String Telescope Concepts
(for Dobsonian Telescopes)
home: dbpeckham.com
Figure 1
(Click for a larger image)
Click the following links to go to the scope and purpose of this document.
Typically, the higher the rigidity of the mirror box / upper ring assembly, the smaller the required strut compression. Smaller strut compression comes with a number of benefits:
Smaller diameter struts
Lower strut weight
Lower center of gravity
Less rigid mirror box
The following table compares relative "rigidity" (relative lateral forces at the upper ring) among various different types of string telescopes. This is not intended to be a comprehensive table of ALL possible designs.
String Attachment Relative to Strut Tops and Bottoms Number of Struts
(Image / Relative Rigidity)
1 2 3 4 Non-Stacked Between-Between not shown not shown Top-Between / Bottom-Between n/a
Top- Bottom n/a n/a n/a
Stacked Top- Bottom n/a n/a
This document describes string telescope concepts. The first string telescope was created by Dan Gray.
Scope: (What is a string telescope?)
This webpage is limited to "String Telescopes" that satisfy the following requirements.
The strings alone define the location of the upper ring with respect to the mirror box.
If the struts are removed you can lift the scope up by the upper ring (holding it near the strut contact points). You can rotate the upper ring with respect to vertical and the mirror box will stay in alignment with the upper ring without any struts in place.
Note: The strings do not stretch so the relationship of the upper ring to the mirror box is absolutely controlled by the strings.The struts provide force on the bottom of the upper ring. If the scope is lifted by the upper ring with no struts, gravity and the weight of the mirror box provide the force that tensions the strings.
Strings must be located in a way that provides both lateral forces and couples.
The mirror box should typically be more rigid than the upper ring. If the upper ring is non-rigid, the upper ring tends to adapt to the shape defined by the string lengths and the more rigid mirror box.
String Telescope Variations Disclaimer:
There are telescopes with strings that do not satisfy the requirements above. Those telescopes may be excellent designs but they are outside the scope of this webpage.
Here is a one strut, three string example that appears to work with my understanding of the roles of strings and struts in a "String Telescope". Note that one string is radial with respect to the "upper ring" centerline (mirror light path) but that two strings are NOT radial. Radial strings typically produce smaller couples than strings that are not radial. This is not intended as a practical design.
(Click for a larger image)
Table of Contents:
How the String Design Works
Component Requirements
Lateral Force and Couples
String Angle Impact on Lateral Stability & Couples (With Vertical Struts)
Radial String Orientation
String Angle Impact on Lateral Stability & Couples (With Angled Struts)
String Length Adjustment
Stacked String Telescope
Rules of Thumb
Clever Designs With Flaws
Relative Rigidity
Some String Telescope PossibilitiesWith string telescopes the "strings" rigidly locate the upper ring with respect to the mirror box. The function of the struts is to provide a vertical (in line with the light path) force at the bottom of the upper ring in order to tension the strings. The struts on string scopes do NOT locate the upper ring.
When the struts are compressed the strings are tensioned. Strings have both a vertical (in line with the light path) and lateral (perpendicular to the light path) force component. The vertical and lateral force components hold the upper ring in place with respect to the mirror box.
With all telescopes the optics (primary mirror, secondary mirror and focuser) must be rigidly located with respect to each other so that collimation is maintained. For string telescopes where with adjustable strut compression, the upper ring optics must be rigidly located with respect to the mirror box optics INDEPENDENT OF STRUT COMPRESSION in order to prevent the need to collimate the telescope each time it is assembled.
The following items impact how rigidly the optics are co-located with a string telescope.
String Stretch
Strings need to be made from a material that does not stretch as the struts are compressed. "No creep" bow string (for example BCY 450 Plus) works well. This string can be doubled several times to assure that it does not stretch with high strut compression. Fabric rope and steel wire stretch.
String Anchor Detail
The strings need to be attached to the upper ring and mirror box using anchors that do not deflect as the struts are compressed. If string anchor deflection varies with strut compression, collimation will vary with strut compression.
Struts
The struts need to be rigid enough so that they do not flex as a function of strut compression. If the struts flex with strut compression, they may also flex due to the weight of the upper ring as the scope moves from vertical to horizontal.
