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Boat Speed in Small Boats: The Physics of Going Faster. Paul Miller Naval Arch & Ocean Engineering Dept. US Naval Academy. The Big Picture in Winning Races. Boatspeed: A useful application of what you learned (?) in physics!. Background:.

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Boat Speed in Small Boats:The Physics of Going Faster

Paul Miller

Naval Arch & Ocean

Engineering Dept.

US Naval Academy

The Big Picture in Winning Races


A useful application of what you learned (?) in physics!


Fact:Dinghy sailors win in more types of boats than big boat sailors?

Why? Assuming you learned something more than starts and tactics in college!


“Boatspeed Blindness” can be detrimental to your racing success!

1996 Int’l Canoe WorldsLemon Tree Passage, Australia

The Start!

The Finish...

The Key Measurement of Racing Boatspeed

  • V = Velocity of boat

  • Vmg = Velocity of boat made good to the next mark (sometimes V “to windward”)

    Which wins boat races?

    They are related by: Vmg = V * cos(f)

Example: Two Boats Beating

In “Point Mode”; V = 5.24 knots, f = 37 degrees

In “Foot Mode”; V = 5.40 knots, f = 40 degrees

Which gets to the weather mark first?


In “Point Mode” Vmg = 4.18 knots

In “Foot Mode” Vmg = 4.13 knots

On a 1/2 mile beat, the “pointer” is 6 seconds

(3 boatlengths) ahead!

How do you find the optimum V and pointing angle, f?

1. Experiment, measure and record

(could be “seat of the pants”)

2. Two-boat-test for relative improvement

(race experience or practice)

3. Predict using a Velocity Prediction Program (VPP)

(IMS and IRM use a VPP to get ratings)

4. Switch to Naval Architecture as a major...

(My chance to put in a plug!)

VPP “Polar”

Provides predicted speeds for all points of sail for common wind strengths.

VPP’s are often customized for different boats types (ex. IACC, IMS, 12m)

Basic Physics of Boat Speed

  • F=m*a !

  • The sum of the forces equals zero F=0

  • The sum of the moments equals zero M=0


    “For every action there is an equal and opposite reaction.”

Sail Force

Where does the force in the sails come from and where does it go?




Note the wind is deflected by the sail!

In Detail:

Force Generated by the Sails = Mass of Wind x

the amount the wind is decelerated by the sails


Force Generated by the Sails = Mass of the boat x the amount the boat is accelerated, (“Thrust”)

plus the mass of the water x the amount the water is accelerated, plus the mass of air x the amount the air is accelerated (“Drag”)

Why is “Acceleration” Important?

Velocity = Acceleration dt

Distance = Velocity dt

And the one that goes the farthest in a given amount of time, or covers the same amount of distance in the shortest time wins the race!

The Goal’s From Physics Are:

  • Take as much from the wind as you can

  • Reduce the mass of the boat as much as possible

  • Disturb the water and wind as little as possible

  • All the while making sure you are maximizing Vmg rather than V!

It isn’t quite that simple(but it’s close)!Quiz 1:Which is faster?

Boat “A”

22 feet

4200 lbs

300 sq ft

Boat “B”

24.5 feet

4200 lbs

300 sq ft

Waterline Length


Sail Area

177PHRF Rating129

Boat B is 48 seconds per mile faster!

Boat A and Boat B


Express 27

If everything else is equal, the longer boat is faster!

The Big Picture in Winning Races

Sail Force

Recall that “For every action…”

As the fluid is deflected past the sail, the sail is deflected the opposite way.

Sail Force

The Magnitude of the force is approximated by Bernoulli’s Equation:

F=½(air density)(wind velocity)2(Sail Area)(Coef. of Lift)

To get more sail force you can increase any of these terms!

1. Sail for the puff, or put up more sails...

2. For most sailors the only “legal” option is to adjust the Coefficient of Lift…

This is accomplished through “sail trim”.

Sail Trim

  • The Direction of the Sail Force depends on how much Lift and Drag the sail is producing.

  • Lift is the force produced perpendicular to the wind

  • Drag is the force parallel to the wind.

Quiz #2Which contributes more to boatspeed; Lift or Drag?

Answer: Both!

Upwind Goal:

High Lift & Low Drag

Downwind Goal:

High Lift & High Drag

Upwind Sail Trim

  • High Lift

    • Full sail

    • High Angle of Attack

    • Even twist

  • Low Drag

    • Flat sail

    • Low Angle of Attack

    • Even twist



Downwind Sail Trim

  • High Drag and Lift

    • Full sail

    • High Angle of Attack (near stall on reach, stalled on run)

    • Even twist

Highest Drag

Tell-Tales(Results from Wind Tunnel Tests)

High Lift/ Low Drag

High Lift/ High Drag

Other Sail Controls

  • Vang (twist, forestay tension, mast and boom bend)

  • Outhaul (lower part of the main lift/drag control)

  • Luff adjustment (flow attachment and lift coefficient control)

  • Mast bend (spreaders, shroud tension)

How do you know when to adjust the controls?

  • Is the twist even?

    • Boom and top batten roughly parallel

  • Is the boat overpowered?

    • Can’t keep it flat, luffing sails

  • What are the faster boats doing?

    • If they are going faster than you, find out why!

The Ultimate Sail?


