Reflecting Telescope Optimizer Suite

Optimizes for telescope, eyepiece, diagonal, baffle, lowrider, center of gravity, rocker including friction of movement, flex rocker and equatorial table.

by Mel Bartels

Selecting a telescope depends on knowing what you want and what you are willing to spend. What telescope will you use the most? Will you use it visually or for digital imaging? Are you planning to observe planets or deep-sky? What type of deep-sky objects? How hefty of a telescope do you want to carry (not, can carry), setup and adjust? Do you need motorized tracking or goto (if imaging, then a resounding yes)? Once you select a telescope then its design can be optimized.

Telescope performance depends on radiance (how bright will the object appear); luminance (the light throughput across the entire field of view or Richest Field effect); resolution (how detailed will the object appear) and on image scale (how big will the object appear).

Telescope design is always a study in compromise. For example, greater aperture results in restricted field of view and a heavier scope; increasing the focal ratio increases the telescope's length raising the height of the eyepiece. A larger diagonal promises more light to the edge of the field, but itself blocks additional light. Even a large tube to avoid vignetting can result in a larger diagonal negating the light gain. Fast lightweight mirrors raise the center of gravity, resulting in bulkier rocker boxes.

To investigate the compromises we need a comprehensive suite of telescope optimizers that allows us to compare any parameter against any other parameter. Shouldn't you be able to pick what you consider the most important factors? Perhaps you care most about the telescope's overall size and weight; perhaps you care most about aperture; perhaps you care most about high magnification views. I wrote this suite of telescope optimizers so that I can quickly compare parameters and fine tune the major aspects of telescope design. Perhaps you will find it useful too.

We begin optimizing the telescope design by starting with the fundamental design parameters of optical performance. These parameters fall into two approaches:

Telescope first Eye and eyepiece first
focal ratio
aperture
true field of view (FOV)
eyepiece field stop
eye pupil
eyepiece FL
eyepiece field stop
aperture
true field of view (FOV)

Note that the first set excludes eyepiece FL and eye pupil while the second set excludes focal ratio.

The 'focal ratio' approach means choosing aperture and focal ratio, then optimizing for best eyepiece by using the 'find widest FOV from eye pupil'. The 'eye pupil, eyepiece FL' approach entails choosing pupil and eyepiece, then optimizing for aperture, focal ratio and FOV.

With these factors set, we optimize our set of eyepieces, then continue by optimizing the diagonal size. Next we calculate baffling and check out the lowrider option. Then we optimize for baffles, then tube assembly weight and center of gravity. Finally we optimize for desired friction of movement at the eyepiece and check the rocker dimensions.

With the full panoply of the telescope design in front of us, we are free to alter the design, trading less important parameters for the parameters that are most important to us.

Each optimizer in turn builds on values entered and calculated in previous calculators. Open the 'Telescope Optimizer', then continue by opening each optimizer in turn (the 'Lowrider Optimizer' can be ignored).

Telescope Optimizer...

Select calculator Use focal ratio Use eye pupil, eyepiece FL

Unit of measurement = imperial metric

Telescope...
limiting magnitude
Focal ratio =
Field of view (FOV) (deg) =

Eye...
Eye pupil (mm) =

Eyepiece...
Select a coma corrector Use coma corrector, x factor =
Select an eyepiece
Focal length (FL) (mm) =
Field stop diameter (mm) = apparent field (deg)

Results:
Derivation, definitions, comparing parameters, magnitudes and resolution...

We are familiar with the standard relationships:

telescope focal length = focal ratio * aperture(better known as, focal ratio = telescope focal length / aperture)

eyepiece focal length = focal ratio * eye pupil(better known as, eye pupil = eyepiece focal length / focal ratio)

Is there a master relationship that allows us to compare essential telescope specifications? And what is the minimum number of parameters?

