Speed Boat Developments From The Past Into The Future
Speed boat development began in the early 1900's with the development of the first gasoline powered piston engines. These engines were large and heavy. Boat hulls were long narrow round bottomed displacement hulls.
As engine design improved, the vee bottomed, hard chined planing hull and the stepped hull were developed. Drive systems included the direct drive, vee drive, stern drive, and surface drive.
The performance of each combination of hull type and drive system can be illustrated by a graph of Performance Factors. (Power Factor vs. Speed Factor) These Performance Factors take into account the running weight, engine horsepower, and measured maximum speed.
For each combination of hull type and drive system, there is a maximum performance line or Limit Line. By comparing the Limit Lines of different combinations of hull type and drive system, we can also see how the efficiency of boats has increased over the years.
The final step is to look at combinations and configurations which might produce even greater improvements in the future. The combination of surface drive and stepped hull will be significantly more efficient than current pleasure craft.
Morley S. Smith
* * *
The history recorded herein, begins at about 1900 when internal combustion piston engines began to replace heavy steam engines and boilers. Many of the examples given herein are race boats. These boats were the most efficient types of their day. The speeds weights and horsepower are often recorded.
At the turn of the century when internal combustion engines were physically large and very heavy, the hulls used were displacement hulls. When a displacement hull moves forward, the sharp narrow bow pushes or displaces the water out to the sides. As the hull passes, the water closes in behind it.
Figure 1 shows the lines of Standard, one of the fastest displacement hulls at that time. 
Length 60 ft. Beam 7'6" 110 hp. Speed 30 MPH. in 1903
These displacement hulls were round bottomed hulls. Viewed in cross section, the tops of the sides were more or less vertical. As the sides move downward, they curve gently into a nearly flat bottom at the keel.
DIRECT DRIVE :
The direct drive engine is located at about mid length in the hull. The propeller shaft goes aft from the engine transmission, through the bottom of the boat, to the propeller which is located aft under the transom.
Refer to Figure 13, for a sketch of Alternate Propulsion Systems.
The performance of a displacement hull is such that the power requirements increase as the speed increases. At higher speeds, the power requirements increase more rapidly, until a speed is reached where great increases in power produce negligible increase in speed.
Figure. 2. illustrates the first basic characteristic of displacement hulls: The greater the length, the higher the limiting speed. If you want to go faster, you build a longer hull.
Luckily the racing rule makers saw what was about to happen. Race boats were already getting absurdly long. New racing rules in 1905 limited the length of Gold Cup and Harmsworth Trophy boats to 40 ft..
Length 40' X Beam 5'-6"  150 Hp. Dry weight = 5,150 Lb. 29.8 MPH in 1904; 32 MPH. in 1906
Designer: Clinton Crane
Note how the very sharp bow cuts through the water, rolling back a nice bow wave. The hull runs level. The ideal displacement hull. (Figure 3)
Since the length of these hulls had been limited, the only way to increase the speed further, was to reduce the weight.
Figure 4 illustrates the second basic characteristic of displacement hulls: "The lighter the weight, the higher the limiting speed." As before, power requirements increase more rapidly as speed increases.
Henry Crane designed and built a large and phenominally light 220 Hp. engine -for a new boat to be named Dixie II. The V-8 engine had 2,477 cubic inch displacement, weighing less than 0.9 pounds per cubic inch.  Compare this to modern automotive engines which weigh about 2 pounds per cubic inch without transmission or exhaust manifolds. The extremely light weight of Crane's 1908 engine was a major engineering achievement. The reason the power output was so low is because maximum speed of the engine was only 900 rpm. (about idle speed for a modern automotive engine).
This light weight engine was placed in an extremely light hull. The 39' 3" hull weighed only 1,130 Lb. It was a huge canoe with planking of only 1/4" on the sides, and 3/8" on the bottom. [I]
In running trim this hull and engine weighed about 15 pounds per horsepower. Less than half of the Weight/Hp. of Dixie I.
Length 39' 3" X Beam 5' 4" 220 Hp. Speed = 37 MPH. in 1908
This combination of high power and low weight allowed the hull to be pushed beyond displacement speeds. At these speeds the bow wave is pushed to the side so forcefully that the water does not close in behind the hull. The bow in effect cuts a trough, and the stern sinks into the trough. The bow rises and tries to climb up on top of the bow wave. The bow is out of the water, and waterline length is no longer the hull length. This round bottomed hull had been pushed to planing speeds.
