StringTelescopeConcepts
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PREFACE

My 'Tensegrity Telescope Structures' presentation at the 2019 Alt-Az Workshop provides an overview of string telescopes without the math.

OVERVIEW

Dan Gray created the first string telescope.  The first string telescope is Example E above.  From my observations, Example C is the most popular string telescope.  I have built Examples F, G, and J.  

This website describes WHAT is happening with a string telescope and WHY. 

Tensegrity string telescopes are robust and typically lighter weight than non-tensegrity string telescopes and have string and strut forces that are 50%-90% lower than non-tensegrity string telescopes.  In addition, tensegrity string telescopes apply zero bending moments to the upper ring and mirror box.

If you are considering building a string telescope, I suggest that look at this Tensegrity String Telescope website first. 

EVOLUTION OF STRING TELESCOPES

(Watch string angle and number of struts)

1. ~1.00 - Dan Gray created the first string telescope in 1998.  This telescope has three pairs of strings and two struts.  The relative strut compression (~1.00) is a value based on string angle and number of struts.  This is Example E. 

2. ~0.67 - This design has three pairs of strings and three struts.  Bending moments are reduced at the upper ring.  This is one of the most common string telescope designs.  The relative strut compression force (~0.67) is lower than the first telescope by 33% because strut compression is spread over three struts instead of two.  You can see examples of this design starting with OSP 2001 Telescope Walkabout.  This is Example C. 

3. ~0.33 - I first heard of this design from Brett Schearer in 2010.  It has a middle ring thus a larger string angle with respect to the struts.  Therefore, the relative strut compression (~0.33) is half the previous design.  Brett's ballscope uses this design and can be seen on this website and the OSP 2014 Telescope Walkabout.  This is Example D. 

Tensegrity String Telescopes, the Next Step 

4. ~0.17 - This is my 3 strut tensegrity design from 2014.  Notice that the relative strut compression (~0.17) is half the previous design because of the larger string angle.  I presented this telescope during the OSP 2015 Telescope Walkabout.  This is Example J. 

5. ~0.08 - This is my 4-strut tensegrity design from 2015.  Notice that the relative strut compression (~0.08) is half the previous design because of the larger string angle and strut force is spread over four struts instead of three.  This is Example K. 

This graphic that shows relative string angles for the telescopes above.  Bigger angle = more robust. 

WHAT IS TENSEGRITY?

Tensegrity is a structure made of strings and rods.  Buckminster Fuller came up with the name tensegrity by combining tension integrity, but he did not invent tensegrity. Tensegrity is also known as "floating compression" because rods are in compression and "float" at the ends of strings.

With tensegrity, all strings are in pure tension and all rods are in pure compression.  There are no bending moments and the structure is ultra-lightweight.  Each string and rod depends on every other string and rod.  If one string or rod fails, the structure fails.

Tensegrity structures are scalable.  Rods are limited by column bending.  If a rod bends, use a larger rod. 

SCOPE:  WHAT IS A STRING TELESCOPE?

A string telescope is a telescope that uses strings (and tubes with tensegrity telescopes) to rigidly locate the upper ring with respect to the mirror box.  The struts provide the compressive force that preloads the strings and the rest of the structure. 

Benefits

• Lightweight

• Few loose parts

• Quick setup

• Maintains collimation between setups

• Compact (disassembled) size for transportation

Non-Tensegrity String Telescopes:

• Strings

  • • Strings alone define the location of the upper ring with respect to the mirror box.

    • Strings are in pure tension.

    • Strings are fixed in length.

• Struts

  • • Struts are in pure compression.  There are no bending moments in the struts.

    • Struts are limited by column buckling.

    • Struts are variable length with the length typically varied by tightening or loosening a screw at the end of the strut.

• Collimation

  • • Collimation is maintained as long as all strings are in tension.

    • Collimation is independent of strut compression, assuming minimum compression to tension the strings.

Tensegrity String Telescopes:

• Strings

  • • Strings plus "middle ring" tubes define the location of the upper ring with respect to the mirror box.

    • Strings are in pure tension.

    • Strings are fixed in length.

• "Middle Ring" Tubes

  • • Middle-ring tubes are in pure compression.

• Struts

  • • Struts are in pure compression.  There are no bending moments in the struts.

    • Struts are limited by column buckling.

    • Struts are variable length with the length typically varied by tightening or loosening a screw at the end of the strut.

• Collimation

  • • Collimation is maintained as long as all strings are in tension, and the "middle ring" tubes are not bowed.

    • Collimation is independent of, assuming minimum compression to tension the strings and "middle ring" tubes.

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.

WHAT TO WATCH

With string telescopes I watch: 

• Weight

• String Angle

• Where Strings Are Attached

Weight

The weight includes the weight of the upper ring, everything attached to the upper ring, and half the weight of the tubes.

String Angle (with respect to strut axis) 

This is a visual way to compare the string tension force [F(string)] and strut compression force [F(axial)] to the lateral force component [F(lat.)]. 

Where Strings Are Attached 

Where the strings are attached determines what bending moments the strings apply to the upper ring and/or mirror box.  If the strings attach to the upper ring and/or mirror box at a point AWAY from the end of the strut, bending moments are applied to the upper ring and/or mirror box.  Bending moments require that the upper ring and/or mirror box be VERY rigid, thus heavier.  Having zero bending moments allows the upper ring and/or mirror box to be less rigid, thus lighter weight.

STRINGS AND STRUTS

String telescopes typically have 2, 3, or 4 pairs of strings. 

Non-Tensegrity String Telescope

Common variables regardless of the number of string pairs:

• The upper ring is rigid. 

• If a middle ring exists, it is rigid, at least in the lateral direction. 