The master equation should involve our eye; the eyepiece; and the telescope's aperture and true field of view. Adding the relationship:

eyepiece field stop = telescope focal length * true field of view

Results in the two master relationships:

aperture * true field of view * focal ratio = eyepiece field stop

aperture * true field of view * eyepiece focal length = eyepiece field stop * eye pupil

Note that the second relationship replaces focal ratio with eye pupil and eyepiece focal length.
Also, the coma corrector is ignored by the second relationship: the coma corrector's magnification only matters for focal ratio and focal length.

Definitions

Aperture is the diameter of the telescope's main mirror or lens.
True field of view is the angle of the sky as seen through the eyepiece when used with the telescope.
Focal ratio is found by dividing the telescope focal length by the diameter of the mirror or lens.
Eyepiece focal length is the distance from the entrance of the eyepiece (where the parallel rays of light begin to converge) to its focal point.
Eyepiece field stop is the entrance to the eyepiece (ring inside the barrel) that limits the apparent field.
Eye pupil is the diameter of the opening of the eye's iris.

Comparing parameters

Let's look at the relationships by comparing parameters.

Example 1: Since aperture, true field of view, eyepiece focal length or focal ratio are all on one side of the equation, they oppose each other. That is, if one increases, another must decrease. Try it: increase aperture then press the 'calc true field of view' button. You'll see the true field of view decrease in response (be sure to turn on 'Use eye pupil, eyepiece focal length' first).

Example 2: Similarly since eyepiece field stop and eye pupil are on the same side of the equation, they oppose each other. That is, if one increases then the other must decrease. Try it: increase the eye pupil then press the 'calc eyepiece field stop'. You'll see the eyepiece field stop decrease.

Example 3: Since aperture and eye pupil are on opposite sides of the equation, if one increases, the other must increase too. Try it: increase aperture then press the 'calc eye pupil'. You'll see the eye pupil increase in response.

Increase aperture: increase eyepiece field stop, increase eye pupil ... decrease true field of view, decrease eyepiece focal length, decrease focal ratio
Increase true field of view: increase eyepiece field stop, increase eye pupil ... decrease aperture, decrease eyepiece focal length, decrease focal ratio
Increase focal ratio: increase eyepiece field stop ... decrease aperture, decrease true field of view
Increase eyepiece focal length: increase eyepiece field stop, increase eye pupil ... decrease aperture, decrease true field of view
Increase eyepiece field stop: increase aperture, increase true field of view, increase eyepiece focal length, increase focal ratio ... decrease eye pupil

Magnitudes and resolution

Stellar limiting magnitude calculated for low power via the equation, 9.8 + 5 * log10(aperture inches). An additional magnitude or more can be gained by going to high power.

I calculate resolution based on the unaided-eye's ability to just barely resolve two arc-minutes.

I avoid the equation, magnification = eyepiece apparent field of view / true field of view, because of the occasional slight inaccuracy in eyepiece specifications. Magnification is defined as the ratio of the object's size to its actual size. I use the equation, magnification = aperture / eye pupil. Also useful is magnification = telescope focal length / eyepiece focal length.

Focusing tolerance

Defocus worsens the wave rating of the optical system. Selecting a degradation of 1/4 wavefront means that focus must be kept within the calculated tolerance.

Coma free diameter

The coma free is defined as the field diameter where the deformation caused by coma is less than the Airy disk diameter. Using a coma corrector increases the coma free field diameter by more than an order of magnitude.

Luminance and radiance

Luminance or etendue is the flux gathering capability of the telescope. The greater the aperture, the greater the true field of view, the greater the luminance, or light flowing through the telescope. If the edge of the field is not sharp, then luminance is wasted. A difference of 20% is probably the minimally meaningful change. While there is a great deal of room to improve luminance in popular amateur telescope designs, ultimately, luminance is limited by the eye's pupil and the eyepiece's apparent field of view. Luminance is calculated in the 'Telescope Optimizer' and vignetted luminance is calculated in the 'Baffle Optimizer'. Radiance is the brightness factor: more aperture means brighter stars and a more zoomed in view. A difference in radiance of 1 is significant, differences less than 0.3 are hardly noticeable.