Dixie II dominated racing; winning the Gold Cup in 1908, 1909, and 1910, and the Harmsworth Trophy in 1908. (Dixie II has been restored and is now in the Antique Boat Museum at Clayton N.Y.)
The next step was to develop a hull shape which would do a better job of climbing up on top of the bow wave and "plane".
PLANING HULL CHARACTERISTICS
Figure 6 shows the lines of a typical planing hull. A patrol boat designed by John Hacker. 
(a) Hard chined hulls have a sharp edge between the hull side panel and the bottom panel. At speed, these hulls tend to throw the bow wave downward rather than push the bow wave out to the side as a displacement hull does. The hard chine keeps the bow wave from wetting the side panel, thus reducing the wetted area.
Less wetted area means less hull drag.
Nearly all of the fiberglass planing pleasure boats made today have a vee bottomed, hard chine configuration.
The concept of the hard chined hull was not new. E. W. Graef published plans for a hard chined, vee bottomed displacement hull named Dolphin.
(b) It was also discovered at about this time that a flat deadrise or flat bottomed hull will have less drag than a highly veed hull . 
Figure 7 shows the Trim and Drag characteristics of a typical direct drive monohull. (Running weight = 2,500 lb.)
As the speed of a planing hull increases, the trim angle, or angle of attack decreases,
(a) This increases the wetted area and greatly increases the drag.
(b) The propeller shaft, shaft strut and rudder also cause drag. Appendage drag. The appendage drag increases as the square of the speed.
Total drag increases very rapidly as speed increases.
When designing very high speed craft, it is important to consider all of the lift and drag forces acting on the appendages.
(Propeller, propeller shaft, shaft strut and rudder.) These forces can greatly affect the position of the center of lift of the hull and the optimum hull proportions. Procedures and references for calculating hull drag and appendage forces are given in the appendix.
PLANING HULL LIMITS
Figure (8) Performance Factors for Direct Drive Planing Hulls
Performance Factors are complex mathematical expressions which combine running weight, engine power and measured maximum speed. These mathematical expressions are derived from model scaling procedures. By using these complex expressions, all size effects are eliminated. (A more detailed explanation of Performance Factors is given in the appendix.)
The Performance Factors show that as the amount of applied power is increased, the speed increases. At high speeds, considerable increases in power produce relatively small increases in speed.
By using these complex numbers we can compare the performance of any size or weight of direct drive planing hull with the maximum performance possible. 
There is a definite limit to how much speed Can be obtained from a direct drive, vee bottomed hull. This is called the Limit Line, and this limit depends upon horsepower and weight. The closer the actual performance comes to the Limit Line, the more efficient the craft.
The graph shows circles which represent test data from actual boats.   There are numerous possible reasons why these data points do not lie on the limit line.
(a) The chine beam of the test boat is not optimum for the power and weight.
(b) The propeller chosen for the test is not optimum for top speed. It might be chosen for best cruise efficiency, maximum acceleration or a compromise.
(c) The engine might not have been producing it's rated power on the day of the test.
(d) The data for running weight is not always accurate.
Nevertheless, I find it surprising that the test data for very different craft is so closely bunched near the limit line.
The racing rule makers banned stepped hulls from the Gold Cup races in 1920 and limited engine displacement to ten litres (or 610 cubic inches). Packard Chris-Craft and similar hard chined monohulls dominated the Gold Cup racing until 1931, when stepped hulls were again al1 owed to compete.
Prominant names include, Baby Bootlegger, Imp, Hotsy Totsy, Rainbow IX, Miss Columbia, Arab VI, and Baby Horace III.
The boats listed here have been beautifully restored or replicated and are in running condition, often appearing at antique boat shows.
The boats were about 25' to 27' long, and averaged about 40 to 45 MPH around the course. Speeds changed very little over a 13 year period, and this is to be expected front looking at the Limit Line on the Performance Factor graph.
Performance Factors and Limit lines can be used to predict the performance of a given hull with different amounts of power. Rainbow IX (Length 25'-10", beam 5' 10") is a good example. 
