I should have paid more attention in math class

[James Mooney]

OK , here goes...

A printer can output a print area of

1cm X 10cm in 25 seconds

1cm X 20cm in 35 seconds and

1cm X 40cm in 55 seconds

How long will it take to print an area of

20cm X 60cm?

I am trying to write a calculation for this and haven't an idea where to start :

Calling on the help of any maths geniuses out there!

[comment]

I think I would approach it this way:

Max ( 20 ; 60 ) = 60;

Div ( 60 ; 40 ) = 1;

1 * 55 = 55;

Mod ( 60 ; 40 ) = 20;

Div ( 20 ; 20 ) = 1;

1 * 35 = 35;

Mod ( 20 ; 20 ) = 0;

Div ( 0 ; 10 ) = 0;

0 * 25 = 0;

55 + 35 + 0 = 90;

90 * 20 = 1800

This is of course assuming the printer is using the same process of determining how to print most efficiently. This is not an easy problem - though I believe in this case it is simplified by having all the strips fixed at 1cm.

[James Mooney]

Many thanks comment.

The full print area is actually 90cm X 60cm, I was using the 20cm X 60cm as an example to illustrate how I might calculate print speed over an VERY varied array of print sizes.

In short we run different products with varying print area sizes through the printer and I'm hoping to find a way to calculate how long each will take so I can calculate a print charge. I am probably asking too much!!

If it makes any difference I know that it takes 5760 seconds (96minutes) to output over the full 90cm X 60cm

Edited August 7, 2008 by Guest
Afterthought

[Fitch]

I'd want to know how long 2x10 or 20x10 takes before attempting a solution. I.e. does that first "row" always take 2.5 seconds/sq. cm, and subsequent sq. cm take 1 sec? That's what it looked like at first glance.

[comment]

The actual print area is not really the issue here. What matters is the division into the pre-defined blocks - 1x40, 1x20, 1x20 in your example. If these are correct, then the calculation above can be applied to any desired size.

[James Mooney]

You're right - it takes 48 seconds to output 2cm X 10cm

[James Mooney]

thanks again comment. I'll play with your suggestion and test it against some examples and see how it goes.

Really appreciate the help and speedy responses.

[comment]

it takes 48 seconds to output 2cm X 10cm

Then we don't know jack. We need some more rules here.

[James Mooney]

I was afraid you would say that : I thought there was a relationship curve between time / area and that if we knew three of the points on that curve we could plot it and take it from there. Back to the drawing board so. Thanks again

[comment]

I have no doubt there *is* some kind of relationship between the area and the time it takes to print it. However, three points are not enough to establish what kind of a curve it might be.

This reminds me of:

http://www.fmforums.com/forum/showtopic.php?tid/193765/post/283678/#283678

[comment]

I should add that it's quite possible there are SEVERAL area/time relationships, depending on the aspect ratio - so 30x60 would not necessarily be printed in the same time as 40x45. And other factors might play role in this too.

[James Mooney]

Yes. that example looks similar to what I was hoping to achieve. Assuming we have the time and means to run a battery of range tests (which we have!) do you have any suggestions as to what would be the best methodology?

I know, I'm grasping at straws here!

[comment]

You need a statistician here. Off hand, I would say make 6 tables like this:

Width = 10cm

Length....Time

10cm

20cm

30cm

...

80cm

90cm

Width = 20cm

Length....Time

10cm

20cm

30cm

...

80cm

90cm

Width = 30cm

and so on, until width = 60cm. Then plot the 6 graphs and see if there's anything meaningful that can be deduced from them by eye. Of course, the finer the resolution, the better.

If you reduce the step size to 1cm (5400 test results), you won't need a formula - you can use the results as a source for a lookup. :laugh:

[comment]

One more thing: it is also possible that the beast prints 10cm strips very quickly, but takes its time printing the <10cm remainders. In such case, the test above would be pretty worthless. It's very difficult to devise an efficient test without knowing at least something about the nature of the beast beforehand. Don't the manufacturers have something to say?

[James Mooney]

comment, you're a star! thanks for all your help. I've been onto the manufacturer to no avail. The machine in question is a laser engraver that outputs a beam of energy at a user determined level from a traveling "print head" so I'm pretty confident that the rate of travel is constant throughout the run or you would get uneven results (slower speed, constant power = more exposure and deeper engraving) I might yet be back on pestering you again :

[comment]

Hm. So it looks like you might have yet another dimension to deal with - the depth. Is it possible that the beam intensity is constant and the depth is controlled by speed of travel?

On a perhaps more practical side: I was kidding earlier about making 5400 tests, but the lookup is actually not a bad idea: instead of trying to figure out a calculation, you could start by a database of say those 54 tests. When a new job comes in, you look up the nearest lengths and widths and make an estimate out of that.

Now here's the sweet part: at the end of the job, you add the data to your database, so that the lookup resolution increases gradually - basically, it's a machine that learns from experience.

[James Mooney]

Ooooh Hal, I like the sound of that. Is there a way to automatically enter the data into lookup table or do you have to go into it maunaly each time. In other words can the lookup table reference a the field "actual time"

[James Mooney]

HIs it possible that the beam intensity is constant and the depth is controlled by speed of travel?

No we control the speed and power of the beam to adjust the cutting depth as required for each different substrate

[comment]

Is there a way to automatically enter the data into lookup table or do you have to go into it maunaly each time. In other words can the lookup table reference a the field "actual time"

I am not sure what you're asking here. You need to enter the data (length, width, time) somewhere.

[James Mooney]

Don't worry - stupid question! I managed to confuse myself in my excitement and thought for a moment we were still talking about writing a calculation