4.12 My Classification Proposal

Let’s get our hands dirty, load up some fountain pens and perform some investigational testing.

The fountain pens tested were:

Parker 105 Flighter, Lamy Safari, Sheaffer Targa 1001XG, Lamy 2000. Except for the Safari, they all have gold nibs.

The test method:

I stuck a sheet of paper on the glass surface of a digital kitchen scale. This helped to determine the vertical load, the writing pressure, and to keep it fairly constant. Then I drew six lines at loads starting at 0.5N, increasing in increments of 0.5N up to 3N. During the drafting, I held the fountain pen at a 45° angle, tilted over the line and pulled it in the direction of the line (instead of moving it sidewards). Furthermore, to keep the line steady in pressure and somewhat straight, I let the ring-finger of the hand holding the pen run along a thick ruler.

Observations:

• Initial trials demonstrated that the speed of writing influenced the line width. Hence, I drew the lines of 100mm length in approximately one second.
• Since the line width varied noticeably, I measured the line width at three places, after 30mm, 60mm and 90mm and calculated the average.
• For lines drawn at low loads, the variation of the line width amounted to up to 20% while the variation reduced to 8% at higher loads.
• Instead of the separation of the tines causing the widening of the lines it was the deeper impression of the nib into the paper at higher loads. Then the tip was more enclosed by the paper prompting more ink to be transferred, and therefore causing the broadening of the lines.
• Except for the Parker, no separation of the tines was noticed. Consequently, I assume that none of the tested fountain pens had flex‑nibs.
• Impression marks on the paper left by the tines were noticeable.

Conclusion: Since a variation in line width occurred without any noticeable separation of the tines (which is needed for determination of elasticity), the results of this test method were exclusively effected by paper and ink, and therefore they didn’t serve their purpose. I decided that a direct measurement of the tine separation as proposed by Senior Campos (in the forum) is more useful.

Therefore, I suggest a static method. I measured the load using my digital kitchen scale again which had an accuracy of a tenth of a gram. The nib was merely is pressed against the scale’s glass surface at a 45° angle.

Photo 6 — Measuring Loupe

How to measure the spread of the tines? The simplest way is with a measuring loupe as shown in photo 6 which I purchased for a couple of dollars. This one has a magnification of 10. Between the two support arms is a bar onto which a tiny ruler is printed. If you place the loupe on the scale before switching it on, you don’t need a tare function to compensate for the loupe’s weight. If that’s a problem, don’t worry because the loupe is very light and hardly influences the measurement. As it may be, now you hold the tip of the nib against it, apply a load and read the tine separation (but remain below 5N, and you are safe not to destroy your nib).

You would need a second person to take the reading of the display of the scale while you look through the loupe. Sure, you could construct a mirror contraption, then, you could read both values at the same time.

Having moved these obstacles out of the way let us return the preload of the tines (see Stresses and Strains), which I will include in this method since it impacts on the value of the spring constant σ which is a standardised expression for a component’s elasticity.

Graph 3 — Determine Preload

I demonstrate this in graph 3 with a hypothetical nib. The blue line is determined with the result of only one measurement where the tine separation of 2.2mm requires a load of 2.2N. The assumption is that this nib has no preload, thus passes through the zero point, the crossing of the axes. Calculating:

σ = load/distance = 2.2N ÷ 2.2mm = 1N/mm, also called the gradient of this line, its inclination.

The red line is determined by the additional measurement at 0.5mm tine separation, which required a load of 0.8N. Here σ is determined through the differences 2.2mm – 0.5mm = 1.7mm and 2.2N – 0.8N = 1.4N from which

σ = 1.4N ÷ 1.7mm= 0.8N/mm.

You may consider this not a great difference, however, with increasing preload the spring rate increases, too. With this method, the preload can be determined as being 0.5N as shown in graph 3.

PS: I should have drawn the graph with the tine separation being the horizontal and the pressure the vertical because in physics it is customary for the horizontal axis to depict the independent variable parameter while the vertical represents the dependent variable. Please forgive me. One day I will correct it.

