# Question about the book 'The Martian', Weir.

sonhouse
Science 24 Nov '15 13:56
1. sonhouse
Fast and Curious
24 Nov '15 13:563 edits
Just started this book, am looking forward to seeing the movie (probably on blue ray, doubt it will still be in theaters).

In the beginning of the book, he talks about a lander being knocked over by a wind storm of 175 kph. The thing that struck me was the low pressure of the Martian atmosphere.

Am I correct in assuming a wind going 175 klicks at 8 torr (roughly Martian pressure) Vs the same speed on Earth, wouldn't the force be linear with pressure, that is to say, suppose a pressure on a body was 1000 Kg on Earth at 175 klicks, Wouldn't then the force on the same body on Mars with the same wind be 1/100th of what it would feel on Earth? Earth=about 760 torr for one Earth atmosphere and Mars, call it 1% for this discussion, then wouldn't the pressure on the same body be 10 Kg on Mars V 1000 Kg for the same wind speed on Earth (175 Kph)?

I guess I am just nit-picking but that seemed like a hole in the plot. Like a disaster happening at the beginning of a story that drove the rest of the story but would never have happened in the first place which places a big hole in the plot.

My visualization of the body having 1000 Kg of force on it from a 175 Kph wind on Earth would be a cylindrical shaped body say 30 meters tall and say 8 meters in diameter, an imaginary rocket set for takeoff weighing in at say 10 tons on Earth but say 3 tons on Mars.

It just didn't seem possible for a Martian wind like that to tip over such a vehicle. Wouldn't the equivalent on Earth be a wind of about 2 Kph? In other words, negligible?
2. Ponderable
chemist
24 Nov '15 15:15
Indeed that was my first idea also, and I still think that that storm is not realistic...it is a storm of narrativum.
3. 24 Nov '15 15:23
Originally posted by sonhouse
Just started this book, am looking forward to seeing the movie (probably on blue ray, doubt it will still be in theaters).

In the beginning of the book, he talks about a lander being knocked over by a wind storm of 175 kph. The thing that struck me was the low pressure of the Martian atmosphere.

Am I correct in assuming a wind going 175 klicks at 8 to ...[text shortened]... vehicle. Wouldn't the equivalent on Earth be a wind of about 2 Kph? In other words, negligible?
When are you Americans going to join the 20th century and learn to use SI units ðŸ˜‰ ðŸ˜›

Ok lets get some handy sources for reference...

http://nssdc.gsfc.nasa.gov/planetary/factsheet/marsfact.html

Surface pressure: 6.36 mb at mean radius (variable from 4.0 to 8.7 mb depending on season)
[6.9 mb to 9 mb (Viking 1 Lander site)]
Surface density: ~0.020 kg/m3
Scale height: 11.1 km
Total mass of atmosphere: ~2.5 x 1016 kg
Average temperature: ~210 K (-63 C)
Diurnal temperature range: 184 K to 242 K (-89 to -31 C) (Viking 1 Lander site)
Wind speeds: 2-7 m/s (summer), 5-10 m/s (fall), 17-30 m/s (dust storm) (Viking Lander sites)
Mean molecular weight: 43.34
Atmospheric composition (by volume):
Major : Carbon Dioxide (CO2) - 95.32% ; Nitrogen (N2) - 2.7%
Argon (Ar) - 1.6%; Oxygen (O2) - 0.13%; Carbon Monoxide (CO) - 0.08%
Minor (ppm): Water (H2O) - 210; Nitrogen Oxide (NO) - 100; Neon (Ne) - 2.5;
Hydrogen-Deuterium-Oxygen (HDO) - 0.85; Krypton (Kr) - 0.3;
Xenon (Xe) - 0.08

https://en.wikipedia.org/wiki/Atmosphere_of_Mars

The atmosphere of Mars is the layer of gases surrounding Mars composed mostly of carbon dioxide. The atmospheric pressure on the Martian surface averages 600 pascals (0.087 psi), about 0.6% of Earth's mean sea level pressure of 101.3 kilopascals (14.69 psi). It ranges from a low of 30 pascals (0.0044 psi) on Olympus Mons's peak to over 1,155 pascals (0.1675 psi) in the depths of Hellas Planitia. This pressure is well below the Armstrong limit for the unprotected human body. Mars's atmospheric mass of 25 teratonnes compares to Earth's 5148 teratonnes with a scale height of about 11 kilometres (6.8 mi) versus Earth's 7 kilometres (4.3 mi).

The Martian atmosphere consists of approximately 96% carbon dioxide, 1.9% argon, 1.9% nitrogen, and traces of free oxygen, carbon monoxide, water and methane, among other gases,[1] for a mean molar mass of 43.34 g/mol.[2][3] There has been renewed interest in its composition since the detection of traces of methane in 2003[4][5] that may indicate life but may also be produced by a geochemical process, volcanic or hydrothermal activity.[6]

The atmosphere is quite dusty, giving the Martian sky a light brown or orange-red color when seen from the surface; data from the Mars Exploration Rovers indicate that suspended dust particles of roughly 1.5 micrometres diameter.[7]

Non-Si
The generic formula for wind load is F = A x P x Cd where F is the force or wind load, A is the projected area of the object, P is the wind pressure, and Cd is the drag coefficient.

