Guillotine Shutters

part 2: Determining Shutter Speeds

 

© 2010 Bill Kumpf for largeformatphotography.info

 

The guillotine shutter offers a simple device to use with a barrel mount lens. It can be quickly constructed from many materials in minimum time. For this article, a report cover provided the material for one while scrap 1/8-inch plywood was used for the second. This article provides a quick method to calculate the effective shutter speed.

 

The guillotine shutter uses a slot to pass across the lens. Being powered by gravity, the drop blade is constantly accelerating as its drops. The leading edge of the shutter opens the lens and the trailing edge closes it. The distance the edges fall determines the drop times.

 

Calculating the drop time, T = equals the square root of (2d/g) where d = drop (in), g=32 feet/sec2

                                                   _______________________________________

Time = √  d x ( 2 / ((32.17405 feet/sec2) x (12 inch / foot)))

 

 Thus for an initial drop of 1.75 inches and a slot with of 4.0 inches;

                                                                                ________________

The leading edge time,  Tl = √ (1.75 x 0.005180)

 

Tl = 0.0952 seconds

                                                                            ____________________

The trailing edge time,  Tt = √ (1.75 + 4.0)x 0.005180)

 

Tt =0.1726

 

For the exposure time T = Tt – Tli

 

T = 0.0774 seconds

To verify the concept I measured the shutter time using a photoelectric eye and an oscilloscope. The leading edge activates the switch while the trailing edge deactivates the switch. With the oscilloscope, the activation time was measured.

 

Two series of tests were conducted. The first used the same initial drop distance with varying slot widths and the second used the same slot width with varying drop distances.

 

The first guillotine shutter provided shutters speeds of 1/15, 1/30, and 1/60 of a second.

 

The slot width was set to give an estimated exposure time:

 

Slot width (in)

0.291

0.6645

1.4425

3.315

Dl=

1.7850

1.7850

1.7850

1.7850

Tl =

0.0962

0.0962

0.0962

0.0962

 

 

 

 

 

dt =

2.0760

2.4495

3.2275

5.1000

Tt =

0.1037

0.1126

0.1203

0.1625

Tl - Tt =

0.0075

0.0165

0.0331

0.0664

 

 

 

 

 

Average Measured time

 

0.0074

0.0168

0.0336

0.067

% Difference

1.89%

-1.91%

-1.38%

-0.93%

 

 

One concern was vertical alignment. How far off the vertical axis could the shutter be orientated before the friction would affect the drop rate? The drop rate was checked at both 5° and 15°. At 5° there was no measurable affect, while at 15° the shutter slowed approximately 5%. This will vary depending on the individual shutter assembly and its internal friction.

 

 

 

Initial Drop

0.1250

5.1250

10.1250

Vertical

Time (sec)

0.0479

0.0150

0.0106

15° Angle

Time (sec)

0.0506

0.0154

0.0110

 

 

 

 

 

 

Difference

-0.0027

-0.0005

-0.0004

 

%

5.64%

3.01%

4.15%

 

 

The second series verified the time distance function and to provide the bases of the following method to determine shutter speed.

 

Drop

1

3

5

7

9

11

Leading edge

0.125

2.125

4.125

6.125

8.125

10.125

Tl

0.0254

0.1049

0.1462

0.1781

0.2052

0.2290

 

 

 

 

 

 

 

Slot Width

0.9955

0.9955

0.9955

0.9955

0.9955

0.9955

Trailing edge

1.1205

3.1205

5.1205

7.1205

9.1205

11.1205

Tt

0.0762

0.1271

0.1629

0.1921

0.2174

0.2400

 

 

 

 

 

 

 

Time (sec)

0.0507

0.0222

0.0167

0.0139

0.0122

0.0110

 

 

 

 

 

 

 

Measured

0.0479

0.02175

0.0164

0.01352

0.01176

0.0106

 

 

 

 

 

 

 

Difference

0.0028

0.0005

0.0003

0.0004

0.0004

0.0004

 

-5.60%

-2.12%

-1.76%

-2.95%

-3.65%

-3.59%

 

 

Trailing

Edge

 
For example, if the shutter design has a leading edge drop of 1 1/2 inches, on the chart find the 1.5 inch line on the vertical axis, cross over to the line and read down to the drop time of 0.0881 seconds. For the trailing edge, add the leading edge drop distance and the shutter slot width and repeat the process. For an opening of 3 inches, the trailing drop distance is 4.5 inches. The time from the chart is 0.1527 seconds. The leading edge time minus the trailing edge time results in a shutter speed of 0.0646 seconds. This is approximately 1/15 second.

 

For reference

f stop

1/8

1/15

1/30

1/60

1/125

Time

0.1250

0.0667

0.0333

0.0167

0.0080

Difference equals the shutter speed

 

Trailing Edge

 

Leading Edge

 


 

 

 


The constant acceleration also varies the exposure during the shutter blade drop. This above process can be applied to the drop / velocity chart to determine the variation in exposure. The same process applied to the “Drop / Velocity” chart will estimate the change in velocity. A doubling of velocity would result in 1 f/stop variation in exposure. For our example above, the Leading Edge velocity is 34.03 in/ sec and the Trailing edge velocity is 58.95 in/ sec. This is a 73.21% decrease in exposure.

                                                       ______________________________________

Velocity= √  d x 2 x (32.17405 feet/sec2 ) x (12 inch / foot)   

 


 

 

 


Leading Edge

 
Hopefully this will help in exploring the world of barrel lens.

part 1: Constructing a simple shutter

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