Don's String Telescope Concepts

String Telescope Concepts
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(Click for a larger image)

Overview:

This document describes string telescope concepts. It describes WHAT is happening with a string telescope and WHY.
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:

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

When 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.

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:

Overview
Scope
Characteristics of Optimum Design
Forces and Couples
String Angle Impact on Strut Force
     With Vertical Struts
     With Angled Struts
String Anchor Location Impact on Bending Moments
Interrelationships Among Strut Force, Bending Moments and Weight
Selectively-Flexible Members
String Length Adjustment
Part Impact on Rigidity
     String Stretch
     String Anchor Detail
     Struts
     Upper Ring Flexibility
     Mirror Box Rigidity
Relative Strut Compression (based on string angle and number of struts)
Radial String Orientation
Stacked String Telescope
Clever Designs with Flaws
Some String Telescope Possibilities
Some of My Astronomy Projects

Characteristics of Optimum Design:

Large string angle (larger string angle allows smaller strut force and lighter weight struts)

Strings attached at tops and bottoms of struts (minimizes bending moments at upper ring and mirror box, which allows lighter weight upper ring and mirror box)

Lightweight assembly (allows smaller strut forces and string tensions)

Collimation maintained independent of strut compression and maintained between setups (variations in strut and string forces do not impact collimation, and recollimation is not required after each setup)

Note: Design requirements ALWAYS take priority over optimum design.  Go ahead and ignore the optimum characteristics if they are in conflict with your design requirements.

Forces and Couples:

All telescopes must maintain collimation while the telescope is being used. Upper ring location, thus collimation, is maintained by the forces and couples at the upper ring.

Forces and couples include:

Vertical (upward) forces at the upper ring from the struts

Vertical (downward) forces at the upper ring from the vertical component of the string forces (result from strut forces)

Horizontal forces at the upper ring from the horizontal component of the string forces

Couples at the upper ring from the horizontal component of the string forces

The following figures shows string and strut forces and couples:

The BLUE arrows are string force arrows. The RED arrow is a strut force arrow.
Fstring (diagonal blue arrow) is the string tension force.

The diagonal "Fstring" force can be replaced by "Fh" (horizontal string force component) and "Fv" (vertical string force component).

All arrow lengths are proportional to the actual forces. For example, the ratio of Fh:Fv is proportional to the arctangent of the string angle with respect to vertical.

The strut force (red arrow) is equal to and opposite to Fv, the vertical string force component.

This example shows only string and strut forces for a single string. The same forces exist for each telescope string.

This figure shows all the forces at the upper ring. There are eight strings so there are:

eight horizontal string force components (blue)

eight vertical string force components (blue)

eight vertical strut forces (red)

The sum of all vertical string force components is equal to and opposite to the sum of all the strut (vertical) force components. This is true regardless of the number of strings and struts.
Note that there are no strut horizontal forces

Forces:
The horizontal force components (Fh) are shown. Note that one force component is shown for each string.
Couples:
There is a clockwise (cw) couple and a counterclockwise (ccw) couple that prevent the upper ring from rotating with respect to the mirror box.

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)

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. Larger string angle and larger number of struts results in smaller strut force.

(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:

Example F has the lowest strut compression.

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

Example C strut compression is more than twice Example H.

Example F strut compression is much smaller than Example C.

String Angle Impact on Lateral Stability & Couples (With Angled Struts):

To satisfy some design requirements such as the decision to use a small upper ring, 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.

(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

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 Anchor Location Impact on Bending Moments:

With string telescopes there is a string vertical force component (red arrow in image below) pulling down on the upper ring, and a strut vertical force component pushing up on the upper ring. The force down equals the force up and the two forces make a pair. Each string of a string telescope has this pair of vertical force components that are applied both at the upper ring and the mirror box. To simplify the example I have only shown the vertical force components for one string.

Note: I have not shown the string horizontal force components because they produce negligible bending moments in the upper ring and mirror box for the string attaching detail shown.

