A New Tack

by popular demand i'm going to switch gears and jump right into designing and creating kites.
i'm going to suggest designs, try them and see if they work. you're welcome to try them also. i've sort of been trying to wing it on a theoretical model for how kites work. this approach is difficult for me and boring for a lot of readers. so, lets have some fun and get out the paper and string.

I'm Still Here

i'm thinking hard on the best aerodynamic model for kite design. so far i've decided to model flow lines across the contoured surface of a kite. this would be a lot simpler if i was using a 3D CAD package, but it's really a challenge using AutoSketch. i would recommend that you use CAD for your kite designs. TurbCad 2D/3D Deluxe seems to be a good choice. personally, I plan to use TurboCad Pro when i upgrade my system.

Bernoulli's Equation

i have given some examples. i think it is
appropriate to explain the principle that explains
how kites fly.
that is, Bernoulli's equation ( a statement of energy conservation
along the streamline of a fluid ).

m*g*h + (1/2) * (d*v^2 )+ p*(Vol1) = m*g*H + (1/2)*(dV^2) + P*(Vol2)

m*g*h and m*g*H represent gravitational potential and are equal so they can be eliminated
so:

(1/2)*(d*v^2) + p*(Vol1) = (1/2) (d*V^2) + P*(Vol2)

(1/2)*(d*v^2)-(1/2)*(d*V^2) = P*(Vol2) - p*(Vol1)

(1/2)*d*(v^2-V^2) = Vol(P-p)

d = density of air
v = initial velocity of air
V = velocity of air after it contacts the kite surface

we are going to assume that the volume of the air remains the same so

Vol = Vol1 = Vol2
p = pressure of air before it reaches the kite surface
P = pressure of air at the kite surface

we are interested in (P-p)

if the surface brings the velocity of air to a completely
perpendicular to the wind surface:
V = 0 -- that is capital V

and

(1/2) (d*v^2)= Vol*(P-p)

or, the difference in pressure DP = (P-p) is proportional to (1/2)(d*v^2)

though there is no complete analytical solution for all
shapes and orientations of surfaces, i am going to
use this equation as a starting point in the
calculations to come.

Dihedrals -- Symmetry and Stability

think about how the dihedral in the diagram enhances the stability of a kite. the keel produced by the two angled faces makes the kite track straight in the wind. solving for the effective area of the dihedral is simple trigonometry A'= cos@*2*A. this of course assumes that the keel between the faces is perpendicular to the wind. there are other ways of improving kite stability but this may be the most common application.

Symmetry -- An All Important Element

when you think of a particular design for a kite, you must always consider the adverse effects of any asymmetry. this applies not only to errors in shape and size between the right and left sides of the kite, but also to the type of fabric and the direction of fabric grain. in short, the right and left sides of a kite should be mirror images of each other in every aerodynamic aspect.

Collecting Pieces

the examples i have given demonstrate the general principles that allow kites to operate and can serve as a starting point for kite design. note that i have only described the force component that is directly resisting the force of the wind. because as this force is deflected, it produces lift on a kite. ultimately the kite achieves a static condition where the weight of the kite is precisely balanced with its lift.

Maxwell Eden has written an excellent book on kite building--THE MAGNIFICENT BOOK OF KITES, Black Dog and Leventhal Publishers,Copyright 1998. on p. 201 Eden gives the following formula for the minimum wind speed required to produce lift.

w = wt. in ounces
A' = effective area in square feet
v = minimum wind speed in mph

v = 7*(w/A')^1/2

note the similarity to the equations we have used so far.
the coefficient of 7 is generally applicable but smaller coefficients ~5 are used for kites designed for light wind.

Simplifying Things

now that we have the basic equation for a force wind exerts on a surface it blows directly against, it's time to illustrate a simple principle. if the surface we're talking about is at an angle to the wind -- as shown above -- the equation F = 1/2(d*A*v^2) becomes
F = 1/2(d*A'*v^2). A' is perpendicular to the wind. this gives you the component of force F opposite to the wind. note that the wind passing through the area A' includes all the wind that will strike surface A. it can be called the "effective area."