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