The bending moment can be determined by the following formula:

Bending Moment = Vertical Force X Offset Between Vertical Forces

Upper Ring Strut And String Details:

Strings Attach At Strut Strings Attach Near Strut Strings Attach Between Struts

Vertical Force = 10* lbs
Offset = 0* in
Bending Moment = 0 in-lbs
*Example specific values Vertical Force = 10* lbs
Offset = 1* in
Bending Moment = 10 in-lbs Vertical Force = 20** lbs
Offset-1 = 6* in
(Offset-1 = half the distance between struts)
Bending Moment = 120 in-lbs

Note that the projection of the string centerline and the projection of the strut centerline intersect close to the upper ring thus an "Offset" close to 0. Note that the projection of the string centerline and the projection of the strut centerline intersect ABOVE the upper ring. This results in an "Offset" (shown) that causes a bending moment for each string-strut pair. Note that the strings are attached half way between the struts. **That means the string angle is cut in half and the strut (and string) vertical force is doubled for the same string assembly stability.

With a bending moment of zero, the upper ring does not flex with a change in strut compression. Thus, collimation does not vary with a change strut compression. Recollimation should not be necessary between setups. The upper ring flex changes as the strut force changes. Therefore, collimation changes as strut force changes unless the upper ring is made more rigid. The telescope will have to be recollimated each time it is set up and each time the strut force changes unless the upper ring is made more rigid. The upper ring flexes as a function of strut compression force. Changing the compression force on any of the struts may require the telescope to be recollimated.
The flex problem can be resolved by making the upper ring VERY rigid.

The upper ring can be non-rigid. The upper ring needs to be more rigid than in the example to the left. Upper ring needs to be VERY rigid to prevent it from flexing with the strings attached at the middle of the upper ring.

Mirror Box Strut And String Details:

Note: The front mirror box member is transparent to show interior detail.

Strings Attach At Strut Strings Attach Near Strut Strings Attach Between Struts

Vertical Force = 10* lbs
Offset = 0* in
Bending Moment = 0 in-lbs Vertical Force = 10* lbs
Offset = 1* in
Bending Moment = 10 in-lbs Vertical Force = 20** lbs
Offset-1* = 6 in
(Offset-1 = half the distance between the struts)
Bending Moment = 120 in-lbs

The string attaches at the bottom of the strut. The string attaching point is near but not at the bottom of the strut. This results in an "Offset" (shown) that causes a bending moment for each string-strut pair. Note that the strings are attached half way between the struts. *That means the string angle is cut in half and the strut (and string) vertical force is doubled for the same string assembly stability.

With a bending moment of zero, the mirror box does not flex with a change in strut compression. Thus, collimation does not vary with a change strut compression. Recollimation should not be necessary between setups. The bending moment is small and the mirror box is fairly rigid.   Recollimation should not be necessary between setups. The bending moment is large so the mirror box will flex unless it is very rigid. Recollimation will be necessary between setups and may be necessary when strut compression changes unless it is made very rigid.

The mirror box does not need to be very rigid. The mirror box needs to be moderately rigid. When the string attaching point is between (not near) the struts the mirror box must be VERY rigid. This is why three-strut string telescopes must have a VERY rigid mirror box.

When do bending moments in the upper ring and mirror box matter?

If your design goals include minimizing the weight of the upper ring, minimizing the the bending moment allows use of a less rigid, lighter weight upper ring.

If your design goals include minimizing the weight of the mirror box, such as with a travel telescope, or converting an existing truss tube telescope to a string telescope, minimizing the bending moments allows use of a less rigid, lighter weight mirror box.

Interrelationships Among Strut Force, Bending Moments and Weight:

The optimum design has:

Minimized strut force

Minimized bending moments (at the upper ring and mirror box)

Minimized weight

Strut force, bending moments at the upper ring and mirror box, and the telescope are interrelated. When one of the three is increased, the other two increase. When one of the three is decreased, the other two can decrease.
Example 1:

When the upper ring weight is reduced, smaller horizontal string forces are required to maintain collimation. When the string force is reduced the strut compression force is also reduced. Smaller strut force means lower chance for the strut buckling, which means the struts can be smaller diameter and lighter weight. Lighter weight means... etc. etc.

