Raingutter Boat Racing - Breathing Life Into Your Boat

Forward Balance

A boat blown through the water by your breath moves water aside. We call this resistence drag. If your boat is to have the best chance of being fast, it must displace as little water as possible and have a shape that makes the drag small. For hydroplanes this is not a problem except at the beginning of a breath and possibly at the end of one. But for all boats that travel with part of their hulls submerged in water it is an important factor in a race. The rest of this page deals with non-hydroplane boats.

Since the sail is above the water line and the part of the hull subject to drag is below it, the two forces tend to tip the boat's bow (nose) down. This tipping is important to know about while designing a boat since it limits the speed of the boat. To model this tipping the concepts of the boat's center of mass, center of pressure, center of pressure drag and center of bouyancy are needed. The relationships among these involve torques which are forces that act through a distance called a lever-arm.

Center of Mass

A boat's center of mass is the point about which it rotates in free space. The raingutter is not free space, but we can still think of the center of mass as the actual rotation point. Depending on the hull shape, the center of mass may need to be lifted since the water can get in the way of a tipping hull! When this is necessary, the weight of the boat opposes this lifting via another torque.

As a practical matter, the center of mass of your boat is near the center of its hull unless you've added weight to get your boat up to the minimum weight. As it will be shown on this page, most boats benefit from a center of mass that is moved back by adding weight toward the back of the hull.

Center of Pressure Drag

The part of your hull in the water is the part that moved water out of the way to make a space for it. The center of that space is the center of mass of the displaced water and acts as a center through which the bouyant force acts. Water pressure is the same on oposite sides of it. The pressure of the water under the hull is equally opposed by the force of the weight of the boat on the area inside the waterline. Because the water pressure in all directions balances out at this point, it is also called the center of pressure drag.

Center of Pressure

Your sail has a similar point where the pressure due to the air movement cancels out in all directions. If you blow into the middle of your sail, it is near its middle, close to but behind the sail (behind being toward the back of the boat). The forces pushing against the sail are considered to act through this center of pressure. "Forces" is plueral because we consider in the models both the driving sail force and the oposing pressure drag of the sail.

Tipping is a balance of oposite torques

Torques fighting to tip a boat forward

It is easy to think about the forces on a regatta boat, but it is less obvious where the lever-arms that make them torques are located. This is partly because each is at a right angle to the direction its force acts in. Each lever arm also passes through a fulcrum or point of turning.

The center of mass is the most important fulcrum, but if the hull is not bowed like the runners on a rocking horse, the water surface toward the front of the boat can become another. But because the amount of tipping can be dramatically reduced by placing a small but optimally sized sail on the deck, it is not likely that we need to consider this fulcrum except in the case where the bow has been swamped with water and the boat is actually in danger of flipping "head over heels".

For a boat designed to reduce tipping, we can write the competition of torques about the pitch axis passing through the center of mass as:

Ss + Dd = Bb where S is the force on the sail including the pressure drag of air, B is the bouyant force and D is the hull or water pressure drag. The lower case letters indicate the length of the forces' lever arms. If the sail's center of pressure is above the boat's center of mass, s has a positive sign. If the center of bouyancy is in front of the boat's center of mass, b is positive. Similarly, if the center of bouyancy is below the boat's center of mass, d is positive.

The sail's torque, Ss, and the torque due to drag, Dd, tip the bow down when they are positive. The bouyant torque, tips the bow up when it is positive. This means the boat must be bouyant enough to balance both the torque cased by blowing and that caused by drag.

The sail and drag forces act parallel to the boat's motion while the bouyant force always acts upward. Let O, theta, be the tipping angle from 0 = parallel to the water surface. As the boat tips, the lever-arms change slighty and because the shape of the sail changes slightly in the flow of air, the breath and air resistence forces also change a little (the pressure drag coefficient changes by a factor of about cosO). Most of the changes are small ones involving a factor of cosO or sinO because of the geometry of tipping.

Let the center of mass of the boat be at y = 0, z = 0, where y is the forward coordinate and z is the vertical one. Then

s = CPy sinO + CPz cosO (CPy is negative)

b = CBy cosO - CBz sinO (CBz is likely negative)

d = CBy sinO + CBz cosO (CBz is likely negative)

So, the full relation accounting for the angle is

ScosO(CPy sinO + CPz cosO) + D(CBy sinO + CBz cosO) = B(CBy cosO - CBz sinO)

This expression must balance, so we can hope to solve for the tipping angle, O. It theoretically can be solved if it is assumed the boat tips no more than plus or minus 20 degrees so the small angle approximations can be used: sinO = O and cosO = \[1-O2] When this is done, the relation becomes fourth order in the angle O and the standard solution for a fourth order single variable equation can be used. For now, the solution is TBD since it is easier to program a calculator to find it iteratively using a simple Newton-Raphson algorithm.

A strategy to use tipping as an advantage!

When the wind begins to blow stronger in the sail, it first levels the boat, then begins to tip it forward. If the bow dips too low, it catches the on coming water and gets swamped which stops it quickly. But if the hull is designed to point up while floating, the downward tipping can be made to balance when the hull is level and O (theta) = 0 (zero). At that point,

Ss = Bb - Dd and B = W

These two expressions reduce to one by substituting W for B,

Ss = Wb - Dd

The weight of the boat is like our human nature and the baggage created as the result of sin in our lives. These react against the buoyant force of Godly character that keeps us afloat in the waters of life.

Likewise, our misunderstandings about God or misdirected attitudes are like the part of the wind's force being directed against our character as well. Indeed the Bible declares that where there is good, evil is present also.

God's refreshing and empowering wind has the ability to drive us forward maintaining a level deck. But we must do our part to maintain the integrity of our hull and the trim of the sail. As God brings us more challenges, we find that our understanding of Him must change and our attitudes bend upward in order to keep our progress level.

[Next Section] [Dry Dock] [Title Page]

Raingutter Boat Racing - Breathing Life Into Your Boat
Copyright © 1997, 2000, 2002, 2004 by Michael Lastufka, All rights reserved worldwide.