# How can I estimate the maximum mass that can be safely handled in low to no g?

Many countries, authorities and companies have the concept of a maximum weight limit for manual handling, both to protect their workers and to protect themselves from lawsuits.

Interstellar Shipping Incorporated (I.S.I.) also has such limits, but their requirements are a little more complicated. As they work on ships that may be accelerating or just floating (at anywhere between 0.5 and 0 g) the weight of the objects in question will obviously be lower.

But the mass of the thing won't, which means that it’s inertia will still make it hard and potentially dangerous to handle. On Earth we forget the inertia in many cases because we’re primarily focused on supporting the weight of the thing. In low to no gravity inertia is the main concern and our normal intuition about how to lift is flawed.

The commonly given example in the health and safety briefings is someone straining to pick up a crate of depleted uranium shells in low g, forgetting that they would have to arrest the forward motion of the crate, and crushing all their fingers between the crate and a doorframe when they couldn’t correct it’s course. The employee also caused damage to the frame of the door, for which they were fired (this may be an apocryphal tale).

So the question I.S.I. has for this site is: what guidance should be given about working in low g to avoid injuries, property damage and lawsuits caused by the disconnect between weight and inertia? Assume this is being given for a maximum of two employees (two man lift limit) and anything above that is covered by lifting machinery.

Good answers will include information on maximum safe mass for some g force between 0 and 0.5 g, necessary lifting techniques and (preferably) some description of how those numbers and techniques were arrived at.

Bonus points if the advice is generalisable to any low value of g. If it isn’t please state what value your advice is for and I.S.I. will compile a suitably comprehensive and not at all overly long winded safety guide.

Note: I’ve tried searching for any existing guidance around manual work on the ISS, but failed to find anything of use. If you find any please feel free to use it as a starting point (and include a link so I can add more useless knowledge to my brain!)

• Good question! This reminds me of various times I've read science fiction with scenes of people manhandling very massive objects in microgravity. It's theoretically possible to move multi-ton objects by hand under those conditions, but if you aren't really careful, the inertia can easily kill someone. I think a good answer will look at force needed to slow it to a stop, which will include force needed (if any) to overcome gravity. Apr 12 '20 at 16:37
• I bet you can safely move a crate of depleted uranium shells in zero-g as long as you do it slowly. You just have to move it slowly enough that you can stop its motion before it crushes your fingers. Apr 13 '20 at 0:06
• Also, items need to be internally solid, or stopping a big box will stop it quickly, and then the box will start moving again once its contents reach the box. Apr 13 '20 at 10:01
• @SimonRichter: Excellent point! “Crates must have no unsecured items prior to moving” is going in the manual! Apr 13 '20 at 13:09
• HUH!?! What is the astronut attached to?
– MaxW
Apr 13 '20 at 20:46

## 5 Answers

I remember my physics book in high school quoting an astronaut about moving large objects in space. He said "they are not heavy, yet one feels they are massive!"

Coming to your question:

How can I estimate the maximum mass that can be safely handled in low to no g?

You state it by yourself

Many countries, authorities and companies have the concept of a maximum weight limit for manual handling

Don't be fooled by the fact that the maximum weight on Earth is expressed in kg or pounds, what that really measures is the Newton (thus force) that needs to be exerted to lift a certain mass.

My educated guess for a first attempt would be:

• take the maximum allowed weight on Earth, say 20 kg
• convert it to force, thus 200 N

This is the limit you have to keep in mind. If you are working in 0.1 g, it means a single person can lift a mass of 200 kg while still being safe.

When it's not strictly about lifting, you can refer to the impulse theorem in its non relativistic and constant mass formulation

$$F \cdot \Delta t = m \cdot \Delta v$$

Knowing the mass of the object, the delta v you want to give it and how quickly you want to give it, you can get the measure of the force you need to apply.

I.e. if you want to move 2000 kg at 1 m/s starting from still, you can safely do it if you have more than 10 seconds to apply the force, since you will be applying less than 200 N. Then of course refinement can come after empirical studies based on real cases and statistics show how microgravity affects the space workers.

• Because in 0g I can (following your guidance) lift anything I want. That’s true, but not necessarily safe unless I’m also thinking about how slowly I should move. Apr 12 '20 at 8:52
• That’s the whole thing I’m trying to safeguard against: people not thinking about inertia because they can’t feel the weight, then not being able to stop an object in time because they’ve misjudged the inertia of the object (as we don’t have a nice intuitive feel for it, being so used to weight). Apr 12 '20 at 9:00
• I think calculating in energy would probably be better. If you calculate in force you have a problem at zero acceleration. A crate coming at you at 100 m/s will surely crush you, but will only experience force once it hits you. Building up the speed can be done gradually without ever going over the force limit. Apr 12 '20 at 9:07
• From a safety perspective, I would imagine you have about 1 meter to slow it to zero velocity. That is if you catch the crate with your hands with your back to the wall. Apr 12 '20 at 9:31
• Another problem you will have in zero-g and one takes for granted in g condition: friction. Apr 12 '20 at 11:11

For ease of use in a practice situation you probably only want one unit as a limit. L.Dutch wrote a nice answer based on force, I will try to do the same from an energy perspective.

