Converting angles in degrees to Newton Metres (Torque)

Probability

Junior Member
We covered the basics many years ago at college but nothing too deeply was ever completed in maths with the formula. We had a formula T = FR which read torque = force x radius.

I'm not a mathematician by any stretch of the imagination hence why I asking if this is at all possible, which it must be as car manufacturers do it!

Angle tighten a bolt and you either get an angle in degrees to work to, or a torque in Newton Metres to torque the bolt to. This now is not always the case you can be given a angle torque only.

You might then ask, why the is the problem with that?

Lets give a real example.

Customer asks for a diagnosis on an engine over heating, you diagnose the cylinder head gasket leaking. You repair the engine and a few weeks later the car returns with the cylinder head gasket leaking again!

You dismantle the engine and find that the 'clamping force' the manufacturer recommended in angled degrees seems to be incorrect. Further investigations on the engine find the cylinder head gasket has not properly been compressed, thus leaks. We contact the manufacturers agent who advises the only information available has been given and we now struggle to find the correct torque data, and given that the manufacturer only gives an angle measurement we cannot compare that to any torque figures!

This then brings me to my question and the formula T = Fr sin (theta)

I'm given an angle measurement 75 degrees. My tool length is 2 m, which is the radius, the force is applied from my arm, which is unknown, thus the torque applied is also unknown.

How then would this problem be solved with two unknowns?

Thank you to anyone who can help me solve this.

HallsofIvy

Elite Member
"Angle tighten a bolt and you either get an angle in degrees to work to, or a torque in Newton Metres to torque the bolt to. This now is not always the case you can be given a angle torque only."

I don't know what you mean by "angle tighten" or "angle torque". I suspect you are misunderstanding what torque" means. If you don't apply enough force to a bolt that is really stuck, it might not turn through any angle at all but you have still applied a non-zero torque to it. Suppose I have a really big wrench with a handle a half meter long, placed on a bar and I really lean into it, applying 20 Newtons force, but the bar doesn't turn at all! I have still applied (0.5)(20)= 10 Newton-meters torque. The angle turned or whether there is any such angle at all is irrelevant.

Subhotosh Khan

Super Moderator
Staff member
We covered the basics many years ago at college but nothing too deeply was ever completed in maths with the formula. We had a formula T = FR which read torque = force x radius.

I'm not a mathematician by any stretch of the imagination hence why I asking if this is at all possible, which it must be as car manufacturers do it!

Angle tighten a bolt and you either get an angle in degrees to work to, or a torque in Newton Metres to torque the bolt to. This now is not always the case you can be given a angle torque only.

You might then ask, why the is the problem with that?

Lets give a real example.

Customer asks for a diagnosis on an engine over heating, you diagnose the cylinder head gasket leaking. You repair the engine and a few weeks later the car returns with the cylinder head gasket leaking again!

You dismantle the engine and find that the 'clamping force' the manufacturer recommended in angled degrees seems to be incorrect. Further investigations on the engine find the cylinder head gasket has not properly been compressed, thus leaks. We contact the manufacturers agent who advises the only information available has been given and we now struggle to find the correct torque data, and given that the manufacturer only gives an angle measurement we cannot compare that to any torque figures!

This then brings me to my question and the formula T = Fr sin (theta)

I'm given an angle measurement 75 degrees. My tool length is 2 m, which is the radius, the force is applied from my arm, which is unknown, thus the torque applied is also unknown.

How then would this problem be solved with two unknowns?

Thank you to anyone who can help me solve this.
Work done by Torque =$$\displaystyle \displaystyle{\int_{\theta_1}^{\theta_2}T \cdot d\theta}$$

Do you understand the equation above?

Do you see the similarity to the equation for work-done by a force?

By the way, I think you are supposed to use a torque wrench!!

Probability

Junior Member
Thanks for your replies, I can see this is going to be difficult, it appears a specialist area of expertise. Just to note that many car manufacturers now don't use torque wrenches, they specify angles of degrees. So if a manufacturer said tighten bolts to 5, 10, 15 and then 35 Newton Metres then that part is easy, but if the manufacturer then says your final part of the tightening sequence is using a angle gauge and turning a bolt 75 degrees, then nobody except the manufacturer knows what that 75 degrees represents!

Hence the cylinder head gasket leaked. If the manufacturer had said angle tighten 90 + 90 degrees or more I could have understood the torque involved would have been more significant, but 75 after 35 n.m is not enough.

I'll do a bit of research with the math you advise above and let you know soon what I think I understand, and if I am wrong, please correct me. Thanks for your help.

Dr.Peterson

Elite Member
I suspect the main issue here isn't math, but understanding what this measurement means. Possibly the manufactures are (or ought to be) the best source of information. It's also possible that there is some defect in the specific product or instructions.

I tried searching for "angle torque" to figure out what you are talking about, and found at least this discussion, whose reliability I can't judge at all: http://user.xmission.com/~kd7olf/torque.html

Probability

Junior Member
I've not managed to look into the details of the above to date, however having purchased another head gasket from another source the instructions in there added another + 90 degrees angle torque. I'm running the car now to see if that cures the problem. It seems on the surface of the problem that the manufacturer does not want the trade repairing their engines when things fail, the manufacturer seems to be trying to work towards a sealed engine and produce an end of life specification. Then they just want you to either buy a new car or a new engine.

HallsofIvy

Elite Member
Thanks for your replies, I can see this is going to be difficult, it appears a specialist area of expertise. Just to note that many car manufacturers now don't use torque wrenches, they specify angles of degrees. So if a manufacturer said tighten bolts to 5, 10, 15 and then 35 Newton Metres then that part is easy, but if the manufacturer then says your final part of the tightening sequence is using a angle gauge and turning a bolt 75 degrees, then nobody except the manufacturer knows what that 75 degrees represents!
To "tighten bolts to 5, 10, 15, and then 35 Newton Metres" you should use a torque wrench and turn until it reads the correct torque. To "turn a bolt 75 degrees" you simply turn the bolt through that angle. You say "nobody except the manufacturer knows what that 75 degrees represents". I assume you mean what torque that would be. I would say that even the manufacturer cannot know what torque would result after turning the bolt through 75 degrees because the manufacturer cannot know what wear has already occurred on the bolt! I would think that, in this case, the manufacturer is saying that "torque" is not relevant- that turning the bolt through the given angle will seat at a given depth and that is sufficient.

Probability

Junior Member
To "tighten bolts to 5, 10, 15, and then 35 Newton Metres" you should use a torque wrench and turn until it reads the correct torque. To "turn a bolt 75 degrees" you simply turn the bolt through that angle. You say "nobody except the manufacturer knows what that 75 degrees represents". I assume you mean what torque that would be. I would say that even the manufacturer cannot know what torque would result after turning the bolt through 75 degrees because the manufacturer cannot know what wear has already occurred on the bolt! I would think that, in this case, the manufacturer is saying that "torque" is not relevant- that turning the bolt through the given angle will seat at a given depth and that is sufficient.