Originally built in 1923 as Packard Chris-Craft II, this hard chined, vee bottomed hull was powered by a 6 cylinder Packard engine producing 250 hp. and achieved a maximum speed of about 45 MPH. This craft has since been restored and repowered with a modern, light weight, 650 hp. V-12 BPM. engine. Even though the craft has about 2 1/2 times its original power, it does not run much more than 10 MPH. faster than it's original speed, (as would be predicted by the limit line).
How do we overcome the performance limitations of direct drive monohulls?
We either change the shape of the hull, or we change the drive system. Regardless of whether we change the hull or the drive, one of the goals is to make the hull run at a higher angle of attack at high speeds. (Refer back to Fig. 7.)
Let us first look at a different hull shape. The stepped hull.
The concept was originally proposed by Rev. Ramus of [Playden Rectory, Rye,] Sussex England in 1872. He proposed both a single step with tandem planing surfaces, and a combination of three pontoons with one forward and two aft. Indications are that these shapes were derived from model tests. Unfortunately, the heavy steam power plants of that day could not push a hull fast enough to plane, and take advantage of the new concept.
As early as 1906 there were published drawings for small stepped hulls with hard chines. William Henry Fauber  obtained a U.S. patent for hulls with multiple steps in 1908, but could find few people in the U.S.A. interested, so he moved to Europe.
Two small boats Solair (12') and Flapper (15') demonstrated the potential of stepped hulls as did the Harmsworth challenger Pioneer (5 steps) in 1910.
(See Data Chart, Figure 12.)
The stepped hull began practical development about at the same time as the hard chined planing hull. A step in the bottom of a hull, raises part of the bottom surface so that it is no longer touching the water. Less wetted area. At the same time, the planing surfaces meet the water at a near optimum angle of attack over a wide range of speeds. The stepped hull is very efficient hydrodynamically.
Refer to Figure 9 : Sketch of Hard Chined Planing Hulls
In the early days of stepped hulls, it was not certain just how many steps should be incorporated. PIONEER had 5 steps in 1910. Maple Leaf IV had 5 steps.
|Maple Leaf IV
Length 39'-11" X Beam 8" Two V-8 engines 350 Hp. each.
In 1912, Maple Leaf IV came over from England, won the Harmsworth Trophy, and took it home. She had no less than five steps, and the driver sat on a pedestal high above the transom in order to see over the bow.
Some hulls had so many steps that they were called "shingled". Rainbow IV (12 steps);
Eventually, model tests showed that a single step would be most efficient if you could locate it in the right position and give it the proper depth.
Length 18'-6" Beam 4' 10" 90 hp. Speed 45 MPH.
The lines shown in Figure 10 are typical of stepped hulls in the 1920's. Note the very flat bottom. This boat raced in a class limited to engines with 1.5 litre displacements.
Gar wood brought the Harmsworth Trophy back to United States in 1920 with the first of his Miss America's. These single stepped craft so dominated the Gold Cup and Harmsworth racing that few other boats attempted to compete. The Miss America series were not really efficient boats, just big boats with huge amounts of power from multiple V-12 Packard engines.
Between about 1915 and 1940, a great many motor torpedo boats and fast patrol boats were built world wide, with stepped hulls.  The performance of these craft varied considerably, with some being very inefficient.
STEPPED HULL LIMITATIONS
The stepped hull maintains a nearly optimum angle of attack over most of the speed range. The hydrodynamic hull drag is almost constant. The drag of the propeller shaft, shaft strut and rudder, (appendage drag) increase as the square of the speed.
Figure 11: Performance Factors for Racing Stepped Hulls.
The graph of Performance Factors shows actual speed data of different prominant racing stepped hulls. The data points are numbered and refer to numbers on the data chart Figure 12. The boats are numbered in sequence according to the year when the speeds were established. The sequential increases in power factor reflect engine development and not hull development. Notice that most of these boats perform almost on the limit line. Gar Wood's Miss Americas were really quite inefficient. Many stepped hulls from England were significantly more efficient and often faster. They failed to win races because of a lack of strength and mechanical reliability. The very streamlined Alagi was slightly more efficient than the others.
Stepped hulls are difficult to design. There are many design variables compared to the design of a vee bottomed monohull. I do not know of any accurate method available to optimize stepped hull design other than by model testing.
