telescope techniques

A Balancing Act for

Dobsonian Telescopes
Achieve perfect balance using springs

instead of heavy counterweights.

By Tom Krajci

M
any of us dream of
building large-aperture,
lightweight telescopes. Such
instruments can easily be
transported to dark-sky sites for awe-
inspiring deep-sky views. Cutting-edge
amateur telescope makers, like Gary Wo-
lanski (S&T: August 1999, page 128), are
constantly incorporating new designs
and materials to make ever-larger instru-
ments more and more portable.
For a Dobsonian telescope to work
properly it has to be balanced. However,
given the layout of many of the new
lightweight designs, every extra pound at
the focuser end of the scope requires five
pounds of extra weight at the mirror end.
Obviously, unless the front of the scope is
very light, or the back very heavy, some
kind of balance problem is likely.
One of the design goals I had when
constructing my 16-inch truss-tube
Dobsonian was that it be transportable
in my midsize car. This necessitated a
low-profile rocker box and altitude bear- Author Tom Krajci holds the 15 pounds of counterweights that would have been needed to
ing assembly. It was apparent early on balance his 16-inch f/6 Dobsonian telescope if he had not implemented his virtual counter-
that such a configuration would make it weight system. All photographs courtesy the author.
difficult to position the scopes center of
gravity at the trunnion axis. To make extra weight. Since I was obviously not that torque generated by the spring varies
matters worse, the upper end of my tube the first telescope maker to run up against linearly as it stretches, but the torque re-
assembly turned out to be heavier than I this problem, I didnt have to look far to sulting from the imbalanced scope varies
had planned. It seemed as if I had paint- find a variety of interesting solutions sinusoidally as the angle of the scope
ed myself into the proverbial corner. from those who had gone before me. changes. However, as Caudell points out,
A search of the amateur literature one need not perfectly match the torque
The Search for Solutions turned up several interesting proposals. caused by the imbalance with that gener-
To look at the situation from another In the June 1981 issue of Sky & Telescope ated by the spring since in most cases
angle, the real problem was that extra (page 549) Thomas Caudell advances the friction in the telescope mount can han-
torque was being applied to the altitude idea of counteracting telescope imbalance dle the remaining imbalance. Thus, the
trunnion by the imbalanced weight of the on a German equatorial mount by using idea of using springs had a lot of appeal.
tube. What I wanted was a method of a spring instead of counterweights. The In the Spring 1996 issue of Amateur
counteracting this torque without adding principal shortcoming of this method is Astronomy (page 50) Barry Peckham

