The twisting power of a wrench never fails to amaze me. Without one handy, I can twist as hard as possible and not budge a nut or fitting of some sort. But slap a 10-inch on that part and it’s child’s play.
Is there a general thumbnail for calculating the extra twisting power of a certain-sized wrench? My WAG is that a wrench might give someone at least 100 times the twisting power, but maybe it’s much more than that.
Can anyone give a rough calculation on a 10-inch wrench?
The problem with answering this question is that a wrench works in two ways. The first is a simple mechanical advantage through a simple level action. Thats easy enough to calculate. The second way a wrench works is that it allows you to use different muscles. To twist something off, you have to rely on the small muscles in your hand and wrist. By using a wrench you can use the big guns, i.e. your pecs, triceps, and in some cases your legs. Unfortunately there is no easy way to calculate the gain from that. That means the only real way to get an accurate answer to your question is to get some wrenches and test it for yourself.
You can buy torque wrenches, right? In that case, it’s just a question of how much money you want to spend to find out the answer to your question.
Grip and Pinch Strength: Normative Data for Adults
I think the grip used to turn bolts most closely resembles a Tip Pinch (table 3). An average man can exert about 18 pounds of force with that grip, a woman, 11.
Applying 18 pounds of force directly to the edge of a 1" diameter bolt (1/2" radius) gives 9 foot pounds of torque.
Applying that same force through a 10" wrench gives 180 foot pounds; a 20 fold advantage.
Its not quite that simple. Pinching something is a compressive force, therefore it would be friction that is providing the torque. The friction force is some fraction of the compressive force that depends on the materials in question. Typical values are between .1 and .3.
Beyond that, no one turns a bolt by just pinching it. They grab it between their thumb and pointer finger. I maintain that the only way to measure this is to empirical test it.
No, you’re right. We need to find measurements of the exact grip. The pinching numbers I gave just get us in the ballpark. Adding in your friction numbers, the advantage of a 10 inch wrench increases from 20 fold to 66 or even 200 fold!
Its not quite that simple either ;). A bolt is angled so its possible to exert some normal/compressive force that results in a torque.
Ignoring the use of muscles et al, I think the difference in mechanical advantage of two wrenches of different lengths can be calculated by (2PiR2) - (2PiR1) where R1 is the radius of the shorter wrench and R2 is the radius of the longer wrench.
I think there are two issues here - grip and leverage.
With a wing nut or thumb screw, you can keep your thumb and finger on the fastener head while applying most of the twisting force you can muster. With a hex nut or bolt, you lose your grip on it long before you’ve reached the limit of the twisting force you can apply. A wrench, on the other hand, virtually never loses its grip on the fastener. Makes a huge difference in what you can do before leverage becomes a factor.
I think the best answer may rely, indirectly, on the suggestion above: get (borrow) a torque wrench.
Instead of using it as a wrench, however, thread several nuts on a short bolt until they are snug against each other. place this inside a suitable socket, and mount the socket on the torque wrench. Now measure the torque as you manually twist the bolt to tighten it. Similar rigs can measure the torque in other cases. e.g. to measure the torque exerted on a nut mounted flush against a board, drill a slightly oversized hole in a small pice of wood, run a bolt through it then thread a nut onto the bolt. You can measure the torque on the bolt or nut by trying to tighten one while the other is held in a socket, while allowing the pice of wood to “free-wheel”
Mechanical advantage, however, is a bit trickier. You’d need a definitive value for the “lever arm” of a hand gripping a bolt, to compare with the more easily defined lever arm of a given wrench. There is fair room for argument and variation, depending on hand size, specific grip and the mechanical model you choose for the hand/arm (e.g. Does the lever end at the palm? The wrist? The elbow?)
– KP “often told to get a grip”
Torque is force applied at a radius, in the direction perpendicular to the arc, times the radius. I don’t see why you are taking the difference of circumference of the circles here; maybe I don’t know understand how you are quantifying “mechanical advantage.”
If we use torque as the way to measure mechanical advantage: Assuming you exert the same force F on two different wrenches, where R2 is x feet longer than R1, the two torques are:
T[sub]1[/sub] = FR1
T[sub]2[/sub] = F(R1+x) = FR1 + Fx* = T[sub]1[/sub] + Fx
So the difference in torque is Fx.
But that’s irrelevant anyway. The OP is what is the difference in torque between a 10" wrench and your bare hands. You would need to do something like take a torque wrench and two nuts connected by a short bolt; put one nut into the wrench socket with the other lug nut sticking out; have a friend hold the wrench steady; then turn the nut with your hand and check the reading on the wrench.
The question asked is underlined. Everyone is overanalyzing with all this talk about which muscles do what and how.
The mechanical advantage (heretofor referred to as “extra twisting power”) is merely the ratio of the lengths of the lever arms. If it takes 10 ft-lb of torque to loosen a nut and if the nut is ½ inch across the lever arm is ¼ in. and 480 lb. are required to exert the required torque. No way can you do that with your fingers. On the other hand with a 10 inch wrench a mere 12 lb. will do the job and you can probably loosen the nut by pushing on the wrench handle with one finger.
In this case the wrench gives 10/(1/4) = 40 times the “extra twisting power.”
But when they do, it hurts like a mother.
The circumference of the circle made by the handle of the wrench is the distance that the wrench handle moves. for a 5" wrench, a 1/2 turn moves the handle about 15.7". For a 10" wrench it moves about 31.4". It’s the same as a compound pulley; if I can pull 20’ of rope and only lift a weight 10’, then it only takes half the force.
This is all off the top of my head and IANAPM.
You simply define “extra twisting power” as mechanical advantage, when I see no reason for you to do so. The advantage from a wrench (without doing any calculations) comes from being able to get a grip and put your back into it, just as much as it does from mechanical advantage.
Are you saying there is no advantage to a longer wrench? Give my wife a 36" breaker bar and she’ll out turn me any day.
No, there is a mechanical advantage but its not necessarily the most important factor. Think of those cheapo hex wrenches. They increase your mechanical advantage by maybe a factor of 2, but they allow you to exert what? 10 times the force? I obviously don’t know exactly, but that would be my guess.
1 torque wrench with 5 ftlb gradiations
1 New, clean 1/2" nut (well 12 mm) and a bolt.
A) Tighten the nut finger-tight then apply the torque wrench and see if I can get a reading before the nut loosens. -Nope.
b) Tighten the nut to 10 foot pounds with the torque wrench, and try to loosen between thumb and forefinger. -No dice.
Now I might be able to loosen it if the nut were the cover plate to a ticking atom bomb and I was willing to sacrifice flesh, but for normal purposes, gripping only to the point of bruising is probably a reasonable approach. A new, clean nut is slippery.
I work in commercial aircraft assembly and we use inch/pounds, not foot/pounds for torque measurements. I have tightened large bolts to only 15 in/lbs and could not break the nut free by hand. That is about 1/10th of a foot/pound. In your scenario with the atom bomb, I would just bend over and kiss my ass goodbye.
I think you do have a point there. If I’m turning a nut by grabbing it with my fingers I can maybe get my forearm into play if I have a good grip, but my forearm is always stronger than my grip. But if I use a lug wrench, I can use both arms and wail on that thing with about half my body weight.