String Telescope Concepts
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Figure 1

(Click for a larger image)

Purpose:

This document describes string telescope concepts.  
Note:  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.

  1. The strings alone define the location of the upper ring with respect to the mirror box.  

  2. 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.

  3. 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.

  4. Strings must be located in a way that provides both lateral forces and couples.  

  5. 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.

Table of Contents:

How the String Design Works
Rules of Thumb  
Lateral Force and Couples
String Angle Impact on Strut Compression Force / Lateral Stability & Couples(With Vertical Struts)    
String Angle Impact on Lateral Stability & Couples (With Angled Struts)  
String Length Adjustment  
Part Impact On Rigidity   
Radial String Orientation  
Stacked String Telescope  
Clever Designs With Flaws   
Some String Telescope Possibilities

How the String Design Works:

With 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. 

Interrelationships:

The (1) Strut Force, (2) Bending Moments and (3) Telescope Weight are interrelated in that reducing one of the three reduces the other two.  Increasing one increases the other two.  For the optimum design strut force, bending moments and weight are minimized.

Make All Three Smaller:

  • Strut force is smaller when the string angle is larger.
  • Bending moments are smaller when the strings attach at the tops and bottoms of the struts.
  • Weight is smaller when parts are inflexible along selected axes but flexible along the other axes.

Rules of Thumb:

Lateral Force and Couples:

Lateral Forces

These are the forces at the upper ring that hold the upper ring in place perpendicular to vertical (vertical being the light path).  The lateral forces are the lateral force components of the tensioned strings.

Couples:

A couple is a torque (force at a distance) or twisting "component".  The strings apply counterbalanced clockwise and counterclockwise couples.

Minimum Lateral Forces and Couples:

These are the minimum lateral forces and couples required to maintain collimation as the telescope is used.  The minimum lateral forces and couples are a "CONSTANT" that is independent of string angle.

String Angle Impact on Strut Compression Force / Lateral Stability & Couples (With Vertical Struts):

This is very important!

The larger the string angle or (to a lesser degree) the larger the number of struts, the smaller the strut compression.  Strut compression is related to the string angle per the following relationship:

Note:  This relationship is independent of the number of struts or strings.

Where:

  • Y is the vertical length of the string

  • X is the lateral length of the string

  • All strings on the telescope are at the same angle with respect to vertical

  • Strings are symmetrically arranged

(Note:  Examples A, C and F are shown)

Smaller strut compression comes with a number of benefits:

  • Less rigid struts, thus smaller diameter and lighter weight

  • Less sensitive to vibration 

Relative Strut Compression (based on string angle and number of struts)

The following table shows relative strut compression for the examples shown below.  It is assumed that all strings within each individual example have the same string angle.

(Click for a larger image)

String
Example X Y NUM
(Number
of Struts)		 Relative Strut Compression
A H x 1 L x 1 2 0.5
B H x 0.5 L x 1 4 0.5
C H x 0.5*** L x 1 3 0.67
D H x 0.5*** L x 0.5 3 0.33
E H x 0.63*** L x 1 2 0.79
F H x 1 L x 0.5 4 0.13
G H x 0.85 L x 1 4 ~0.29
H H x 1 L x 1 4 0.25
I H x 0.54*** L x 1 4 0.46

*** Depends on string orientation w/r to altitude movement.

Observations:

  1. Example F has the lowest strut compression.  

  2. The strut compression for Example A is the same as Example B.

  3. Example C strut compression is more than twice Example H.

  4. Example F strut compression is much smaller than Example C.

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:

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)N		 Ftotal Normalized
(divide by 32)		 Couple =
(B+B+G)(A)(N)		 Couple
Normalized
(divide by 256)

H

 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 H in the table above has an offset of zero.
  • 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.

String Length Adjustment:

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.)

Part Impact On Rigidity

The following items impact how rigidly the optics are co-located with a string telescope.

  • String Stretch

Strings should 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.

The string is selectively flexible because it is inflexible in tension but flexible in other directions.

  • String Anchor Detail

The strings should 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 should 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.

With the stacked design the struts are selectively flexible because they are inflexible in compression but flexible in the lateral direction.

  • Upper Ring Flexibility

It may be acceptable for the upper ring to be selectively flexible if the upper ring is inflexible in the lateral direction and flexible in the vertical direction.

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.

Radial String Orientation:

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)

Stacked String Telescope:

My stacked string telescope is finished.  Stacked string telescope.

The stacked string telescope design works better with large F number telescopes where the tube length is short compared to the width of the mirror box.  However, the stacked design can also be used reduce strut compression with small F number telescopes.

  • 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.  

Some Stacked String Telescope Advantages Over Non-stacked:

  • Larger string angle (with respect to light path) so lower strut compression, lighter weight struts

  • Struts captured at the middle so lower smaller diameter struts without buckling, allows yet lighter weight struts

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)

Clever Designs With "Flaws":

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 string telescope.

Figure 12

(Click for larger image)


Some String Telescope Possibilities:

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.  The strut compression force is twice the force with four struts and the strings at the same angle .

Example A

 

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 in Example H.  Therefore, the strut compression force is twice the force of Example H.

Example B

(Click for larger image)

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 Example H.  Therefore, the strut compression force with this design is more than twice the force for Example H.

Example C

(Click for larger image)

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 strut compression is half the strut compression with Example C.

Example D

(Click for larger image)

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.

Example E

(Click for larger image)

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 Example H.  Therefore, the strut compression force is half the force with Example H.

The middle ring captures the middles of the struts and reduces buckling concerns.  Therefore, smaller diameter struts may be used.

Example F

(Click for larger image)

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.

Example G

(Click for larger image)

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 Example C with three struts.  Therefore, the strut compression force is ~half the strut force with Example C.

Example H

(Click for larger image)

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 angle of the strings is smaller than the angle of the strings in Example H where the strings go from the tops to the bottoms of the struts.  Therefore, the strut compression force is twice the force of Example H.

Example I

(Click for larger image)

Some of my astronomy projects:

12.5" F4.5 String Telescope       
8" F6 Stacked String Telescope (Successfully built)    
Flex Ring (Flexible upper ring used with four strut string telescope)

Last updated:  26 June 2010
Don Peckham
email:  don@dbpeckham.com