So I imagine the safety involves not being crushed by big crates. For fingers and such complete other rules apply, as well as for sharp or tiny things (You can't catch a bullet).

So if you are are in danger of being crushed by a crate hurling towards you in zero g you have your arm's length (about 1m) to catch the crate and slow it down to a complete stop. If you can benchpress 80 kg on earth you exert a force of 800 N if you use a gravitational acceleration $$a$$ of 10, according to,

$$F = m a$$.

The work needed to do this can be calculated with,

$$W = F s$$,

where $$s$$ is the distance along which the force is exerted and $$W$$ is the work done in Joule. So bench-pressing 80 kg in earth's gravity costs 800 J.

So 800 J would be the energy limit for objects

So for moving crates in zero g only the mass and velocity matter since they don't experience force until you push against it. So the energy (here we will assume work is equal to energy, basically ignoring the directional component of work) of a crate can be calculated with,

$$E = \frac{1}{2} mv^2$$.

So you can calculate what the maximum velocity of a crate is allowed to be depending on the mass. In practice a table with a certain safety factor involved is probably better. So some safety limit speeds of different masses can be:

Mass (kg)    Max Velocity (m/s)    Max avg. Acceleration (m/s^2)
8             7.1                    100
80            2.2                    10
800           0.7                    1

As suggested by Morgen I have added the maximum average acceleration a worker should apply over 1 m (arms length) to the crate. This is all assuming the worker has some way of counter balancing the force.

So for working safely you would need to remember some numbers and be able to judge the velocity of an object. It works for other gravities as well as long as the force direction of gravity is perpendicular to the plane the crates are being moved in.

• I am deviating from it since those safety limits are meant for a gravity environment. The 800 J is coming from the calculation of based on bench pressing 80 kg. I have a feeling that this should be a stoppable weight, but you can always reduce/recalculate the numbers if you feel the margins are to tight. To me it would amount to stopping a 80 kg crate floating on an air hockey table within a meter. This seems quite reasonable. If you cover the crate with needles with a 1 cm^2 area pointing out it becomes less reasonable. Apr 12 '20 at 14:55
• Defining the limits in terms of maximum safe speed for any given mass is a sensible 0g option. That’s an appendix for the I.S.I. safety manual right there. Apr 12 '20 at 15:44
• @D.J.Klomp: I guess there are two safety factors: How hard should I push before I’m going to hurt myself, and how fast can I go before I’m likely to hurt others. The first is all we worry about under 1g load because we can’t often go fast enough for the second to be an issue! Apr 12 '20 at 19:07
• It feels like this is half the answer. Once you know the max safe energy a thing can have, feeding that back into the appropriate calculations to get the max mass that a standard worker can accelerate to a velocity which would cross that threshold seems like it would complete the answer. Realistically, regs that say, "don't throw something with greater mass than X, using the Approved Yeeting Technique" make much more sense than, "don't catch anything with more energy than X" - mass doesn't change, and can be clearly labelled be safe gravity thresholds Apr 12 '20 at 19:14
• @Morgen The nice thing about this answer is that no matter what size object you're handling, you are allowed to accelerate it using exactly one shove, which means that the person on the other end can also decelerate it to a complete stop using exactly one reverse-shove. You don't really need to worry about acceleration values, since no matter how hard you push, so long as you only push once, you can also stop the object by only pushing once. If you keep the impulse constant, the relationship between mass, speed and acceleration is irrelevant. Apr 13 '20 at 15:37

L.Dutch gave an excellent answer about the basic physics of the situation, so I'll take a different approach.

In no gravity or very low gravity environments, it's unlikely you would be "lifting" or even directly moving heavy objects, in the same manner you are used to on Earth.

Any attempt to push the object will push you back with the same force and you won't stop until you hit into something, any attempt to lift the object would result in it flying "upwards", with you unable to stop it. On Earth we have gravity to anchor us and that gravity restricts our up-down motion (z-axis) and also allows for friction which restricts our (x-y) motion. Thus we see gravity enacts a lot of restrictions on the motion of an objects along it's degrees of freedom.

Of course in Sci-fi you can have some fancy work-around to some of these issues, such as magnetic boots (there are a host of reasons these are impractical IRL), which seem to be popular in sci-fi. But anything short of artificial gravity does not solve the issue.

For objects, whose mass is much smaller than our own, Newton's third law ensures that moving them around in low-g/no-g environments isn't too big of an issue, this can be seen in videos of astronauts/cosmonauts doing their thing on the ISS for example.

