13.pdf


Aperçu du fichier PDF 13.pdf - page 3/52

Page 1 2 34552



Aperçu texte


uses the E approach, as well as the ON4UN LOW BAND
SOFTWARE modules dealing with boom strength and torque
balancing.
Curt Andress, NI6W (now K7NV)wrote an interesting
software package that addresses all of the mechanical issues
concerning antenna strength. YS (Yagi Stress) is easy to use,
has lots of data about materials and tubing in easy-to-access
form. For information contact K7NV@contesting.com. A
free trial download can be obtained from WXØB’s website at
www.arraysolutions.com/Products/yagistress.htm.
All of these tools deal with static wind-load models. The
question, of course, is how reliable all these models are in a
complex aerodynamic situation. As Leeson puts it, “. . . but
we’re not dealing with mathematical models when the wind is
roaring through here at 134 mi/h. Either model (C or E) results
in booms that break upward in the wind if you ignore vertical
gusting...” In particular locations, such as hilltop QTHs, there
may be vertical updraft winds that can break a boom unless
three-way boom guys are used. But these are rather extreme
conditions, not the run-of-the mill situations.
The real proof of the pudding is in the building of big
antennas, and even more so keeping them up year after year.
The mathematics involved in calculating all the structural
aspects of a low-band Yagi element are rather complex. It is
a subject that is ideally suited for computer assistance. To­
gether with my friend R. Vermet, ON6WU, I have written a
comprehensive computer program, YAGI DESIGN, which
was released in early 1988 and updated a few times since.
In addition to the traditional electrical aspects, YAGI
DESIGN tackles the mechanical-design aspects. This is espe­
cially of interest to the prospective builder of 40 and 80-meter
Yagi antennas. While Yagis for the higher HF bands can be
built “by feel,” 40 and 80-meter Yagis require much closer
attention if you want these antennas to stay up.
The different modules of the YAGI DESIGN software
are reviewed in Chapter 4 on low-band software. This book is
not a textbook on mechanical engineering, but a few defini­
tions are needed in order to better understand some of the
formulas I use in this chapter.
3.2.1. Terms and definitions
Stress: Stress is the force applied to a material per unit
of cross-sectional area. Bending stress is the stress applied to
a structure by a bending moment. Shearing stress is the stress
applied to a structure by a shearing moment. The stress is
expressed in units of force divided by units of area (usually
expressed in kg/mm2 or lb/inch2).
Breaking Stress: The breaking stress is the stress at
which the material breaks.
Yield Stress: Yield stress is the stress where a material
suddenly becomes plastic (non-reversible deformation). The
yield stress to breaking stress ratio differs from material to
material. For aluminum the yield stress is usually close to the
breaking stress. For most steel materials the yield stress is
approximately 70% of the breaking stress. Never confuse
breaking stress with yield stress, unless you want something
to happen that you will never forget.
Elastic Deformation: Elastic deformation of a material
is deformation that will revert to the original shape after
removal of the external force causing the deformation.
Compression or Elongation Strain: Compression strain

is the percentage change of dimension under the influence of
a force applied to it. Being a ratio, strain is an abstract figure.
Shear Strain: Shear strain is the deformation of a
material divided by the couple arm. It is a ratio and thus an
abstract figure.
Shear Angle: This is the material displacement divided
by the couple arm. As the angles involved are small, the ratio
is a direct expression of the shear angle expressed in radians.
To obtain degrees, multiply by 180/π.
Elasticity Modulus: Elasticity modulus is the ratio
stress/strain as applied to compression or elongation strain.
This is a constant for every material. It determines how much
a material will deform under a certain load. The elasticity
modulus is the material constant that plays a role in determin­
ing the sag of a Yagi element. The elasticity modulus is
expressed in units of force divided by the square of units of
dimension (unit of area).
Rigidity Modulus: Rigidity modulus is the ratio shear­
stress/strain as applied to shear strain. The rigidity modulus is
the material constant that will determine how much a shaft (or
tube) will twist under the influence of a torque moment (eg,
the drive shaft between the antenna mast and the rotator). The
rigidity modulus is expressed in units of force divided by
units of area.
Bending Section Modulus: Each material structure (tube,
shaft, plate T-profile, I-profile, etc) will resist a bending
moment differently. The section modulus is determined by the
shape as well as the cross-section of the structure. The section
modulus determines how well a particular shape will resist a
bending moment. The section modulus is proper to a shape and
not to a material. The bending section modulus for a tube is
given by:
S = π×

OD 4 − ID 4
32 × OD

(Eq 13-1)

where
OD = outer diameter of tube
ID = inner diameter of tube
The bending section modulus is expressed in units of
length to the third power.
Shear Section Modulus: Different shapes will also
respond differently to shear stresses. The shear stress modulus
determines how well a given shape will stand stress deforma­
tion. For a hollow tube the shear section modulus is given by:
S = π×

OD 4 − ID 4
16 × OD

(Eq 13-2)

where
OD = outer diameter of tube
ID = inner diameter of tube
The bending section modulus is expressed in units of
length to the third power.

3.3. Computer-Designed 3-Element
40-Meter Yagi at ON4UN
Let us go through the design of a very strong 3-element
full-size 40-meter Yagi. This is not meant to be a step-by-step
description of a building project, but I will try to cover all the
Yagis and Quads

Chapter 13.pmd

3

2/17/2005, 2:49 PM

13-3