In this chapter, I will bring together, all that has been said before.
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.
In case the nib is attached to a fountain pen, the ink is offered from below, it bulges out of the capillary at the top of the feed 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 slit is narrower than the capillary, its attraction forces pull the ink into the slit and forward to the tip.
When the nib is attached to a holder, the ink is brought to it through dipping the nib into a well. In regards to photo 1, I would like to draw your attention to the inwards curve of the tines… this reduces the pressure at the start of a line. See pressureless writing in the chapter Nib Mechanics. Whatever amount of ink adheres to the nib after dipping is what is available for writing.
In photo 2 you can see that the inside of the nib has been roughened, so to change the surface reaction of the metal, thus to increase the contact angle and the adherence of ink. As a refresher, go to Surface Tension.
The same has been done to the top of the nib in photo 3.
In my early years of writing, I had been fascinated by the Gothic font. The line width varied between half a millimetre to 5 mm (for the hanging capitals at the front of a paragraph) and the ink was used up very quickly.
I found a small clip-on tray, which sat on top of the nib, similar as shown in photo 4. At its lower end it had a beak, covering most of the length of the slit. It was filled with an eye dropper, holding just about two or three drops of ink. I could write comfortably five to seven letters of about eight to ten millimetres height.
The Cross Section of a Nib
… and its effect on stiffness
Photos 5 to 7 show older style 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 in, photo 6.
In photo 5, the shadow lines show the inwards curve of the tines.
Photo 7 showing the feed from underneath.
In drawing 2, I show how the nib’s profile changes from a partial circle with a radius R1, to the wide radius R3.
At R1 the profile is circular to slide on top of the round feed into the grip-section. The profile starts flaring out towards the tip, from around the location of the ‘breather-hole’ R3.
The profile continues to flatten to a larger circular or oval contour at R2. , which significantly determines the softness and responsiveness to pressure.
You can see, how, all along its length, the nib rests on a cylinder made from purple circles.
The feed may follow this change like in drawing 3 or remain circular .
I would encourage you to use the toilet-paper-centre-role-nib-model from the chapter on Nib Mechanics and change its radius of curvature. You will find: the smaller the radius the stiffer. When you gradually increase the radius, there will be a point, when the nib kinks over, with a flip.
This shows, when designing a nib, the curvature and its change is not merely a matter of aesthetics.
A good example for an almost flat nib is this modern nib in photos 8 a – b. It is not inserted into the grip section but clings onto the feed with two flaps. This design with flaps has its advantages during manufacture and material usage, in particular gold, especially, when in traditional designs up to half of the gold is hidden. However, there are other draw-backs.
When the nib reaches into the grip section, its metal structure determines the stability of the front end of the fountain pen. Whereas, in the above design it solely relies on the strength of the plastic of the feed. Since immediately inside the grip sections the capillary chambers start, the feed is prone to breaks.
More about Elasticity of a Nib
I have already elaborated on elasticity in the chapter Material Technology. Here, just briefly:
Elasticity is the type of deformation which causes a component to return to its original shape after the deforming load has been released. If it does not, or not completely, then the component has experienced a degree of plastic deformation. In reference to nibs, we want to keep the deformation within the elastic range. If the nib has been designed well, normal writing would not be a challenge.
More important for writing is not that much the elasticity, but the consequence of it: the widening of the tines, thus the broadening of the written line.
In the chapter Nib Mechanics, I explained how the slit widens. Combining this with the information presented in Materials Technology, I will now show, how the responsiveness of the nib to writing pressure can be adjusted.
Diagram 4 was the final diagram in the chapter Nib Mechanics. It demonstrates the necessity of the angle in order for the tines to move apart at W when the writing force F increases. The larger the angle, the stronger the effect.
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 solid: 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 application of the force F
- distortion distance d
This is a standard mechanical ingeneering arrangement, well documented and certified with equations.
The standard equation in question contains the modulus of elasticity and certain shape characteristics. We can neglect them, because now, we do not want to calculate any specific nib but get an understanding, how varying certain dimensions effect nib behaviour. We keep the material and its condition the same. The slimmed down equation is shown in equation 1:
d ≈ (F × l3 )÷(b × t3 )
Discussion of equation 1: The distortion distance d increases
- proportionally with the applied force F
- by the length cubed, meaning: if originally l was 2, 2 cubed is 8. If l is increased to 3, 3 cubed is 27 then, when applying the same force, d is 27/8=3.375 times larger. If you double l then d increases by by factor 8.
- inverse proportional with the width b… if originally b was 2 and is widened to 3 then d reduces by 1.5
- by the inverse of the thickness cubed. Let’s say, if you double t, d reduces to an eighth of the original.
Applied to the nib this means: lengthening the slit or increasing the thickness have a significant, cubed effect. If you change both by the same proportion they compensate each other.
Two things to consider:
- The length of the slit is not necessarily affecting the length of bending. In the next section, I will look at this aspect, specifically.
- If you reduce the thickness through hammering, the material becomes work-hardened and the material’s condition is changed. In order to apply the above, to reduce the thickness, the excess material would need to be machined away.
What we have discussed so far, will affect the elasticity of the nib, which could be called the softness or hardness of the nib. Diagram 4 shows how the deformation widens the slit.
Diagram 6 shows the correlation of dimensions:
- W is the width of the slit,
- d the deformation and
- α the angle the tine is bent along the axis.
W = 2 × d × sin α
Let’s discuss equation 2. For example: When α or αF respectively, is 30° then sin 30° is ½ … meaning the widening of the slit W equals the deflection.
For a rounded nib the angle αR can be established through approximation.
In most cases nibs are not flat roof shaped, even there is nothing wrong with that. I believe that the reason behind curved nibs is a thousands of years old tradition, 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.
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 is? How to predict where the break will happen?
Looking at diagram 5, we see, the bend is gradual, it isn’t a specific line. As a basis for discussion, you can see in diagram 7 several suggestions of possible areas of bending.
The width of the bending area is shorter than suggestion b, however, the radius of curvature is smaller, therefore, this section is stiffer and bending will not occur.
Even it offers the longest length of bending, the width is wider than at suggestion c.
This is the most likely area of bending. In comparison with a and b, it has the largest radius of curvature and the narrowest width. When you look at diagram 8, you can see how the change in thickness and in profile can move the bend principle c further back and therefore it increases the length of bending.
Why not this one, you ask rightly, the radius is the largest and the width the smallest. Remember, the thickness of material is often not constant. I show you a diagram from the Nib Manufacturing, which explains it.
The thickening 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.
The other advantage is that the slit opening is not curved but straight, through having the thickness about double, which makes this section 8 times stiffer.
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!
8 June 2016