Ross Sackett's amateur telescope making
Ross Sackett's amateur telescope making
Articles
Which is stiffer, wood or metal? Some telescope makers design all-metal telescopes in the belief that they will be
stiffer than ones built substantially from wood. Even among those who use wood extensively in telescopes there is a
widespread belief that metal cell parts are somehow inherently better (usually meaning stiffer and stronger) than
wooden ones.
Unfortunately, these beliefs confuse two very different things—the inherent elasticity of materials and the stiffness of
the parts made from them. Stiffness (that is, resistance to deflection under load) is determined by not only the
elasticity of the material, but also by the length and sectional properties of the parts. Since the length of most
telescope parts is set by the design, it is mainly the differences in material and section that determine differences in
stiffness.
In big telescopes weight is at a premium; we want the most stiffness for a given weight, or the least weight for an
acceptable amount of flexibility. So pound for pound how do wood and metal parts compare? It turns out that the
answer has a lot to do with the kind of stress the part needs to resist. Here we will compare a part loaded in pure
compression and tension, as in a truss pole, with a part loaded in bending, like a load-spreading bar in a mirror cell.
Table 1: Typical material properties
----------------------------------------------------------
Material E Density
----------------------------------------------------------
Steel 29,000,000 psi 0.284 lb/in3
Aluminum 10,000,000 0.099
Softwood1 1,500,000 0.0176
Hardwood2 1,830,000 0.026
----------------------------------------------------------
1 Average of spruce, pine, and fir
2 Average of maple and red oak
Tension and compression: truss poles
A truss pole is loaded from the ends, ideally exactly through the long axis of the pole. Such a pole responds to
ordinary loads by stretching or squashing. Only at very high loads does it begin to bend (through Euler buckling), but
by that point the telescope is likely to be so strained as to be optically useless anyway. Consider a typical aluminum
truss pole for an 18” telescope: 1” OD, 0.049” wall thickness, 50” long. Such a pole would weigh a little less than three-
quarters of a pound. Holding length constant the stiffness of column like a truss pole is proportional to the elasticity of
the material (E) times its cross-sectional area (A). Table 1 presents the properties of several common materials used
in telescope construction.
Such an aluminum tube would have an AE of 1,464,000. How much steel, softwood, and hardwood would it take to
match this? Table 2 compares this aluminum tube to a thin-walled steel tube and square solid wooden tubes with the
same overall stiffness.
Table 2: Truss poles of similar stiffness
-------------------------------------------------------------------------------------
Material Dimensions Weight Relative weight1
-------------------------------------------------------------------------------------
Aluminum 1” OD, 0.049” wall 0.725 lb 1.00
Steel 1” OD, 0.025” wall 0.715 0.99
Softwood 0.99 X 0.99” 0.860 1.19
Hardwood 0.89 X 0.89” 1.04 1.44
-------------------------------------------------------------------------------------
All poles 50” long
1 Compared to aluminum pole
We see that when loaded in compression or tension metal has an advantage over wood, weighing 20-50% less than
wooden poles of similar stiffness. It isn’t surprising that truss poles are usually made of aluminum (thin-walled steel
poles would work as well, but are usually not available and may be less resistant to buckling and damage). But also
note the clear advantage of softwood over hardwood—pound-for-pound it is considerably stiffer. In fact, the softwood
pole weighs only about 20% more than the aluminum pole, and may have advantages in cost and ease of
construction. One should note that truss poles are only a small fraction of the total weight of a telescope, and in an
18” instrument substituting wood for aluminum poles would increase the total optical tube weight by a little over a
pound, an increase of only some 1% overall.
Bending: load-spreading bars
The bar used to spread the load in mirror cells is supported in the center on a collimation bolt, and is loaded at the
ends (through pads or triangles) by the mirror. Loaded in this manner the bar acts as a beam, bending under the load
(unlike a column squashing under an axial load). Bending puts the upper portion of the bar in tension and the lower
part in compression; the middle of the bar is not stressed. In general, the thicker the bar the better able it is to resist a
bending load. The bending of a beam is proportional to the second moment of the cross-section (I) times the elasticity
of the material (E). The second moment depends on the distribution of material in the cross section relative to the
plane of bending. For a rectangular beam I equals the width of the beam multiplied by the cube of the depth, divided
by 12. Since we are multiplying by the cube of the depth a small increase in the thickness of the beam can bring huge
rewards in improved stiffness.
