Torque Wrench Extension - physics

Need some help in the calculation of the torque multiplication if you use an extension.

I am referring to an extension that increase the length of the toque wrench AFTER to place where you normally attach a socket (not an extension in the same axis as the socket to reach into a deeper hole/gap).
In all this I am using a “click” type wrench and an extension (e.g. another spanner) that is connected to form a straight line with the wrench handle.
Now, if you apply turning force with your hand half way down the torque wrench handle, or add a “cheater” bar, the wrench will click at exactly the same applied torque at the nut. This logical, fits with my understanding of levers, and seems to be the accepted wisdom.
If I use an extension that increases the length after the torque wrench, this will increase the applied torque at the nut/bolt when the wrench “clicks”. Again no arguments
However, in order to calculate the multiplication, most calculators/formulae take into account the original wrench handle length along with the extension length I can’t see why thee original handle has any bearing on the new value, especially as the effective handle length does not affect the setting in normal use.
If I set the wrench to 100Nm, and use a 1m extension, I assume I will get 200Nm at the bolt. Or do I need to use the original handle length in the calculation to get the ratio?

If you apply a force perpendicular to the handle, the torque is that force multiplied by the length of the handle (between the pivot point and the point where you apply the force). So if you have a 0.5 meter handle and apply a force of 4 Newtons, the torque is 2 Nm. If you add a 1 meter extension, so you extend the total handle length to 1.5 meters and apply the same 4 N force, the torque is 6 Nm.

I understand the basic principle of levers, and the case you describe is a simple lever. So the longer the distance from the point where force is applied to the socket/bolt, the greater the torque.

But while I am using a long lever, I am applying the force up until the torque measured by the wrench reaches a particular value. So agreed I will have to push harder the shorter the handle, but the wrench “clicks” at the same torque value. Hence my point about cheater bars etc.

If I extend the lever length AFTER the point at which torque is measured, the torque applied to the bolt will be greater than the torque setting of the wrench. But I can’t see why the handle length of the original torque wrench, or cheater bar, or where I hold it has any effect on the point at which the wrench “clicks”, and therefore why that value (original handle length) changes the effective torque at the end of the extension (i.e. at the bolt)

the mechanism which indicates the set torque has been reached is right where the handle attaches to the head. if it’s set to 20 ft-lbs, it’ll click at 20 ft-lbs whether you use the standard handle or put a 100’ cheater bar on it. So I’m not sure I understand what you mean by “extend the lever length AFTER the point at which torque is measured.”

There’s the torque on the nut and the force required to achieve that. As long as you do nothing to mess with the way the torque on the nut is measured, you’re good. Use a lever long enough and a place to stand and you can torque the Earth. Or something like that.

OP is trying to figure out why a regular torque wrench is completely agnostic in terms of where you place your hands (apply 20lbs force at 1ft, or 1lb force at 20ft, you get the same torque applied at the bolted joint), but once you attach something like a crows foot to the end, all of the sudden it matters whether or not you can choke up on the wrench or add a cheater in order to get an accurate reading

The reason why is that there are two components to this that the joint is reacting against - the torque and the linear force. Push down at the end of a 1 foot torque wrench at 20 lbs, and the joint has to push back up at 20 lbs, in addition to resisting the 20 ft-lbs of torque.

But with a normal torque wrench, it doesn’t really matter what the linear force is- the torque wrench just reads the torque part of the equation. The joint takes up the linear force. Nobody really cares about the linear force, as its not important for bolt tension. If you had a socket extension you would probably have to place another hand right at the rotational axis in order to steady it (resisting the linear force), or if the whole thing was on wheels you may have to stop it from rolling in the direction you’re pushing on the wrench, but again, that doesn’t really matter to the bolt.

But once you add in a crows-foot extension, everything gets out of whack. That linear force now applies it’s own additional torque across the length of the crow’s foot, in addition to the torque that the wrench is reading, and the joint/bolt sees the sum of both torques. So now all of the sudden it matters whether you had originally applied 20 lbs@1ft or 1 lb@20ft, as that “bonus” torque can be 20x less for the latter. And the torque wrench has no inherent way of distinguishing between them, unless you assume a fixed lever arm.

I know the physics, but I don’t know the tool. Can anyone link to a good diagram or the like of a crow’s-foot extension, and how it differs from a simple pipe slipped over the handle?

