# White space scan increasing adds more time?

So when i am using the white space scan im not sure why but increasing the speed gives alot of different results… speed in mm/min… 1500=4 hours 2000 = 6.5 hours 3000 = 5 hours 4000 = 4.5 hours 9000=4 hours… can someone explain why this is?

Short answer: Increasing the whitespace speed pushes the engraver to spend more time accelerating and decelerating. It can also add time by ‘overscanning’ as it overshoots the edge of the image at speed to decelerate to zero. This increases the travel distance.

Without getting into too much fun with the algebra maybe we can look at it like this.
v0 = zero speed 0mm/min
v1 = engraving laser speed say 1000mm/min
v2= white space scan speed (laser off) say 5000mm/min
n= number of speed changes between v1 & v2 (example here say 3000)
a0= allowed acceleration and deceleration rate.

Let’s say this is a really simple block of whitespace : engrave : whitespace.

1500 whitespace events : 1500 engrave events : 1500 whitespace events.
but where the engraving stops and starts there are acceleration events.

1500 whitespace events
1500 deceleration events
1500 engrave events
1500 acceleration events
1500 whitespace events

but wait… there’s more.
It’s bidirectional to save time so it switches direction and stops on each end.
1500 acceleration events (stop to v2)
1500 whitespace events (v2)
1500 deceleration events (v2 to v1)
1500 engrave events events (v1)
1500 acceleration events (v1 to v2)
1500 whitespace events (v2)
1500 deceleration events (v2 to stop)

The acceleration and deceleration events will take longer as the whitespace scan speed increases and they will be done in the whitespace and in the overscan as they can’t be done during the engrave event. I’m going to put a couple more assumptions in and clean up the units a little bit.

let’s say the thing engraves for 10 seconds on a pass.
10 seconds * 1500 events = 15000 seconds (250 minutes)
1000mm/minute *250 minutes = 250,000mm (or 250 meters)

Same distance for pre-engrave whitespace (250m) and post engrave whitespace (250m).

500m whitespace (before reductions caused by accelerations) in the graphic.
500m is 500,000mm /5000 mm/min= 1000 minutes

now the fun part. The acceleration.

let’s say the engraver accelerates at 1000mm/(sec^2).
the time to change speeds under linear acceleration is given by:
t=(Vf-Vi)/a
so the different intervals are:
t=(v0-v2)/a0 = (5000 mm/s)/1000mm/second squared = 5s
t=(v2-v1)/100 = (5000-1000)/1000 = 4s

Since speeding up and slowing down takes the same time we can re-use our accelerations.

1500 acceleration events (stop to v2) 5s x 1500= 7500 s = 125 min
1500 whitespace events (v2) 1000 minutes
1500 deceleration events (v2 to v1) 4s x 1500= 6000s = 100 min
1500 engrave events events (v1) 1000 minutes total
1500 acceleration events (v1 to v2) 100 minutes (same as above)
1500 whitespace events (v2) included in whitespace calc above
1500 deceleration events (v2 to stop) 5s x 1500= 7500 s = 125 min

2450min or 40.8 hours of which 450 min or 7.5 hours is accelerating and decelerating.

But wait… there’s less…

There is a minor time savings that isn’t accounted for yet. the white scan time consumed by the acceleration between the whitespace speed and the engrave speed should be subtracted.

The time difference caused by 100 minutes of accelerations stealing part of the whitespace - to calculate this we have to get to distance.
distance consumed by accelerations:
distance = 4 seconds 5000mm/s - (1/2) (1000mm/(sec^2))(4s)^2
distance = 4 5000 - 0.51000
4*4 = 20,000mm-8,000mm = 12,000mm
the time at full whitespace speed:
12000mm/(5000mm/s)= 2.4s
4-2.4=1.6s

1.6 seconds*3000 events= 4800 seconds = 80 minutes… or 1 hour and 20 minutes.
2450-80 minutes) = 2370 minutes = 39.5h (still 7.5h accelerating and decelerating)

The zero to Whitespace speed happens outside the graphic so it’s simply added.
It’s 1 AM. I’ll double check my math another day.

here’s a link to an explanation of the acceleration vs time formula.

Here’s a link to the distance given a speed and an acceleration

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