130 November 1999 Sky & Telescope

 (A) and the length of the wire rope need
careful planning. If the rope is disconnect-
ed from point D and the spring is allowed
D to completely relax, the end of the rope
should be at pulley C. With this adjust-
ment we see that in attaching the spring to
D we must pull the rope a distance x from
the pulley, stretching the spring by an
equal amount. When j = 0, the spring is
still stretched, but by a minimum amount
where x = d. Since the force due to a
spring is proportional to the amount it is
C stretched from its relaxed length, we can
write F = kx, where F is the force applied
B to point D (as transmitted through the
rope) and k is the spring constant a
measure of the stiffness of the spring.
A Fields analysis shows that a combina-
tion of proper spring pretensioning, loca-
tion of the attachment points, and pulley
geometry can transform the springs lin-
ear torque into the sinusoidal torque re-
The spring counterweight system as applied to Tom Krajcis Dobsonian. A is the anchor point quired. Here was a solution I could use!
for the spring that is attached to a wire rope at B. The rope bears against the pulley at C before Unlike earlier spring counterweight solu-
being attached to the telescope at D. tions, this method exactly counterbal-
ances the telescope at all altitudes. Best of
demonstrates that spring counterweights counterbalancing at all telescope eleva- all, it is simple no specially made cams
can work on a large Dobsonian to fine- tions, but I was not eager to fabricate the or exotic hardware are needed.
tune the scopes balance, an idea that necessary cam.
Chris Westland takes a step further in the Posting a query regarding spring coun- Springing into Action
Winter 1998 issue. Westland carefully an- terweights to the ATM e-mail list pro- The first step in implementing this virtual
alyzes the forces involved in an imbal- duced a number of solutions, including counterweight system is to determine the
anced telescope and shows that a specially one by Stuart Field, a physics professor at exact amount of imbalance in your tele-
designed cam, spring, cable, Colorado State University. Field proposed scopes tube assembly. An excellent book,
and pulley arrangement the general layout of the spring counter- The Dobsonian Telescope (Willmann-Bell,
could allow a telescope weight system shown in the illustration 1997) by David Kriege and Richard Berry,
to defy gravity. This below. A spring is fixed at one end, A, gives detailed instructions in chapter 3,
was the first solu- and is connected to a wire rope page 59, on how to calculate the required
tion I had come at its other end, B. The rope counterbalancing. The method is pretty
across that pro- then passes around a pulley straightforward. All you need to know is
vided exact at C and is finally connected how much the pieces weigh and how far
to the altitude bearing at D. they are from the desired balance point.
Points C, D, and the center of the For example, if your finderscope weighs 3
altitude bearing are collinear when pounds and is positioned 60 inches away
the telescope points straight up and from the balance point, then it has a
angle j = 0. Thus j is the angle of the torque of 180 inch-pounds. To counter its
scope as measured from its vertical posi- weight you will need an equal amount of
R tion, so that the torque induced by any torque on the other side of the balance
R weight imbalance is proportional to sinj. point. This could mean a 15-pound
D In order to balance properly, the spring weight 12 inches from the pivot point, or
device must provide a countertorque that a 7 12-pound weight 24 inches from the
x is also proportional to sinj. balance point the choice depends on
d The position of the attachment point the configuration of your particular
scope. Add up all the inch-pounds on one
C This schematic shows the spring counter- side of the balance point and compare the
weight system proposed by Stuart Field, pro- result with what you have on the other
B fessor of physics at Colorado State Universi- side. The difference is the added counter-
ty. Field was able to show mathematically weighting you need.
that this arrangement produces a torque Since I was building my scope from
that varies sinusoidally exactly what is re- scratch I knew the weight and position of
quired to balance a telescope. all the components. However, if you al-

A Sky & Telescope November 1999 131

telescope techniques
Tom Krajcis spring counterweight system is
shown here in action. Note that when the
telescope is pointed straight up, the spring is
not completely recoiled. When the telescope
is pointed horizontally (bottom image), the
spring reaches its maximum length. It is im-
portant to determine beforehand how far the
spring can safely stretch.

ready have a completed tube assembly

you can easily determine the amount of
imbalance by laying your tube horizon-
tally on top of a broom handle on the
floor. Position the tube so that the center
of the altitude trunnions is positioned di-
rectly over the broom handle. Use a scale
and measure how nose-heavy the tube as-
sembly is. Make note of the distance from
the bearing axis to the scale and multiply
the weight by that distance. For example,
3 34 pounds and 70 inches will give you
26212 inch-pounds of torque.
The next step is to acquire a spring and
determine its spring coefficient (k) and
stretch length. The value for k can be de-
termined by hanging an object of known
weight from the spring and measuring
how far the spring stretches. Simply di-
vide the weight by the stretch distance
and you have k in pounds per inch. Some
springs come pretensioned their
coils are tight against each other when
the spring is relaxed. With such springs
you need to initially add enough weight
to extend the spring a small amount from
its retracted position. Now youre set to
find k as before; just dont count this first
weight in your calculation. I used two
identical, pretensioned springs on my
telescope, each with a k value of approxi-
mately 1.13 pounds per inch. I also had to
keep spring tension above a minimum of
4 pounds to keep the springs from fully
retracting. Since both springs worked to-
gether, in tandem, they provided a total k
of 2.26 pounds per inch.
The second spring parameter you have
to determine is maximum safe stretch
length. This is the point beyond which
the spring will permanently deform and
never return to its original length. Youll
need to test one spring to destruction to
determine this. The springs I purchased
could stretch about 18 inches before de-
forming. I chose 16 inches as a safe limit.

