Fountain Pen Design

Function, Development, Construction and Fabrication

051-7-2 Quantitative Classification – 5-7

So far we have addressed classifications, which were mainly based on comments of writers experienced in writing with flex‑nibs.  Not many have this experience, and in discussions, misunderstandings happen even amongst the elite.

I said it before, I am an ingeneer, and when there is something to be understood, then I like to find out.

5. Technical Approaches

In this chapter, I summarise the more technical approaches, which I found in various discussions.  At the forum on this topic, a 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.

A line was drawn with no pressure exerted to the nib, and its width was measured.  A second line was drawn with a load, which would spread the tines to a degree that the test performer considered to be close to the maximum. At the time of writing the pressure was measured and the line width, afterwards.

The summary of results is shown in Table 2, and since the force data were presented in gram (and not in Newton); I did not change it.

  Table 2 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.  I show this in Table 3 where I added the column Spring Constant (often abbreviated with σ (sigma)), a unit quantifying the flexibility, the springiness of a component.  It is the quotient of the load and the amount of flexing.

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 at, the more it responds to a load.

For easy comparison, it is common to display results in a graph as shown in Graph 2.

Since the shape of nibs and their tines is intricate, 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.  Such a chart can be used to graphically determine the load/width characteristic of a nib.  Table 4  shows the graphic approximation of the loads required to achieve a line-width of 1.5mm. Utilising the spring constant, calculation provides more accurate results when linear correlations are present, as we have chosen it to be the case in this example.

Table 4 writing force 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

In real life situations, the characteristic curve of the nib/tines flexing can be drawn with values resulting from the measurement of load-width correlations at several, often equal intervals.

Another method proposed by Salvador Maturana Campos is called A simple method to evaluate the flexibility of a nib where he also 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.  Valuable observations have been gathered, which I will include in my proposal such as the constant writing angle.  I have elaborated on the relationship among writing pressure, the positioning of the pen and the spreading of the tines in a later chapter, 9. When one Applies Sufficient Force.

The proposed classifications are undoubtedly useful, much better than “sloppy noodles”.

The fall down of the method is the high loading.  There are some rigid nibs, even flex‑nibs, which had not been designed to open 1mm, and they would be damaged if they were forced to such degree.  Further to that, I could imagine that mechanical damage occurs to the pen at forces over 750g.  For this reason, I would like to suggest to reduce the standard spreading of the tines to 0.5mm.  The force values would be around half, but the same classification can still be applied.

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

6. Useful Line Width

I would like to suggest this expression when deciding on the broadest line one can draw or write with a nib: “The widest, useful line width is the one which still leaves a full line.”  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 greater useful width, the designer 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 message would prevent damage. Here I would like to refer back to Table 1 where I discussed four scenarios of use/misuse.

When deciding on the maximum useful width, should one consider the type of ink, the feed and paper?  I would suggest: no and yes.  Mechanically, the tine separation is independent of ink and paper, but in practical terms, a recording medium is needed.  If ink and paper are used we know that they influence the line width.  As long as there is a standard of ink and paper the data are comparable.

As ink, I always used a run of the mill blue.  As a standard paper, I suggest one as it is generally used in a test machine, which is common in the writing instrument industry.  In the next chapter 7. Useful Writing Pressure, I show you this machine.  It finds application mainly in the testing of ballpoint and roller refills, but it also is suitable for fountain pens.

The paper standard

  • ISO 12757 + JIS S 6039 as well as ISO 9706-1994 requirements for consistency
  • 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

Someone will need to do the homework to find out who of the paper manufacturers produces paper, which comes close to it.  We used to buy it from the machine manufacturer, and it cost an arm and a leg.

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, the field I used to work in.  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 — Test Machine for Writing Instruments

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 it so that it suited fountain pens and that the writing angle was variable from 30 to 60° in 7.5° increments.  My standard was 45°.

Figure 1 — Writing Angle δ

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.  Then, I didn’t know that there were fountain pens with flex‑nibs.  It’s incredible that the machines have not changed much during this time span.

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

V = F × sin δF × 0.7

Applying this formula where δ = 45° the range of the useful writing pressure is 3.5‑280g or 0.035‑2.8N, admitting that the lower end is a bit useless because a fountain pen alone weighs about 20‑30g / 0.2‑0.3N.  Did you notice however so gently I introduce the Newton?

In the next chapter, I distil the above and instil my own thoughts and suggest My Proposal on flex nib classification.

Ω

Amadeus W.
Ingeneer

15 December 2017
cropped-cropped-ink-pen-writing_wide113.jpg

Continue reading about  My Classification Proposal chapt. 8
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