Upper Ring Flexibility
If string anchors attach to the upper ring at the same points** as compression struts, upper ring rigidity is not very important. However, if string anchors attach to the upper ring AWAY FROM the strut contact points, the upper ring must be rigid enough to prevent the upper ring from deflecting as the struts are compressed*.
**Note: In order to minimize bending, the centerline of the string and the centerline of the strut should cross at the point the strut attaches to the upper ring (and mirror box).
(Note: For both photos the strut compression is the same.)
GOOD - In the photo at the left, the centerline of the string crosses the centerline of the strut at the upper ring. Note that the ring is NOT bowed.
NOT OPTIMUM - In the photo at the right, the centerline of the string crosses the centerline of the strut a couple of inches ABOVE the upper ring. This introduces a bending moment when the strings are tensioned. Notice the bow in the ring.
(Click for larger image)
Mirror Box Flexibility
If string anchors attach to the mirror box at the same points** as compression struts, mirror box rigidity is not very important. However, if string anchors attach to the mirror box AWAY FROM the strut contact points, the mirror box must be rigid enough to prevent the mirror box from deflecting as the struts are compressed*.
String Requirements
All strings must be on an angle with respect to vertical (the light path) in order to provide both a vertical and a lateral force component when the struts are compressed (strings are tensioned). A string that aligns with vertical does not provide a lateral force component.
As a rule, strings should be NOT RADIAL with respect to the center of the upper ring. Strings that are radial with respect to the center of the upper ring produce a smaller couple than strings that are not radial.
There is typically an even number of strings with a minimum four strings. Three strings can work although if all the strings are radial the lateral forces and couples at the upper ring will be small. An odd number of strings can work.
Strut requirements
There must be at least one strut. Designs with two, three or four struts are more common.
Struts must be rigid enough to not buckle when loaded in compression.
Rigidity - Upper Ring / Mirror Box
*Disclaimer:
For the following examples the goal is to be able to progressively load the struts in compression without any corresponding flex in the upper ring or mirror box. For some string telescope designs the struts are not progressively loaded in compression. The strut compression is a fixed value controlled by a spring at each strut. Some string telescope designs intentionally allow the upper ring or mirror box to flex correspondingly as the struts are progressively compressed.
RIGID Upper Ring / Mirror Box
If the upper ring and mirror box are VERY rigid, the placement of the string anchors with respect to the tops and bottoms of the struts is unimportant. Such a string telescope could have any combination of struts and strings as long as the struts and strings do not interfere with each other. Some combinations could include:
Two struts and four strings, six strings, eight strings, etc. Jane's string telescope is an example of this design.
Three struts and four strings, six strings, eight strings, etc. Dan Gray's 28" string telescope is an example of this design.
Four struts and four strings, five strings, six strings, etc.
Non-RIGID Upper Ring / Mirror Box
In order for the upper ring to be less RIGID, the string anchors MUST be located in close proximity to the tops of struts. In order for the mirror box to be less RIGID, the string anchors MUST be located in close proximity to the bottoms of struts. Some combinations could include:
Two struts with four strings attached to the upper ring close to the tops of the struts. Note that the upper ring could be less RIGID, but the mirror box would have to be VERY rigid.
Three struts with six strings attached to the upper ring close to the tops of the struts. Note that the upper ring could be less RIGID, but the mirror box would have to be VERY rigid.
Four struts with eight strings attached to the upper ring close to the tops of the struts and to the mirror box close to the bottoms of the struts. Both the upper ring and the mirror box could be less RIGID. Don Peckham's 12.5" string telescope is an example of this design.
Four struts with eight strings attached to the mirror box close to the bottoms of the struts and to the upper ring away from the tops of the struts. Note that the mirror box could be less RIGID, but the upper ring would have to be VERY rigid.
Lateral Force
This is the force at the upper ring that holds the upper ring in place perpendicular to vertical (along the light path).
Couples:
A couple is a torque (force at a distance) or twisting "component". The strings apply counterbalanced clockwise and counterclockwise couples.
String Angle Impact on Lateral Stability & Couples (With Vertical Struts):
This is VERY important! The string angle has a very large impact on the rigidity of the telescope.