Consider a typical steel load-spreading bar in a cell for an 18” mirror, 1/4” deep, 1” wide, and 6” long. Since the width
and length are pretty much set by the design, we can hold stiffness constant by varying the depth to compare bars of
different materials. Table 3 compares bars of similar stiffnesses.
Table 3: Load-spreading bars of similar stiffness
-------------------------------------------------------------------------------------
Material Dimensions1 Weight Relative weight2
-------------------------------------------------------------------------------------
Steel 1/4 X 1 X 6” 0.426 lbs 1.00
Aluminum 0.3565 X 1 X 6” 0.212 0.50
Softwood 0.6710 X 1 X 6” 0.071 0.17
Hardwood 0.6279 X 1 X 6” 0.099 0.23
-------------------------------------------------------------------------------------
1 Depth X width X length
2 Compared to steel bar
Here we see the relative advantages reversed: when stressed in bending, wood parts can be considerably lighter than
metal ones. Wooden cell parts can weigh only one-quarter to one-fifth of steel parts of similar stiffness. Lower density
metals like aluminum have considerable advantage over steel, and softwoods perform better weight-wise than
hardwoods.
So which is better?
The brief answer is that when we are trying to minimize weight parts loaded in pure compression and tension should be
made of metal (whether steel or aluminum makes little difference), while parts loaded so as to bend should be made of
wood.
In practice things can get a little more complicated, however. Sometimes parts that need to bend need to be strong
(especially against concentrated loads) as well as stiff, and thus should be made of metal since wood fibers might
crush. If so, lighter metals like aluminum have the advantage over denser metal like steel. Sometimes substituting
hardwood for softwood might be enough, however.
Where cost and ease of construction are important issues wood might have an overall advantage over metal even for
compression members such as truss tubes. In compression the advantage of metal over wood is relatively slight; by
contrast, the advantage of wood over metal in bending may be considerable.
Copyright 2009 Ross Sackett
stiffer than ones built substantially from wood. Even among those who use wood extensively in telescopes there is a
widespread belief that metal cell parts are somehow inherently better (usually meaning stiffer and stronger) than
wooden ones.
Unfortunately, these beliefs confuse two very different things—the inherent elasticity of materials and the stiffness of
the parts made from them. Stiffness (that is, resistance to deflection under load) is determined by not only the
elasticity of the material, but also by the length and sectional properties of the parts. Since the length of most
telescope parts is set by the design, it is mainly the differences in material and section that determine differences in
stiffness.
In big telescopes weight is at a premium; we want the most stiffness for a given weight, or the least weight for an
acceptable amount of flexibility. So pound for pound how do wood and metal parts compare? It turns out that the
answer has a lot to do with the kind of stress the part needs to resist. Here we will compare a part loaded in pure
compression and tension, as in a truss pole, with a part loaded in bending, like a load-spreading bar in a mirror cell.
Table 1: Typical material properties
----------------------------------------------------------
Material E Density
----------------------------------------------------------
Steel 29,000,000 psi 0.284 lb/in3
Aluminum 10,000,000 0.099
Softwood1 1,500,000 0.0176
Hardwood2 1,830,000 0.026
----------------------------------------------------------
1 Average of spruce, pine, and fir
2 Average of maple and red oak
Tension and compression: truss poles
A truss pole is loaded from the ends, ideally exactly through the long axis of the pole. Such a pole responds to
ordinary loads by stretching or squashing. Only at very high loads does it begin to bend (through Euler buckling), but
by that point the telescope is likely to be so strained as to be optically useless anyway. Consider a typical aluminum
truss pole for an 18” telescope: 1” OD, 0.049” wall thickness, 50” long. Such a pole would weigh a little less than three-
quarters of a pound. Holding length constant the stiffness of column like a truss pole is proportional to the elasticity of
the material (E) times its cross-sectional area (A). Table 1 presents the properties of several common materials used
in telescope construction.