Stepped hulls dominated race boat design until about 1938 when Adolph Apel patented the three point hydroplane configuration. Ventnor three point hydroplanes dominated small limited class racing, yet stepped hulls were running competitively in Unlimited class racing up until 1949. In 1950, Slo-mo-shun demonstrated "prop riding" and boosted the world speed record significantly. (More on 'prop riding' later.)
Stepped hulls definitely have the potential of being significantly more efficient than monohulls.
Compare the Limit Lines on the Performance Factor graphs. There are a number of reasons why stepped hulls did not become popular for pleasure boats.
(a) Complexity of design, and the costs of development.
(b) Stepped hulls were banned from gold cup racing from 1920 to 1931. Wealthy race boat owners were not investing in stepped hull development.
(c) There were quite a few relatively small stepped gentleman's racers* built, but few of these were really efficient.
(d) There were many huge war-surplus aircraft engines available after the first world war, at reasonable prices, and few light weight marine engines available. It was easier, (and possibly cheaper) to buy a big engine for a monohull, than to develop an efficient stepped hull.
Three point hydroplanes and other more modern hull configurations such as tunnel hulls, use aerodynamic lift to improve the efficiency of the craft. Any weight supported by air, does not have to be supported by the water. Air has much less drag than the water. In order to obtain significant aerodynamic lift, it is necessary to have light weight and to run at very high speeds. (Race boats with modified engines or outboard motors.)
Aerodynamics of high speed boats is an extensive subject all it's own and will not be dealt with further in this paper. 
Let us look at the different drive systems and see how they affected the performance of planing hulls. We have seen how stepped hulls increased the angle of attack of the hull at high speeds, (compared to the direct drive monohull). An increase in trim angle can also be achieved by moving weight, (the engine) aft, or by changing the direction of propeller thrust. This is what alternate drive systems do.
Figure 13 shows Alternate Drive Systems
Engine weight is at about mid length in the hull. Propeller thrust is upward.
Having the engine weight forward on a monohull, helps the boat get up onto plane more quickly, as does the lifting component of propeller thrust. The direct drive layout is still in use today on boats which specialize in towing water skiers. At high speed, the forward weight and upward propeller thrust reduce the angle of attack and increase the hull drag. (Fig. (5))
The direct drive is the least expensive of the drive systems.
The engine is located aft in the hull.
The output shaft runs forward to a gear box, and then aft from the gear box, through the hull bottom to the propeller located aft under the transom.
(a) Some early stepped hull race boats were equipped with vee drives and located the crew aft of the engine. Liberty The Second, Miss Daytona, Miss Minneapolis, Arab IV, Prowler Jr.,  (These boats have been restored or replicated.) and most of Gar Wood's Miss America's.
(b) Other layouts put the engine right back against the transom. The drive shaft runs forward between the crew^which sits forward of the engine.
This was a common layout for English stepped hulls such as Miss England II, Miss Britain III, Delphine IX, and Bluebird I.   
The use of a vee drive in a stepped hull shows no increase in performance compared to a direct drive stepped hull.
Vee drive systems were common on many modern flat-bottomed racing monohulls and drag boats.
Engine weight is aft of raid length, and the propeller shaft angle is less inclined than with a direct drive. Having the weight aft tends to lift the bow of the boat, as does the more level thrust line of the propeller. The hull becomes more efficient at high speed than the direct drive monohull.
The engine is aft against the transom with the drive shaft going aft through the transom above the water line into a right angle gear box mounted aft of the transom. The drive goes down into another right angle gear box which contains the propeller shaft.
Engine weight is full aft, and the propeller thrust line is basically parallel to the keel. Modern designs are hydraulically adjustable so that the propeller shaft angle can be varied up or down. Upward thrust of the propeller helps a monohull get up on plane.
Downward thrust of the propeller helps to lift the bow at high speeds. (More efficient for this hull.)
The stern drive is the most common drive system (with inboard engine) for modern planing pleasure craft. A hard chined monohull with a stern drive, is almost as efficient as a stepped hull. (With the same deadrise and a practical power range.)
