Well, there they were: After a night of
serious drinking, my party of would-be
adventurers had woken in the dismal
hold of a ship at sea, victims of a press
gang. Possessed of nothing more than
their hangovers, these brave souls were
ready to begin one of their greatest
adventures.

And then, to fill in the details, I turned
to the Waterborne Adventures section of
the DMG, nodding
my way down the lists of size, winds,
movement. . . . But when I got to the
SPEED Table, there was a moment of
shock.

For there, in black and white, were listings
showing that smaller boats of all
types had a greater maximum speed
than that of their larger cousins. This, I
said to myself, must be the mistake of
some itinerant landlubber — not those
old salts up at TSR. So I quickly wrote a
letter to the people at DRAGON™ Magazine
and offered to explain the laws of
fluid mechanics and the worship of the
great Froude, God of Marine Engineering,
to their many good readers. Unfortunately
for me, they just wrote back and
said, “‘Sure, sounds like a good idea.”
So, here goes:

Most boats float in water. This statement
was, of course, more true in olden
times than it is today, but in the AD&D™
game there are very few hovercraft and
jetboats. Slower boats, especially those
that are either sailed or rowed, float
because their hulls displace a volume of
water equal to the weight of the ship.
Failure to do this simple thing is often
called, by laymen, “sinking.”

When a boat pushes its way through
the water, it also pushes the water. This
movement tends to build up a high wave
at the bow, the first point on the boat to
meet the water, and one or more secondary
waves later on. While these waves
are often quite picturesque, the energy
needed to raise them is taken directly
away from the boat, which is very wasteful
from the sailor/boatman’s point of
view.

As the boat picks up speed, the height
of the bow wave increases, raising the
water in the wave farther above the level
of the surrounding sea. The water in the
wave has a property called mass, which
means that gravity acts upon it, seeking
to pull it back down. This mass of water
takes a certain amount of time to fall
back to sea level, and because of inertia
(the tendency of a mass in motion to
keep on moving) it actually goes below
sea level.

In this way a wave is born. But although
a wave will appear to be moving across
the surface of the sea, the water in the
wave stays in pretty much the same
place, moving mostly just up and down.
Of course, the larger a wave is, the
longer it takes the water in it to fall, and
then to rise again. This increases the
length of the wave, which for our purposes
can be measured as the distance
between one wave crest, the highest
point, to the next.

When a ship or boat goes faster, it
creates a larger and longer wave. By
using models of ships under controlled
laboratory conditions, the great British
marine engineer William Froude discovered
in the late 1800’s that there was a
relationship between the velocity and
the length of a wave. And he found that
this “Froude Relation” could be used to
determine the best speed for a ship.
To put it simply but scientifically, the
inertial force divided by the gravitational
force is equal to the velocity squared
divided by the length of the ship. This
gives one the appropriate “Froude Number”
(best speed) for any watergoing
vessel. Translated into real-world terms,
this means that a longer ship will have a
higher best speed than a shorter one.

For example, let’s say we have a sailboat
that is 25 feet long at its waterline.
When our small boat starts off at an easy
4 knots (4 times 6,076.10 ft. per hour), the
waves it makes are about 10 feet long.
Our boat will be riding, then, on top of
three wave-crests: one at the bow, one
10 feet back from the bow, and another
one 20 feet back, near the stern.
If we increase the boat’s speed to 6
knots, the distance between wave crests
is about 20 feet, and we will have lost the
support of the third crest. Luckily, two
crests are enough to still keep the boat
fairly level, especially since each of them
is larger than each of the crests were
when they were 10 feet apart.

At 6.75 knots, we have one wave-crest
at the bow and one wave-crest precisely
at the stern. This, of course, still keeps
the boat in good balance, but note that a
boat shorter than this one would only be
riding up on its bow wave.

Now the wind becomes stronger, we
start to go faster, and our wave length
becomes greater. Once we go over 7
knots, the distance between the bow
wave and the second wave becomes
greater than the length of the boat. With
the bow on top of its wave, and the stern
down in the low water between two
crests, we are now sailing uphill.

Sailing uphill naturally takes more
power, and, what’s worse, the faster we
try to go, the steeper the hill gets. So the
best, most comfortable, most economical,
speed for this boat is just under 7
knots, where we still have two waves
supporting the hull.

Of course, if you buy (or, for those with
piratical tendencies, steal) a larger boat,
for instance one that is 30 feet long at the
waterline, at 7 knots the boat will still ride
on two wave-crests and can speed along
quite nicely — until you hit about seven
and a half knots. And a 100-foot-long
ship would do fairly well until the distance
between wave crests becomes
more than 100 feet (this occurs at about
13.5 knots).

To figure out the best speed for a ship
you’ve built, borrowed, or otherwise acquired
for AD&D adventuring, all you
have to do is to take the square root of
the length (waterline) and multiply by
1.35 (a “fudge factor” which can be used
in place of going through Froude’s complicated
calculation). This gives a rough
approximation of the boat’s best speed
in knots. (Translating this into miles per
hour, a measurement which a true sailor
never uses, yields a slightly higher number,
but it is of course exactly the same
speed.)

To answer the understandable question
about the difference between fast,
narrow ships and slow, wide, bulky ones:
Yes, a narrow ship requires less energy
to reach its best speed than a fat one. But
the overriding factor, once that speed is
attained, will always be the length of the
boat.