As previously noted, all strings must be on an angle with respect to vertical (the light path) in order to provide a lateral force component. The larger the string angle with respect to vertical, the larger the lateral force component. A larger lateral force component results in a more rigidly located upper ring for the same strut compression.
The sketch below (Figure 2) shows a strut with three strings. One string is anchored at length L1 (half the length between the struts). A second string is anchored at length L2 (the length between the struts). A third string is anchored on at the middle ring. When this string is projected to the mirror box it is "anchored" at length L3 (two times the length between the struts). The lateral force component in the string is proportional to length (L1, L2 or L3) shown. For this example, L2 = 2 x L1. Therefore, the string at L2 has a lateral force component equal to 2X the lateral force component for the string at L1. The string at L3 has a lateral force component equal to 4X the lateral force component for the string at L1.
L1 - Four Strut - Strings Attached At Tops Of Struts, Between Bottoms of Struts
L2 - Four Strut - Strings Attached At Top & Bottom of Struts
L3 - Stacked Four Strut - Strings Attached At Top & Bottom of Struts
When choosing the string angle, it is suggested that you choose as large a string angle as will fit the telescope.
(Click for larger image)
The following compares relative lateral forces and couples with four different sting/strut combinations numbered #1, #2, #3 and #4.
#1 has two struts and four strings, with the strings attached close to the tops of the struts but away from the bottoms of the struts.
#2 has four struts and eight strings, with strings attached close to both the tops and bottoms of the struts.
#3 has four struts and eight strings, with strings attached close to the tops of both struts but away from the bottoms of the struts.
#4 has three struts and six strings, with strings attached close to the tops of both struts but away from the bottoms of the struts.
(click for a larger image)
Assumptions:
The mirror box is a square with dimensions L x L
A = the moment arm of a couple as measured from the center of the mirror box (see Figure 3). The total couple results from adding all couples.
All strings in a particular example are at the same angle with respect to vertical (the light path)
All struts in a particular example have the same compression force.
Note that the total strut compression (force) value depends on the number of struts.
The following sketch (Figure 4) shows lateral force components (red arrows) for each example. The lengths of the arrows are proportional to the string forces. Notice that the arrows in examples #1 and #2 are the same length, but there are twice as many struts/strings/arrows/arrows in example #2.
Examples #4a and #4b are actually the same example. #4a shows the red arrows lined up with x-y coordinates. Each of these red arrows includes a small number. A larger view of these numbered arrows is shown in Figure 4a and Figure 5a. #4b shows forces lined up with the strings. This example makes it easier to visualize the couples.
(Click for larger image)
Figure 4a Example #4a
The sketch below (Figure 5) shows a top view of the four examples that are shown above. However, all the red arrows have been moved to the centers of the upper rings, and green arrows are added to show the couples for each example. A couple is a force at a distance so notice the distance between the upper ring centers (centers of red arrows) and the respective green arrows for each example.
Things to notice:
Notice the lengths of the red "force" arrows, the green "couple" force arrows, and the moment arms of the couples.
Examples #1 and #3 have the equivalent forces and couples although different numbers of struts and strings.
In Example #4 notice that each red arrow is numbered. Also see Figure 4a and Figure 5a.
In Example #4 the horizontal arrows are a different length than the vertical arrows. That is because the horizontal strut spacing is 0.866X the vertical strut spacing.
The relative force and couple values are shown for each example.
(Click for larger image)
Figure 5a Example #4
Conclusions:
Example #2 has a minimum two times the force of the other examples for two reasons:
There are four struts (mores struts than all except example #3)
The string lateral length is larger than all except example #1)
Example #2 has a minimum two times the couple of the other examples:
In addition to there being four struts and a higher string lateral force, the moment arm is larger than the other examples
Example #4 has a lower x-direction force than the other examples
Example #4 has a lower couple than any of the other examples
The force and couple values can be increased by increasing the strut compression force which may mean larger diameter (heavier) struts.
Strings oriented radially with respect to the center of the upper ring result in significantly lower lateral forces and couples than strings located perpendicular to a radial line from the center of the upper ring. This is in part because there is not much space to locate radial strings without increasing the size of the upper ring or mirror box. The following sketch compare the forces with radial and perpendicular strings.
