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Everyone who deals with screws and screwdrivers knows that long screwdrivers are stronger than short ones. However, I can't find any relationship between length of a screwdriver and mechanical advantage. For a wrench, it's obvious: Long arms produce more torque. But in case of a screwdriver, it is not so simple.

For this question, my point is not originally about screwdrivers. I'm actually going to design a simple machine that has a relatively long arm connected to an electric motor. It's intuitive that the long arm weakens the motor (Or maybe I'm wrong?). The answer of my question about screwdrivers will help me undrestand the mechanism behind this case, and solve the problem.

Moctava Farzán
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    Huh ? I don't know that long screwdrivers are stronger than short ones. I don't see any reason for them to be to be stronger, and I see many reasons explaining that the length does not matter appart from reaching screw deep inside a hole. – TZDZ Nov 28 '14 at 12:37
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    It's a good question, for a screwdriver of a given material with a shear modulus $G$, the torque from turning it an angle $\theta$ is approximately $\tau=\frac{\pi r^4G}{2L}\theta$ where $r$ is the radius of the shaft and $L$ is the length of it. So it would seem that increasing the length decreases the torque and makes the screwdriver easier to twist and deform. Really makes you wonder why, other than accessing deep screws, they'd make them longer – Jim Nov 28 '14 at 15:00
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    Length matters mostly for this reason: For the screwdriver tip to strongly lock into the slot/recess of the screw the screwdriver must be directly in line with the screw and not canted off to one side or the other. A longer shaft makes it easier to visually verify that the screwdriver is lined up and it also minimizes the effect of any lateral motion of the handle. Aside from that, a longer shaft (within reason) makes it easier to grasp the screwdriver and put your arms in a position that achieves maximum torque. – Hot Licks Nov 28 '14 at 20:58
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    In regards to the matter of size, I thinks it's commonly acknowledged that it's not really the length that is most central to performance, but the girth. Longer tools to tend to have a larger girth as well, and length is a vivid and easily visualized quality, but it's really issue of correlation vs causality here. Either way, most of them do their job fine regardless of the variances in length or girth, and success it's mostly a matter of technique and adaptation to what you are screwing. – Alex Nov 29 '14 at 10:10
  • @Jim really? Where did that formula come from? – Mark Pattison Nov 29 '14 at 18:34
  • @MarkPattison $\frac{\pi r^4G}{2L}$ will give you the torsion constant for a given cylindrical length of material with a given radius. $\theta$ is the twist angle - the amount the base of the shaft twists relative to the handle. The formula I listed will give you the torque applied by the screwdriver if the screw does not turn. Alternatively, you can isolate the equation for $\theta$ and notice that for any applied torque, the screwdriver twists and deforms more with a longer shaft (although the $r^4$ term can easily be used to compensate for that) – Jim Nov 29 '14 at 20:02
  • @TZDZ Length matters for more than just hole depth. Depending on where the screw is situated, either a long or short shaft may not allow the screwdriver to be positioned properly to touch the screw. For instance, for tight spaces parallel to the screw plan, a short driver is best. But if there is a close plane perpendicular to the screw a longer shaft reduces the angle needed to prevent the handle from bumping into that plane. – Michael Nov 30 '14 at 05:40
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    I vote the comment from @Alex as the comment of the millennia! –  Nov 30 '14 at 10:12
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    "It's intuitive that the long arm weakens the motor." Perhaps your intuition is telling you that, but your intuition is leading you astray. Other than air friction and any additional bearing friction due to the weight of the shaft, the length of the shaft has no effect on the power delivered at the far end. – Hot Licks Nov 30 '14 at 12:40
  • @Jim Just to clarify: For longer screwdrivers, the torque achieved for a given twisting angle is smaller, or, from an other point of view, the twisting angle at which a particular torque is achieved is larger. But of course, the torque that needs to be applied to the screwdriver in order to start turning a particular screw is still the same. – andreasdr Dec 01 '14 at 08:34

5 Answers5

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For a long screwdriver the inclination angle may be smaller, so you do not loose your force due to applying a part of it in a wrong (perpendicular to the rotation axis) direction.

Vladimir Kalitvianski
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    Thanks. I believe that this answer is totally right, but I had to mark @SridharEvo's answer, because he pointed at a bigger effect, compared to this one. Thank you, again. – Moctava Farzán Nov 28 '14 at 14:52
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    Actually, the answer @shridhar posted was from here : link –  Nov 28 '14 at 15:21
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From this site:

Torque is in units of force times distance, but the distance of course is not distance along the axis of rotation (the screwdriver shaft) but instead distance away from the axis. This is one reason screwdrivers have handles; the bigger the handle, the more torque to the shaft is provided by a given force. (though actually the more important issue might be the friction force that your hand can produce, which is proportional to the surface contact area, which is itself of course determined by the length and radius of the handle.)

