62

68/71/Sp

68/79/Sp

And finally...
Mild sloped beach (1 foot rise per 50 feet horizontal distance)

ht \period->

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

2

2/3/Sp

2/2/Sp

3/2/P

3/3/P

3/3/P

3/4/P

3/4/P

3/4/P

4/5/P

4/5/P

4/4/P

4/4/P

4/5/P

4/6/P

4/7/P

3

3/4/Sp

3/4/Sp

3/4/Sp

4/4/P

4/4/P

4/4/P

4/5/P

5/5/P

5/6/P

5/6/P

6/6/P

6/6/P

6/6/P

7/7/P

7/7/P

4

4/7/Sp

4/5/Sp

4/5/Sp

5/5/P

5/6/P

5/6/P

6/6/P

6/7/P

6/7/P

7/8/P

7/8/P

7/8/P

8/8/P

8/8/P

5

5/6/Sp

5/6/Sp

6/6/P

6/7/P

6/8/P

7/8/P

7/8/P

8/8/P

8/9/P

8/10/P

9/10/P

9/10/P

9/11/P

6

6/7/Sp

6/8/Sp

7/8/Sp

7/8/P

7/9/P

8/10/P

8/10/P

9/9/P

9/10/P

10/11/P

10/11/P

10/11/P

10/12/P

7

7/9/Sp

7/9/Sp

7/9/Sp

8/9/P

8/9/P

9/10/P

9/11/P

10/11/P

10/11/P

11/12/P

11/12/P

11/13/P

12/13/P

8

8/10/Sp

8/10/Sp

8/10/Sp

9/10/Sp

9/10/P

10/11/P

10/12/P

11/12/P

11/13/P

12/14/P

12/13/P

13/14/P

13/14/P

9

8/11/Sp

9/11/Sp

9/11/Sp

10/11/Sp

10/11/P

11/12/P

11/13/P

12/14/P

12/14/P

13/15/P

13/14/P

14/15/P

14/15/P

10

9/12/Sp

10/12/Sp

10/13/Sp

11/13/Sp

11/12/P

12/13/P

12/14/P

13/15/P

13/15/P

14/17/P

14/15/P

15/16/P

16/16/P

11

10/13/Sp

10/14/Sp

12/14/Sp

12/14/Sp

12/14/P

13/15/P

14/16/P

14/16/P

15/18/P

15/17/P

16/17/P

17/17/P

12

11/15/Sp

11/15/Sp

12/15/Sp

13/16/Sp

13/15/P

14/16/P

15/17/P

15/17/P

16/19/P

16/19/P

17/19/P

18/19/P

13

12/16/Sp

12/16/Sp

13/16/Sp

14/16/Sp

14/17/Sp

15/17/P

16/17/P

16/18/P

17/20/P

17/20/P

18/20/P

19/20/P

14

13/17/Sp

13/17/Sp

13/17/Sp

15/17/Sp

15/18/Sp

16/17/P

17/18/P

17/19/P

18/21/P

18/21/P

19/22/P

20/22/P

15

14/18/Sp

14/19/Sp

14/19/Sp

15/19/Sp

16/19/Sp

17/18/Sp

18/19/P

18/20/P

19/22/P

20/23/P

20/24/P

21/24/P

16

14/19/Sp

15/21/Sp

15/20/Sp

16/20/Sp

17/20/Sp

18/19/Sp

18/19/P

19/21/P

20/23/P

21/24/P

21/25/P

22/26/P

17

16/24/Sp

16/21/Sp

17/21/Sp

18/21/Sp

19/21/Sp

19/20/P

20/22/P

21/24/P

22/25/P

22/26/P

23/27/P

18

17/26/Sp

17/22/Sp

17/22/Sp

19/22/Sp

19/22/Sp

20/21/P

21/23/P

22/24/P

22/25/P

23/27/P

24/28/P

19

17/28/Sp

18/23/Sp

18/24/Sp

19/23/Sp

20/24/Sp

21/22/P

22/24/P

23/25/P

23/26/P

24/28/P

25/29/P

20

18/29/Sp

19/25/Sp

19/25/Sp

20/24/Sp

21/26/Sp

22/24/Sp

22/24/P

24/26/P

24/27/P

25/29/P

26/30/P

21

19/30/Sp

20/27/Sp

20/26/Sp

21/25/Sp

22/27/Sp

23/25/Sp

23/25/P

24/26/P

25/27/P

26/30/P

27/31/P

22

