4.11 Quantitative Classification

So far we have discussed several classifications mainly based on comments of writers experienced in writing with flex-nibs. There are not many, and in discussions even amongst the elite, misunderstandings happen, because not only differ their experiences but also the words they use in formulating their findings differ, too.

I said it before (I think), I am an ingeneer (“I think, therefore I am!” but I assume Descartes referred to something else), and when there is something to be understood, then I like to find out. How can one determine which of two suggestions, viewpoints or solutions is the better and at the same time remain free of bias? If this is a topic which interests you: A friend of mine has written about Occam’s Razor, a widely applied scientific method for deciding on which one is the better choice.

5. Technical Approaches

In this section, I summarise the more technical approaches, which I found in several discussions. At the forum on the topic of flex nibs, a YouTube video was shown: “Measuring & Rating fountain pen flex nibs (quantitatively)” presenting results from testing three flex nibs. Let me introduce the test method briefly as I understood it, still, I recommend you watch the video. “A picture says more than a thousand words.” Old saying amongst ingeneers, and since you are on the path to be one, it serves well to have some slogans under your sleeves.

Here about the video: “A line was drawn with no pressure on the tip and its width was measured. A second line was drawn with a load on the nib that spread the tines as much as the person performing the test considered as close as possible to the maximum. At the time of writing, the pressure and afterwards the line widths were measured.”

I reformatted the table shown in the video. The summary of the results is shown in table 2; since the force data was given in grams (not Newtons); I haven’t changed it.

*Table 2*	Fountain Pen	Line Width	Line Width	100g = 1N
Nib		load-free	loaded	load
1	Waterman Ideal 2 fine	0.5mm	2mm	300g
2	No name medium	0.7mm	2.5mm	230g
3	No name fine	0.5mm	3mm	200g

My comments: The measurement of importance for the flexibility of the nib is the increase of the line width, not the actual line width, hence, any ratio between an increase in linewidth and a corresponding difference in writing pressure is useful to establish the Spring Constant (often abbreviated with σ (sigma)), a unit quantifying the flexibility, the springiness of a component. It is the quotient of the load [usually N] and the amount of flexing [mm]. I show this in table 3:

Spring Constant σ = Load at loaded width ÷ (loaded width – load-free width)

	Table 3
Nib	increase of line width	load	spring constant
1	1.5mm	300g	200g/mm
2	1.8mm	230g	128g/mm
3	2.5mm	200g	80g/mm

Graph 2 — for Table 3

The smaller the value of σ, the less force is needed to flex the nib, alternatively, the more the nib flexes, the more it responds to a load.

For easy comparison, it is common to display results in a graph as shown in graph 2. As a result of the intricate shape of nibs and their tines, the lines would not be straight but slightly curved in a sagging form. For the purpose of this exercise, we do not need to consider this. You can see that the higher the spring constant, the steeper the inclination.

Graph 2 also permits the prediction of the flexing behaviour of the three nibs. Such a chart can be used to graphically determine the writing-load/line-width characteristic of a nib as shown in table 4. As an example, I selected the desired line-width of 1.5mm, and I graphically approximate the three loads required to achieve this.

*Table 4*	writing force required for creating a line width = 1.5mm
Nib	graphic approximation	calculated load using spring constant σ
1	200g	1.5 – 0.5=1× 200g/mm = 200g
2	105g	1.5 – 0.7=0.8× 128g/mm = 102g
3	95g	1.5 – 0.5=1× 80g/mm = 80g

Since we’ve chosen the three nibs to present linear correlations, utilising the spring constant and calculating the values provides more accurate results.

The low spring constant is depicted as the shallowest line, the determination of the intercept point is more vague, sliding or imprecise. This can be improved by stretching the vertical, the load axis. In real-life situations, the characteristic curve of the nib/tines flexing is drawn with more than one value but with several resulting from the measurements of load-width correlations at several, often equal intervals. In that case, the graphic determination outperforms the mathematical.

Another method proposed at an “issuu” page by Salvador Maturana Campos is called “A simple method to evaluate the flexibility of a nib” where he introduces the Rigidity Index RI. While holding the fountain pen at an angle of 45°, a load is applied and increased until the tines spread by 1mm. At this point, the load is registered. As a result of testing nibs of all kinds and repeated measurements, he suggests the following Table 5.

Table 5 — Rigidity Index

This method’s main advantage is its simplicity, and it can be easily applied by anyone who has an accurate kitchen scale. Valuable observations have been gathered, which I will include in my proposal for a standard classification for flex nibs. There, like Señor Maturana I propose the constant writing angle during testing.

I have elaborated on the relationship amongst writing pressure, the positioning of the pen and the spreading of the tines in a later “chapter 9. When one Applies Sufficient Force” on the page The Technical Side.

Indubitably, this proposed classification is useful, it certainly surpasses expressions such as “sloppy or wet noodles” or “nails”. It provides a big improvement when discussing nibs’ characteristics amongst non-technical experts, and it helps to concentrate on the subject rather than debating over the confusion imprecise expressions always lead to.

Where the method needs improvement is in the measurement of the 1mm. Señor Maturana reads the separation of the tines with a steel ruler, a method which is influenced by parallaxes and the acuteness of the tester’s vision. A more precise method would be the application of a 1mm stainless steel drawn wire which can be purchased at high accuracy. After the wire is pushed between the tines, the gentle force 20N ≈ 200grams) would pull on the wire. Then the writing force is applied. When the wire begins to slide the gap would be 1mm which would be the moment of reading the writing load. The method is well-known as measuring with a feeler gauge.

