If a screw is very tight, you use a screwdriver with a longer shaft. 
I'm told this is because it increases the torque on the screw.  How
does this work?  Do we assume a perfectly rigid shaft?

IIRC, we measure power in (weight * distance / time) and torque in
(weight * distance).  I know that you can use a block and tackle, for
example, to keep the power the same while trading off between weight
and distance.  But that doesn't seem to be related to what's happening
here, unless the shaft is elastic and stores force over distance.

I've seen a page on howstuffworks.com about this, where they were
multiplying by the length of the shaft to get torque.  But this
doesn't make sense to me.  We're concerned with the force on the
screw, parallel with the direction of the turning of the screw.  The
distance of my hand from the screw is orthogonal to what we're
interested in.  Obviously if we were using a wrench its length would
be important.

This is what I would think would be absolutely trivial mechanics, but
I have yet to see a cogent explanation of it.  I bid $10 -- since my
Google Researcher application was turned down on the basis that my
expertise were not specialized enough, I'm assuming an expert in
classical mechanics will be answering this and it will take her 5
minutes -- but I'll pay more if it takes you longer and your answer is
good.

-Carl

This link http://www.sciencenet.org.uk/database/Physics/0104/p01521d.html
basically says what my original thought was, namely that a longer
screwdriver in itself doesn't help, but that often a longer
screwdriver will help you get yourself in a better position to apply
torque.

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.

http://www.cromwell-tools.co.uk/tool_tips/screwdrivers.html, among
other helpful screwdriver purchasing tips, suggests that more torque
can be applied with a longer screwdriver because the handle part is
longer (again, because the limiting factor is the hand-handle
friction).  Again, this only matters until the handle gets as long as
your hand is wide, though I suppose two-handed screwdriver operation
is possible in extreme cases.  (though at that point, you should find
a socket wrench!)

searches used: "longer screwdriver"

---

Request for Answer Clarification by beefman-ga on 11 Jun 2002 00:43 PDT

So the torque is the same, excluding the ability to grip the driver. 
I could believe this, except that I had the tires on my car changed,
and the mechanic used "torque sticks" on his impact wrench:

< http://autos.yahoo.com/repair/results/ques003.html >

"There are also special torque-limiting extension sockets called
"Torque Sticks" that can be safely used with an impact wrench to
accurately tighten lug nuts. But a plain impact wrench should never be
used for the final tightening of the lug nuts because most provide no
control whatsoever over the amount of torque applied to the nuts."

This page has pictures showing sticks of roughly the same length
(unlike my memory of the set belonging to my mechanic):

< http://www.procutinternational.com/html/torqstik/torqstik.html >

"The amount of torque is determined by how fast the the nut end can
catch up with the drive end. The stiffer the stick, the higher the
torque. By strictly controlling the diameter of the stick shaft and
the material used the output torque can be controlled."

So it seems we cannot assume a rigid shaft.  According to their graph,
shaft elasticity causes the torque to slowly build up to, and later
exceed only very slightly, the torque of a rigid shaft.  So if
increasing the length of a screwdriver shaft increases its elasticity,
this would seem to only decrease the torque...

Comments?  Then we'll wrap it up. . .

-Carl

---

Clarification of Answer by davidmaymudes-ga on 11 Jun 2002 01:30 PDT

the "TorqStiks" appear to be for a very specific purpose; apparently
an "impact wrench" works by basically hitting the nut with a small
hammer repeatedly to turn it, and the TorqStiks work by delaying some
of the force of the hammer impact....  I don't think they would work
if you were using a hand wrench.  In any case, I think they're made of
much more flexible material than a screwdriver shaft would be.

With the constant applied torque of a hand wrench, as the wrench
turns, the torque stick would just keep twisting until it either
broke, or until it was putting enough torque on the target nut to turn
it.  (or until the spring force was so great that it ripped the wrench
back out of your hand and hit you with it.  I don't think it's a good
idea to try this.  :-)

So anyway, I think you're right in principle that the shaft could
twist, but I don't think it happens in practice.  (first, the skin on
your hand will bend and the handle will slip.)

Let me know if you have any further questions, it's an amusing topic.

--David

I too have heard the theory that a screwdriver with a longer shaft is
an advantage with a tight screw. Actually in terms of Physics the
screwdriver exerts a moment on a screw although the net force is zero,
the reason being that a couple is involved. Therefore apart from the
access/grip practical considerations in the Answer by davidmaymudes-ga
there is no truth in the theory.
A couple consists of two equal and oppositely directed parallel
forces, not in the same straight line. A couple can produce only
rotation.
The moment of a couple is equal to the product of one of the forces
and the perpendicular distance between them. Therefore one can see
that using a screwdriver with a larger diameter handle is an advantage
since the perpendicular distance between the forces is greater.

