# Does thread angle modulate ease of (rotational?) penetration in a screw?

Forgive me if this question is too simple, I'm a complete outsider to the field of engineering and mechanical engineering.

A friend of mine had said that the thread angle of a screw modulates how easily a screw is able to penetrate a certain material. I think he was talking of mechanical advantage in screws, and had said that it's essentially like an inclined plane or an axe, it'll go through easier/with less work if the angle is decreased.

I just wanted to verify if this is true, and if the length of the (flank?) or just triangle if we think of it in simple terms, also needs to increase, in the same way an inclined plane's length needs to increase in order to modulate the angle and also reach the same height, and that will allow a person to go up the plane with less effort.

EDIT:

I made a GIF to (hopefully) more clearly state what I want to understand: Here I am scaling the Z-axis. Would this scaling (making it thinner) result in a horizontal force that allows the screw to penetrate a material with less work? Would the major diameter also have to change to bring it up to the same length/height?

In other words can this angle here: Be thought of in the same way in relation to the angle of an incline plane? (the lower the angle is, and the longer it is, the less energy to climb up it? Similar to an axe? (A sharper, longer axe will go in with less energy), here I'm mapping the crest of a thread to the crest of an axe.

• It would help if you added what type of screw, and what material? Are we talking self tappers in wood, a bolt in to a tapped hole in steel? Etc
– Drew
Jul 26 at 15:41
• @Drew I didn't even know those existed, thank you! He didn't mention any specific type, I thought he was talking of a kind of general rule of thumb. But I'd be curious in all those cases if it applies or doesn't apply. I think he meant that the threads themselves would penetrate into the material rotationally with less work, rather than the vertical ease of penetration (though I could be wrong or misinterpreted what he meant here, he didn't explicitly say this).
– Hmm
Jul 26 at 15:43
• Above a certain angle the thread “locks” ie won’t self rotate, below that it will turn when loaded. So for a car jack for example it is a good idea they don’t self rotate. Jul 26 at 16:41
• I presume your friend means the pitch of the thread, which isn't the same as the "thread angle" Jul 26 at 16:50
• Interesting. Would thread pitch modulate ease of penetration horizontally or vertically? I’m mainly thinking of the/ concerned with the horizontal force of the thread crest/tip, like an axe going into wood, and thinking of the angle of the tip as modulating the ‘sharpness’ + if we’re increasing the height of the tip, the major diameter, both modulating the ease of penetration horizontally.
– Hmm
Jul 26 at 17:05

Let's forget about the friction for now and say the resisting force of the material, P, the screw is being driven into acts only at the tip while the screw smashes the material or pushes it out of the way.

If we unwind one thread from the screw, stretched it flat, it is going to work as a ramp with the slope angle of $$\alpha = pitch/2\pi r$$

And the force needed to drive the screw $$F= P*sin \alpha$$

Hence the torqu $$\tau = F*r$$

So the smaller the pitch the flatter the slope and easier to drive the screw.

However, there is a range of optimal pitch depending on the hardness of the material and the utility of the screw as a fastener.

For example too tight a pitch can eat away the threads and weaken the grip. Too wide a thread can unwind under the load.

• Thanks! this is very enlightening with regards to the vertical force, or going into the material vertically. However I am curious about the horizontal force. For example the sharpness/angle of the crest of the threads. The crest of the thread has (or can have) a triangular shape, which to me implies something like an incline in that instance as well. What I'm most curious about is when it comes to the crest itself pushing into the material/shoving away elements, would pitch also control the horizontal force of the crest, contributing to the ease (like an axe?) or would that be something else?
– Hmm
Jul 26 at 20:08
• Also I assume here that the smaller the pitch, the higher the threads per inch?
– Hmm
Jul 26 at 20:11
• the shape of the threads vary according to the material and utility. obviously to sharp an edge would bend under heavy loading. but the actual attack edge of top thrrad near th tip of the screw is feathered to zeor to make the turning easier. and of course the smaller pitch means more threads. Jul 26 at 21:29

## Thread Angle Helix angle and self locking

What controls the effort required to move the the screw is not the thread angle but the helix angle. You can see the difference in the following image. Figure 1: Lead or Helix Angle (source fastenerdata)

The lead angle $$\lambda$$ is calculated from:

$$\lambda = \arctan\frac{p}{\pi d_p}$$

where:

• $$p$$ is the pitch
• $$d$$ is the pitch diameter **Figure 3: Calculation of helix angle (source : cadcamengineering.net) **

For a constant pitch, if you change the thread angle, you need to change the length of the flank. 