The monohull is much easier to design than a stepped hull. When we consider that the number of designers of good stepped racing hulls in the past was probably no more than a half dozen, we can understand why the large volume boat manufacturers of today avoid such complex designs.
Figure 14, shows Performance Factors for Stern Drive Pleasure Boats The small circles represent data points from actual boat tests published in 1992. The limit line is also shown. The boats tested in 1984 and prior years were significantly less efficient. The limit line was further to the left. 
The general characteristics of the Limit Line are similar to what we have seen for direct drive monohulls and direct drive stepped hulls. As the speed increases, the power requirements increase.
A surface drive is one in which only the lower half of the propeller is in the water. This was tried by Albert Hickman on his Sea Sleds in the late teens and on Rainbow IV in 1924.  In these applications, the propeller shaft went aft from the engine and through the transom just above the bottom of the boat. As the propeller rotates, only one half of the blades are in the water at a time. A three or four bladed propeller is used in order to reduce the vibrations caused by blade impacts. It is a characteristic of surface piercing propellers to shoot a great plume of water out behind the boat.
The "Roostertail" is evident in photos of Rainbow IV (1924) and of Hickman's SeaSleds (1920- ).  Surface piercing propellers must have a larger diameter than submerged propellers because not all of the blade area is working at any one time.
The advantage of the surface drive is that it eliminates the drag of the propeller shaft and shaft strut, and part of the rudder area. Neither craft just described exibited any really significant gains in speed. (This will be explained later.)
The surface piercing propeller was rediscovered almost by accident by three different race boats, in three different countries in the late 1940's.
In 1939 Sir Malcolm Campbell set a world speed record of 141.7 MPH. in a three point hydroplane designed by Adolph Apel of Ventnor fame.   In 1949, his son Donald began testing the same boat, and found that at 145 MPH. the transom started to lift. The transom mounted engine cooling water pickup would come out of the water and the engine would overheat. With the water pickup relocated to a forward sponson, a speed of 160 MPH. was achieved. When the stern lifted, the propeller came part way out of the water and became a surface piercing propeller.
As the propeller rotates, the blades come out of the water, travel through the air, and then come down out of the air and into the water with considerable impact force. This impact force is seen as a lifting force on the propeller shaft. It is this lifting force which supports the aft end of the boat. The aft end of the boat rides on the propeller force, thus the name "Prop Rider*.
The propeller shaft, shaft strut and part of the rudder are lifted out of the water. This eliminates much of the appendage drag and allows a considerably increase in speed.
The angle of the Bluebird's sponson bottoms was then changed so that they would have an efficient angle of attack after the stern lifted off the water. A speed of 170 MPH. was reached before the craft hit a floating log and was too badly damaged to rebuild.
(B) Miss Canada IV
In 1948 Harold Wilson established a North American record of 138 MPH. in a two step hydroplane designed by Doug Van Patten.  Almost the same speed that Malcolm Campbell had achieved with a three point hydroplane in 1939.
With some changes in propeller, this boat achieved 173 MPH. before the propeller shaft broke. Photos of this run show a distinct roostertail. The boat was prop riding but no one seems to have been aware of it.
Harold made one more try and exceeded the 170 MPH speed, but an overspeeding engine destroyed the gear box before speed measurements could be made. The expense of rebuilding the equipment to withstand these significantly higher speeds prompted Harold to retire from racing.
(C) Slo-mo-shun IV
The story of how this boat was developed by designer Ted Jones and owner Stanley Sayers has not been revealed in detail.
It just seemed to appear in June 1950, and set a world speed record of 160.3 MPH. Again, the roostertail revealed that this boat was 'prop riding*. After having the angle of the sponsons adjusted, Slo-Mo boosted the record to 178.5 MPH in 1952.
Here we have three boats which exhibited almost 40 MPH. (or 29%) increase in speed as a result of prop riding. These three boats demonstrate the gains to be had by combining a surface drive with a stepped hull.
Why not apply a surface drive to a pleasure boat?
In recent times, manufacturers such as Arneson and Dan Arena have packaged surface drive systems which locate the engine back at the transom and put the propeller about 30' aft of the transom. On the Arneson system the short propeller shaft is pivoted about a vertical axis for steering. These drives exibited some speed increase when installed on Offshore racing tunnel hulls, but nothing near the speed increases seen on three point hydroplanes. Rainbow IV and the Seasleds did not exibit great increases in speed in their day either.