Summary

Check magnification for image scale; look at the resolution in arc seconds for ability to resolve tight detail, up to your local seeing conditions; look at the luminance for the scope's ability to deliver larger scale nebulae; and look at the radiance for the brightness of small nebulae, galaxies and stars.

Eyepiece Optimizer...

Select Manufacturer Type FocalLength FieldStop ApparentField ExitPupil TrueFOV Magnification Resolution MagnitudeLimit Luminance
Some thoughts on magnification...

A range of magnifications are key to using a telescope properly.

Magnification is the ratio of the apparent size to actual size of an object. For example, looking through a magnifying lens the spider appears three times bigger. That's a magnification of 3x.

Magnification depends on telescope focal length and eyepiece focal length. Calculate magnification by dividing the telescope focal length by the eyepiece focal length. For example, a 6 inch or 15cm telescope of 48 inches focal length used with a 9mm eyepiece yields a magnification of 48 inches * 25.4mm per inch / 9mm = 135x.

Astronomical objects are very far away and very faint. Both magnification and aperture are needed to view and image objects.

Astronomical objects are either point sources like stars, too small in diameter to ever be resolved in a telescope, or extended sources like nebulae.

There is a practical limit to both lowest magnification and highest magnification.

The lowest magnification is simply the ratio of the telescope's aperture to the eye's dark adapted pupil. The lowest possible magnification for a 6 inch or 15cm aperture is 6 inches * 25.4mm/inch / 7mm eye-pupil = 22x.

A useful highest magnification is the magnification where the eye's resolving power is fully utilized. A telescope's resolution is limited by interference caused by the aperture. The interference creates a disk of light surrounded by ever fainter rings of light. The radius of this Airy Disk is ~ 1.2 times the wavelength of light divided by the aperture. For a 6 inch or 15cm aperture scope the Airy Disk is 0.75 arc-seconds. The eye can resolve 120 arc-seconds. The magnification that matches the eye's resolution to the telescope's resolution is 120 arc-seconds divided by 6 inches aperture or roughly 27x per inch of aperture (roughly 68x per cm of aperture).

Some observers prefer up to twice this amount so that the eye isn't strained (54x per inch of aperture or 136x per cm of aperture).

Magnification above this is termed empty magnification: the object is made larger but nothing more can be resolved. In certain cases such as double star observing increasing magnification above this amount makes measuring the separation between the stars easier, but otherwise the image becomes softer, fuzzier and displeasing to the eye.

Shimmering in the atmosphere, called seeing also limits magnification. If the jet stream is overhead or the upper atmosphere otherwise disturbed, magnification can be limited to 250x regardless of aperture. Steadier nights allow for increased magnification. The number of nights where 500x or higher can be employed are few in number and highly prized by observers. Nights where 2000x and higher can be used come once a decade. For example see The Night of 6000x at the 1997 Oregon Star Party. For more on seeing and the atmosphere, see my article on atmospheric turbulence.

A useful range of magnification for many telescopes is 50x to 250x. Richest Field Telescopes and binoculars employ lowest power for the widest fields.

Stars (other than our Sun) are so far away that they are not resolvable regardless of magnification. They remain point sources. Extended objects (Moon, Sun, planets, nebulae, galaxies), however, are resolvable. As magnification increases, their light is spread over a larger area, decreasing brightness at any single point. The Moon, Sun and planets are so bright that increasing magnification doesn't consign them to invisibility. Nebulae and galaxies are a different matter.

Let's use the Andromeda Galaxy, visible as an elongated smear in dark skies to the unaided-eye. It's about 3x1 degrees apparent size with an integrated or overall magnitude of 3.5. The galaxy has an average surface brightness of 22.2 magnitudes per arc-second square. Let's use our 6 inch, 15cm, aperture at lowest magnification of 22x. At 22x the Andromeda Galaxy now appears 66x22 degrees in size and will comfortably fit within a 80 degree field of view eyepiece. The telescope brightens the galaxy by the ratio of the square of the telescope's aperture to the eye's aperture, or (6 inches of aperture * 25.4 mm/inch / 7mm eye-pupil) squared or 484 times. But the magnification of 22x decreases the object's brightness by the identical 484 times amount, leaving the apparent average surface brightness unchanged at 22.2 magnitudes per arc-second. Yet the view through the 6 inch is immeasurably richer. Why?