There is a good explanation of the physics of couples using a
screwdriver example in the Southern Methodist University's Dept of
Mechanical Engineering Course ME2310 Statics at the following link (MS
Word 97 or Word 97 for Macintosh recommended):
www.engr.smu.edu/me/2310/4-4_4-5.doc


I searched with the following keywords:
"moment of a couple" + screwdriver
://www.google.com/search?hl=en&q=%22moment+of+a+couple%22+%2B+screwdriver&btnG=Google+Search

I tried a range of screwdrivers (from the same manufacturer, and with
handles that differed only in length).

There's no doubt that tough screws are easier to move with the longer
screwdrivers. I put this down to two factors.

Firstly, as davidmaymudes-ga pointed out, a longer handle offers your
hand a better grip. This made a big difference on my "test screws".
But I still gained a further advantage from a longer shaft when the
handles were
identical.

I'm fairly certain that this is due to the ability of the shaft to
twist slightly. This elasticity seems to soak up the irregularities in
the force that I can apply with my hand, and enables me to apply a
steady high torque without so accidentally twisting the screwdriver
head out of the slot.

I'm no expert in classical mechanics. As I said, the above is from my
own observation. But try it and I think you'll agree - it's the slight
elasticity of the longer shaft that makes possible the the steady
application of a higher torque.

Can't resist another comment!
My preference is to use long-shafted screwdrivers, since like
eiffel-ga I find it easier to keep the tip seated in the slot in the
screw head. However I attribute this to the better control one has
with a long screwdriver. Specifically, when one is applying one's
maximum force the screwdriver tends to wobble and its axis moves out
of alignment with the axis of the screw. Obviously for a given
off-axis displacement of the handle-end, the angular displacement will
be greater for a short screwdriver than for a long one.
As David says "...its an amusing topic"

Torque sticks refer to a widely different use of force, impact
wrenchs. If you are able to create the amount of pressure and action
of an impact wrench you would in fact need a long handled screw driver
to effect torque. Oddly enough, your theory on torque sticks seems to
be backwards. Torque sticks are used to reduce torque, to assure that
a bolt is not overtightened by an impact wrench. They are not longer
to provide this ability, they normally are thicker for higher torque.

http://www.sarveshwari.com/ts_torque_sticks.htm
"Assures an equal torque on all wheel nuts and bolts with pneumatic
impact wrenches. The resulting shaft flexes in synch with the blows of
an input wrench, once the correct torque has been reached."
(search words "torque sticks" on google)

If you were hoping prove this would assist in loosening, it would do
just the opposite in my thinking, it would limit the amount of torque
that you are able to apply based on the thickness of the shaft.

Also thinking this is a amusing topic which should not close.

Mother911-ga

mother911-ga and David

My idea when I asked about elasticity in the original question was
that flex in the shaft of the driver would store energy over
distance/time and then release it suddenly, since to break the
friction on a tight screw you probably only need to get over a certain
threshold very briefly.  But as I say in the post on torque sticks,
they do the opposite thing.  According to the site, 'If the torque
from the wrench continued, the torque at the end of the stick would
eventually *equal* it, but since the impact wrench works by periodic
bursts, the torque at the end of the stick can never catch up.'  I
would expect that if the impact wrench were continuous, the torque at
the end of the stick would exceed that of the wrench at some point --
indeed their graph shows it going slightly higher, but not much.  I
suppose the elastic motion of the stick is slow enough to conserve
power but keep the max torque down.  No telling if a screwdriver shaft
behaves the same way. . .  David, torque stick shafts appear to be
made out of metal at least as stiff as screwdriver shafts.

My personal experience with screwdrivers agrees with eiffel-ga.  I
have a set of Craftsman drivers with the same handles but different
shafts.  I'm not sure I understand the comment by west-ga.

-Carl

I'll try to summarise the gist of my two previous comments.
There can definitely be an advantage in using a long scewdriver where
a screw is tight. Possible benefits are as follows:
 1.To enable comfortable access.
 2.Sufficient length of handle to obtain a firm grip.
 3.Improved ability to keep the screwdriver axis closely aligned with
the axis of the screw, thus ensuring the tip of the screwdriver
engages correctly with the slot and is less likely to slip out.

Additional helpful points:
 1.Use the largest practical diameter of handle consistent with a firm
grip.
 2.Ensure that the shape and size of the tip closely match the slot in
the screw head.

Well, we're left with exactly what could/would/should have happened
on the usenet, except there's all this $ flying around.  This is a
sad, sad, day.

Shame on Google.  Never thought I'd catch myself saying that.

-Carl

Sorry for the multiple copies of my last comment; I don't know why
refreshing the page after the comment form is gone and I'm just
viewing the page should cause this.

-Carl

As the shaft of the driver gets longer, it allows for greater torsion,
which is the twisting force much like wringing out a washcloth. Each
unit of length is capable of supporting some amount of torsion against
the restoring forces, and more length means more units, each carrying
its own little torsion contributing to the whole.  As eiffel
mentioned, this stores up potential energy, allowing a greater torque
overall.