Why My Rocket Wont Reach Rocksim Projected Altitude

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You point out an important distinction! Water vapor, a gas of individual molecules, is invisible. But mist (or clouds or fog), is liquid water in small droplets (hugely massive compared to an individual molecule). If you can see it, it's not vapor (i.e. a gas).
I wouldn't call it a mist (or clouds or fog) either which has precipitated. It's just humidity that gives the air a glow when the sun is low in the horizon. When Kilauea erupted in 2018, it gave the air a yellow glow from the sulfur when the Kona winds blew from the south. We're bracing ourselves again for whatever Mauna Loa is planning to do.

https://www.usgs.gov/media/images/h...mauna-loa-monitoring-data-august-october-2022
 
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Response from my professor friend. Basically, the water molecules do not displace the nitrogen and oxygen because the water concentrates into micro-droplets between the space created by the heated air. High humidity creates more drag on the rocket. This goes back to my theory that rockets go higher in the desert than they do in the tropics. This assumes the air isn't too dusty. I lived in Vegas for 5 years and it takes several months to get used to low humidity and dusty air.

First let me begin by stating the difference between solids, liquids and gases; A solid consists of atoms or molecules that are close enough to each other that inter-molecular forces dominate. As such, the particles of the solid are pretty much locked in place, and there is not much room between the particles. Liquids on the other hand have a larger space between the particles. There are still inter-particle forces acting on the particles, but they are nowhere near as strong as for a solid. As such, the particles that make up the liquid are free to move round each but are not really free to escape from the neighborhood (that is unless of course, they acquire so much kinetic energy that the can - evaporation). For gases, the particles are so very far apart that they effectively exert no forces on each other. As such, gases expand to fill any container that they may occupy.

My interest in this started when I asked a meteorologist friend of mine if the partial pressures of oxygen and nitrogen change with humidity. The answer was NO. Since pressure (and partial pressures) depend on the populations of particles, this indicates that the particle displacement argument does not hold. When a water molecule evaporates, and goes into the gas above its surface, it does so because there is space for it to occupy. It (the water molecule) does not displace another molecule. Why is there such confusion about this? Basically, the misconception that is being propagated here is that the cart is being put in front of the horse. The thought that high humidity leads to lower pressure should be reversed; lower pressure leads to higher humidity. When heated the atmosphere expands. In fact, this can be seen (measured) from space. Since density is the ratio of mass to volume, this expansion leads to lower density. Lower density leads to a larger distance between particles that make up the gas. Because there is more volume for evaporating water molecules to occupy – and because of LaChatlier’s principle (a system that was in equilibrium when stressed will react by lessening the stress) – the particle population of the gas will increase by including more water molecules. Now, one could argue that the atmosphere is not in equilibrium – in fact, we do have weather – but on a local scale, this argument does work. This is why weathermen are always following low pressure systems (they call them troughs) - low pressure systems gather water leading to high humidity. It is not that large concentrations of humidity produce low-pressure systems. So, yes, higher temperatures correspond to lower densities and consequently higher humidity BUT not because of particle displacements.

Now how does this impact the drag on a rocket? Firstly, we need to consider the polar nature of water. Nitrogen, oxygen, and the carbon dioxide molecules that make up the atmosphere, are all strictly non-polar. Water however, is polar. Because of this, when water molecules have a concentration that is high enough, they can exert forces on each other, and gather to form micro-droplets. Drag in high humidity is because there are many more of these collisions occurring as the rocket passes through the air column. Now for those of you who don’t like this argument, let's look at the math: D = 1/2 C r A v^2. On one hand, you could look at the density (r) and say since the density is decreasing Drag should be less. True to a point, the problem is that the drag Coefficient (C) depends on something called the Reynold’s number, which depends on something called the viscosity. As humidity increases so does the drag coefficient. When the humidity gets high enough, the drag coefficient becomes greater than any increase due to a decrease in density.
 
Response from my professor friend. Basically, the water molecules do not displace the nitrogen and oxygen because the water concentrates into micro-droplets between the space created by the heated air. High humidity creates more drag on the rocket. This goes back to my theory that rockets go higher in the desert than they do in the tropics. This assumes the air isn't too dusty. I lived in Vegas for 5 years and it takes several months to get used to low humidity and dusty air.
Makes sense. Droplets about the size of a wavelength of visible light, ~ 1um, scatter light causing visible haze. Now I wonder what range droplet density can take, i.e. how much mass they add to a given volume of air...
 
This is a pretty well developed academic article dealing with density of air for three conditions: dry air, humid air, cloudy air.
https://journals.ametsoc.org/config...002fatsc$002f68$002f10$002fjas-d-11-085.1.xml
Conclusion?
Humid air is less dense than dry air.
Cloudy air (visible moisture) is more dense than humid air.
Cloudy air may be more or less dense than dry air, but:
“We are once again led to considerations set out following Eq. (15), and to the conclusion that clouds are more often than not lighter than dry air, in the sense that in the field of gravity the smaller density of clouds implies their buoyancy with respect to the same amount of displaced dry air.”
 
This is a pretty well developed academic article dealing with density of air for three conditions: dry air, humid air, cloudy air.
https://journals.ametsoc.org/config...002fatsc$002f68$002f10$002fjas-d-11-085.1.xml
Conclusion?
Humid air is less dense than dry air.
Cloudy air (visible moisture) is more dense than humid air.
Cloudy air may be more or less dense than dry air, but:
“We are once again led to considerations set out following Eq. (15), and to the conclusion that clouds are more often than not lighter than dry air, in the sense that in the field of gravity the smaller density of clouds implies their buoyancy with respect to the same amount of displaced dry air.”
All things being equal humid air is less dense than dry air and provides less drag. Professional baseball players know this. 13.2ft more distance on home runs with every 15% increase in RH.

https://www.daytondailynews.com/wea...re-home-runs-baseball/oP4c9mGNHtBAo1gYDpFODJ/
 
Response from my professor friend. Basically, the water molecules do not displace the nitrogen and oxygen because the water concentrates into micro-droplets between the space created by the heated air. High humidity creates more drag on the rocket. This goes back to my theory that rockets go higher in the desert than they do in the tropics. This assumes the air isn't too dusty. I lived in Vegas for 5 years and it takes several months to get used to low humidity and dusty air.

You also have to account for the elevation. Many desert communities, such as Vegas, are a few thousand feet above sea level. Air is ~91% as dense at Lake Lucerne as it is at the beach.
 

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