Balancing aperture with magnification is as if a rocket ship takes us 22 times closer. We see more detail and the object overall is much brighter. But fly too close and the eyepiece can no longer fit the object into the field of view. Using the same telescope at increasing magnification means more detail at the cost of brightness. See my comparison of the Sombrero Galaxy, M104, with 6 inch and 13 inch telescopes at is aperture king?

Table of lowest and highest magnifications per aperture.

Lowest magnification is given for 7mm and 5mm pupils, older people's eyes being closer to 5mm. Magnifications starred with an asterisk * may be limited by seeing conditions.

Aperture Lowest Mag Lowest Mag Highest Mag Highest Mag
inches 7mm pupil 5mm pupil
doubled
0.3 1 1 7 15
1 4 5 27 54
2 7 10 54 108
4 14 20 108 216
6 22 30 162 324*
8 29 40 216 432*
10 36 50 270* 540*
13 45 63 338* 675*
14 51 71 385* 770*
16 58 80 432* 864*
18 65 90 486* 972*
20 72 100 540* 1080*
22 79 110 594* 1188*
24 86 120 648* 1296*
25 90 125 675* 1350*
28 101 140 756* 1512*
30 108 150 810* 1620*
36 130 180 972* 1944*
40 144 200 1080* 2160*
48 173 240 1296* 2592*
60 216 300* 1620* 3240*

Choosing magnification and aperture.

Start with an object in mind. Three examples...

Saturn. Since Saturn is a planet, select for highest useful magnification for your telescope, given seeing conditions. For example at my home, some of time I can I am limited to 250x, sometimes I can get up to 500x, occasionally I can reach 1000x before the image turns fuzzy thanks to seeing.

North American Nebula. The NAN is an extended wide field object, spanning 120 arc-minutes.

Compute the highest magnification such that the entire object plus a border fits into the eyepiece. For this we need to know your eyepieces apparent field of view.

Eyepiece apparent field of view is object size in arc-minutes is

Highest magnification is and largest aperture is

Dumbbell Nebula. This planetary nebula is a favorite of observers. Its size is about 8 arc-minutes. Enter its size in the calculator above. The calculator will give a value of 240x-600x depending on the eyepiece's apparent field of view. The calculator will also give an aperture value far greater than your telescope. In this situation, use the largest aperture you have, setting its magnification to the calculated amount.

If the object is too faint, then use a slightly lower magnification. If the object is too fuzzy because of turbulence in the atmosphere or perhaps because the telescope is performing poorly, then lower the magnification. Be careful to not over-magnify the object such that it overfills the field of view. This can cause a faint object to disappear.

Here is a table of magnification and aperture for objects of different size. The aperture is based on a 7mm eye pupil. For 5mm eye pupil, increase magnification by 1.4 and decrease aperture by 1.4. Magnifications starred with an asterisk * may be limited by seeing conditions.


Eyepiece apparent field of view

60 degrees 80 degrees 100 degrees
Object size
arc-minutes
magni-
fication
aperture
inches
magni-
fication
aperture
inches
magni-
fication
aperture
inches
180 16x 5 22x 7 27x 8
120 24x 7 32x 9 40x 12
60 48x 14 64x 18 80x 23
45 64x 18 85x 24 107x 30
30 96x 27 128x 36 160x 45
15 192x 54 255x* 71 319x* 89
8 359x* 100 478x* 133 597x* 166
4 717x* 200 956x* 266 1194x* 332
2 1433x* 399 1911x* 531 2388x* 664
1 2866x* 796 3821x* 1062 4776x* 1327

The strategy is to select the highest magnification that frames the object in the eyepiece's field of view, subject to seeing conditions and telescope capabilities. Then select the largest aperture available. Starting with a given aperture, select for the highest magnification that frames the object, subject to seeing. If the object is invisible, then try a lower magnification. This rarely happens. Much more common is a failure to properly frame the object. Use filters, go to dark skies and improve your observational skills.