Current holder of the

“Little America’s Cup”

Routine speeds of 20 knots

in 15 knots of breeze!

“World’s Fastest Raceboat”

IACC/Int’l Canoe Mast Project

The Big Picture in Winning Races

Foil Basics

  • F=0

  • So Side Force generated by the sails is balanced by the side force (Lift) of the Foils (Centerboard and Rudder)

Foil Lift and DragCenterboard and Rudder

  • The same concept as sails

  • Bernoulli’s Eqn for force (Lift or Drag) magnitude

  • Vector addition of lift and drag components for direction

  • Goal is high efficiency

    • (High Lift/Drag ratio)

Lift and Drag on Foils

Foil Drag Components

  • Friction (Viscosity)

  • Pressure (Lift induced, eddies)

  • Aspect Ratio (Span2/Area)

  • Planform

The Drag Equation from Bernoulli’s is:

Fdrag=½(water density)(boat speed)2(Foil Area)(Coef. of Drag)

The two easily-changed variables are area and Cd!

Foil Frictional Drag

Two things for sailors to think about:

  • Smoothness (1/c Huffman: EN245A)

    • Smoother the better

    • Laminar vs Turbulent

    • Min sand w/400 grit

    • All coatings were worse

  • Area

  • Polished

    Sanded with 180 grit


    Angle of Attack

    Example of Area Reduction

    Centerboard area is approximately 10% of the total wetted surface.

    In light air “wetted surface drag” is approximately 80% of total drag.

    A 420 Running:

    Raising the board 90% of the way will reduce drag 7%! Giving 0.14 kt!

    This assumes you don’t increase rudder drag due to loss of steering control!

    Foil Pressure Drag

    • Keep angles of attack small so as to stay in low drag area of foil performance. (High Lift/Drag ratio)

    High Drag


    In a 420, increasing the rudder angle from 2o to 6o will cost 0.1 kt!

    Low Drag


    Example of How to Minimize Angle of Attack

    “Steer with your weight”

    “Steer with the sails”

    This minimizes the foil drag.

    Think of the rudder as a brake.

    The Big Picture in Winning Races

    Hull Resistance

    • Friction

    • Pressure (eddies)

    • Wave Making

    • Spray

    Typical Dinghy Resistance Curve


    Int’l Canoe

    Hull Friction Drag

    • Like foils, make it as smooth as possible! (Min 400)(Benefit is not as great as foils)

    • Reduce area by heel or trim (flat areas out, round sections in)

    Hull Pressure Drag

    • Reduce eddies by not letting transom drag (look for “clean” flow off stern)

    • Move forward if possible

    Hull Wave-Making Drag


    • To make waves takes a lot of energy!

    • Energy used in making waves is based on:

      • Wave length

      • Volume of water displaced

    When beating in a 420 in light air, the lighter crew (~50 lbs) is 0.15 knots faster!

    Example of Weight/Length Effect

    Cal 20 and Moore 24 (originally)

    Same Weight and Sail Area: Different Length

    Moore 24 is 1.5 minutes a mile faster! Moral is, “Think Light!”

    Research in Length

    “New” Navy 44 Research

    The Big Picture in Winning Races

    Saving the best for last!

    Effect of heel on drag

    Increased yaw moment

    Increased leeway

    Increased rig drag

    Increased wave making

    StabilityThe most important factor in speed?

    Except in light air and flat bottomed boats, heel is slow!

    StabilityThe most important factor in speed?

    Effect of heel on thrust

    • Reduced sail area

    • Reduced rig efficiency

    How stability fits with physics

    F=0,  M=0

    h x SF = weight x t

    Thrust=SF x sin(B)

    B=sail trim angle


    Thrust =(w x t x sin(B))/h

    There will not be a quiz at the end!

    Example: Effect of Hiking

    How much more sail force can we develop if we hike just 3” farther out on a 420?

    Thrust =(w x t x sin(B))/h

    If “t” goes from 3’ to 3’3”, then Thrust goes up 1%!

    That gives us 2 boatlengths/beat on a short course!

    If “t” goes from 3’ to 6’, Thrust is doubled!

    Hence the value of a trapeze!

    Effect of Crew Weight on Speed

    Crossover at about

    the point when

    whitecaps start

    “Nothing’s new in Naval Architecture”





    Sliding seat

    So what do you do when you have too much wind, knowing that heeling is slow?!


    • Decrease Sail Area or Cl- Smaller sail, reef , twist or flatten

    • Increase weight or “t” - Bigger crew or hike farther out

    • Decrease “h” - “Lower” sail or raise centerboard

    • Increase B - Lower traveller, barber haul, ease sheet, twist sails

    From the basic equations...

    F=½(air density)(wind velocity)2(Sail Area)(Coef. of Lift)

    h F = w t

    Thrust =(w t sin(B))/h

    “Something new in naval architecture…”(Actually proposed by L. F. Herreshoff in 1947)



    best uses



    Note also bow

    and stern


    V=28+ kts!

    The Big Picture in Winning Races

    Key points to remember about boatspeed:

    • Reduce drag of sails, hull and foils

      • Wetted surface, rudder angle, sail fullness, total boat weight

  • Adjust power to match righting moment

    • Proper twist

    • Hike harder, sail flatter

    • “Flat is fast and fast is fun!”

  • Just for fun, what would happen if you got in the way of a Navy 44?

    Have fun and think fast!

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