Such an aluminum tube would have an AE of 1,464,000. How much steel, softwood, and hardwood would it take to
match this? Table 2 compares this aluminum tube to a thin-walled steel tube and square solid wooden tubes with the
same overall stiffness.
Table 2: Truss poles of similar stiffness
-------------------------------------------------------------------------------------
Material Dimensions Weight Relative weight1
-------------------------------------------------------------------------------------
Aluminum 1” OD, 0.049” wall 0.725 lb 1.00
Steel 1” OD, 0.025” wall 0.715 0.99
Softwood 0.99 X 0.99” 0.860 1.19
Hardwood 0.89 X 0.89” 1.04 1.44
-------------------------------------------------------------------------------------
All poles 50” long
1 Compared to aluminum pole
We see that when loaded in compression or tension metal has an advantage over wood, weighing 20-50% less than
wooden poles of similar stiffness. It isn’t surprising that truss poles are usually made of aluminum (thin-walled steel
poles would work as well, but are usually not available and may be less resistant to buckling and damage). But also
note the clear advantage of softwood over hardwood—pound-for-pound it is considerably stiffer. In fact, the softwood
pole weighs only about 20% more than the aluminum pole, and may have advantages in cost and ease of
construction. One should note that truss poles are only a small fraction of the total weight of a telescope, and in an
18” instrument substituting wood for aluminum poles would increase the total optical tube weight by a little over a
pound, an increase of only some 1% overall.
Bending: load-spreading bars
The bar used to spread the load in mirror cells is supported in the center on a collimation bolt, and is loaded at the
ends (through pads or triangles) by the mirror. Loaded in this manner the bar acts as a beam, bending under the load
(unlike a column squashing under an axial load). Bending puts the upper portion of the bar in tension and the lower
part in compression; the middle of the bar is not stressed. In general, the thicker the bar the better able it is to resist a
bending load. The bending of a beam is proportional to the second moment of the cross-section (I) times the elasticity
of the material (E). The second moment depends on the distribution of material in the cross section relative to the
plane of bending. For a rectangular beam I equals the width of the beam multiplied by the cube of the depth, divided
by 12. Since we are multiplying by the cube of the depth a small increase in the thickness of the beam can bring huge
rewards in improved stiffness.
Consider a typical steel load-spreading bar in a cell for an 18” mirror, 1/4” deep, 1” wide, and 6” long. Since the width
and length are pretty much set by the design, we can hold stiffness constant by varying the depth to compare bars of
different materials. Table 3 compares bars of similar stiffnesses.
Table 3: Load-spreading bars of similar stiffness
-------------------------------------------------------------------------------------
Material Dimensions1 Weight Relative weight2
-------------------------------------------------------------------------------------
Steel 1/4 X 1 X 6” 0.426 lbs 1.00
Aluminum 0.3565 X 1 X 6” 0.212 0.50
Softwood 0.6710 X 1 X 6” 0.071 0.17
Hardwood 0.6279 X 1 X 6” 0.099 0.23
-------------------------------------------------------------------------------------
1 Depth X width X length
2 Compared to steel bar
Here we see the relative advantages reversed: when stressed in bending, wood parts can be considerably lighter than
metal ones. Wooden cell parts can weigh only one-quarter to one-fifth of steel parts of similar stiffness. Lower density
metals like aluminum have considerable advantage over steel, and softwoods perform better weight-wise than
hardwoods.
So which is better?
The brief answer is that when we are trying to minimize weight parts loaded in pure compression and tension should be
made of metal (whether steel or aluminum makes little difference), while parts loaded so as to bend should be made of
wood.
In practice things can get a little more complicated, however. Sometimes parts that need to bend need to be strong
(especially against concentrated loads) as well as stiff, and thus should be made of metal since wood fibers might
crush. If so, lighter metals like aluminum have the advantage over denser metal like steel. Sometimes substituting
hardwood for softwood might be enough, however.
Where cost and ease of construction are important issues wood might have an overall advantage over metal even for
compression members such as truss tubes. In compression the advantage of metal over wood is relatively slight; by
contrast, the advantage of wood over metal in bending may be considerable.
Copyright 2009 Ross Sackett
Wood Or Metal?
[Need to reformat tables]