Returning to our test method: The procedure involves two measurements of loads at two different amounts of tine spread. Preferably the first load measurement should be at a point when the tines just start to separate, somewhere around 0.2‑0.5mm. For accuracy, the second distance measurement should be at a load causing a separation of at least 0.5mm wider than the first measurement, as long as the load does not exceed 3N.

The more significant the tine separation per load, (the softer the nib is), the lower the value of the spring constant σ.

The advantages of the suggested method are:

The value of the points of measurement can be adjusted to the style of nib.
The value of σ is not influenced by the choice of measurement points.
The spring constant σ is a standard value in material physics and permits comparison across any nib data.
It allows the determination of the preload.

Now we have two technical ways of describing a nib’s behaviour, as it is determined by its shape and material:

1. The spring constant σ gives us a precise result expressing the elasticity of a nib, or more technically speaking: It is an exact value that represents the proportional correlation about how the variation of the line width responds to a variation of writing pressure.

2. The preload tell us about the amount of writing pressure that needs to be applied to a nib before the line begins to widen or point when the tines start to separate. Or in other words, its willingness to respond in the lower range of changes in writing pressure, thus, changes in line width must be intentional.

3. There is a third characteristic I would like to add which is answered by performing the following tests:

(a) How far can the tines spread under a sensible writing pressure of up to 3N?

(b) At what spreading and correlating writing pressure is the written line interrupted?

The test setup: Affix a sheet of paper to a kitchen scale. Draw a more or less straight line with increasing writing pressure. At one point, you reach either the chosen writing pressure limit (3N) or the line will be interrupted. These will be the necessary test results for tests (a) and (b). Luckily, if that happens, test (c) does not need to be performed.

I suggest calling the test result showing the smallest value of spreading of the tines the Useful Tine Separation.

Knowing σ, we can calculate the tine separation, the “Useful Tine Separation”. You can also determine it graphically following Graph 4. I used the same sample nib as in Graph 3.

Graph 4 — Useful Tine Separation

Comments to Graph 4

As we know, σ = F ÷ s, with F being the writing pressure and s the resulting tine separation. The equation can be solved to s = F ÷ σ

The red line represents σ like in Graph 3, only the scale of the axes is different. It starts at 0.5N, the preload. The gradient is defined by the intersect-point of the two values obtained by the measurement from above (2.2N writing pressure and 2.2mm tine separation).

The useful tine separation UTS is the maximum separation at which no permanent distortion occurs, meaning, once the writing pressure is removed, the tines return to their original shape and preload. The useful line width equals the useful tine separation plus the tip width.

A practical application is shown with the dashed line. One after the next load, the writing pressure is increased incrementally until the tines have been spread above the point of no return, let’s say 3.5N. The dashed line starts at the load measured just before the overload occurred, 3.2N, resulting in the useful tine separation of 4.6mm.

The Useful Line Width can be approximated by adding the tip width to the Useful Tine Separation.

Now we have three technical characteristics, which describe the properties of a nib in a standardised way, which permits comparison and classification.

A Joint Effort

From here, where to next? Now we need data obtained from a selection of fountain pens with all kinds of nibs.

I hope that a group of several enthusiastic collectors with a range of fountain pens will find each other, and who will acquire the above-mentioned equipment, perform the test with their fountain pens and pass their data on to me.

After the data are grouped, a correlation between the data and the writers’ experience will be established. This will provide a classification based on measurable, technical terms as well as individually evaluated opinions.

I would collate the results and complete this job in the form of a table, like table 6 (an example). the first column will contain agreed names for a number of nib styles, may they be as romantic as we like, as long as we agree. Then the data for the spring constant, the preload, and the max. tine spread will be added.

The values in the example-table are sort of sensible suggestions only to fill the columns, they don’t originate from performed tests.

*Table 6* sample only	Nib Style Definitions
Styles	Spring Constant [N/mm]	Preload [N]	Max.Tine Spread [mm] @ 5N
Hard, Nail	1.2	2	0.2
Semi-Flex	1.6	1	0.5
Superflex	2	0,8	1
Moderate Superflex (noodle)	2.5	0.6	2
Soft Superflex (soft noodle)	3.2	0.4	3
Easy Full Flex	4	0.2	4