20/32/Sp

21/29/Sp

21/27/Sp

22/27/Sp

23/28/Sp

23/26/Sp

24/26/P

25/27/P

26/28/P

27/31/P

28/32/P

23

21/34/Sp

22/31/Sp

22/28/Sp

22/28/Sp

23/29/Sp

24/28/Sp

25/28/P

25/27/P

27/29/P

28/31/P

29/33/P

24

23/35/Sp

23/33/Sp

23/30/Sp

23/29/Sp

24/30/Sp

25/30/Sp

26/29/Sp

26/28/P

28/30/P

29/32/P

29/34/P

25

24/37/Sp

23/35/Sp

24/31/Sp

24/31/Sp

25/31/Sp

26/31/Sp

27/30/Sp

28/29/P

28/30/P

30/33/P

30/35/P

26

25/39/Sp

24/36/Sp

25/33/Sp

25/32/Sp

26/32/Sp

27/32/Sp

28/31/Sp

29/30/P

29/31/P

31/34/P

31/36/P

27

26/39/Sp

24/38Sp

26/42/Sp

26/33/Sp

27/33/Sp

28/33/Sp

28/32/Sp

30/32/P

30/32/P

32/35/P

32/36/P

28

27/40/Sp

27/50/Sp

27/34/Sp

28/35/Sp

28/34/Sp

29/34/Sp

31/34/Sp

31/33/P

32/35/P

34/37/P

29

28/40/Sp

28/48/Sp

28/35/Sp

28/36/Sp

29/35/Sp

30/35/Sp

32/35/Sp

32/34/P

33/36/P

35/38/P

30

29/41/Sp

29/47/Sp

29/37/Sp

29/38/Sp

30/36/Sp

31/37/Sp

33/37/Sp

33/35/P

34/37/P

36/39/P

31

29/41/Sp

29/46/Sp

29/39/Sp

29/39/Sp

31/37/Sp

32/38/Sp

33/38/Sp

34/36/P

34/37/P

36/39/P

32

30/42/Sp

30/47/Sp

30/40/Sp

30/40/Sp

32/39/Sp

33/39/Sp

34/39/Sp

35/38/Sp

35/38/P

37/40/P

33

31/42/Sp

30/48/Sp

31/42/Sp

31/41/Sp

33/40/Sp

34/40/Sp

35/40/Sp

36/40/Sp

36/39/P

37/40/P

34

32/43/Sp

31/50/Sp

32/47/Sp

32/42/Sp

33/41/Sp

35/41/Sp

36/42/Sp

37/41/Sp

37/40/P

38/41/P

35

33/52/Sp

33/43/Sp

34/43/Sp

35/42/Sp

37/44/Sp

37/43/Sp

38/41/P

39/42/P

36

34/57/Sp

34/44/Sp

34/45/Sp

36/43/Sp

38/45/Sp

38/44/Sp

40/43/Sp

40/43/P

37

35/62/Sp

35/45/Sp

35/47/Sp

37/45/Sp

39/46/Sp

39/46/Sp

41/44/Sp

41/44/P

38

36/60/Sp

36/47/Sp

36/48/Sp

38/47/Sp

39/46/Sp

40/47/Sp

42/46/Sp

42/45/P

39

37/58/Sp

37/48/Sp

37/49/Sp

39/48/Sp

40/47/Sp

41/48/Sp

43/47/Sp

43/46/P

40

38/58/Sp

38/50/Sp

38/50/Sp

39/50/Sp

40/48/Sp

42/50/Sp

43/48/Sp

44/47/P

41

38/60/Sp

39/51/Sp

39/51/sp

40/51/Sp

41/49/Sp

43/51/Sp

44/49/Sp

45/49/Sp

42

39/62/Sp

40/56/Sp

40/51/Sp

40/52/Sp

42/50/Sp

44/52/Sp

44/50/Sp

46/50/Sp

43

39/62/Sp

40/61/Sp

41/52/Sp

41/53/Sp

43/51/Sp

45/53/Sp

45/51/Sp

47/52/Sp

44

40/67/Sp

42/53/Sp

42/54/Sp

44/52/Sp

46/54/Sp

46/53/Sp

48/53/Sp

45

41/72/Sp

43/55/Sp

43/56/Sp

45/54/Sp

46/55/Sp

47/55/Sp

48/55/Sp

46

41/77/Sp

44/56/Sp

44/57/Sp

45/55/Sp

47/56/Sp

48/57/Sp

49/56/Sp

47

45/57/Sp

45/58/Sp

46/56/Sp

47/57/Sp

49/58/Sp

49/58/Sp

48

46/58/Sp

46/59/Sp

46/57/Sp

