Just like engineers, throw around a bunch of equations without really knowing what's going on.

Here is the way an actuary explains it:

I am going to keep this all in metrics so it is easier to follow.
Let's say your mass is 75 kg. (that is about 165 lbs here on earth).
Now, you suppose you fall 10 meters (about 30 ft).
Let's say you are caught by the rope, and with all of the slippage in the system and rope stretch, from when the rope first starts to catch you until you actually stop is 1 meter (about 3 ft.).

Now, let's look at the forces:

First, we have to figure out your final velocity during this big whipper.

We will use the equation:
(final velocity)^2 = (initial velocity)^2 + 2 X (accel.) X (distance)
initial velocity = 0
Accel. = 9.8 m/sec^2 is the acceleration due to gravity on earth.
Distance = 10 meters
so, (final vel)^2 = 2 X (9.8 m/sec^2) X 10m
Solving this gives us the final velocity = 14 meters/sec

Now, we need to figure out our decceleration when we stop. We will use the same equation above:
(final vel)^2 = (initial vel)^2 + 2 X (Decceleration) X distance
Now, the initial velocity is 14 m/sec and the final velocity is 0 m/sec. because we are stoppping.
The distance to stop is 1 meter (given at the beginning due to stretch and slippage)
so, our equation is:
0 = (14)^2 + 2 X (Decceleration) X 1
solving gives Decceleration = -98 m/sec^2 (which is about 10 g's, well within our tolerance)
Almost done!
Now, plugging this decceleration into our formula for force:
Force = Mass X Acceleration give us:
Force = 75 kg X -98 m/sec^2
= 7350 Newtons = 7.35 Kilonewtons (force is always positive)
So, this 30 foot fall by a 165 lbs. person where the rope/system stretches 3 feet causes about 7.35 Kilonewtons of force on our system.

Whew! All of this math knowledge and I am stuck pricing insurance?!?

So, for your ten meter fall, one meter arrest of a 75KG climber, the answer is 8.085 kN.

Sure, after you've seen the answer.

Extreme actuary, the deceleration is not constant. It increases linearly with rope stretch. That's why there is a peak force at the very end instead of a constant one. The correct answer is twice what you calculated.

When I was in college, I was a pre-med student. One day, my math professor came to me and told me I should go into math instead of medicine. I was flattered. I asked him "Do you really think I am good enough at math?"
He responded "No, but you make so many mistakes you'd kill somebody if you went into medicine."

Hasn't rgold already covered this?

This thread is a good example of why so many sensible,intelligent people think they can't understand math and physics.

...

Consider this: The word pound was used to describe force for many, many years, and the cars, and airplanes, and a whole lot of other things, designed using the word pound as a unit of force, worked just fine.

...

Now torques are given in newtons, and pounds are no longer a unit of force, and somehow we are supposed to believe that if we use pounds as a unit of force, nothing will work and the engine will come apart.

This thread is a good example of why so many sensible,intelligent people think they can't understand math and physics. The problem isn't that math, or physics, is difficult. It isn't. What is actually going on is about as basic, and understandable as any subject could be. The problem is that people in the field refuse to explain it in understandable terms.

Latch onto this concept: The principles; the reality; that math was invented to describe, existed exactly as they are for quite a few billion years before there were humans or language. The words mathematicions, and physicists, use to describe what is going on, are just noises made with the mouth, or weird markings on a paper. They have no intrinsic meaning in themselves.

Mass and force really are two separate things. There are times when speaking as if they are the same, or using the same unit titles to describe them, can cause confusion. This is particularly true for astrophysicists. Remember, whether or not we use the same word to describe a certain amount of mass, and or a certain amount of force, is up to us. It is something we just decided to do, or not do.
We seem to get along using the same word for different things, like boat that floats on the water, and gravy boat, that holds gravy; and using different words for pretty much the same thing, like cup and mug; but scientific academecians think if we use the same word for an amount of mass; or weight- that is, mass under the influence of gravity on earth; and the amount of force it takes to support that mass when it is on the earth, that we are going to get hopelessly confused. Because they care deeply about us, they decided to help us out of this confusion by introducing a new set of terms that make no sense to anyone who has not gone to some considerable effort to understand them.