Another suggestion I would like to offer is for testing in the high load specifications. There are some rigid nibs, even flex‑nibs, which have not been conceptualised to open 1mm, hence, they would be damaged if they were forced open to such degree. Further to that, I could easily imagine that mechanical damage occurs to the pen at forces over 750g. For this reason, I would like to suggest reducing the standard spreading of the tines to 0.5mm. The force values would be around half, but the same classification can still be applied (even though 500g for the highest test load is still a lot). For an accurate measurement even for a 0.5mm gap, the wire pull method from before can be as easily applied.

The correlation between load and tine width must be considered in any evaluation of a nib’s properties. However, rather than loading any arbitrary pressure on a pen or spreading the tines to a specific value, I would like to remain within practical, useful parameters. In the next chapter I would like to define:

6. Useful Line Width

When deciding on the broadest line one can draw or write with a nib I would like to suggest this definition: “The widest, useful line-width is the one which either still leaves a full line, or is caused when applying a reasonable writing pressure, whichever comes first.” The nib geometry and material may allow more flexing but when the ink flow interrupts, what’s the point of further spreading of the tines?

If the nib had been intended to operate at a wider useful width, the ingeneer would have constructed the nib in such fashion. The termination of ink flow could be regarded as the indicator for the predetermined limit of tine separation; respecting this hint would surely prevent damage.

What’s a reasonable writing pressure? I throw in the results, table 6, of a brief test I performed right now with my everyday fountain pen:

Table 6 Writing Style	Writing Pressure [g]	[N]
Everyday writing	30-80	0.3-0.8
signature	80-200	0.8-2
straight line with emphasis	350-400	3.5-4
causing a spread of 0.2mm	550	5.5
causing a spread of 0.4mm	800	8.0

Yes, the nib is on the firm side. Trying to suggest one significant number for the adjusted test of Señor Maturana, I propose 350g, the weight of a 12-ounce beer can (with metal) which is not only well in the upper range of general writing pressure but also readily available; not everyone has a pressure gauge in the kitchen drawer. PS: two servings of wine make 300g, but it’s easier to juggle a beer can on your fountain pen than two wine glasses.

Photo 5 — Test Machine for Writing Instruments

If ink and paper are used in a test, we know that they influence the line width. Someone needs to perform a test to demonstrate the test’s degree of dependency on the variation of ink and paper. It could well be that their influence is negligible.

Be this as it may, in my fountain pen tests I always used a run-of-the-mill blue ink; is this enough of a standard? The standard paper is the one as it is generally used in a test machine, which is common in the writing instrument industry, see photo 5. It finds application mainly in the testing of ballpoint and roller refills, but it also is suitable for fountain pens. Have you got one in your kitchen?

The paper standard, shown in table 7:
ISO 12757 + JIS S 6039 as well as ISO 9706-1994 requirements for consistency

Table 6 Criterion	Value	Standard
Grammage	80 ± 5g/m²	ISO 536
Smoothness PPS	3 ± 0.25µm	ISO 8791-4
Ash residue at 900°C	11 ± 1 %	ISO 2144
Cobb 45	18 ± 2g/m²	ISO 535
Thickness	80 ± 5µm	ISO 534
Colour	white
pH value	7 ± 0.5
Composition	100 % wood, cellulose fibre, bleached

Did you know that paper specification includes so much detail? We used to buy it from the machine manufacturer, and it cost an arm and a leg. Since we don’t want to go that far… someone will need to do the homework to find out which paper manufacturers produce a paper, which comes close to it. Or perhaps not, if our test about the impact of paper on the test shows no need for it.

After having defined the useful line width, let’s investigate the other main parameter:

7. Useful Writing Pressure

I would like to refer to test standards in the writing industry. There, writing instruments are designed obeying a framework of parameters considering the needs and customs of the writer community and pens are tested accordingly.

Photo 5 shows a typical writing test machine as they are used for testing ball pen refills. At the end of the holders for the refills, you can see the weights to apply a writing pressure ranging from 5‑400g (0.05‑4N). One of these machines was in my laboratory. I modified to suit fountain pens which includes an adjustable writing angle, variable from 30 to 60° in 7.5° increments. My standard was 45°.

Figure 1 — Writing Angle α

This machine would have been perfectly suitable to measure the elasticity of nibs, but in 1978 my focus was on the ingeneering development of a fountain pen, the nib had been predetermined, unfortunately. Then, I didn’t know that there were fountain pens with flex‑nibs; I had been a true blue fountain pen novice. It’s remarkable that these test machines have not changed much during this time span (since 1980). It shows how far the change or consistency of user demand impacts even on the equipment of the research laboratories.

One point to consider is that in this machine the force F was applied axially to the pen (figure 1) along the angle α while the writing force V acts vertically to the paper surface. A bit of trigonometry helps: V = F × sin α

Applying this formula where α = 45° — V ≈ F × 0.7 and the range of the writing pressure applicable with this machine ranges from 3.5‑280g or 0.035‑2.8N. Admittingly, the lower end is a bit useless because a fountain pen alone weighs about 20‑30g / 0.2‑0.3N. Let me summarise the useful writing pressure: As I introduced it a bit prematurely in the topic on useful line-width, I trust, the beer can value is the most appropriate; 3.5N, the weight of a 12 once beer can (with metal).

Did you notice however so gently I introduce the unit Newton? The ratio is not quite 100:1 but rather: 1Newton is ≈ 102grams, the weight of a bar of chocolate with its silver wrapper.

In the next chapter, I distil the above and instil my own thoughts and suggest Fountain Pen Flex Nibs — Classification Proposal on flex-nib classification.