Force and gravity

Ruler.  (Cropped from the original image by Ejay in . License: CC Share Alike 3.0)
Ruler. (Cropped from the original image by Ejay in . License: CC Share Alike 3.0)

In this world, the unit is often the source of confusion. Climbing is no exception. As an example, here is an extract from Andy Kirkpatrick's solo attempt in Troll Wall, where he had a hard time as vividly described in his own words:

[After hand-drilling a hole to place a bolt:]

I slid the bolt onto the hanger, then pushed it into the hole, but found it was a little too big to fit easily, so tapped it in with my hammer. I felt it trying to resist, but eventually felt it begin to give way. Then, after only a centimetre, it started to bend.

I'd blown it.
My first bolt was a dud.

[Then, in the third attempt:]

Tap tap tap.

I held it up against the hole and tapped it — just a little — striking it as if it was made of glass. Gently. Carefully. With love.
As if my very life depended on it.
The bolt bent.
I couldn't feel my knees.

[Andy Kirkpatrick:
Cold Wars — Climbing the fine line between risk and reality (2011)]

Why was that? Because the sizes of drill and bolts are not consistent with each other — one is in metric (like milli-metre) and the other is in imperial (like inch).

In wider fields, there have been consequences in a grand scale. Arguably the most famous one is Mars Climate Orbiter developed and launched by NASA in 1998. The mission failed ultimately due to the inconsistency in the units used in a crucial software — metric and imperial — which means the waste of some 660 million US-dollars.

Or, close to you, I am sure you have encountered the cases feet and metres were confused, if you climb in Britain regularly. You had been told or believed it would be only 30 feet, but it turned out to be 30 metres, and so on.

Units are like language. If two parties speak different languages to each other, and if they believe they are speaking the same language, that only produces a confusion and miscommunication. Imagine an American guy talking about pants, then what he means is probably not knickers…. Let's make the units right always.

Unit of force

So, here in this post, I summarise arguably the most important physical unit used in climbing, as the starting point.

First, throughout all my posts I only use the metric unit, called SI (or MKSA) unit, and I do not use imperial ones. Climbing is the world-wide activity, so let's keep them universal.

The standard unit for the force in the metric system is Newton, denoted as N. In the field of climbing, kN, namely the unit of 1000 N, is usually used, as that is the range we encounter in most of the real climbing situations.

What is 1 kN? It is the gravitational force the earth pulls an object of the weight of roughly 102 kg (or 225 pounds in the imperial unit, or roughly 16 stones) at the surface towards its centre, namely, vertically downward. As a rough and easy-to-remember guide, the static weight of 100 kg corresponds to 1 kN.

1 kN ≈ 100 kgf

A little deeper in physics

For those who have a basic knowledge of physics, this relation is easy to remember. For the gravitation, F = mg, where F is a force in Newton, m is a mass in kilo-gramme and g is the gravitational-acceleration constant of 9.8 [m/s²] (you must have learnt this value to death!). Hence 1 kg corresponds to 9.8 N, or more roughly, 10 N. So, 100 kg corresponds to 1 kN.

There is another expression of the force: kgf, which stands for kilo-gramme force. As you would expect, 102 kgf is 1 kN. I might use this unit occasionally, quoted in a pair of parentheses as a reference, following the main value in (kilo-)Newton, to help readers have a clearer idea of the number, but will never use this unit alone.

In some (climbing) books or literature you may see an expression like the force of 102 kilo-gramme. That is wrong. kilo-gramme (or gramme, tonne etc) is a unit of mass and not that of force. They are different. As an extreme case, in the International Space Station (ISS) you would happily hold a matter of 300 kilo-grammes or whatever, because nothing has a weight in the ISS and hence everything floats around unless tied to some structure. So, the expression of the force of 102 kilo-gramme should really be stated as (the force of) 102 kgf, instead, or better, (the force of) 1 kN.

Comment on Physics

Very strictly speaking, in physics inertial mass and gravitational mass could be different from each other, though it could be indeed identical (Equivalence Principle). The former is the measure of how hard a matter is accelerated and the latter is that of how strong it reacts with and generates the gravitational field, or universal gravitation. In reality, it is known both of them are consistent with each other as far as humans have examined so far with the highest precision possible, and there is no evidence they are different.

kilo-Newton in climbing

An adult climber, combined with the gear to wear or carry, typically weighs a little less than 100 kg (or congratulations, if you weigh a lot less than that!). Therefore, 1 kN is the absolute minimum value to support your body weight with a little margin.

For example, RP 0 is rated as 1 kN. Providing the crack in rock the RP 0 is put in is hard and absolutely sound, you could take your weight off completely (in other words, aid-climb) with the RP 0 in a crack, as long as you do it very smoothedly with the absolutely minimum shock load.

The thing is, any jerky move can multiply the applied peak-force by a couple of folds! In this case of RP 0, there is very little margin — 20 per cent only for an averaged adult climber with the weight (with gear) of 80 kg. So, in reality, it would be an absolutely terrifying experience if your life depends on a RP 0, even if the rock is perfect, let alone if not. But if it is RP 1 (rated 2 kN), and if you are sure of the rock and placement, you should be reasonably comfortable to rely on it.

Next post

will be about an application of this measure of force in climbing — required strength of belay anchors.


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