The Math of Torque Wrenches

[Papa]

There was a post in the main roadster forum about how to torque the front hub nuts to the indicated 250 ft. lbs.. I'd always been told that where you grip the wrench affects the accuracy of the actual torque applied. I also had been told that using an extender would change the applied torque and incorrectly assumed this was applicable to using a cheater or extension on the handle of the wrench. The engineer in me wanted to do the math, so here is what I learned while researching this question.

1. The formula for calculating applied torque vs. desired torque (setting on the wrench) is:

https://farm1.staticflickr.com/798/40374795754_b8c49507f5_b.jpg (https://flic.kr/p/24vMo9b)

2. The reference to extension is applicable to an extension at the wrench head, not to the length of the handle.

3. With no extension on the head of the wrench, the effect of the length of the handle is 0, meaning that the torque setting on the wrench is what is applied at the bolt.

https://farm1.staticflickr.com/786/40190574755_b751c2eb0e_z.jpg (https://flic.kr/p/24evcE4)

4. Adding an extension at the wrench head and then changing the length of the handle does make a difference.

https://farm1.staticflickr.com/820/39275295330_e54b21a490_z.jpg (https://flic.kr/p/22QC9Yj)

Of course, the plot is exaggerated to show the effects, but the effect is clear. If an extension is used, the torque applied at the bolt will be different than what the wrench is set to. It also matters what angle the extension is relative to the handle. The above calculations assume the extension is in-line with the handle. As the angle approaches 90 degrees, the effect is reduced with no effect at 90 degrees.

So, there you have it.

Dave

[Just puttering]

I am no engineer but i will ask anyway,

The click style wrench you show above is made to click when a certain amount of pressure (torque) is applied at the handle. If the handle past that point is extended, it makes the torque easier for the person (more leverage) but it shouldnt change the torque value when it clicks having a longer handle should just make it easier to accomplish???? Now I am going to have to get my torque wrench out and do some experimenting with a bolt in a vice and see if it stays consistent with an extension!

Second thought, L in the formula is the lenght that is engineered into the wrench for the torque setting, not where you put your hand?? My assumption would be that chart 4 is the same as chart 3 but would show the lower value from the multiplication factor (L / A ratio)

Third thing, this may be a wives tale but guys in our shop (a long time ago) said using an extention on the socket itself would throw off the torque?

Side note- We had a torque multiplier that looked like a fat socket that went between the wrench and socket, but i do not remember much about its multiplication or how that was accomplished.

I have never seen an adapter like you show above (i know sheltered life) but the formula to use one is a great thing to have listed here. I read the post you mentioned, and thought that should start some good discussion about angles and leverage! Thank you for all the research you did and posting it!

[Boydster]

I have never seen an adapter like you show above (i know sheltered life) but the formula to use one is a great thing to have listed here. I read the post you mentioned, and thought that should start some good discussion about angles and leverage! Thank you for all the research you did and posting it!

The adapter (and the math examples used above) is used on air cooled aircraft engines; specifically the cylinder base nuts. There's not enough room for the torque wrench head to get in there, so you need the extension. There's also 2 different size nuts... so with this extension, you can just flip it as your going through the torque sequence. And yes, you have to do it at different angles, so have to work out the math for each one. The good mechanics will do it quickly in their head...

https://thefactoryfiveforum.com/attachment.php?attachmentid=83206&d=1522310314

[Papa]

I am no engineer but i will ask anyway,

The click style wrench you show above is made to click when a certain amount of pressure (torque) is applied at the handle. If the handle past that point is extended, it makes the torque easier for the person (more leverage) but it shouldnt change the torque value when it clicks having a longer handle should just make it easier to accomplish???? Now I am going to have to get my torque wrench out and do some experimenting with a bolt in a vice and see if it stays consistent with an extension!

Second thought, L in the formula is the lenght that is engineered into the wrench for the torque setting, not where you put your hand?? My assumption would be that chart 4 is the same as chart 3 but would show the lower value from the multiplication factor (L / A ratio)

Third thing, this may be a wives tale but guys in our shop (a long time ago) said using an extention on the socket itself would throw off the torque?

Side note- We had a torque multiplier that looked like a fat socket that went between the wrench and socket, but i do not remember much about its multiplication or how that was accomplished.

I have never seen an adapter like you show above (i know sheltered life) but the formula to use one is a great thing to have listed here. I read the post you mentioned, and thought that should start some good discussion about angles and leverage! Thank you for all the research you did and posting it!

I think we're saying the same thing. The L term is a moment arm. Force x Moment arm = Torque The length of the handle itself isn't what changes the force, but the length of the moment arm does. This is the measurement from the pivot axis to the point where force is applied (hand position).

Dave

[Flyguy561]

Just to chime in, adding an extension does not change the torque value. Using a torque adapter at a 90 degree angle to the torque wrench will not change the torque value either. Anything else you must do the calculation.As long as you pull or push the torque wrench anywhere on the handle you are good to go, change the length at with a bar you must recalculate. I hope this may help. I use torque wrenches every day and check them on torque testers all the time.

[Al_C]

Dave,

I am not an engineer either. Nevertheless, I agree more with "Just Puttering". Here's the thing: the formula essentially says that "A" - an extension, is going to modify the true torque applied. I agree with that part, as it is on the "business" end of the wrench. However, most of us are putting an extension on the other end: extending the "handle" of the torque wrench. So, if my math is correct, and we extend the length of the handle, we have this equation: R = 250 (torque) x 48 (total length of the handle) / 48 (total length of the handle) + 0 (extension on the socket end of the wrench). We can cancel out the 48s, and are left with R = 250. No?

My interest in this is that I used a pipe on the end of the torque wrench because I couldn't get enough weight into the wrench to get it to click at 250. With the handle extension, I could. Please tell me I don't have to re-do this.

[Just puttering]

Papa,

I have no idea, im just thinking

Part one, without a torque adapter you could use an extention on the handle and the torque will stay the same - seems to make sense. You are adding to the moment handle but reducing the force so the torque stays the same?

Part two, with a torque adapter and the wrench lined up with the adapter if part one is correct, it should tranfer to part two that the torque would stay the same although be multiplied?

My thought is the wrench is set to click with what ever torque setting you use and useing a handle extender just reduces the force to get to that point?

Not trying to be smart, just curious.

[Papa]

Dave,

I am not an engineer either. Nevertheless, I agree more with "Just Puttering". Here's the thing: the formula essentially says that "A" - an extension, is going to modify the true torque applied. I agree with that part, as it is on the "business" end of the wrench. However, most of us are putting an extension on the other end: extending the "handle" of the torque wrench. So, if my math is correct, and we extend the length of the handle, we have this equation: R = 250 (torque) x 48 (total length of the handle) / 48 (total length of the handle) + 0 (extension on the socket end of the wrench). We can cancel out the 48s, and are left with R = 250. No?

My interest in this is that I used a pipe on the end of the torque wrench because I couldn't get enough weight into the wrench to get it to click at 250. With the handle extension, I could. Please tell me I don't have to re-do this.

You're good! Using an extension on the handle has no affect on the applied torque as long as no extension is used on the head of the wrench. This is demonstrated in the first plot where the torque is the same regardless of the length of the handle.

Dave

[Jeff Kleiner]

... Please tell me I don't have to re-do this.

You don't have to re-do it.

Happy now? :)

Jeff

[Al_C]

You don't have to re-do it.

Happy now? :)

Jeff

Yes ! :)