But with large (having large volume) and/or massive (having large mass) objects, as compared to ourselves, moving them around safely would be a fairly serious and difficult issue. The speed at which something is moving is not easy to gauge and allowing massive objects to be moved around with no physical restrictions of motion along at least some of their degrees of freedom is a disaster waiting to happen.

In the case of the ISS or space-shuttle, moving large objects in space is accomplished with small rockets and tethers. The same would be the case for moving around crates on the docking bay of a transport ship. The iconic scenes that are a trope of sci-fi in which a wide docking bay has smaller ships docking and taking off while busy crews load and unload crates as seen in films like Star Wars simply couldn't happen in a low-g or no-g environment. (I know there are artificial gravity in most of these films, but I'm using the imagery)

The most likely solution would be a network of cable paths, along which all things are moved along. Crates would be hooked to the cables and guided or reeled along specific paths, junctions would allow paths (and hence the cables the crate is hooked to) to be switched.

There would be guidelines which would be strictly adhered to governing the properties and conditions of the cables and the mass and size of the crates which are allowed on cables of various ratings. Crews would have to adhere to equally rigorous procedures when moving things around. This would remove the burden of manually calculating forces, energies and speeds (presumably on the fly) away from crew members (robots maybe, but certainly not humans) and instead "procedurize" the process to optimize for safety and efficiency.

• So, you’re placing the limit at ‘objects whose mass is much lower than our own’, if I understand your answer. Apr 12 '20 at 15:45
• @Skyler An excellent, point. But rather than counter my point I think this story highlights it. The bulk of moving the Westar was accomplished with the mechanical arm and only the final step of fitting the satellite into the cargo bay had any difficulty. Allen didn't move the satellite by carrying it, but rather he helped stabilize it, acting as an anchor point, while attached to the mechanical arm which was controlled by Fisher. By some accounts the procedure took 90 minutes so the forces on Allen were problem very low. Apr 14 '20 at 1:38
• Sources I used: Apr 14 '20 at 1:39
• hughesscgheritage.com/… Apr 14 '20 at 1:39
• nytimes.com/1984/11/15/us/… Apr 14 '20 at 1:39

I propose that you replace the weight limit in 0g with a limit on moving technique. The key is that putting something in motion and then stopping it will take the same amount of effort. So you encode the following rules of thumb as laws:

1. You push objects while standing in a single spot. No following something with you magnet boots to give it an extra oomph. This means the receiving end can stop the object from a single spot, eg. if they're stuck between the object and a door.
2. Only one person does the initial (and only) push, preferably the physically weakest. Means everyone else can do the stopping push on their own.

You can then safely push ridiculously large things, even the whole space station, but it will have to move atrociously slow.

• Exactly! There should also be a time limit on how long you push/pull, probably not more than 3 seconds. And the administrative rule that goes with it should be: If you violate this rule and live, you will be fired. If you violate this rule and kill, you will be executed. Apr 12 '20 at 23:37
• I was thinking along these lines also but I think this still permits too much energy. It assumes you catch perfectly and that your catching position is just as good as your tossing position. Even if you can do it you're going to have a problem with stopping at exactly the right time, you're probably going to toss it back slowly. Apr 13 '20 at 4:22
• This is similar to what I was going to answer, however, the OP asked for mass not handling procedures so I would add that the maximum mass is that which can be reasonably handled within the procedures and still achieve a velocity high enough that it doesn't float in traffic moving at a snails pace. So there should be a defined minimum (and max) velocity to move through busy rooms and hallways. Apr 13 '20 at 16:30

As D.J. Klomp points out in their answer, the important value is the energy of the object. However, there is a catch: You cannot easily judge the velocity, and thus its energy, in a hand-handling-cargo situation. I mean, when you handle a box, do you think "Hmm, I think this box is moving at 2.4m/s now"? Most certainly not, and even if you did do this estimation, you would not be very accurate with it.

However, another observation comes to the rescue: Humans have a typical max. velocity that they use when handling cargo. And if you combine that max. velocity with a max energy, you get a max. safe mass.

So, let's assume that a worker can safely exert a force of 500N (= 50kg) with their arms, over a distance of 0.5m (about one arm's length). That's 250J. (I'm being much more conservative here than D.J. Klombs answer, we are talking about safety regulations after all!) Now, let's assume that humans move heavy object at a max velocity of 2m/s (that's 7.2km/h - faster than walking, slower than jogging). Then we find a max. weight by solving the formula 250J = m * (2m/s)^2 / 2, which yields m = 125kg.

Now, this is a weight that I can stop from crushing me when my back's against a wall, and I have time to prepare for the impact. A safety regulation, however, must err on the safe side. Now we note that 125kg is actually quite close to the weight of a human being. Which makes sense, for we routinely handle an object of our own weight all day long! As such, I would expect the I.S.I. to set the max. safe weight for manual handling to 75kg. (This is the weight that's typically assumed for an average human being. For instance when declaring how many persons are allowed to ride a lift together.)