Figure 6
(Click for larger image)
As can be seen below, lateral forces and couples are significantly smaller with radial oriented strings than perpendicular oriented strings.
Figure 7
(Click for larger image)
String Angle Impact on Lateral Stability & Couples (With Angled Struts):
With the four strut design it may be necessary to use angled struts instead vertical struts. The following table compares relative lateral forces and couples with struts at different offsets (angles).
Vertical struts have only a vertical force component. Angled struts have both a vertical force component and a lateral force component. The vertical force component applies to the strings. The lateral force component provides a lateral force at the upper ring but does not impact string tension.
Figure 8
(Click for larger image)
Table 1
These values are used for the following table, but the resulting forces and couples are "normalized" so they can be compared to the force and couple values in Figure 5:
H = Strut Height (not length) = 40
L = Mirror Box Length/Width = 16
F = Strut Compression (axial) = 1
N = Number of Struts = 4
Figure 9
Example O
Offset
(length)B = sin(45)(O)
(length)C =
atan(B/(L-B))
(degrees)A =
(L/2)-B)
(length)G = L-B
(length)Ftotal =
(G+B+B)NFtotal Normalized
(divide by 32)Couple =
(B+B+G)(A)(N)Couple
Normalized
(divide by 256)#2
0.00 0.000 0.00 8.000 16.000 64.00 2
512.00 2
0.50 0.354 1.29 7.646 15.646 65.41 2.044 500.19 1.954 1.50 1.061 4.06 6.939 14.939 68.24 2.133 473.56 1.850 2.00 1.414 5.54 6.586 14.586 69.66 2.177 458.75 1.792 2.50 1.768 7.08 6.232 14.232 71.07 2.221 442.93 1.730 3.00 2.121 8.69 5.879 13.879 72.49 2.265 426.12 1.665 Conclusions:
- Notice that example #2 in the table above, with an offset of zero, is the same example #2 in Figure 4 and Figure 5.
- The larger the strut offset ("O", offset with respect to vertical), the greater the lateral force at the upper ring.
- The larger the strut offset, the smaller the couple.
- Offsetting struts has a minimum POSITIVE impact on lateral force at the upper ring, and a moderate NEGATIVE impact on the couple at the upper ring.
Three points define a plane. A string telescope with RIGID upper ring and mirror box and four or more strings requires some way to compensate for tolerances in string lengths and tolerances in string anchor locations. The first three strings define a plane but some means must be provided to compensate for the fourth, fifth, sixth, etc. string length / string anchor location variations.
Here are some possible solutions to compensate for string length / string anchor location variations:
Put turnbuckles in (some of) the strings
Provide a way to shim (some of) the string anchors
Allow the upper ring and/or mirror box to flex. (Note: Allowing the upper ring and/or mirror box to flex may result in the need for more frequent collimation.)
My stacked string telescope is nearly finished. Stacked string telescope.
The string telescope design works better with large F number telescopes where the tube length is short compared to the width of the mirror box. Therefore, I suggest a "stacked" design with large F number telescopes. I am currently building this design.
The stacked design is essentially two string telescopes stacked one on top of the other. The middle example (see sketch below) is a four strut design with sixteen strings. The eight strings in the lower half of the telescope connect between the mirror box and the middle ring. The eight strings in the upper half of the telescope connect between the middle ring and the upper ring.
With a stacked design each stacked section of the telescope should be close to the same height. For example, in the middle and right sketches notice that the upper and lower parts of the telescopes are the same height. String forces depend on the angle of the strings with respect to vertical. If the upper and lower assemblies are different heights, the string angles will be different with the upper and lower assemblies. The assembly with the smaller string angle will determine the string forces.
Theoretically, this design will work with a triple stack, quadruple stack, etc. The number of stacks will determine the lateral force at the upper ring if the strut compression is the same for each of the following:
Single height string telescope - Lateral forces at upper ring = F
Double stack string telescope - Lateral forces at upper ring = 2 x F
Triple stack string telescope - Lateral forces at upper ring = 3 x F
Quadruple stack string telescope - Lateral forces at upper ring = 4 x F
Sketches Below:
Left - The sketch at the left is of an ~F4 telescope. Notice that focal length is short with respect to the mirror diameter. Also, notice the length of the force arrows.
