4.8 How to… for Nibs

In this chapter, I bring together all the information on nibs and discuss their correlations.

Let me start with a few general observations.

From Above or Below

The nib does not care in which way the ink arrives at the slit, from below the nib or the top, from the back or the front.

Drawing 1 — Nib feed cross-section showing the ink cross-over

In case the nib is attached to a fountain pen, the ink is offered from below, it bulges out of the capillary because it ends there due to the weight of the hydrostatic column from the top of the ink level in the reservoir to this point, drawing 1.  Since the width of the nib’s slit is narrower than the capillary in the feed, the slit’s capillary attraction pulls the ink in and forward to the tip.

When the nib is attached to a holder, the ink is brought to it by dipping the nib into a well.  With regard to photo 1, I would like to draw your attention to the inwards curve of the tines, you can notice it through the change of the light’s reflection like on a domed surface … this reduces the required pressure when starting to write a line.

Photo 1 — Nib holder – Nijomu

See pressureless writing in the chapter Fountain Pen Nib Mechanics.

Whatever amount of ink adheres to the nib after dipping is what is available for writing. In photos 2 and 3 you can see that the front part of the nib has been roughened, on the inside as well as the outside.  Its main reason is to deburr the slit and the stamped hole.  As a side effect, the surface reaction between metal and ink changes, more specifically: to decrease the contact angle thus increasing the adherence of ink.

Photo 2 — With grind marks

Photo 3 also shows the change of surface behaviour between ink and metal at the upper region where you can see the ink bulge, the sign of higher surface tension while at the lower end the crossover is levelled.  As a side-effect, the surface reaction between metal and ink changes, more specifically: to increase the contact angle and the adherence of ink.

Photo 3

Most importantly, this only offers an advantage when the grinding has followed the axis of the nib. When the lines go across, the ink is pulled into the grooves and stays there because the capillarity of the grooves is higher than that in the slit. Often this shows through dried ink patches remaining on the nib. As a refresher, go to Surface Tension.

There is no need for the process of grinding, a clean tumbled finish is quite adequate, moreover, grinding is labour intensive and may cause uneven thickness of the nib.

Photo 4 — Nib with Reservoir on nib holder

In my early years of writing, I had been fascinated by the Gothic font.  The available line width varied between half a millimetre to 5mm (for the hanging capitals at the start of a paragraph), and the ink was used up very quickly.

Some nibs accepted a small clip-on reservoir or tray (could be bought separately) to be attached to their tops (clip-on for easy cleaning), which was loaded with an eyedropper, similar as shown in photo 4.  The ink was held inside the tray due to capillary forces.  At its lower end, it had a beak which gradually approached the tip of the nib whereby covering most of the length of the slit.  This assured the transport of the ink, prevented dripping (as long as one moved the nib gently), extended the length of writing and prevented drying to some degree.

The holding capacity was around three drops, which, for normal writing, supplied enough ink for a line or more without interruption.  I used it for calligraphy when writing five to seven letters, a complete word in one go, was a treat.

The Cross-Section of a Nib

… and its effect on stiffness

Photos 5 to 7 show traditionally-styled nibs.  Their method of attachment to a fountain pen is like to a nib holder, they have the shape of a full or partial circle and slide over the feed into the section, photo 6.  Without any problem, they could be attached to a nib holder

Photo 5 – Pelikan Nib – inwards curved tines

In photo 5, the shadow lines at A radiating out from the “breather hole” indicate the inwards curvature of the tines; the darker shadows at B show the same.  The effect is the same as the bulges in photo 1but more so here it also brings stiffness to the tines, which causes the slit to open straight rather than curved permitting the capillary action to be more efficacious.  The softness of writing is encouraged by flattening the active cross-section between hole and scallop, see also photo 6.

Photo 6 — Typical drawing, flex nib

The nib in photo 6 shows a typical flex nib.  Characteristic is the narrow distance between the breather hole and the outer edge of the nib, which makes it very flexible, together with the thin material and of course the material’s properties.

Photo 7 — Pilot Custom 823 fine nib (FPQuest.com)

Photo 7 shows the feed from underneath but more importantly, the flaring out and flattening front part of the nib.  These are the characteristics of a softer nib.  Another example of a nib with flat tines is shown in photo 8 further down, where the tines are almost flat, which should result in a more flexible nib; however, the active cross-section (photo 6) ends up in a sharp kink, which counteracts the softening and produces a rather hard nib.

Drawing 2 — Change of Radii and area and length of bending

In drawing 2, I show the nib’s contour change from a partial circle with a radius R1 to the flatter radius R3.   At R1 the profile is circular to slide on top of the round feed into the grip-section.  Then, from around the location of the breather-hole R3, it starts flaring out towards the tip.  The dimensions d3 and d2 show how the centre of the larger radii R3 and R2 move away from the centre of the original radius R1.