Modern surface drives use supercavitating propellers. On a supercavitating propeller, the water separates from the suction face of the blade and leaves an air cavity between the water and the blade face. The cavity extends aft of the trailing edge of the blade. Sometimes the trailing edge of the blade is made very blunt or flat. These are called cleaver propellers.
It all goes back to the factors which limit the performance of any vee bottomed planing hull. The angle of attack of the hull planing surface relative to the water surface.
The surface drive has two factors working against the monohull. The propeller lift forces (which are well aft of the transom on the Arneson drive), and the propeller thrust line which is high and near the bottom of the hull. Both these factors tend to push the bow of the hull down, flatten the trim angle and make the hull less efficient. Any gains from reduction in appendage drag are offset by an increase in hull drag. The boat does not travel significantly faster. The reduction of one set of drag forces is offset by the increase in another set of drag forces.
The idea is to combine the efficiency of the surface drive with a hull that will have maximum efficiency, in spite of the prop lift of the surface drive. This requires a stepped hull.
I call the combination of surface drive and stepped hull, a Surf-Step. The potential gains from such a combination are considerable.
Now you can see why a study of hull design history is desireable. It enables us to look at the overall advance of technology without getting hurried in minute details.
Figure 15, Performance Factors of Different Configurations
Figure 16, Horsepower Vs Speed for different configurations.
Figure 16 shows the potential speeds for four different types of boat in the 18' to 20' length range. The hull weight is fixed. The running weight is adjusted for engine sire, and drive type weight. By using a single boat size, the numbers should be more meaningful to the average reader.
The Surf-Step is about 8 MPH. faster than a stepped hull, or 12 MPH faster than a stern drive with the same power. This magnitude of gain is worth pursuing.
General design Characteristics On modern surface drives, the propeller is located 30" or more aft of a hull planing surface. At low speeds, especially when the boat is 'getting up onto a plane', the hull assumes a steep angle of attack. This submerges the aft located propeller more completely so that more blade area is working. The pressure loading per square inch of blade area is reduced and 'runaway cavitation' is less likely to occur.
I prefer to extend the hull bottom aft on either side of the propeller to reduce hull drag during the process of getting up onto a plane. This should further reduce propeller loading at that critical speed.
A further enhancement would be to place a shroud around the upper section of the propeller. A lip on the shroud aft of the propeller will help pressurize the water at the propeller diameter.
If the shroud extends out to the hull side extensions, the propeller will be operating in a truncated tunnel.
The designer must be aware of the fact that a propeller draws in water from a disc area which is significantly larger than the propeller diameter.
The primary hull step must be located forward of the effective center of pressure in order to prevent porpoising.
The large lifting forces produced by the surface piercing propeller, move the center of pressure well forward of the static center of gravity.
Consider the cross section of the hull at the primary step. This portion of the hull will be running at near optimum trim when at maximum hull speed. A conventional vee section would be running chine-dry. The outboard portions of the bottom near the chine provide no lift, but are wetted by spray. I prefer to cut away that portion of the bottom which is not working. The wetted area is given a relatively low deadrise of about 10 degrees. Research has shown that wave impact forces are greatly reduced when the beam is reduced.   The edge of the wetted area is defined by a spray fence. Model tests have shown that spray fences can reduce the drag of a stepped hull by as much as 10 percent. Lift strakes do not have this effect.
The portion of the hull outboard of the spray fence will have a much higher deadrise. (Thirty degrees is shown.) In rough water, the craft can be expected to operate at lower speeds. There will be more wetted area. The outboard portions of the hull with their high deadrise will be operating at much less than optimum trim. These portions of the hull will contribute very little to wave impact forces.
An alternative to a dual deadrise surface is a convex hull section. The continuous curvature will be more rigid than a dual deadrise sur-face. The spray -fence which defines the beam of the high speed wetted area can be moved depending upon the power and loading of any given particular application.
The performance of any combination of hull type and drive system has definite Performance Limits. In order to increase performance beyond the limits of presently common boats, we must develop new combinations of drive and hull.
Some combinations do not promise significant improvements in Performance Limits. A stepped hull with a stern drive is only slightly better than a monohull with a stern drive. The monohull with a surface drive is only slightly better than a monohull with a stern drive.
