# How can I calculate the density of Mars' atmosphere during dust storms?

I have been searching to try to estimate the air density of the atmosphere on Mars during a dust storm.

I am trying to use this dynamic pressure equation to calculate the pressure on a theoretical structure during a dust storm on Mars.

$$q=\frac{1}{2}\times p\times v^2$$
where
$$q=\text{dynamic pressure}$$
$$p=\text{air density}$$
$$v=\text{air velocity (TAS)}$$

I know the atmospheric pressure on Mars is very small, something like $$600$$ $$Pa$$, and the atmospheric density is small too, around $$0.020$$ $$kg/m^3$$. Sustained wind speeds can be high, around $$60$$ $$mph$$.

My question is, how can I factor the increased density due to suspended dust into this equation?

• These are not the same as your question about the correction due to the dust, but you might find the math and results interesting: Could you feel the wind on Mars? and How feasible is wind energy generation on Mars? and Is wind-power a viable backup power source for Mars One? – uhoh Jan 29 '19 at 22:29
• Yes, not quite the same, but thank you for the resources! :) – RealDiels Jan 29 '19 at 22:34
• You may need to look at mine ventilation engineering or environmental protection documentation. They are two fields that consider at dust laden air - particularly how to mitigate it. From that you might be able to extrapolate something for dusty air on Mars. One problem you will have is the bulk density of the dust-air mixture will depend on how much dust is in the atmosphere. I'm not confident that just considering dynamic pressure & velocity will given you want you want. – Fred Jan 30 '19 at 14:05
• You may need to look into the physics of tornadoes & hurricanes. – Fred Mar 9 '20 at 19:30

One thing you might want to do is be prepared for some low numbers. Even during a storm, the density of Martian dust in the air is much less than that of the gases. According to Martin[1]:

During the peak of the 1977b storm, a total dust mass of approximately 4.3 × 10^(14) g was suspended, equivalent to 4.3 × 10^(−4) g/cm^2, or a layer 1.4 μm thick. During a local dust storm near Solis Planum at LS 227°, approximately 1.3 × 10^(13) g of dust were lofted, equal to about a 6‐μm layer in that vicinity.

The larger density of the local storm still amounts to only about $$0.002\text{ g/cm}^2$$ or $$0.02\text{ kg/m}^2$$. The average surface gas pressure of $$610\text{ Pa}$$ at the Martian surface gravity corresponds to about $$190\text{ kg/m}^2$$ of gas in the air. Martian dust storms get their impressive appearance from the very fine particles of the dust, on the order of a micron in size, which gives a lot of surface area for reflection and scattering of light; and our foreshortened view of the atmospheric dust when we see pictures of the storm from afar.

Reference:

1. Terry Z. Martin, "Mass of dust in the Martian atmosphere", Journal of Geophysical Research: Planets, Vilune 100, Issue E4. https://doi.org/10.1029/95JE00414