Middle - The sketch in the middle is of an ~F8 telescope. Notice that the lateral forces at the upper ring are the same with both the left and middle sketches.
Right - The sketch at the right is of an ~F4 telescope with a middle ring. Notice that the force arrows are twice as large as the force arrows in the sketch at the left because the magnitude of forces at the upper ring depends on the angles of the strings with respect to vertical. Notice that the string angles in the right sketch are larger with respect to vertical than the strings angles in the left sketch. Since the forces are larger in the right sketch, it may be possible to use smaller diameter struts with the stacked design (right sketch) than the non-stacked design (left sketch).
Figure 10a
(Click for larger image)
This is an innovative use of the stacked design with a three strut telescope, suggested by Brett Schaerer.
Notice that with the stacked design the strings at the mirror box and upper ring attach close the the strut contact point. Therefore, the struts take the vertical loading so the mirror box and upper ring do not need to be very rigid.
The string angle with respect to vertical (light path) is larger than with the non-stacked three strut telescope, therefore the lateral forces and couples at at the upper ring are twice those of the non-stacked three strut telescope.
The middle ring captures the middle of the struts which reduces buckling, so smaller diameter struts can be used to reduce weight.
Figure 10b
(Click for larger image)
Strut Compression - The higher the strut compression the higher the lateral forces and couples at the upper ring, thus a more robust design.
String Angle - The larger the string angle the higher the lateral forces and couples at the upper ring, thus a more robust design.
Number of Struts - More struts means more force pushing up on the upper ring, thus a more robust design.
Radial vs. Perpendicular String Orientation - Perpendicular typically results in a more robust design than radial.
Stacked Telescopes - A stacked telescope has at least twice the lateral forces and couples of an equivalent non-stacked telescope.
Note that Strut Compression, String Angle, Number of Struts, etc. can be traded against each other. For example, a larger string angle may allow lower strut compression. Higher strut compression may allow fewer struts or a smaller string angle. A more struts may allow lower strut compression or smaller string angle. Etc.
Here are some clever designs with "flaws". These designs do not satisfy the requirements in the scope of this webpage. Depending on the user's requirement, some of the flaws may be considered acceptable, and other of the flaws make the design unusable.
Center strut with radial strings - This design looks like it will work. We have all seen radio and TV antennas with this design. However, this design has no couple at the upper ring. If the upper ring is rotated with respect to vertical, there is no couple to hold the upper ring with respect to the mirror box.
Figure 11
(Click for larger image)
Strings wrap around adjacent struts - I'm particularly fond of this design and I built a full scale mockup. It is SIGNIFICANTLY more rigid than other three strut and four strut designs. The strings run from the bottom of a strut, around the middle of the adjacent strut, and to the top of the opposite strut. There is a floating internal "ring" that snaps into place at the mid points of the struts. This design is quick to setup and more robust than any of the other designs I've seen. The mid point of each strut is captured and reduces buckling issues, thus smaller diameter (lighter weight) struts can be used. There is only one "flaw":
The upper ring location is not repeatable from setup to setup because the string does not go straight from the top anchor to the bottom anchor. That means the telescope with this design will have to be recollimated every time it is setup. This recollimation may be OK for a travel telescope considering the significant advantages of the design.
Note that this design led to the idea for the stacked telescope.
Figure 12
(Click for larger image)
Some String Telescope Possibilities:
Three Strut - Strings Attached At Top of Struts and Between Bottoms of Struts
This design has three struts. Strings go from the top of each strut to points on the mirror box that are between the bottoms of the adjacent struts. The upper ring does not need to be particularly rigid. However, the mirror box needs to be rigid.
The angles of the strings with respect to vertical is smaller than the angles of the strings with the four strut design where the strings go from the tops to the bottoms of the struts. Therefore, the lateral components of the string force is half the lateral force components where the strings go from the tops to the bottoms of the struts.