It is the combination of surface drive and stepped hull which can produce significant improvements in efficiency for pleasure craft. (Up to 40% less power required.)
The task of designing an effective Surf-Step craft will require the combined effort of hull designer and propulsion system designer. Much of the technology is available. The drive system is complex. Stepped hulls are much more difficult to design than monohulls, and some of the design secrets which have passed on with the old designers might have to be relearned. Don't expect the first prototype to perform at the Limit Line. The potential gains are still substantial.
 D.W. Fostle, 'Speedboat' Mystic Seaport Museum, 1988
 Lindsay Lord, 'Naval Architecture of Planing Hulls', Cornell Maritime Press. 1954
 Daniel Savitsky, 'Hydrodynamic Design of Planing Hulls', Marine Technology, October, 1964
 Morley S. Smith, How Fast Will It Go?', Society of Small Craft Designers, 1986
 Powerboat Magazine, Gerald Christian Nordskog Publisher
 Trailerboat Magazine Poole Publications
 William T. Campbell Jr., A Speedboat Scrapbook-Mystic Seaport Museum, 1992
 Kevin Desmond, Power Boat, Orion Books (Crown Publishers)1988
 Uffa Fox, 'Sail And Power', Peter Davies Ltd., 1936
 'Fast Fighting Boats'
 Morley S. Smith, "The Aerodynamics of High Speed Boats" S.N.A.M.E. Oct.1985
 Leo Villa & Kevin Desmond, 'The World Water Speed Record', Pitman Press., 1955
 Donald Campbell, 'Into The Water Barrier', Odhams Press. 1955
 Harold Wilson, 'Boats Unlimited' Boston Mills Press, 1990
 Savitsky, 'On The Seakeeping of Planing Hulls', Marine Tech. April, 1968
 Ward P. Brown & R.L.Van Dyk, "An Experimental Investigation of Deadrise Planing Surfaces with Re-entrant Vee Step", Davidson Lab Report 664, Stevens Inst. Dec. 1964
 Eshbach, "Handbook of Engineering Fundamentals", John Lilley & Sons, New York, 1952
 Eugene P. Clement & James D. Pope, "Stepless and Stepped Planing Hulls" Hydrodynamics Lab R & D Report 1490, 1961
 Daniel Savitsky, "Procedures for Hydrodynamic Evaluation of planing Hulls in Smooth and Rough Water" Marine Tech. Oct. 1976
 Donald L.Blount & David L. Fox, "Small-Craft Power Prediction", Marine Technology January, 1976
* * *
Performance Factors were developed so that the performance or efficiency of one boat design can be compared to that of another. Performance is expressed in terms of maximum speed, rated power and running weight. These are factors which are usually readily available for existing boats. Factors such as overall length and maximum beam have very little to do with the actual performance of a boat. Factors such as location of the center of gravity, chine beam at the center of gravity, or deadrise at the center of gravity are seldom known.
Performance Factors are derived from model scaling relationships. Ulhen a prototype hull design is scaled down to produce a model for tank testing, the proportions of the model must maintain a fixed relationship to the proportions of the prototype. These relationships are controlled by the "Rules of Similarity". 
All length dimensions (length, beam, location of center of gravity etc.), must be decreased in the same proportions.
Areas - decrease as the square of the length scale factor.
Volumes - decrease as the cube of the length scale factor.
Weights - decrease as the cube of the length scale factor.*****
The model is towed and the drag is measured at different speeds.
Because the model has been scaled according to the rules of similarity, the model drag and power requirements are scaled also.
Horsepower - decreases as the length scale factor to the 3.5 power (Mathematically)
Speed - decreases as the square root of the length scale factor, or the length scale factor to the 1/2 power (mathematically)
Naval architects usually plot the hull drag against a speed factor. The speed coeff. is commonly expressed as a speed/length ratio or a speed/beam ratio.
Where g is the acceleration due to gravity. (32.2 ft/sec²) The introduction of g makes the speed coefficient non-dimensional.
The model and the prototype run at the same speed coefficient.
The problem with such coefficients is that they do not allow the comparison of the performance of two different hulls with significantly different proportions. Consider a hypothetical example. Two identical hulls. Same weight, same drag versus speed curve, same power and same top speed.