A table of best speeds

Length at waterline  (in feet)	Best speed  (in knots)	Best speed  (in miles per hour)
10	4.3	4.9493
15	5.2	5.9852
20	6.0	6.906
25	6.8	7.8268
30	7.4	8.5174
35	8.0	9.208
40	8.5	9.7835
45	9.0	10.359
50	9.5	10.9345
60	10.5	12.0855
70	11.4	13.1214
80	12.1	13.9271
90	13.0	14.963
100	13.5	15.5385
150	16.5	18.9915
200	19.0	21.869
250	21.5	24.7465
300	23.5	27.0485
400	27.0	31.077

<Knot = 1 nautical mile per hour (Knot)

1 nautical mile = 1.150779 miles (statute) (exact: 57,875/50,292 miles) (Nautical mile)

Note: The Best speed (in mph) column, was added, and figured from 1.151, to start. 1" = 3 mph.>

Holes in the hull

Dear Editor:
Bruce Evry’s article “The hull truth about
speed” (issue #70) is true, but has very little to
do with AD&D or D&D.

A vessel’s best speed is its most efficient
cruising speed, rather than any sort of a top
speed. The table he refers to in the DMG follows <link>
the table he produced up to the level of
small galley, at which point maximum speed
falls off. This follows thousands of years of
experience that, as a general rule, large boats
are faster than small boats, but small ships are
faster than large.

Up to the level of a small galley, the wave
effects Mr. Evry talks about give a speed near
the top speed. Larger vessels tend to sink
more deeply into the water, so that friction
becomes the principal limiting factor. Before
the 19th century, most of the speeds Evry sets
forth were beyond the abilities of large ships
that might have reached them.

As an example, one need only contemplate
the War of 1812. The American frigates were
bigger and more heavily armed than anything
the British could spare from Europe. The
smaller classes of vessels reflected much the
same relationship as among the frigates. The
British used the same tactics in the War of
1812 that worked against the German “pocket
battleships” in 1939-40: Teams of smaller vessels
which could cope with their larger opponents
so long as one American faced two British.
The British had little trouble catching
their larger opponents. Nor, as a rule, were
the American frigates able to run down small
(that is, smaller than a frigate) British vessels.

In the context of a D&D or AD&D campaign,
the sailing vessels available are simply not
capable of reaching speeds above 12 knots,
and the higher best speeds are irrelevant.
They might be useful in dealing with the more
sophisticated vessels of the 18th-19th centuries,
when speeds of up to 181 knots were
achieved. But a clipper ship would be as out of
place as a revolver in such surroundings.

Jack R. Patterson
Roanoke, Va.
(Dragon #72)
 
 

THE HULL TRUTH ABOUT SPEED: Larger ships make faster frigates
    By Bruce Evry

By using models of ships under controlled conditions, the great British marine engineer William Froude discovered in the late 1800's that there was a relationship between the velocity and the length of a wave.

For example, let's say we have a sail-boat that is 25 feet long at its waterline.
When our small boat starts off at an easy 4 knots (4 times 6.076.10 ft. per hour), the waves it makes are about 10 feet long.
Our boat will be riding, then, on top of three wave-crests: one at the bow, one 10 feet back from the bow, and another 20 feet back, near the stern.

If we increase the boat's speed to 6 knots, the distance between wave crests is about 20 feet, and we will have lost the support of the third crest.
Luckily, two crests are enougth to still keep the boat fairly level, especially since each of them is larger than each of the crests were when they were 10 feet apart.

At 6.75 knots, we have one wave-crest at the bow and one wave-crest precisely at the stern.

Once we go over 7 knots, the distance between the bow wave and the second wave becomes greater than the length of the boat.

So the best, most comfortable, most economical speed for this boat is just under 7 knots, where we still have two waves supporting the hull.

Of course, if you buy (or, for those with practical tendencies, steal) a larger boat, for instance one that is 30 feet long at the waterline, at 7 knots the boat will still ride on two wave-crests and can speed along quite nicely - until you hit about seven and a half knots. And a 100-foot-long ship would do fairly well until the distance between wave crests becomes more than 100 feet (this occurs at about 13.5 knots).

To figure out the best speed for a ship you've built, borrowed, or otherwise acquired for AD&D adventuring, all you have to do is to take the square root of the length (waterline) and multiply by 1.35 (a "fudge factor" which can be used in place of going through Froude's complicated calculation.)

A table of best speeds

Length at waterline (in feet)	Best speed (in knots)	Best speed (in miles per hour)
10	4.3	4.9493
15	5.2	5.9852
20	6.0	6.906
25	6.8	7.8268
30	7.4	8.5174
35	8.0	9.208
40	8.5	9.7835
45	9.0	10.359
50	9.5	10.9345
60	10.5	12.0855
70	11.4	13.1214
80	12.1	13.9271
90	13.0	14.963
100	13.5	15.5385
150	16.5	18.9915
200	19.0	21.869
250	21.5	24.7465
300	23.5	27.0485
400	27.0	31.077

Knot = 1 nautical mile per hour (Knot)

1 nautical mile = 1.150779 miles (statute) (exact: 57,875/50,292 miles) (Nautical mile)

Note: The Best speed (in mph) column, was added, and figured from 1.151, to start.