Should you ever select for less aperture? That's equivalent to stopping down the aperture to improve the view. Stopping down by using an off-axis mask to reduce the deleterious effects of bad seeing helps. Stopping down to improve deep-sky views does not help. While objects can be detected at diminished apertures, there is a general loss of detail. See my results at Is aperture king?

As long as you can select for the largest aperture, you are in telescope mode. Once aperture is constrained, you are in eyepiece mode. Well equipped amateurs who have a number of eyepieces should also consider equipping themselves with a range of apertures.

Note that wider angle eyepieces allow for greater aperture.

Diagonal Optimizer (and off-axis mask calculator)...

Focuser...
Select a focuser

Telescope tube...

Diagonal...
Acceptable magnitude loss =

Results:

Off-axis mask results:
Interpreting diagonal sizes...

For the complete picture, the chart includes light lost from the diagonal obstruction. Larger diagonals improve off-axis illumination but cost light across the entire field.

Use the magnitude scale; avoid percentages of illumination: the eye responds logarithmically, not linearly. It's a mistake to be upset over a 5% light loss when in fact from the eye's perspective the light loss is an imperceptible 1/20 magnitude.

I find light loss of less than 0.3 magnitude hardly noticeable. For extended objects where both the background and object drop equally in magnitude, the contrast or ratio is unchanged, meaning that the eye's ability to detect the object remains largely unchanged. For instance, compare a 10 inch to a 12 inch telescope - the magnitude drop is 0.4. I can detect this difference when comparing views on borderline objects. A drop of 0.5 magnitude or more is not readily detectable on brighter objects. However, the difference between a 10 inch and a 11 inch telescope is much smaller at 0.2 magnitudes and not readily apparent.

An object's detectability depends on contrast between object and sky, apparent size of the object and the object's brightness. The contrast is the ratio between the object's brightness per area (typically one arc-second squared) added to the sky background brightness that is in front of the object and the sky background brightness adjacent to the object (contrast=(object+sky) / sky). When a star or extended object is dimmed as it approaches the edge of the field of view, so is the sky background. Contrast remains the same. Experiments that I have conducted show that the object's detectability is not diminished as much as the raw magnitude loss suggests. Besides, if critical detection is required, then the object can be brought to the center of the field. Read more on visual detection and limits at the eyepiece.

Diagonals act to degrade optical performance, the larger the diagonal, the worse the degradation. A one-third obstruction, a much larger ratio than the customary visual Newtonian uses, degrades the optical quality by one-sixth wave. Changes less than one-eight wave are very difficult to see. However, a smaller diagonal does not always result in improved views. Check out my secondary size experiment.

The offset is the distance that the diagonal needs to be moved away from the focuser and the distance that the diagonal needs to be moved towards the primary mirror. For a detailed explanation including graphics, see my diagonal offset study.

Thoughts on an off-axis mask...

Stopping down by using an off-axis mask is a time honored way to beat seeing and to cut the dazzling light of the Moon and bright planets in large aperture scopes.

Stopping down is less popular today. This could be so because of drifting preferences. It is also a testament to learning how to use large Dobsonian mirrors in the dropping night time air by cooling them with fans.

The maximum diameter of an off-axis mask is set by taking the primary mirror’s diameter and subtracting the diagonal’s minor axis size then dividing the result by two. For example, a 16 inch with a 3.5 inch diagonal has a maximum off-axis mask diameter of (16 – 3.5) / 2 = 6.25 inches.

The light throughput is the inverse of the mask diameter to primary mirror diameter squared. Using the numbers from above, (off-axis mask diameter / primary mirror diameter) squared is (6.25 / 16) ^2 = 0.15 or 15% light throughput. That dims the Moon’s brightness by two magnitudes.