Figure 13
(Click for larger image)
Stacked Three Strut - Strings Attached At Top and Bottoms of Struts
This design has either three long struts or six short struts. There are twelve strings. Six strings go from the mirror box to the middle ring. Six strings go from the middle ring to the upper ring. Since strings at the top and bottom attach close to the struts, the upper ring and mirror box do not need to be particularly rigid.
The lateral forces and couples at the upper ring are twice those of the non-stacked design.
If the middle ring captures the mid points of the struts, strut buckling is reduced so it may be possible to use smaller diameter struts.
Figure 14
(Click for larger image)
Four Strut - Strings Attached At Top & Bottom of Struts
This design has four struts. Strings go from the top of each strut to the bottoms of the adjacent struts. The string loading is taken up by the struts. Therefore, the upper ring and mirror box do not need to be particularly rigid.
The angles of the strings is larger than the angles of the strings with the three strut design above. Therefore, the lateral component of the string force is twice the lateral force component with the three strut design above.
Figure 15
(Click for larger image)
Stacked Four Strut - Strings Attached At Top & Bottom of Struts
This design has four struts or eight half-height struts. There are sixteen strings. Eight strings connect from the mirror box to the middle ring, and eight strings connect from the middle ring to the upper ring. All strings connect from the tops of struts to the bottoms of struts. Therefore, the upper ring and mirror box do not need to be particularly rigid.
The angles of the strings is larger than the angles of the strings with the four strut design above. Therefore, the lateral component of the string force is twice the lateral force component with the non-stacked four strut design above.
The middle ring captures the middles of the struts and reduces buckling concerns. Therefore, smaller diameter struts may be used.
Figure 16
(Click for larger image)
Four Strut - Strings Attached At Top & Bottom of Angled Struts
This design has four angled struts. Strings go from the top of each strut to the bottoms of the adjacent struts. The string loading is taken up by the struts. Therefore, the upper ring and mirror box do not need to be particularly rigid.
This design has slightly higher lateral forces but slightly lower couples than the similar design with vertical struts.
Figure 17
(Click for larger image)
Four Strut - Strings Attached At Bottoms of Struts, Between Tops of Struts
This design has four struts. The strings go from the bottoms of the struts to points on the upper ring that are BETWEEN the upper ends of the struts. The mirror box does not need to be particularly rigid. However, the upper ring must be very rigid or it will flex when the struts are compressed.
The angles of the strings is smaller than the angles of the strings where the strings go from the tops to the bottoms of the struts. Therefore, the lateral component of the string force is half the lateral force component where the strings go from the tops to the bottoms of the struts. The lateral force component is equal to the three strut design.
Figure 18
(Click for larger image)
Four Strut - Strings Attached At Tops Of Struts, Between Bottoms of Struts
This design has four struts. The strings go from the tops of the struts to points on the mirror box that are BETWEEN the bottom ends of the struts. The upper ring does not need to be particularly rigid. However, the mirror box must be very rigid or it will flex when the struts are compressed.
The angles of the strings is smaller than the angles of the strings where the strings go from the tops to the bottoms of the struts. Therefore, the lateral component of the string force is half the lateral force component where the strings go from the tops to the bottoms of the struts. The lateral force component is equal to the three strut design.
Figure 19
(Click for larger image)
Two Struts - Strings Attached Top of Struts and Bottom Between Struts
This design has two struts. The strings are connected close to the tops of the struts and between the bottoms of the struts. The upper ring can be non rigid but the mirror box must be VERY RIGID.
Figure 20
Two Strut - Strings Attached Top and Bottom Between Struts
This design has two struts. The strings are connected BETWEEN the ends of the struts both at the upper ring and the mirror box. Both the upper ring and the mirror box must be VERY RIGID.
This example has six strings and two struts. If this telescope was added to the table above, the Relative Force and Relative Couple values would be 2/3X the values for the three strut design because there are two struts instead of three.
Figure 21
(Click for larger image)
Some of my astronomy projects:
12.5" F4.5 String Telescope
8" F6 Stacked String Telescope (Work in process)
Flex Ring (Flexible upper ring used with four strut string telescope)Last updated: 22 February 2010
Don Peckham
email: don@dbpeckham.com
