Aperture calculation

[bomberbaz]

Is this calculation correct when comparing various scope types, think I have asked similar before but such as my age is, I forget far too easy these days.

Simple frac 100 - Pi x Rsq =  3.14 x 50sq = 7854

OTA with central obstruction, this time a 6" CC with a 58mm central obstruction.

1) CC 150 - Pi x Rsq =  3.14 x 75sq = 17671  minus 2) central obstruction  58 - Pi x Rsq =  3.14 x 29sq = 2642 

Therefore you get 1 - 2 = 15029 total area for the CC.

Is this right?

TIA people

Steve

[johninderby]

An article by Damien Peach that might be of interest. 

An examination of the effects of optical aberrations, obstruction and seeing on real Planetary images.

http://www.damianpeach.com/simulation.htm

 

Used an area calculator and came up with the same answer of  15,029

Edited February 16, 2022 by johninderby

[vlaiv]

Yes, those are correct.

Depending on what you need that for - you might want to include various other losses in the system.

If you for example want to see what sort of refractor will provide you with same light gathering as 6" CC then it would go like this:

You have calculate area of CC to be 15029mm2 but did not account for mirror reflectivity - according to FLO that is 95% for both primary and secondary mirror.

Effective aperture is then 15029 * 0.95 * 0.95 = ~13563.67mm2

For doublet refractor - you have x4 air/glass surface (two lenses - each having front and back surface) and if they are properly coated - they transmit light at ~99.7% efficiency.

We now do things in reverse:

square_root( ( 13563.67 / (0.997*0.997*0.997*0.997) ) /PI ) = sqrt( 13727.67 / PI) = sqrt(4369.65) = 66.1 being radius in mm

So diameter is 132.2mm

130mm refractor will have roughly the same light gathering as 6" CC.

Do pay attention that light gathering is not the same as resolved detail. Above does not mean that 130mm refractor will show the same planetary image as 6" CC. Other things come into play when calculating which one will show more detail.

[bomberbaz]

2 hours ago, vlaiv said:

130mm refractor will have roughly the same light gathering as 6" CC.

 

Two big differences here would be price for a Doublet refractor and more importantly for me, size/ ease of storage. 

I don't doubt both will give superb views, also that the 130mm frac would give better views overall.    

I have also read @johninderby's link regarding many aspects appertaining to OTA with a central obstruction and found this very useful. 

Originally I was considering an 8" CC but after much thought I feel this is going to be too big, hence this thread. 

Theree was also a very lot of useful info in this current thread. 

Thanks why I love SGL, in this instance (and for a change) I am actually thinking myself out of an impasse 😅

Thanks for the info vlaiv and @johninderby, it is proving very useful.

[johninderby]

You just have to accept that every scope is a compromise and no one scope does ot all so it’s more about finding the best comprimise rather than the perfect scope. Also explains why most have more than one scope. 😁

[Louis D]

And don't forget that some Maks use undersized primary mirrors, so they don't actually operate at the aperture of their corrector which diverges the incoming rays and requires an oversized primary to collect all of them.  For instance, the Synta 127mm Maks actually operate at about 118mm from what I've read.  The JOC 127mm Maks do actually operate at 127mm from what I've read.

[bomberbaz]

1 hour ago, johninderby said:

You just have to accept that every scope is a compromise and no one scope does ot all so it’s more about finding the best comprimise rather than the perfect scope. Also explains why most have more than one scope. 😁

sshhhh, everyone needs at least 7 days worth of scopes, Sunday through to Saturday, everyone know that. Even my wife

[Mr Spock]

Mak correctors bend the light outwards. I know an OMC-140 has a 150mm primary to compensate for this. Skywatchers don't.