This is what they look like. Link

Now I understand why it’s actually complicated. The OP had me thinking pipe over the handle, which isn’t complicated at all.

Crowfoot Wrenches

Just a way to convert a socket wrench into an open end wrench. Typically you won’t use the ratchet function of the handle.

It throws off the torque reading because it moves the center of rotation away from the gauge, whether ‘click’ style or flexing shaft.

The reason an extension on the handle doesn’t mess with the reading is that even though it takes less force to operate, you have to move further. It’s a force times distance calculation. Decreasing on variable necessitates increasing the other.

Sorry if my explanation wasn’t too clear. I now try to clarify, but it’s late and I’m a couple of glasses of cabernet down so let’s hope…

Please see

I can see how the extension ( from the second link) E changes the torque at the bolt, but I don’t get why L matters given that the torque is measured/set at the original end of the wrench (left end of L).

If E is one length unit ( a foot for lb/ft or a meter for Nm) then I can see why that doubles the effective torque. L should be irrelevant. Or please explain why it isn’t!

I’ve worked at a lab that calibrates torque tools. You can’t use a crowfoot socket with a tool that either indicates (live/peak display or dial) or signals (beep, click, cams) without calibrating that pair together. The torque applied to the fastener is different from the measured torque at the tool’s drive point.

If you need a wrench instead of a socket, there are single torque setting (not adjustable) tools for that. These are very common in assembly production environments.

A calculator that I’ve used multiple times for torque wrench setting vs torque on bolt. Long story short, handle extensions don’t matter, but anything on the drive end changes the torque applied (depending on angle it’s attached)

yes, and here they still say that L matters. Why? For my logic, only E matters

Torque = force x distance.

In this configuration, the torque wrench is measuring F x L, but the torque on the screw is F x (L + E).

Imagine E was 3 ft and L was 5 inches. The torque on the end is far greater than the torque measured by the torque wrench, because it’s the same force multiplied by a much greater lever arm. On the other hand, if E was 5 inches and L was 3 ft, the measured torque and torque on the end will be almost exactly the same.

Or more to the point: the torque wrench isn’t applying torque on the extension. It’s applying lateral force to the extension.

It sometimes helps, in cases like this, to consider the extreme cases. One extreme case would be a zero-length crow’s foot: In this case, the torque at the nut will be the same as the torque measured by the torque wrench. Another extreme case would be a very long crow’s foot, but where you hold the combined tool right at the measuring head: In this case, the measuring head will read no torque at all, but the nut will still feel a torque. So it’s clear that, when you have a crow’s foot beyond where the torque is measured, you’ll get different readings when you’re holding it at different spots: If you hold it close to the measuring head, then the reading will be much less than the torque at the nut, but if you hold it very far out (much greater than the length of the crow’s foot), then the reading will be very close to the torque at the nut.

Again, you’re ignoring the linear force component of this. That’s perfectly fine to do when its just a standard torque wrench where the axis of rotation lines up perfectly with the torque measurement, since the bolt doesn’t care about the linear force, and you’re measuring torque right at the bolt.

But once the axis of rotation is offset from the torque measurement, you need more data than just the Torque and “E”, since the bonus (unmeasured) torque on E depends on the total linear force applied across distance “E”. You need a breakdown of the measured torque (knowing either force or distance “L” in addition to the torque will automatically get you the other one), and its easier to assume a fixed distance than it is to assume a fixed force (If you knew the force, you wouldn’t need a torque wrench to begin with!)

It’s the ratio of the new length to the old length that matters.

Obviously, the torque at the nut depends no the new length: clearly the torque at the click/measure point depends on the old length.

Tm is the torque measured by the wrench
Ta is the torque applied to the bolt
F is the force applied at the handle

L and E are as described on the calculator; assume the angle is 0

Tm = F*L, solve for F = Tm / L

Ta = F*(L+E), substitute for F to get Ta = Tm*(L+E)/L

or, if you want the wrench setting for a particular applied torque solve for Tm = Ta*L/(L+E)

Once case where handle extensions do matter, if you do not reach the click point while the bolt is turning your torque value will not be accurate. This is due to the difference for static friction and extensions can typically lead to this situation due to the throw. Click type torque wrenches when clicked while the bolt is not turning will be under torqued.

Oh, and I missed this:

Units shouldn’t matter. What if you had a torque wrench that had a display that showed both American and metric units? Would you expect that an E of 1 meter or 1 foot would both double the effective torque?