Everyone should make a black cardboard mask with a one inch off-axis hole. The Airy disk and rings look beautiful. But that costs resolution. Of course this resolution is wasted at low magnification.

What is the relationship between the off-axis mask’s resolution and the telescope’s magnification? What size should the off-axis mask be to resolve all that is possible at a particular magnification?

Since the eye's entrance pupil at best resolution is 1mm in size, the eyepiece's exit pupil is the factor that the primary mirror's aperture can be reduced. For example, an exit pupil of 6mm (the exit pupil is calculated by taking the eyepiece's focal length in mm and dividing by the primary mirror's focal ratio) means that the off-axis mask should be 1/6 the diameter of the primary, an exit pupil of 3mm means that the off-axis mask should be 1/3 the diameter of the primary. This leads to the conclusion that the smallest exit pupil to use with the maximally sized off-axis mask is 2-3mm.

There is also a very simple and easy to remember relationship between aperture and magnification with respect to resolution. And it is this: the telescope will resolve all that the human eye can see when the aperture in inches equals the magnification divided by 25. For example, at 100x, the off-axis mask should be at least 4 inches in diameter, 100 / 25 = 4.

For the 16 incher’s off-axis mask mentioned above, the optimal magnification is 6.25 * 25 = 156x.

That’s it! Now you can make those off-axis masks understanding the brightness reduction and the best fitting magnification (or what diameter to make the off-axis mask given a desired magnification).

Note: double star observing with smaller apertures can double even quadruple the optimum magnification, up to the seeing limit of the sky, in order to better see the Airy disk and rings.

Baffle Optimizer...


Results:
Discussion on baffles...

We want the 'good' light to reach our eye, the 'rogue' light to be blocked. Some rogue light we simply cannot block because it comes from the upper atmosphere exactly between the object and our telescope. This includes sky glow and reflected light pollution. Other rogue light strays into our eyes. This we can block with a hood or by cupping the eyepiece. The remaining rogue light can sneak past the diagonal into the eyepiece and sneak past from behind the primary mirror, bouncing off the diagonal to fog the eyepiece.

The rogue light sneaking past the diagonal can be blocked with a baffle. This baffle is called the projected focuser baffle or diagonal baffle. And rogue light sneaking past from behind the primary mirror can be blocked by baffles that surround the primary mirror upward. These baffles are called the primary mirror baffle. The baffle optimizer calculates the minimum size for these baffles based on geometric light ray traces. An additional baffle, not shown and not calculated, can be placed just below the focuser to tighten up the projected focuser or diagonal baffle.

Using an idea by Larry Shaper in Amateur Astronomy magazine, Issue #91, Summer 2016, page 52-53, the edges of the baffle can be tilted to direct light away from the focuser's tube bottom aperture. Larry concludes that the flattest black paint always looks gray while a baffle painted in gloss black with tilted sides looks truly black. You can see that the tilt angles light past the focuser tube and is long enough that light reflected at a narrow angle face on is also directed away from the focuser tube. Since the optical tube assembly can be open, I tilt the projected focuser baffle on both sides.

Discussion on vignetted luminance...

The telescope's light flux or throughput is vignetted by the diagonal, both from the diagonal's obstruction and from falling off-axis illumination. The vignetted luminance integrates the light loss to arrive at a vignetted luminance value. For comparisons, since all telescopes have two reflecting surfaces with minor light loss from each coating and a token light loss caused by the eyepiece's lenses, it's not necessary to adjust the luminance. The actual luminance or light flux or throughput can be calculated by multiplying the vignetted luminance by the reflectance of the coatings and subtracting the eyepiece's light loss, e.g., let's say that the theoretical luminance is 2000 and after diagonal vignetting does to 1680. If the coatings reflect 90% each and the eyepiece absorbs 5%, then the actual luminance is 1600*0.9*0.9*0.95=1293.

Lowrider Optimizer...


Results:
Discussion on lowriders...

By increasing the diagonal's angle, we can aim move the focuser a little closer to the primary mirror, lessening the eyepiece's height above the ground.

