simple maths, yet I fail

[Ags]

I thought I would quickly write a simple start trail calculator... but my calculation keeps giving too much trailing. I can't see my error, I will probably spot it directly after posting this, so here goes:

        int sensorWidthPixels = 4000;
        double sensorWidthMm = 22;
        double fovFactor = 57.3;
        double lensLengthMm = 50.0;
        double acceptableTrailingPixels = 1;

        double degreesFov = sensorWidthMm * fovFactor / lensLengthMm;
        System.out.printf("Field of view is " + degreesFov + "mm.\n");

        double secondsFov = degreesFov * 4 * 60.0; //seconds of time not arcseconds
        System.out.printf("Field of view is %.3f seconds, or %.3f minutes.\n", secondsFov, (secondsFov / 60.0));

        double pixelsPerSecond = sensorWidthPixels / secondsFov;
        System.out.printf("Drift rate is %.3f pixels/second, or %.3f pixels/minute.\n", pixelsPerSecond, (pixelsPerSecond * 60.0));

        double secondsBeforeTrailing = acceptableTrailingPixels / pixelsPerSecond;
        System.out.printf("Seconds before adjustment is required %.3f seconds.\n", secondsBeforeTrailing);
 

I get this output:

Field of view is 25.212 degrees.
Field of view is 6050.880 seconds, or 100.848 minutes.
Drift rate is 0.661 pixels/second, or 39.664 pixels/minute.
Seconds before adjustment is required 1.513 seconds.
 

For a 50mm lens I would expect 6 seconds...?

[ronin]

Why do you expect 6 seconds?

As in where does that value get derived from.

Little puzzled by:

double secondsFov = degreesFov * 4 * 60.0; //seconds of time not arcseconds

Why the *4, which would make the value 4x bigger and as it is used later as a division in

double pixelsPerSecond = sensorWidthPixels / secondsFov;

Would cause the result of that to be 1/4 the value so then 1.513 would be 6.052

[Ags]

Experience :-)

[Mr Spock]

Wouldn't 1.5 seconds apply only if the star image was contained on a single pixel?

[Ags]

No, with one or two pixels of trailing star shapes are already looking funny.

I find 8 adjustments per minute at 50mm is sufficient to keep the stars round. My maths does not agree with my experience... but now that I have done the maths I fear that I will no longer be able to track at 50mm with my barn door anymore :-(

@Ronin, it takes roughly four minutes for a star to drift through 1 degree (celestial equator). So my calculation finds the number of seconds for a star to drift through the whole image, then this is divided into the number of pixels to get pixels per second.

[happy-kat]

Why do you think your won't be able to use your barn door any more?

[Ags]

I've proved mathematically that I can't do it :-)

Like the mathematician that 'proved' bumblebees can't fly.

[happy-kat]

I am not deterred. Hands over eyes...

[JamesF]

I've proved mathematically that I can't do it :-)

Like the mathematician that 'proved' bumblebees can't fly.

It didn't stop bumblebees flying though

James

[JamesF]

Ignoring the fact that  you've approximated some of your constants, because I don't think they'll have that much of an effect, if the maths is correct (which it appears to be to me) and is inconsistent with your experience then I think you must question your assumptions.  As Holmes was so fond of saying: "When you have eliminated the impossible, whatever remains, however improbable, must be the truth".

I think my next step would be to take a single frame exposure of a star close to the celestial equator (perhaps a three-second exposure -- something that won't show significant trailing).  Then without moving the camera do the same after a minute, or two, or five, depending how patient you are.  Compare the two frames and count the pixels between the images of the same star.  If the result you get in terms of the distance between the images is consistent with the maths then your assumption that trailing of a single pixel is visible may well be wrong.  If the result is inconsistent with the maths then we both may need to go back to school

James

[JamesF]

Come to think of it, debayering might act to blur the edges of the stars and hide a small amount of trailing depending on the algorithm in use.

James

[Ags]

I can do it on one frame actually... open the shutter, count three dial ahead one rev on the barn door, count three, dial two revs ahead, count three, dial four revs ahead, count three, dial one more, count sixty, close shutter.

I know the barn door tracks at sky rate so I don't need to wait for the sky to move. The last 60 second trail is to check that assumption.

[JamesF]

I was thinking that it would be easier to measure and minimises possible sources of error to do it on two frames.

James