The profile continues to flatten further to a circular or oval contour at R2, which significantly determines the softness and responsiveness to writing pressure.  You can see, how, all along its length, the nib rests on a conceivable cylinder made of purple circles.  The dotted line d starting from the breather hole to the outer edge displays the area/line of bending while the green line l depicts the length of bending.  More about this is in the chapter on Fountain Pen Nib Mechanics.

Drawing 3  —  Nib Feed cross-section

The feed may follow this change towards ovality like in drawing 3 or remain circular.  Advantageously, the nib has a larger radius than the feed which permits the nib and feed to touch at their capillaries, which helps the ink to cross over.  Not all fountain pens use this simple trick.

Further down this page, I discuss the various positions for the nib to bend and show, which one is most likely; see diagram 7.

I would encourage you to use the toilet-paper-role-centre nib-model from the chapter on Fountain Pen Nib Mechanics and change its radius of curvature. You will find: the smaller the radius around the start of the tines, the stiffer they are.  When you gradually increase the radius, there will be a point, when they kink over, with a flip. That was too much.

§

The next example shows, when designing a nib, the curvature and its change is not merely a matter of aesthetics.  This nib is almost flat; see photos 8a – b.  It is not inserted into the grip section but clings onto the feed with two flaps.

Photo 8a  — Nib with flaps: bottom view

This design with flaps has its advantages during manufacture and in material usage. There is a significant cost advantage for nibs made of gold because traditional designs hide up to half of the material inside the grip-section.  However, there are other drawbacks.

Photo 8b

Like in most traditional designs where the nib reaches up inside the grip section, the nib’s metal structure determines the stability of the front end of the fountain pen.  Whereas, in the design of photo 8 the stability solely relies on the strength of the plastic of the feed.  Since the overflow slits start immediately inside the grip sections, the cross-section of the plastic is very small hence, the feed is prone to breaks. The strength offered through the hole bearing is negligible.

I have discussed already why this nib ended up being somewhat stiff; being a nail as some fountain pen enthusiasts call it.

More about Elasticity of a Nib

I have already elaborated on elasticity in the chapter Fountain Pen Nib Technology.  Here, I summarise just briefly:

Elasticity describes the type of deformation of a material where a component returns to its original shape after the deforming load has been removed.  If the component does not recover completely, then it has experienced a degree of plastic distortion.  In reference to nibs, we want to keep the deformation sufficiently within the elastic range which is assured by the ingeneer’s understanding of material physics, mathematical competency and conversance with testing.  Then, regular writing is no challenge.

For writing, elasticity is not that much significant, you could write with a “nail”. However, the consequence of elasticity causes a varying line width under changing writing pressure.

In the chapter Fountain Pen Nib Mechanics, I explained how the slit widens.  Combining this with the information presented in Fountain Pen Technology,  Now I will now show, how the responsiveness of the nib to writing pressure can be adjusted through alteration of its dimensions, and not the change of material.

Diagram 4 —  Angled wings (tines)

Diagram 4 was the final picture in chapter Nib Mechanics.  It demonstrates that the wings (the tines) need to be angled to each other so that to move apart at W when the writing force F increases.  The larger the angle, the more the widening at the same writing pressure… almost, there is a bit more to it.

Now, let us investigate how the dimensions of the wings influence the responsiveness.

For a start, let us look at a flat spring attached immovably to something (a brick wall): along the line X – Y.  In mechanics, this arrangement is known as the cantilevered beam.

You have seen this diagram 5 already in the chapter Nib Mechanics. This time let’s add dimensions to it.

• Thickness t
• width b
• length l from X-Y to the application of the force F
• distortion distance d

Diagram 5 — Deformation of a flat Spring

Diagram 5 shows a standard mechanical ingeneering arrangement, well documented and certified with equations.

The equation in question contains the modulus of elasticity and characteristics of the shape (Moment of Inertia).  For now, we can neglect these items because we do not want to calculate a particular nib, but we rather want to develop an understanding, how varying individual dimensions affect a nib’s behaviour.  Furthermore, we can remove those two items because we keep the nib’s material and shape the same.

The slimmed-down equation is shown in equation 1:
d ≈ (F × l³ )÷(b × t³ ÷ 4)        Equation 1

Discussion of equation 1:  The distortion distance d increases

1. proportionally with the applied force F while keeping all other variables constant.
2. by the length to the 3rd power (cubed), meaning: When applying the same force, if l would be 2 then d is 8 times bigger. If l is increased to 3 then d is times 27 bigger.

it decreases

1. inverse proportional to the width b… if b was 2 and is widened to 3 then d reduces by 1.5
2. by the inverse of the thickness to the 3rd power (cubed).  Let’s say, if you double t,  d reduces to an eighth of the original deflection.

Applied to the nib, this means: lengthening the bending length or increasing the thickness have both significant, cubed effects on the deflection of the tines.