One hull is given flared sides so that the measured beam at the shear is greatly increased (without any increase in weight) If these hulls are compared on the basis of drag versus a speed/beam coeff., the performance will not be comparable. The wide hull will appear to have more drag at the same speed/beam ratio. In reality, the speed performance of the two hulls will be exactly the same. Similarly, a long raked stem can upset a speed/length comparison.
It is because of these disparities that other speed coefficients needed to be developed.
This is close to the Speed Factor which I use. I divide the weight by a factor of 1,000 just to produce more manageable . numbers.
Naval architects commonly express the efficiency of a planing surface in terms of the drag produced in order to hydrodynamically support a given amount of weight. The drag/lift ratio. The amount of drag is roughly equal to the component of propeller thrust which is parallel to the keel. The thrust is proportional to the driving horsepower (and speed).
Because the horsepower of an existing hull is known, and the actual hull drag is not known; it is logical to express the hull efficiency as a power/weight factor.
Power - varies as the 3.5 power of the length scale factor.
Weight - varies as the 3rd power of the length scale factor.
Power - varies as the (3.5 / 3.0) power or the 1.1667 power (mathematically) of the WEIGHT scale factor.
Speed - varies as the square root or 1/2 power of the length scale factor.
Weight - varies as the 3rd power of the length scale factor.
Speed - varies as the (1/2 divided by 3) or the 1/6 power of the WEIGHT scale factor.
Figure 18 Shows weight raised to these two power levels.
At low planing speeds, th® appendage drag, the aerodynamic drag, and the appendage li-ft forces are small compared to the hydrodynamic drag. The usual procedure for designing a low speed boat is to optimize the hydrodynamic drag of the hull. There is little to be gained by trying to improve or optimize anything but the hydrodynamic drag.   
On high speed boats, the appendage drag, aerodynamic drag, and appendage lift forces can be very large. [These forces increase as the square of the speed.)
Lift produced by the angled propeller shaft of a direct drive system shifts the effective center of gravity <or center of hydrodynamic pressure seen by the hull), forward. The angle of attack of the hull decreases, and the hull drag increases. The rear optimum chine beam for this high speed hull will be different than it would be if shaft lift were ignored in the calculations. The whole system must be considered during the design stage of high speed boats. 
The limit lines shown on the graphs are mathematical expressions which are valid for the particular combination of hull type and drive system being investigated. One equation should cover all of the craft of a given combination.
The naval architect can develop a mathematical equation which will closely approximate the limit line. The basis of the equation is that the horsepower put out by the engine equals the total of all of the losses and drag forces in the system. This equation includes factors such as: transmission losses, propeller slip, aerodynamic drag, hull drag, appendage drag, (rudder, propeller shaft, strut, etc.)
By using such equations, the naval architect knows where the horsepower goes and which losses are greatest.
When calculating the hydrodynamic drag of a planing hull, the designer must take into account the lift forces on the inclined propeller shaft and rudder, and the suction forces produced by the propeller on the hull.
Consider a direct drive hull. The aerodynamic drag, propeller shaft drag, strut drag and rudder drag all increase as the square of the speed. Individual drag coefficients can be developed using methods outlined in . When the effects of propeller shaft and rudder lift, and propeller suction are taken into account, it was determined that the hull drag also increases as the square of the speed - (in the power range for which I have data).
Horsepower is calculated at different speeds using this equation. This data is then converted to Power Factor and Speed Factor for plotting on the graph.
Similar procedures can be used to establish the mathematical equation for the limit line of other configurations.
STEPPED RACE BOATS
The data collected usually provides total weight of hull and engine. I have estimated crew and fuel weight to arrive at an approximate running weight. The hull hydrodynamic drag is assumed to be constant at maximum speed. Equal to the drag of the step deadrise at optimum trim plus ten percent.
Most of the boats recorded, used an aft propeller shaft bearing mounted in the rudder. This essentially eliminates the drag of the shaft strut.
Reference  shows test data and limit lines for offshore performance boats, outboard powered vee bottomed hulls and outboard powered tunnel hulls.
(Reprinted from Speed Boat Developments from the Past Into the Future by Morley S. Smith, Freeville, NY)