# If an astronaut got stuck in the middle of a space station, can he propel himself towards a wall by blowing air out of his mouth?

Consider the astronaut as floating in the middle of the "Kibo" (ISS module) without him having any initial motion. The module has a diameter of 4.2 m (inner), and the goal is to reach any of the module's walls by only blowing air through his mouth. Is it possible for him to reach any wall? If it is, how long would it take him to do it, given that he inhales for about 4-8 seconds and exhales it fully for nearly half a second?

• Comments are not for extended discussion; this conversation has been moved to chat. Aug 20, 2020 at 16:39

Just a naive and very approximate calculation:

If you neglect friction, google that human lung capacity is around $$6\text{l}$$, air density around $$1\text{kg m}^{-3}$$, take the inhalation time $$6\text{s}$$ and approximate that the nostrils have area around $$1\text{cm}^2$$, then the velocity of inhaled air will be $$\frac{6\text{l}=6000\text{cm}^3}{6\text{s}\cdot 1\text{cm}^2}=10\text{m s}^{-1}.$$ The momentum transferred on inhalation is thus around $$10\text{ m s}^{-1}\cdot 0.006\text{m}^3\cdot 1\text{kg m}^{-3}=0.06\text{kg m s}^{-1}.$$

The same computation on exhalation with duration $$0.5s$$ gives $$0.72\text{kg m s}^{-1}$$. The momentum gained is thus $$0.66\text{kg m s}^{-1}$$, which for man of weight $$66\text{kg}$$ gives you velocity $$0.01\text{m s}^{-1}$$.

So on one breath you would reach the wall (assuming you are in the middle and have a distance around $$2\text{m}$$ to go) in $$200\text{s}=3\text{min}20\text{s}$$.

Now, you can make a breath each $$7\text{s}$$, which adds another $$0.01\text{m s}^{-1}$$ to your velocity. Thus the distance traveled is $$7\text{s}\Rightarrow 7\text{cm}$$ $$14\text{s}\Rightarrow 7\text{cm}+14\text{cm}$$ $$21\text{s}\Rightarrow 7\text{cm}+14\text{cm}+21\text{cm}$$ And so on. From this the time for traveling distance $$2\text{m}$$ is around $$50\text{s}$$.

• No one trying this would breath in through their nostrils. They'll use their wide open mouths instead. The open-mouthed inhalation allows quick intake of lots of air without any significant momentum transfer, so the 6s figure is way off. On the other hand, people would also use their mouth for blowing, which tends to produce a larger opening than the nostrils. This allows for better focusing of the air stream, but reduces the momentum transfer on the blow action. Aug 19, 2020 at 10:18
• @cmaster-reinstatemonica: Are you sure that the torque component wouldn't affect the linear momentum? It seems that some of the energy would go into increasing the angular momentum if the expelled air stream is not in line with the center of mass. Similar to how a cylinder moving down an incline will accelerate slower when rolling than if sliding without friction. Aug 19, 2020 at 11:59
• Comments are not for extended discussion; this conversation has been moved to chat. Aug 20, 2020 at 16:39