Is my maths right?

[Demonperformer]

I am trying to get some idea of scale on the AZ adjustment bolts on the EQ6.  I think I have it sussed, but would be grateful if anyone can spot any mistakes.

The centre of the AZ tripod peg is about 40mm from the centre of the mount.

The circumference of the circle prescribed at this distance is therefore about 251.3mm [πd].

There are 6 threads per cm on the bolt, meaning that a complete circumference would require 1508 complete turns of the bolt.

Every turn of the bolt therefore equates to 0.287 degrees [360/1508], which is about 14.3’.

So if AT says my AZ adjustment is 49.2’ out, I would need to turn the bolts just under 3.5 times [49.2/14.3].

In reality, the figures I have used are far more “accurate” than is practical in the real world (I guess I could get it to within about 1/8 turn fairly accurately - which would appear to equate to about 1.8'), but this is just to give me a guide as to the sort of amount of movement required.

If these figures are right, that is a lot more turns than I was expecting (based on no evidence whatsoever!) and could account in part for my difficulties with PA.

Thanks.

[LeeB]

looks like you cm and mm are mixed, 6 per cm and circumference in mm

[Moonshane]

I think this is right but I keep contradicting myself.

25.13cm circumference = (25.13x6) = 150.96 turns to go all the way around

one turn = 360/150.96 = 2.38 degrees = 142.8 minutes

your 'error' is 49.2 minutes so you need 142.8/49.2 = 2.9 turns to get there. I suppose just a smidge under three is easy enough.

[Demonperformer]

Thanks for the replies.

Yes cm/mm confusion (pretty typical for me).

Shane, I agree with the calcs (143' per turn seems a lot more likely to me than 14.3'), up to the last line, which I think is upside down? Should this not be 49.2/142.8, i.e. about 1/3 of a turn?

Thanks.

[LeeB]

close I make the last bit, 49/142 for 1/3 of a turn (timing!!!!) both posting together

[Moonshane]

sorry, yes. my common sense check obviously went AWOL!  if one turn is approx 3x your error......doh!  snatching defeat from the jaws of victory is something my football team (Manchester City) tends to do more than me thankfully.

Ironically, I am considering the purchase a copy of Stroud's Engineering Mathematics to try and understand physics forumlae a little better (i.e. at all). maybe I need to revisit O level maths first!

[Moonshane]

I suppose the easier way to think about it was that if your turn measurement parameter was out by a factor of ten then so must your answer be. therefore 3.5/10 = approx 0.33

[Cornelius Varley]

Almost right in the end. The pitch of the bolt (M10 coarse series) should be 1.5mm. (6.66/cm)or 1.25mm (M10 fine series)

http://www.roymech.co.uk/Useful_Tables/Screws/Hex_Screws.htm

[Demonperformer]

I just did a rough count against a ruler - which is always dependent upon how 'square' one holds it - so I accept your amendment without complaint .

So that produces a result of about 129' per turn.

[Gina]

That sounds about right.

[wookie1965]

Are you sure this is not "A" level math`s i got an "O" level and this is beyond me i cannot get my head around it.

[Moonshane]

well cirumference = pi (3.142 approx) x D (diameter).

diameter = 40mm x 2

one circle = 360 degrees

one degree = 60 minutes of arc (or 60')

6.6 turns of the bolt pushes out by 1cm

see if you can work it out 

[Cornelius Varley]

You lost me on "well"

[Moonshane]

LOL

not only is my maths bad, I cannot spell either.......

[wookie1965]

Now i understand well almost i would have to do this a few more times get the hang of it.

[jambouk]

In practice, I've found to correct a PA error of 45 minutes or so, I think a third of a complete turn would be too much. My experience is it would be much less of a turn needed.

James

[Gina]

well cirumference = pi (3.142 approx) x D (diameter).

diameter = 40mm x 2

one circle = 360 degrees

one degree = 60 minutes of arc (or 60')

6.6 turns of the bolt pushes out by 1cm

see if you can work it out 

OK   I like a challenge   Now then - where did I put my brain (or waht's left of it) ???

One turn of the bolt = 1/6.6 cm = 10/6.6 mm (I work in mm).

With an 80mm diameter the circumference = Pi x 80 mm

One turn of the bolt = (10/6.6) / (Pix80) x 360 degrees rotation of the mount (I think)

Rationalising = 10 x 360 / ( 6.6 x Pi x 80) degrees = 10 x 360 x 60 / ( 6.6 x Pi x 80) minutes of arc = 130.21768071155072926545035185024

So to change the azimuth by one minute of arc would require 360 / 130 degrees = 2.8 roughly

So turning the bolt a mere 3 degrees changes the az PA by an arc minute.  Which just goes to demonstrate how difficult it is to get good PA with these coarse controls

[jambouk]

So to correct 45 arc minutes of error, would require 3 * 45 = 135 degrees turn, which is about a third of a complete turn, which still seems too much from my limited experience.

James

[Clockwork_Orange]

Ah all this talk of pies is making me feel very hungry

anyways dont use Pi use percentages instead if you take 150 over 7 rather than 22 over 7.

You see 150 over 7 = 21.482 still with me, so if the the peg is 40mm from the centre then the square it would fit into would measure 80mm wide, the perimeter of the square would equal 320mm, ok still with me then deduct 21.482% off this to arrive at the maximum sized circle that fits inside the square of 251.2576mm.

more than one way of skinning a circle

I worked this out myself btw

John 

[Gina]

Well, I'm assuming the quoted figures for the thread pitch and centre to az peg measurements are correct.  I can't remember now and I'm not venturing out in this attrocious weather to go and measure it! - so there!

[Gina]

I like pies   Anyway the Win 7 OS calculator has Pi on it so I use it

[jambouk]

Actually, on second thoughts, a third of a turn might not be that far from the truth if we are talking 45 arc minutes.... I was having a very blond [well ginger] moment and was thinking of last set of numbers on the right when the skywatcher handset gives the Mel and Maz errors, and of course that is arcSECONDS.... Stupid, sorry.

Does anyone manufacture a reticle eye piece, high power (short focal length) which has graduations along its east-west and north-south axes? That way, if you know the fov in that eye piece was say 14 degrees, then each half of east-west would be 7 degrees, and that could be graduated into seperate degree markers, and each degree could be etched into 10 arc minute segments; then when one knew the error, slew back to polaris, centre polaris bang in the middle of the fov, then use the azimuth (and then the elevation) to get polaris to move the appropriate amount of error in the appropriate direction, which would probably get you to 2-5 arc minutes away in terms of accuracy. You could then use the same reticle eye piece to re-do the star alignment and re-establish the error again of the PA.... Adding a 2x barlow or greater multiple would allow a new fov to be worked out and would beed the divisions on the reticle to be re-calulated as to what they then represented in terms of arc minutes....

Just a thought.

James

[Demonperformer]

Does anyone manufacture a reticle eye piece, high power (short focal length) which has graduations along its east-west and north-south axes?

James

something like http://www.firstlightoptics.com/specialist/baader-microguide-illuminated-reticle-eyepiece.html ?

[jambouk]

That would do it.

Blimey, £165.

James