If you have a firm grip on the screwdriver, then your forearm and the screwdriver act as a unit, and the torque then depends on how far your elbow is from the axis of rotation. If the screw in question is, say, inside a computer case, a longer screwdriver may let you get your forearm at a right angle to the shaft and thus as far away as possible; a short screwdriver, conversely, may restrict you so that not only is your arm at a shallower angle, but you might need to apply force with your wrist instead of your whole arm, combining the reduced force of a weaker set of muscles with the reduced lever arm, and producing much less torque.

Also this might be due to the ability of the longer shaft to twist slightly. This elasticity seems to soak up the irregularities in the force that you can apply with hand, and enables you to apply a steady high torque without so accidentally twisting the screwdriver head out of the slot.

Sridhar Evo
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  • So what about motors? Consider an electric motor or a tiny electric armature. Will it produce the same torque when connected to shafts with different lengths? It's not really intuitive for me. – Moctava Farzán Nov 28 '14 at 13:38
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    I'm surprised to hear that the steel shaft of a screwdriver would elastically deform (twist) to any noticeable extent under the torque that can typically be applied by the human hand. Any calculations to support this? – RedGrittyBrick Nov 28 '14 at 15:08
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    Sridhar, Plagiarism is bad and is deprecated here. I'll just edit your post and give proper attribution. –  Nov 28 '14 at 15:11
  • That quote seems dubious. The mechanical effort is not coming from your elbow but from either your wrist or your shoulder so the distance from your elbow to the axis of rotation doesn't seem to be a factor, at least in terms of basic physics. – David Richerby Nov 29 '14 at 12:30
  • @RedGrittyBrick, try to unscrew a very tightly-screwed screw with a screw driver that has a very thin shaft. You can feel your hand rotate and see the screw not budging. Not a scientific proof, but you could experiment and see for yourself. – Shahbaz Nov 30 '14 at 14:52
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For screwdrivers, a significant limit is the amount of angle which can be tolerated before the screwdriver rocks out of the slot. When exerting a large force, humans cannot keep the centre of rotation completely steady. A longer driver means the angle for a given wobble is less, so the driver stays in its slot at higher torque.

I personally have found that I can sometimes get better torque with a high quality miniature screwdriver ( with a narrow handle that has a rotating end ) held with one hand turning and the other hand pressing rather than a larger driver in one hand - preventing the head 'camming out' is more important than the leverage. I also haven't found the same effect with hex or socket drives, only flat and cross head screws which can cam out.

In terms of a long shaft driven by a motor, then it won't have much effect if the shaft is driving something with it is firmly attached to. Adding a flexible coupling between the the motor and the shaft though will have a somewhat similar effect in that it will allow the motor to rotate in its bearings' axis and the shaft in its axis even if there is a small misalignment.

Pete Kirkham
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Everyone who deals with screws and screwdrivers knows that long screwdrivers are stronger than short ones.

I own and use screwdrivers but I don't know that to be true.

I'm reasonably sure the torsional strength of a screwdriver shaft does not depend on length. At least not appreciably so within the range of screwdriver shaft lengths I have encountered (say 1cm to 20 cm).

It depends on material and diameter. Different types of steel will have different strengths.

Maximum torsional stress $ T_{max} = ( \frac \pi {16}) \tau_{max} D^3 $ where $\tau_{max}$ is maximum shear stress of material and D is diameter of a solid rod with circular cross-section. Ref

Your hand may be able to exert more torque on a larger handle but ungripped shaft length has no significant effect on the torque you can deliver to the bit end. In general I'd expect shorter drive shafts to be stronger, not weaker.

RedGrittyBrick
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The answers above explain almost all of the points but let me try to put it all together.

It is not necessarily true that long screwdrivers have more strength in all cases. It all depends on the cross section of the shaft, length of the shaft and material property. In fact shorter screwdrivers are stronger for a similar cross section and flexural stiffness. You can refer torsional stiffness, polar moment of inertia, bending stresses and shear strength of a material to get a better understanding how it influences the strength of an object.

Often you would find that longer screwdrivers are used commonly to loosen/tighten larger screws and they come with thicker cross-section. Which is one of the reason why they are stronger. They also provide higher bending resistance due to thicker cross section so you will find it hard to snap them. But that being said longer screwdrivers with thinner cross sections do exist to tighten/loosen up screws at a larger depth. Also a larger screwdriver comes with a thicker handle, this allows more torque to be applied. This is because you apply the force on the periphery of the handle and that slight distance from periphery to centre of shaft does make a difference.

Further, you can increase the strength of a screwdriver by simply choosing a stonger material.

Abhishek P G
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