48/58/Sp

50/59/Sp

50/59/Sp

49

47/59/Sp

47/60/Sp

47/58/Sp

49/59/Sp

51/60/Sp

51/60/Sp

50

48/60/Sp

48/61/Sp

48/59/Sp

50/61/Sp

52/61/Sp

53/62/Sp

51

49/62/Sp

49/62/Sp

49/60/Sp

51/63/Sp

53/62/Sp

54/64/Sp

52

50/62/Sp

50/63/Sp

50/61/Sp

52/64/Sp

53/63/Sp

55/66/Sp

53

50/66/Sp

50/62/Sp

52/66/Sp

54/64/Sp

56/68/Sp

54

51/69/Sp

51/63/Sp

53/67/Sp

54/65/Sp

57/69/Sp

55

52/72/Sp

52/65/Sp

53/68/Sp

55/66/Sp

58/71/Sp

56

53/74/Sp

53/67/Sp

54/69/Sp

56/67/Sp

59/72/Sp

57

54/70/Sp

54/70/Sp

57/68/Sp

59/73/Sp

58

55/72/Sp

55/71/Sp

58/69/Sp

60/74/Sp

59

56/74/Sp

56/73/Sp

59/70/Sp

60/75/Sp

60

57/74/Sp

60/71/Sp

61/76/Sp

61

58/76/Sp

61/72/Sp

61/77/Sp

62

62/73/Sp

62/79/Sp

Once a wave breaks, it will reform as a new, smaller wave.  Spilling waves reform at 1/2 their previous height, and plunging waves reform at 1/3.  Surging waves just surge onto the shore and dissipate fully that way.  The new wave will then break according to its new height, and may reform several times before ultimately splashing onto land.

Also keep in mind that sandbars, reefs, and submerged rocks act as localized ocean floor, and waves will break over them even if the depth in the general area is too great for breakers to form.  For example, suppose we have an outcropping of rock 8' below the sea surface, with the surrounding area at a depth of 15' or more, gradually sloping toward shore, when an 8' wave with a period of 10 seconds passes through.   On a mild slope, this wave will break in 12' of water, so it passes normally through most of the area.  The rock outcropping is a steep slope (way more than 1:10 slope, but we only have three tables, for simplicity's sake).  On a steep slope, this wave breaks in 10' of water, rising as high as 12' in a plunging breaker.  A smart sailor will see the breakers in this area and steer well away.

One last point here: the wave heights listed here (and in other wave tables I've published) are measured from the bottom of the lowest point of the wave to the top of the highest point.  The depth listed is a baseline drawn where the water level would be at rest, without wave action.  So in the example above, the water in the 15' depth would vary between 11' (4' less than baseline) and 19' (4' more than baseline) as the 8' waves passed over, and the water over the rocks would vary between 2' and 14' as the waves built to 12' and broke over them.