Remember, the people who decided that the word pound, or kilogram, would absolutely not do to describe force, are the same people who consider it important , and worth arguing at length about, whether or not Pluto should be called a planet. Pluto does what it does, and is what it is, with no regard whatsoever to what anyone says about it. Forces, and weights, do what they do with no regard whatsoever to what terms are used to describe them.


Consider this: The word pound was used to describe force for many, many years, and the cars, and airplanes, and a whole lot of other things, designed using the word pound as a unit of force, worked just fine.
When torque readings for tightening bolts were given in foot pounds, a whole lot of people working on their cars without torque wrenches handy, knowing about how much force it took to lift 50 lbs, for instance, and knowing they had a 1 foot wrench, were able to come reasonably close to getting the torque right on bolt that specified 50 ftlbs. This worked just fine for many decades. Now torques are given in newtons, and pounds are no longer a unit of force, and somehow we are supposed to believe that if we use pounds as a unit of force, nothing will work and the engine will come apart.
I still have a torque wrench calibrated in foot pounds, and the engines I build hold together just fine.

In summary: 1kn=the force exerted by 225 pounds at rest, on earth, in a downward direction, and knowing this can give a pretty good idea of how strong something is, which is what we were concerned about in the first place.

If you fall, and after all the math, it in reality turns out that you exert the amount of force that we call 10 kn, then if your anchor will hold exactly 2260 pounds, hanging from it statically, then you are ok. If your anchor will hold only 2240 pounds, hanging from it without movement, then you are in trouble.

Thank you for allowing me to vent. I feel much better now.

valarc and j, thanks for the correction. I feel better now, knowing the world is in this small way somewhat less screwed up than I had thought. Seriously, I'm not being sarcastic.
It's been a long time since I took physics, and I'd gotten the impression something had changed.

So why are we stuck with strength of climbing gear being given in KNewwtons, instead of the much more relatable kg or lbs? I'm old enough to have been in the industry when those were the units on the hang tags and in the literature, and no one ever questioned what what they actually meant, as so many do with Kn.
My rant may have been misguided, but I'm still convinced Kn is a poor unit to use for conveying an important piece of information.

valarc and j, thanks for the correction. I feel better now, knowing the world is in this small way somewhat less screwed up than I had thought. Seriously, I'm not being sarcastic.
It's been a long time since I took physics, and I'd gotten the impression something had changed.

So why are we stuck with strength of climbing gear being given in KNewwtons, instead of the much more relatable kg or lbs? I'm old enough to have been in the industry when those were the units on the hang tags and in the literature, and no one ever questioned what what they actually meant, as so many do with Kn.[/email]
My rant may have been misguided, but I'm still convinced Kn is a poor unit to use for conveying an important piece of information.

As to why gear is now usually rated in kN, I don't know for sure. Like I said, it's likely only to be a problem for Americans, anyway. But the kN is the official international unit of force (whereas kg is the unit of mass), so, I imagine that the practice is becoming, or has become, standard worldwide. Or it simply might be required by the EN under which the gear is certified.

Jay

The english system of units SUCKS ASS, and their common usage sucks even MORE ass.

So why are we stuck with strength of climbing gear being given in KNewwtons, instead of the much more relatable kg...

if only all you americans would switch from your silly and backwards english system all this confusion would be avoided.

You had me feeling better until you said Kg wasn't a unit of force. If pounds can be a unit of force, so can kg. All you have to do to make it so, is for people to agree that it is. The physics stays exactly the same.
1kg=2.20462lb . 1lb=.45359kg. The law of identity says that whatever is on one side of the equation can be substituted for whatever is on the other side. They are the same thing.
For those who say kg is not a unit of force, I say it can be used as such, and it works just fine.
Go back to may origional post, substutute ".45359kg" everywhere you read pounds, and I stand by it.
It's not that I don't understand what is being said. I think it is confusing to force people into acting as if there is some distinction that is only there in outer space.
All definitions of units of force that I know of go back to expressing it in terms of the effects of gravity on a certain mass.

To those who say weight does not equal force, I ask: How is weight measured? By a scale. What does a scale actually indicate? The downward force being applied to it by the object being weighed.
A scale, which measures weight, and, on earth, mass, does not scan the object, calculate the density of it's molecules, then count those molecules to come up with some figure. It measures the force being applied to it, and we know that that force is the same as the mass, or weight.

Why is it in KN?