Making It Work
Before you can start drilling holes and
mounting springs, its a good idea to
make a scale drawing of your setup so
that you can determine values for R (see

132 November 1999 Sky & Telescope

the illustration on page 131) and d to
make sure that your rocker box is large
enough to accommodate the length of
the fully stretched spring. R normally
cant be larger than the radius of your al-
titude bearings and d cant be too large
or youll need to build a larger rocker
box. (As a starting point, I recommend
that R be no more than 80 percent of
your altitude bearings radius and that d
be approximately 35 percent of R.)
Fields analysis shows that the spring
will generate a maximum torque that is
equal to kR(R + d). With my scope I need-
ed 264 inch-pounds to properly balance
the tube. The maximum total length the
spring will need to stretch is approximated
by R + 2d. With the spring I had chosen,
this length could not exceed 16 inches.
The maximum amount of stretch room
you need on your rocker box is approxi-
mated by R + d. I had about 12 inches of
available stretch room on my rocker box
with a diagonal spring placement.
Arriving at a working solution is a
classic case of solving multiple equations
that contain several variables. The best
strategy is to try to vary only one para-
meter at a time. If you have already cho-
sen your spring and built your rocker
box, then you just need to find values for Advertisement
d and R that produce the torque needed
to balance your scope while staying with-
in the spring safety and stretch-room
constraints described above.
To avoid having to play around with a
lot of numbers, I put together a spread-
sheet to test various combinations and
found many possible solutions for d and
R. I settled on R as 9 14 inches and d as 312
inches. This generated a torque value of
266 12 inch-pounds within 1 percent
of my required value! Further analysis
showed that the spring would have to
stretch a maximum length of 15 34 inches
(just under my safety limit) and that I
needed 12 inches of stretch room in my
rocker box. With this information I was
finally ready to build my spring counter-
balance system.
The pictures on page 132 show my re-
sults. On opposite sides of the rocker box
are identical counterbalance devices that
share equally in providing the necessary
torque. Each spring is attached to a wire
rope that passes around a pulley wheel.
All parts were obtained from a local
hardware store.
Since my telescope is balanced for
heavy, 2-inch eyepieces, what do I do
when I use lighter, 114-inch eyepieces?

Sky & Telescope November 1999 133

 In order to minimize the amount of counterbalancing needed, it is important to ensure that
the instruments spider-cage assembly is as lightweight as possible. Krajcis fondness for his
heavy 2-inch Nagler eyepiece meant that some counterweighting would be necessary in spite
of his lightweight upper-tube design.

Simple. I temporarily disconnect one of for a range of maximum spring torques.

the two springs. Since both springs to- If this all sounds too good to be true,
gether counterbalance about 334 pounds you should be aware that the design does
of excess weight in the upper end of my have its limitations. A spring counter-
tube, using only one spring results in al- weight system does not change the center
Advertisement most a 2-pound change in torque the
difference between my heaviest and
of gravity my scope is still front-
heavy. If the center of gravity is too far
lightest eyepieces. Another solution forward, the instrument could become
would be to make the distance of the at- unstable and in extreme cases even tip
tachment point (D) adjustable to allow over! These potential problems are worst
when the telescope tube is horizontal. I
One way of minimizing the weight of the di- have noticed my scope is slightly less sta-
agonal cage of a truss-tube Dobsonian is to ble when aimed near the horizon than
eliminate the heavy clamping mechanisms when pointed near the zenith, but this
favored by many telescope makers. Krajcis effect is hardly objectionable.
simple solution is effective and lightweight. This spring-counterweight system will
Note the single ring of plywood that holds not be needed on every Dobsonian tele-
the whole upper cage together. scope, but for those trying to design light-
weight, compact instru-
ments it may make the
difference between a scope
that can be transported to
a dark site and a scope that
has to stay at home.

Tom Krajci is an avid ama-

teur astronomer and telescope
builder. Additional aspects of
his scope can be seen at http://
coeweb1.g su.edu/spehar/
FOCUS/Astronomy/krajci/
krajci.htm. He invites reader
inquiries by writing krajcit@
3lefties.com, or 1688 Cross
Bow Circle, Clovis, NM
881101.

134 November 1999 Sky & Telescope