Why a folded reflector (popular name, 'low rider')? It's all about convenience: the eyepiece height above ground is shortened. This can make the difference between ladder and no ladder or between high up a ladder and stepping up onto a stool.

An early example of a folded (or low rider) reflector is Ed Danilovicz's 12 inch, featured in Sky and Telescope magazine, April 1976 pg 278.
Ross Robert's folded 16 inch was featured in the Oregon Star Party Walkabout of 2008 here http://www.bbastrodesigns.com/osp08/RossRoberts-16.jpg.
Dan Gray's bent 28 inch is a popular scope at the Oregon Star Party. The eyepiece is a couple of feet closer to the ground because of the folded design. http://www.siderealtechnology.com/28inch/.
Pete's 25 inch folded scope as posted on the atm-free discussion group, from 2006. He's since added side panels and a tertiary mirror to angle the eyepiece directly outward.

Center of Gravity Optimizer...

Part Weight Distance



Results:

Rocker Including Friction of Movement Optimizer...

Altitude movement...
Altitude bearing separation (deg) =
Altitude bearing materials
Azimuth movement...
Azimuth bearing materials



Results:
Discussion on friction of movement...

An essential feature of John Dobson's telescope design is that the telescope moves smoothly and precisely about the sky, staying put once the operator let's go. There is no clamping or locking down. Tracking an object across the sky consists of periodic adjustments by pushing the scope very small distances while looking through the eyepiece. His design depends on an interesting property of Teflon on pebbly Formica, namely that the friction of movement is about the same as the friction that begins a movement. In other words, the dynamic friction equals static friction. Most materials stick worse than they move, leading to jerky motions.

The force to move the telescope should not be so great as to demand a great deal of effort, particularly when making very tiny high magnification adjustments by hand, nor should the force be so slight that wind can move the telescope. Ideally the force in both azimuth and altitude axes is roughly the same so that the axes 'disappear' as the scope is moved to and fro.

The force to move the scope in azimuth increases as the scope is pointed upward. I set the angle at 48 degrees or halfway up the sky. This is the optimum pointing angle given the range of altitude movement, area of sky and seeing conditions. Keep in mind that as the scope is pointed further upward that the azimuth resistance to movement becomes quite stiff.

I like a frictional force of two to three pounds (1 to 1.5 kilos). This gives me a smooth and not-too-stiff touch at the upper end of the scope, avoids balancing issues with heavy eyepieces and resists weathervaning from wind gusts.

The altitude friction can be adjusted by varying the bearing angle and the altitude bearing radius. The azimuth friction can be adjusted by varying the distance from the pads to the pivot (the azimuth bearing radius) and by changing the material pairing. Bearings can be substituted for one or more of the bearing points with a proportionate reduction in friction. For instance, the azimuth friction can be reduced by two-thirds if two of the three bearing pads are replaced with roller bearings. More unusual is to build a trolley with a pad on one end and a roller bearing on the ther. By moving the pivot location closer to the pad the friction can be increased and by moving the pivot location closer to the bearing the friction can be decreased.

The formula and concept is from Richard Berry's article in Telescope Making 8, page 36-.

The size of the pads modestly affects the quality of motion. It's a long standing rule of thumb that 15 PSI (pounds per square inch) is idea.

The key here is to have a favorable static to dynamic friction ratio where the friction to begin the movement is less than the friction to continue the movement. This feels like 'butter' at the eyepiece.

Discussion on telescope value...

Initially telescopes were judged by their focal length culminating with Helvelius' 150 foot. Since then telescopes have been rated by their aperture initially in inches now in meters. But I don't feel that this completely captures a telescope's value. A combination of telescope performance factors along with ergonomic factors seems more comprehensive. combining luminance, radiance and telescope weight seems to capture the comparative value better. This combined value explains the lasting popularity of the Astroscan, Edmund Scientific's little red ballscope. It has an luminance-radiance-weight value (in pounds) of roughly a 1000. Many amateur scopes are closer to a value of 300. It's important that each amateur understand what will maximize their value. For some it is the most transportable aperture, for others it's wide fields, for many it's aperture regardless of the cost. Time under the stars is precious. Use it wisely by optimizing your telescope design.