Two things to consider:

• The length of the slit, however, does not necessarily affect the length of bending l.  If the slit progresses into the section where the nib has a partial tubular shape it has hardly any effect.  In the next section, I will look at this aspect, specifically.
• If you want to apply the above equation, to reduce the thickness, the excess material would need to be machined away, through grinding, for example. Reducing the thickness through hammering or roll-forming, the material becomes work-hardened, and the material’s condition is changed.  In that case, the modulus of elasticity must be taken into consideration.

§

What we have discussed so far, will influence the flexibility of the nib, which could be called the softness or hardness of the nib.  Diagram 4, further above, shows how the deformation widens the slit.

Diagram 6 —  Deformation of a nib — left side of the drawing depicts a nib with curved tines, right with flat tines.

Diagram 6 illustrates the correlation of dimensions applied to the design of a nib where the tines are angled towards each other:

• W is the width of the slit,
• d the deformation and
• α the angle alpha, the degree the tine is bent along the axis of the nib.

W = 2 × d × sin α          Equation 2

Let’s discuss equation 2.  For example:  When α_R or α_F respectively, is 30° then sin 30° is ½ … meaning the widening of the slit W equals the deflection.

For a rounded nib, the representative angle α_R can be established through approximation.

In most cases, nibs are not flat or roof-shaped, even though there is nothing wrong with that.  I believe that the reason behind curved nibs is a tradition of many thousands of years when nibs were cut from quills (tubular), which has turned into a consumer expectation, the icon of writing.

A flat nib is more predictable in behaviour.  As I said further up, a rounded nib snaps over at a certain point.  Not nice.  Flat nibs give gradually and pass over into plastic deformation. Not good either, but avoidable through good ingeneering. I would not mind a flat nib like the Parker 180, but it was very stiff. It appeared as if they didn’t know what they were doing.

How to determine the length of bending?

It’s a bit like: The chain breaks at its weakest link.  They all look the same.  How to determine, which one it will be?  How to predict where the break will happen?  In nib terms, we do not want the nib to break, but we want to be able to determine where and by how much the nib is going to bend.

The physics of bending I have discussed around diagram 5, where we see that the curve is gradual, it isn’t a particular, given line.  As a basis for discussion, you can see in diagram 7 several suggestions for possible areas of bending.  As a refresher:  Keeping the force constant, the degree of bending is determined by the cross-sectional area along the line of bending where the cross-section area is the product of the thickness of the material and the length of the width of bending. The lines of bending I suggest could be at a, b, c or d.

Suggestion a

The width of the bending is shorter than in suggestion b; however, the radius of curvature is smaller (light blue); therefore, this section is stiffer, and bending will not occur there.

Suggestion b

Even it presents the longest length of bending (distance from the tip, therefore longest lever and highest momentum) as well as a flatter radius (dark blue), the width (length of the purple line) is almost twice as long as in suggestion c.

Diagram 7 — Radii of bending

Suggestion c

This is the most likely area of bending in this shape of nib.  In comparison with a and b, it has a larger radius of curvature, and the width is narrower (the green dotted line).  In diagram 8, you can see how the change in thickness and profile can move the bend area c further back because the thickness of the material increases the bending force by the power of 3.  In addition, moving the bending area back also increases the length of bending.

Diagram 8 — Variation of thickness and hardness in the rolled blank and the formed nib

Suggestion d

Why not this one, you ask rightly, the radius is the largest and the width the smallest, but the length of bending is very short.

Remember, the length of bending affects the degree of bending by the 3rd power.  Furthermore, the thickness of the material is often not constant, see again diagram 8.

The thickening of the nib around the length of the tines makes them stiffer, doubling makes them eight times stiffer. This has two advantages, at least.  It shifts the area of bending further back; the longer the length of bending the more responsive the nib is, see equation 1, the relationship is l cubed.

Diagram 9

The other advantage is that the slit opens with its sides being straight which evens the change of its capillarity, diagram 9. Hence, prevents the retraction of ink. Bending the tines inwards has the same effect, as I have shown with the Pelikan nib in photo 9; the change of light reflection indicates the inwards curvature.

Photo 9 — Reflection on Tines

Summarising the information about the possible, most significant area of bending for this style of nib can be concluded to lay in the range as indicated in diagram 10 (the pink section, the location which I described in the suggestion (b) in diagram 7.

Diagram 10 —  Area of bending

This last chapter also demonstrates that there are many intervening aspects to consider, too many, to rely on mathematics and material technology alone, for sure, they are a good start.  The feel for it comes with taking risks and making mistakes ignited by a passionate curiosity.

§

I feel a sense of saturation.  It was a lot to digest for you.  Tell me your questions, and I will continue expanding on this topic.

Until then, this is the last chapter on nibs, pheeooo, done!

News: There is a new chapter on flex-nibs. Here is the link: Fountain Pen Flex Nibs

Above all: Enjoy!

Ω

Amadeus W.
Ingeneer

8 June 2016

Ready for more? Go back to the start page Homepage and Content and see what’s on offer.

▲  top