A is the projected area of the object. It is the two-dimensional area of the three-dimensional object that the wind is hitting.[4] Its units are feet squared (ft2).

P is the wind pressure in pounds per square foot or psf.[5] It can be calculated using wind speed and a conversion factor.

Cd is the drag coefficient for an object and is determined based on the size and shape of the object subjected to the wind.[6] It does not have units.

The site has more complex formulas used for different purposes and is quite interesting to read.

http://projects.knmi.nl/hydra/faq/press.html

SI
The wind pressure can be approximated by: Pressure = ½ x (density of air) x (wind speed)2 x (shape factor)

The density of air is about 1.25 kg/m3. {for Mars read ~0.020kg/m3}
The shape factor (drag coefficient) depends on the shape of the body. It has order of magnitude 1 and is dimension less.
The wind speed must be expressed in m/s. In that case the pressure has units kg/m/s2, i.e. N/m2.

Fd = (1/2)*p*(v^2)*A*Cd

Fd is the force against any surface or shape.
p is the density of the air,
v is the speed of the air against the object,
A is the area of the object which the air is blowing against,
Cd is the drag coefficient,

This is the same as the last, but the 'shape factor' has been expanded.

Using these last two, we can see that the force is proportional to the air density.

Earth air density is ~1.25 kg/m3
Mars air density is ~0.02 kg/m3 or ~1.6% of the Earth's.

So the force on Mars due to any given wind speed on any given structure is going to be 0.016 times the equivalent on Earth.
The weight of any object on Mars is going to be ~0.378 times the equivalent on Earth [although the mass will of course be the
same].
So overall, the force to weight ratio will be ~0.042 for any given wind speed, or ~4.2%.

However we are talking here about a very high wind speed of ~48.6 m/s [175km/h]
And the force increases by the square of the velocity.

Assuming for simplicity a shape factor coefficient of 1.

We get the force of roughly ~23.6N/m2 or the equivalent of a Force 4 on the Beaufort scale. This is the relevant number if what
is important is the mass, and not the weight.
However if we factor in the difference due to the lower gravity we get an equivalent of ~62.5N/m2 or a Force 5 on the Beaufort scale.

Which shouldn't be an issue for any Earth like structure.

Which means we now get to some intangibles [particularly seeing as I haven't seen the film or read the book yet]...

Is the structure tied down?
Is it shaped to generate lift [can the wind get underneath it?]
Would picking up enough sand in a sand storm increase the density factor enough to make a significant difference?
And, given that it's ultra ultra light, to have been shipped from Earth, is such a relatively gentle wind strong enough to
blow it over?

The wind forces do look to be stronger than you estimated, but still not strong enough to worry any kind of Earth structure.
However, as this is supposed to be a very light structure brought from the Earth [assuming they didn't weigh it down with
materiel from Mars on arrival, which would seem sensible] that has a very large surface area to mass ratio. And particularly
if air could get underneath it, and given Mars' low gravity... It might still be plausible.
4. sonhouse
Fast and Curious
24 Nov '15 15:551 edit
When are you Americans going to join the 20th century and learn to use SI units ðŸ˜‰ ðŸ˜›

Ok lets get some handy sources for reference...

http://nssdc.gsfc.nasa.gov/planetary/factsheet/marsfact.html

[quote]Surface pressure: 6.36 mb at mean radius (variable from 4.0 to 8.7 mb depending on season)
[6.9 mb to 9 mb (Viking 1 Lande ...[text shortened]... ly
if air could get underneath it, and given Mars' low gravity... It might still be plausible.
Nice analysis! Hadn't run into the Beuufort scale before, don't see how a force 4 would topple anything though, even on Mars. I used Kilometers per hour to duplicate the statements in the book.
5. sonhouse
Fast and Curious
27 Nov '15 15:121 edit
Originally posted by sonhouse
Nice analysis! Hadn't run into the Beuufort scale before, don't see how a force 4 would topple anything though, even on Mars. I used Kilometers per hour to duplicate the statements in the book.
This site claims the fastest winds noted on Mars were about 90 klicks, or about 30 meters per second.

That puts a big hole in the plot right there.

http://quest.nasa.gov/aero/planetary/mars.html
6. 27 Nov '15 15:28
Originally posted by sonhouse
This site claims the fastest winds noted on Mars were about 90 klicks, or about 30 meters per second.

That puts a big hole in the plot right there.

http://quest.nasa.gov/aero/planetary/mars.html
Only if you assume that we have seen the strongest winds possible on Mars.

If you allow for this being an exceptional one in a hundred year kind of event
then the events in the story may merely be improbable, rather than impossible.

Given how short a period we have been observing Mars, it would be unlikely that
we have already seen the worst possible Martian weather.
7. sonhouse
Fast and Curious
28 Nov '15 15:52