Soil Experiments
Attempts To Duplicate The Properties Of Martian Soil, Part 6
At last, we have reached the end of the soil simulation experiments. Everything so far has indicated that the Martian soil seen in many of the images is wet or at least damp. And, simple tests show that in order to produce the texture and appearance of the soil surface, a spray of fine, high speed droplets must be used. No other combination of elements will produce this unique soil surface texture.
It seems to imply that it must rain on Mars, and that the rain drops must be very small and fast. Can we find support for this prediction? To do so, we must find out some things about the Martian atmosphere and how rain is formed on Earth.
Water droplets in clouds will not fall due to their small size and the resistance they encounter in the air. This is because air, like any fluid medium, has a resistance to objects passing through it. This is called "drag". Once the droplets in a cloud begin to come together and form larger raindrops, they pass a critical size and can no longer be supported by the drag. This is when they fall.
The presence of an updraft can allow the droplets to remain aloft for greater periods of time, and this can allow the droplets to become much larger.
For very thin air, the droplets will fall very easily and cannot become very large. Also, for thinner air, the droplets will fall much faster since they do not encounter as much drag, or resistance from the air. On Earth, the droplets can fall with speeds typically between 10 and 25 mph, determined by the size of the droplets. The mathematical description of falling raindrops is fairly complex but can be done with a pocket calculator.
Let's start out with the basic aerodynamics of falling objects.
Any falling body will accelerate due to gravitation. On an airless body like the Moon, that acceleration is "pure"- all you need to know is the strength of gravity and the time something is falling. Technically, the falling body equation is:
V = at where V is velocity, a is acceleration, and t is time. In other words, the longer something falls, the faster it will be moving. On Earth, that speed will increase by adding about 9.80 meters per second to your downward velocity for every second that you fall. On Mars, that will be reduced to about 3.72 meters per second for every second you fall.
But when an object falls through the air, it encounters resistance. The amount of resistance depends on the density of the air, the area of the object falling, and the speed at which it is moving. The object falling will accelerate until the resistance matches the force of gravity- then it can neither speed up or slow down, and has reached "terminal velocity".
The terminal velocity can be determined by this equation:
Vterminal = sqrt { (mg) / (AD1/2P) } where m is the mass of the falling object, g is the force of gravity, A is the cross sectional area of the falling object, D is the drag coefficient, and P is the density of air.
On Earth, the air density varies with altitude, but skydivers use the value for the altitude they are at, or where they expect to be when they open their parachutes. There would be no real difference on Mars, and the equations needed to do skydiving on Mars are not hard to do.
To determine the resistive force on a falling body, you would calculate the following equation:
R = (mgv2) / Vterminal where R is resistive force called drag. Drag is different for different atmospheres. The density of the atmosphere and the temperature as well will each play parts in determining the drag coefficient. In order to figure it out, we need to know about the atmosphere at various altitudes. What we need is an atmospheric model of the Earth, and one for Mars. This will provide us with the air density values we need. Here is an atmospheric model for Earth, and here is one for Mars.
Once we have done these equations, we find that for Earth, a typical terminal velocity is about 192 kph (or 120 mph). For Mars, however, due to the thinner air, the terminal velocity works out to about 990 kph (or 618 mph). In other words, things will have roughly 5 times the terminal velocity on Mars that they do on Earth. This result holds for raindrops, just as it does for human skydivers.
Now, we have determined that raindrops on Mars would have to fall when they are smaller because there is far less drag in its atmosphere. This confirms that Martian rain would have small droplets. Also, we have determined that rain on Mars would have to hit the ground about five times faster than rain on Earth, once more due to the lack of drag. Where rain on Earth hits at 16 to 40 kph (10 to 25) mph, Martian rain would hit at between 80 to 200 kph (50 and 125 mph).
An interesting result of the terminal velocity calculations shows that larger droplets, if they could form in the Martian atmosphere, would break up into smaller droplets due to the drag that they would encounter falling at high speeds.
To explore flight characteristics on Earth and on Mars, you can use this flight simulator written by NASA.
References
Dynamics of falling raindrops -
1 Department of Physics, West Virginia University, VA, USA
2 Department of Mathematics, West Virginia University, VA, USA
Small Raindrops: Falling Bodies With Weak Air Resistance - James Martino, Johns Hopkins University
Skydiving On Mars - Kim Gordon