Torque Wrenches - my answer... (Fifield, Douglas)

[Orin Eman]

> 
> OK, so using your numbers SJ and my formula:
> 
> TW = (NT * LT) / (LT + L2079)
> 
> TW = 258 * 1.46 /  (1.46 + 1.0)
> TW = 153 ft-lbs
> 
> So  instead of using the 258 ft-lbs on the torque wrench, you will use 
> 153 ft-lbs when you have the 2079 tool on the end. It makes sense - the 
> 2079 tool extends the torque wrench by ~60%, so there is a reduction on 
> the setting by 60%.

Huh?  258 is the spec for the indicated torque setting on a torque wrench
attached to a 2079.  Your numbers would be correct if you used torque at
the bolt rather than 258.

Yet again:

Torque at bolt = Torque wrench setting * (length of 2079 + length of torque wrench) / length of torque wrench

You can find that formula in the instruction sheet for almost any decent
torque wrench.

Torque wrenches measure force.  Period.  Either directly by deflection
with a beam type, or by comparing to the force generated by the
internal spring for the clicker type (setting the clicker type preloads
the internal spring).  The scale on a torque wrench takes account of
the the length of the wrench.

So how is the above formula derived?

Assuming that the magic Audi torque wrench is 42" long or 3.5 ft.
What force is required to make it read 258 ft-lb?  About 74 lb force
at the handle.  It matters not whether the torque wrench's square drive
is attached to a 2079 or clamped in a vise.  Now for a clicker type
wrench, assume it is just about to click - everything is still solid,
we have a bit less than 74 lb of force on the handle.  What does this
mean for the bolt?  Well, it sees the force of 74 lb 4.5 ft away
giving a torque of 332 ft-lb.

Turning those numbers into letters:

Ti = indicated torque
Lw = length of torque wrench
Le = lenght of extension ie 2079
Ta = actual torque

Fw = force on wrench = Ti / Lw
Ta = Fw * (Lw + Le)	[2]

Substitute for Fw in [2]

Ta = Ti * (Lw + Le) / Lw

BTW, clicker type wrenches have a pivot point somewhere along the length
of the wrench.  The mechanism could be said to measure torque about
this pivot with the distance from the pivot to the square drive being
a built in extension.  The _scale_ on the wrench would take this built
in 'extension' into account of course...

Orin.