A tube has a minimum diameter. There is also a minimum and maximum length. However they depend on each other. The figure below shows the principle.
The thick pink line at the bottom symbolizes the primary. The red cone on top of it is the area covered by the Field Of View (FOV). To prevent vignetting, the tube may not enter this area.
The blue line shows the position of the secondary, this is for clarity only it has no impact on the tube dimensions.
The green line on the left side symbolizes the first lens of the eyepiece. The thick black lines surrounding it show the focuser with the focuser baffle. (For more on this see "Focuser Baffling"). The orange/brown area extending from it, shows the area from which the eyepiece-lens can be seen directly. The tube (or upper cage of a truss-tube) should block all light that could enter the lens this way. This is to achieve the best possible contrast.
(Note: As a compromise, it is also possible to use the size of the fully illuminated area at the focal point. See "Focuser Baffling" for more information.)
The upper edge of a tube should thus be in the green area.
First choose a tube diameter. Use it (the radius) in the following formulas to determine the minimum length. To avoid tube currents and to have some place for baffles, it is advised to choose an inner diameter 50-100 mm (2"-4") larger than the aperture.
The following formula(s) can be used to calculate the minimum tube length:
To the above formulas:
- The variable "k" is not alway's known, or can at least fluctuate. One could also use the diameter of the fully illuminated area, or the largest field stop of the used eyepieces. If you do, the the value "e" should be the distance between the tube centerline and the plane in which "k" lies.
Check with the following formula if the value obtained above is below the maximum length.
The following formula can be used to calculate the maximum length:
If the minimum length is greater than the maximum length, then choose a bigger tube diameter and rerun the calculations.
It would ofcourse be possible to derive a formula to calculate the minimum tube diameter, but the formula would be rather complicated. It is easier to make one or two itterations.