Flex Rocker Optimizer...

Altitude bearing separation (deg) =
Altitude bearing materials
Azimuth bearing materials



Results:
Discussion on flex rockers...

Imagine the altitude bearing getting bigger and bigger. The rocker's weight shrinks, which is good but so does the height, lessening its rigidity, which is bad. But what if the altitude bearing points are placed at the rocker's corners and under each corner an azimuth bearing is placed resulting in four azimuth bearings that ride on a rigid ring? In fact, the altitude and azimuth bearings can be combined into a single block with the rocker reduced to merely holding the bearing blocks in relative position. We can have our ultralight rocker with good rigidity. Additionally, the mirror box can swing down through the base to lower eyepiece height when pointing near the zenith. Check out some examples.

Equatorial table optimizer...

Equatorial table optimizer work in progress...

Latitude (deg) =
Tracking time (minutes) =



Results:
Discussion on equatorial tables...

Equatorial table discission...

The polar axis must pass through the combined center of gravity of the tube assembly, rocker and the equatorial table's platform.

Values for a four corner equatorial table are calculated where a tracking arc is situated at each corner of the equatorial table.

Other table designs include three arcs (two on the north side of the platform, one on the south side), two arcs on the north side and a pivot on the south side, and finally, two pivots, one on the north side and one on the south side.

Optimizer summary...

Telescope...
Magnitude limit =
Radiance (brightness) =
Resolution (Dawe's Limit) =
Luminance (Richest Field effect) =
Vignetted luminance =
Vignetted luminance-radiance-weight =

Aperture =
Focal ratio =
Telescope focal length =
Telescope diopter =

Optimized eyepiece =
Eyepiece focal length =
Eyepiece apparent field =
Eyepiece field stop =
Coma corrector =
Coma free diameter =
eye pupil =
FOV =
Magnification =
Useful magnification =

Diagonal and focuser...
Focal plane to diagonal distance =
Diagonal (m.a.) size =
Diagonal offset (towards primary mirror and away from focuser) =
Focuser =
Racked in height =
Focuser tube travel =
Barrel tube inside diameter =
Barrel tube length =
Inward focusing distance =
Focusing tolerance =

Telescope tube outside diameter =
Telescope tube thickness =
Mirror sagitta =

Manufacturer Type FocalLength FieldStop ApparentField ExitPupil TrueFOV Magnification Resolution MagnitudeLimit Luminance
Off axis mask...
Maximum diameter =
Highest magnification =
Dawe's Limit =
Magnitude limit =

Baffle...
Baffle opposite focuser diameter =
Tilted baffle opposite focuser:
Baffle primary mirror extension (measured from mirror's front edge) =

Low rider...
Primary mirror front edge to eyepiece distance =
Primary mirror front edge to secondary mirror distance =
Primary mirror front edge to end of tube distance =
Bending angle =
Secondary mirror size =

Weight and center of gravity...
Tube assembly weight =
CG =
CG sensitivity =
CG to eyepiece distance =
CG to back corner of telescope tube (distance for tube to clear rocker bottom) =

Dobsonian rocker...
Rocker dimensions:
Rocker weight:
Altitude friction of movement at eyepiece =
Azimuth friction of movement at eyepiece =
Azimuth pad size =

Flex rocker...
Rocker dimensions:
Base ring dimensions:
Rocker weight:
Altitude friction of movement at eyepiece =
Azimuth friction of movement at eyepiece =
Azimuth pad size =

Equatorial table...
Latitude (deg) =
Tracking time (minutes) =
Max tilt:
South tracking arc:
North tracking arc:
Platform size:
Platform weight =
Total weight =

For more, see...

Bartels' equation for telescope value
The analyzed telescope
Tips to improve your telescope
Richest Field Telescopes
A new way to look at things
Visual detection

For my telescopes and more articles, see my Telescope Making page.

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