Observatory Calculations

[astrosathya]

Since I do not have a telescope at the moment, I thought to give my brain some exercise. What exactly is involved in the design of a domed observatory? Specially the calculations involved for the gores and ribs as they are of different arc lengths. My plan is to design a dome with the opening built in, rather than build a dome and cut the opening out. Has anyone built one for themselves? if so, please do advice, if not we could make this a topic of discussion.

I am looking to understand the mathematics of design, not just "how to cut and glue plywood". The design phase I believe is the most important one, but I am still confused. It is good to build a complete hemispherical dome and then cut the slots out, but I would like to investigate the mathematics of the other design wherein the rib sizes are calculated and then the gores attached.

Clear Skies,

Astrosathya

[JamesF]

Ok, this is going to be hard without drawings to refer to, but let's have a go...

Draw a plan view of the dome to scale, with the centre and the slot marked. You can then measure off the horizontal distance that the remainder of any rib must cover (call it "s"), and from that you can work out how much of the horizontal span to the centre that it doesn't cover, but subtracting that value from the dome radius r.

You can then work out the angle between the horizontal and the radius of the hemisphere ending at the point where the outside edge of the rib ends (where the slot edge starts) by trigonometry. IIRC, and don't quote me on this, it'll be cos^-1 (( r -s ) / r ). Call the angle a.

That angle gives you the outside length of the rib as πra/180.

I think

James

[JamesF]

Actually, knowing the width of the slot and the angles between the ribs you can calculate s using trigonometry, too, so you'd not even need to draw it. Though it make well make more sense if you do.

James

[pete_l]

Not quite what you're asking about, but there are some online calculators for geodesic domes. Briefly, you plug in the dimensions of the dome, choose the type of geodesic you want (half-dome, 5/8s etc. whether you want to make it out of triangles, penta/hexagons). The program then spits out designs for the various parts, including the dimensions and numbers for the various shapes as their are some non-obvious angles involved.

[pete_l]

Doops: s/their are/there are/

+1 vote to bring back the editor

[astrosathya]

Hi Guys,

Thank You James for the trig calculations. Just to confirm, is that cos "inverse" or is it cos (off) 1/ (xyz value)? I have looked at geodesic domes, but they are not quite "dome enough" for my liking. I am more into the old world charm of observatories.

I did find calculator for Hemispherical parachutes. That may help too.

sathya

[JamesF]

It's inverse cos. I'd really check the maths is sane before relying on it though I don't exactly have a lot of need for trigonometry these days and may have misremembered. Doubtless I'll have to learn it all again once my children start doing it at school.

James

[JamesF]

Thinking about this a little more, regardless of the calculated value I'd make these ribs perhaps 50-100mm longer than they need to be, then trim them down to the correct size once the entire frame is built.

James

[nytecam]

I am looking to understand the mathematics of design, not just "how to cut and glue plywood". The design phase I believe is the most important one, but I am still confused. It is good to build a complete hemispherical dome and then cut the slots out, but I would like to investigate the mathematics of the other design wherein the rib sizes are calculated and then the gores attached. Clear Skies, Astrosathya

Perhaps some useful info in attached pics/sketch of my 10ft DIY frameless [no ribs!] dome - it shows gore dims/trig that can be scaled. Gore size from economic cut of 8' x 4' x 3mm ply sheet. Good luck

ps: currently planning demise of dome and reroofing 'hole' to return as garage/workshop. My 12" Meade SCT dome remains.

Little girl in pic is my middle daughter - the family celebrated her 50th last week - how time flies !

[Gina]

I like that I always think a dome looks like a "proper" observatory but for me the shed style with roll off roof and attached warm room, is more practical. I guess I'm a bit of a square

[nytecam]

I like that I always think a dome looks like a "proper" observatory but for me the shed style with roll off roof and attached warm room, is more practical. I guess I'm a bit of a square

Thanks Gina - as my big dome is going, I thought I should weigh it with the trick of placing a set of bathroom scales under one edge whlist it's supported on the opposite side by the dome track - the scales recorded 8st = 50Kg or double that eg 100Kg for whole dome. So that's the gross weigh to be lifted off the roof is 50Kg when dome is halved into two sections - a bit more than I thought Removing the shutter and shutter fixed back section should reduce it a few Kg so just about manageable

[astrosathya]

Hi All,

Thank you for sharing your experiences. Would love to hear from more of you out there. I started this topic so that we can have something our brains can chew on when the weather Gods are on holiday.