• The mirror box is rigid. 

• The pairs of strings attach directly from the rigid mirror box to the rigid upper ring.

3 Pairs Of Strings (The most common choice for non-tensegrity string telescopes.)

• The top end of each pair of strings traces an arc in space.

• There is only one place in space where the upper ring can attach to the three pairs of strings.

• This design is self-correcting in that it works regardless of string length tolerances (within reason).

2 Pairs Of Strings (Not very common.)

• The top end of each pair of strings traces an arc in space.  However, there are only two pairs of strings.  Therefore, the attached upper ring is located by only two points (a line). 

• If the telescope has two struts, the upper ring must be constrained in some way to prevent it from rotating about the line between the two string-attaching points.  This may mean attaching the upper ring to the top few inches of the struts, which may result in bending moments being applied to the tops of the struts.

4 Pairs Of Strings

• The top end of each pair of strings traces an arc in space.  Three points define a plane, which means one of the four pairs of strings will likely not fall in the same plane as the other three pairs of strings.  Something must be done to compensate for the location of the third pair of strings.

• Possible solutions may include:

  • • Add turnbuckles to one pair of strings.

    • Only use three pairs of strings to locate the optics on the upper ring.

    • Note:  I used a flex ring on my telescopes to solve this problem.

    • ???

Tensegrity String Telescope

Common variables regardless of the number of pairs of strings:

• Upper ring is rigid.

• "Middle ring" is floating tubes - (This is important)

• Mirror box is rigid.

4 Pairs Of Strings - Tensegrity

• The top end of each pair of strings from the mirror box traces an arc in space.

• The bottom end of each pair of strings from the upper ring traces an arc in space.

• The "middle ring" is four floating tubes.  The floating tubes can shift as required to compensate for tolerances in string length.  For example, floating tubes can shift to a parallelogram shape.  Also, the ends of some of the floating tubes can be higher or lower than the ends of other tubes.

• This design is self-compensating regardless of string length tolerances (within reason).

3 Pairs Of Strings

This "floating tube" middle ring is similar to a rigid middle ring of non-tensegrity string telescopes (Example D) with the following exceptions:

• The floating tubes weigh less than a rigid middle ring.

• The floating tube middle ring is larger than the rigid middle ring.

• The larger floating tube middle ring allows string and strut forces to be approximately 50% lower than with the rigid middle ring of Example D.

RELATIVE STRUT COMPRESSION (based on string angle and number of 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:  H/L is approximately equal to the mirror's F-Number. 

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.  A larger string angle and a larger number of struts result in a smaller strut force. 

DOS AND DONT'S

It is suggested that the string centerline should intersect the strut centerline.  If not, bending moments will be applied at the upper ring and/or mirror box.

Note:  This is a suggestion.  The choice to have or not have bending moments is a design decision.  Bending moments are OK if the upper ring and/or mirror box are rigid enough to handle them. 

Strings must be inflexible.  If strings are flexible collimation will not be maintained.  I suggest that the strings be made using BCY 450 Plus bowstring.

Strings should attach directly to string anchors.  Do not use chain links or rings between strings and string anchors.

With tensegrity string telescopes, strings, and middle ring tubes should NOT contact struts. 

On telescopes with a middle ring(s), separate strings are required above and below the middle ring.  

CLEVER DESIGNS WITH "FLAWS"

Here are some clever designs with "flaws".  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.

• • Strings wrap around adjacent struts - I'm particularly fond of this design and I built a full-scale mockup.  It has the same rigidity as the stacked string design.  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 midpoints of the struts.  This design is quick to set up and more robust than any of the other designs I've seen, except tensegrity. The midpoint 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 set up.  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. 

SOME STRING TELESCOPE POSSIBILITIES

Note:  This is not intended to be a comprehensive list of all possible string telescope designs. 

• Four Strut - Strings Attached At The Top & Bottom of Struts

  • • • • The large string angle results in small strut forces that allow a lighter-weight upper ring and mirror box.

        • Weight is minimized.

Strings are attached at the tops and bottoms of the struts so bending moments are zero at the upper ring and mirror box.  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 are larger than the angles of the strings in Example C with three struts.  Therefore, the strut compression force is ~half the strut force in Example C.

Warning:  Something must be done to account for the fact that there are 4 pairs of strings. 

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

Warning:  Something must be done to account for the fact that there are 2 pairs of strings. 

• • • • • 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 are smaller than the angles of the strings in Example H.  Therefore, the strut compression force is twice the force of Example H. 

• • • • • 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 is 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 are smaller than the angles of the strings in Example H.  Therefore, the strut compression force with this design is more than twice the force for Example H. 

• • • • • Stacked Three Strut - Strings Attached At Top and Bottoms of Struts

This design has large string angles and the strings are attached at the tops and bottoms of the struts.  Therefore, bending moments are close to zero and strut forces are low.

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 in Example C. 

Another variation of this design is shown in Example J.  I am currently building a mockup of this design.  The strut compression is 25% of the strut compression in Example C. 

• • 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. 

• 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 are larger than the angles of the strings in Example H.  Therefore, the strut compression force is half the force with Example H.

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

• 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.

Warning:  Something must be done to account for the fact that there are 4 pairs of strings. 

• 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 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.

Warning:  Something must be done to account for the fact that there are 4 pairs of strings. 

• Tensegrity 3 Strut String Telescope

This design has significantly (75%) lower string tension and strut compression than a typical string telescope.  For more details about tensegrity string telescopes see this webpage. 

• Tensegrity 4 Strut String Telescope

This design has significantly (~85+%) lower string tension and strut compression than a typical string telescope.  For more details about tensegrity string telescopes see this webpage. 

My tensegrity string telescopes Google Sites