Example 2:

When bending moments are reduced at the upper ring/mirror box, the rigiditiy of the upper ring and mirror box is reduced, which means the weights of the upper ring and mirror box are reduced. Lighter weight mirror box means... etc. etc.

Example 3:

When the strut force is reduced the bending moments are also reduced. Lower bending moments means less rigid upper ring and mirror box, which means lower weigh upper ring and mirror box. etc. etc.

Conclusion: Strut force, bending moments and telescope weight should be minimized.

Selectively Flexible Members:

String telescopes have "selectively-flexible" members. "Selectively-flexible" members are inflexible along one axis but flexible along another axis. Flexible parts typically weigh less than rigid parts so using selectively-flexible parts reduces the weight of the telescope. Selectively-flexible members allow additional benefits not allowed by rigid members. Here are some examples of selectively-flexible members:

Strings:

Strings are inflexible in tension so they can rigidly locate the upper ring with the struts in place. When the struts are removed the strings are flexible so the strings remain attached to the upper ring and mirror box for compact storage and quick setup.

Flex-Ring:

The "Flex-Ring" lower ring is inflexible in the horizontal direction but flexible in the vertical direction. The vertical flexibilility compensates differences in string lengths so prevents the need for turnbuckles in the strings.

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 or all 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. String and strut forces would have to be VERY high for this design to work. 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.

(Click for larger image)

As can be seen below, lateral forces and couples are significantly smaller with radial oriented strings than perpendicular oriented strings.

(Click for larger image)

Stacked String Telescope:

My stacked string telescope is finished. Stacked string telescope.

The stacked string telescope design works weil 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 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).

(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.

(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.

(Click for larger image)

Strings wrap around adjacent struts - I'm particularly fond of this design and I built a full scale mockup. It has the same rigidity of 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 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.

(Click for larger image)

Some String Telescope Possibilities:

Four Strut - Strings Attached At Top & Bottom of Struts

This design satisfies the requirements of the "optimum design":

Strings are attached at the tops and bottoms of the struts so bending moments are zero at the upper ring and mirror box.

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

Weight is minimized.

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)

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 .
Example A

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

Example B

(Click for larger image)

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 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)

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 with Example C.
Example D
(Click for larger image)

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.

Example E

(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 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)

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.

Example G

(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 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)
Truss Tube to String Telescope Conversion
Greg's Right Angle Telrad

Last updated: 29 March 2011
Don Peckham
email: don@dbpeckham.com

	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.

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

Strings Attach At Strut	Strings Attach Near Strut	Strings Attach Between Struts
Vertical Force = 10* lbs Offset = 0* in Bending Moment = 0 in-lbs *Example specific values	Vertical Force = 10* lbs Offset = 1* in Bending Moment = 10 in-lbs	Vertical Force = 20** lbs Offset-1 = 6* in (Offset-1 = half the distance between struts) Bending Moment = 120 in-lbs
Note that the projection of the string centerline and the projection of the strut centerline intersect close to the upper ring thus an "Offset" close to 0.	Note that the projection of the string centerline and the projection of the strut centerline intersect ABOVE the upper ring. This results in an "Offset" (shown) that causes a bending moment for each string-strut pair.	Note that the strings are attached half way between the struts. **That means the string angle is cut in half and the strut (and string) vertical force is doubled for the same string assembly stability.
With a bending moment of zero, the upper ring does not flex with a change in strut compression. Thus, collimation does not vary with a change strut compression. Recollimation should not be necessary between setups.	The upper ring flex changes as the strut force changes. Therefore, collimation changes as strut force changes unless the upper ring is made more rigid. The telescope will have to be recollimated each time it is set up and each time the strut force changes unless the upper ring is made more rigid.	The upper ring flexes as a function of strut compression force. Changing the compression force on any of the struts may require the telescope to be recollimated. The flex problem can be resolved by making the upper ring VERY rigid.
The upper ring can be non-rigid.	The upper ring needs to be more rigid than in the example to the left.	Upper ring needs to be VERY rigid to prevent it from flexing with the strings attached at the middle of the upper ring.