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This has a look of an empirical formula. The overall form might, indeed, be motivated by something from statistical mechanics, but odds are, numbers just come out from fitting this curve to data points. Outside of making this formula fit the data, these numbers have no meaning.

Edit: Quick search confirms that this is derived from empirical formulas: https://en.wikipedia.org/wiki/Arden_Buck_equation

Edited by K^2

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1 hour ago, K^2 said:

This has a look of an empirical formula. The overall form might, indeed, be motivated by something from statistical mechanics, but odds are, numbers just come out from fitting this curve to data points. Outside of making this formula fit the data, these numbers have no meaning.

Edit: Quick search confirms that this is derived from empirical formulas: https://en.wikipedia.org/wiki/Arden_Buck_equation

I don't think that is precisely correct.

I mean, first of all, it's clear that 273.15 is a correction to Kelvin.

And the reference that Ars actually posted shows some of the derivation. It does start from what is probably an experimentally-derived correlation for saturation pressure versus temperature, but then it factors in physical values for water (molecular weight of 18.02) and ideal gas law relationships and ends up with the equation as described.

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44 minutes ago, mikegarrison said:

I mean, first of all, it's clear that 273.15 is a correction to Kelvin.

Because the original empirical equations were derived in Kelvin, because, obviously. Then somebody combined these empirical relationships and converted the units to get a convenient humidity formula, which is why you get a few familiar looking numbers in there mixed in with the rest. But these start with Buck's relations, and the numbers in these are purely from data. You cannot derive these from fundamental properties of materials involved. The fact that you later did a bunch of math on them to convert to a different set of units doesn't magically make this formula less empirical.

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Yes, I just read Buck's 1981 paper, and it's pretty clearly a curve-fitting exercise. But the equation that Ars posted isn't Buck's equation.

Quote

Strategy for computing absolute humidity, defined as density in g/m^3 of water vapor, from temperature (T) and relative humidity (rh):

1. Water vapor is a gas whose behavior approximates that of an ideal gas at normally encountered atmospheric temperatures.

2. We can apply the ideal gas equation PV = nRT. The gas constant R and the variables T and V are known in this case (T is measured, V = 1 m3), but we need to calculate P before we can solve for n.

3. To obtain a value for P, we can use the following variant[REF, eq.10] of the Magnus-Tetens formula which generates saturation vapor pressure Psat (hectopascals) as a function of temperature T (Celsius):

Psat = 6.112 × e^[(17.67 × T)/(T+243.5)]

4. Psat is the pressure when the relative humidity is 100%. To compute the pressure P for any value of relative humidity expressed in %, we multiply the expression for Psat by the factor (rh/100):

P = 6.112 × e^[(17.67 × T)/(T+243.5)] × (rh/100)

5. We now know P, V, R, T and can solve for n, which is the amount of water vapor in moles. This value is then multiplied by 18.02 – the molecular weight of water ­– to give the answer in grams.

6. Summary:
The formula for absolute humidity is derived from the ideal gas equation. It gives a statement of n solely in terms of the variables temperature (T)  and relative humidity (rh). Pressure is computed as a function of both these variables; the volume is specified (1 m3) and the gas constant R is known.

You can see here that they use a the "Magnus-Tetens formula" to get Psat, then they derive the rest of the equation from the ideal gas law and the physical characteristics of air and water.

The equation you referenced is a replacement for step 3. It's a different equation to find Psat as a function of temperature. That's still only one step of linking RH to absolute humidity.

Edited by mikegarrison

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Small fireworks rockets are basically solid fuel rockets, like a drastically downscaled version of Space Shuttle's SRBs (Only much less sophisticated). If a civillian pick Space Shuttle's SRBs as reference and try to upscale the size of regular fireworks rocket into SRB size, at which point the size of upsized firework rocket becomes illegal to own by civillian and no longer classified as fireworks and start to classified as actual rockets? (Because when it comes to firework rockets, the tiny ones that fits into your hand and the one attached to external tank is basically similar in operating principle: burn all propellant until there's nothing left)

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1 hour ago, ARS said:

Small fireworks rockets are basically solid fuel rockets, like a drastically downscaled version of Space Shuttle's SRBs (Only much less sophisticated). If a civillian pick Space Shuttle's SRBs as reference and try to upscale the size of regular fireworks rocket into SRB size, at which point the size of upsized firework rocket becomes illegal to own by civillian and no longer classified as fireworks and start to classified as actual rockets? (Because when it comes to firework rockets, the tiny ones that fits into your hand and the one attached to external tank is basically similar in operating principle: burn all propellant until there's nothing left)

Judging by the model rocketry code, I’d say that more than 4 oz (~110g) would require a permit. I don’t know what sort of permit is required for amateur rockets

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https://www.nar.org/high-power-rocketry-info/

Quote

A rocket exceeds the definition of a Model Rocket under NFPA 1122 and becomes a High Power Rocket under NFPA 1127 if it:

Uses a motor with more than 160 Newton-seconds of total impulse (an “H” motor or larger) or multiple motors that all together exceed 320 Newton-seconds; or

Uses a motor with more than 80 Newtons average thrust (see rocket motor coding); or

Exceeds 125 grams (4.4 ounces) of propellant; or

Weighs more than 1,500 grams (53 ounces) including motor(s); or

Uses a hybrid motor or a motor designed to emit sparks; or

Includes any airframe parts of ductile metal.

Note that high powered rockets are not illegal to own by civilians. They do however require licenses and permits.

Edited by mikegarrison

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34 minutes ago, mikegarrison said:

Exceeds 125 grams (4.4 ounces) of propellant; or

I was close, I was going by ~30 year-old memories. But the max mass went up a lot, I seem to recall it was 16oz max. But again, that’s old NAR code

Edited by StrandedonEarth

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Pretty cool 10 minute overview video of Curiosity's journey that Youtube recommended to me today:

Quote

We follow the Curiosity Rover on Mars as it climbs up a Martian mountain named Mount Sharp. We have selected only the clearest footage from Mars to give you a sense of actually being there alongside Curiosity. All the places that NASA has explored have been given nicknames, which you will see in the video. Some of the images have been 'white balanced' by NASA to give geologists a clearer view of the rocks.

 

 

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On 2/14/2020 at 12:57 PM, ARS said:

Small fireworks rockets are basically solid fuel rockets, like a drastically downscaled version of Space Shuttle's SRBs

Firework rockets and most hobby model rocket engines are based on gunpowder or something similar, and have exhaust velocity around the speed of sound. You'll notice that they have no bell on their nozzle, because the later only makes sense with supersonic exhaust. Exhaust from SRB is 5-6 times faster, which also means they operate with way higher pressure. Outside of both being solid fuel motors, they are actually very, very different rockets. You can launch an SRB into space. You cannot launch a firework rocket into space, no matter how big you make it.

 

On 2/14/2020 at 12:43 AM, mikegarrison said:

Yes, I just read Buck's 1981 paper, and it's pretty clearly a curve-fitting exercise. But the equation that Ars posted isn't Buck's equation.

You can see here that they use a the "Magnus-Tetens formula" to get Psat, then they derive the rest of the equation from the ideal gas law and the physical characteristics of air and water.

The equation you referenced is a replacement for step 3. It's a different equation to find Psat as a function of temperature. That's still only one step of linking RH to absolute humidity.

Tetens formula is another empirical formula, which is also just a result of fitting. Except, you can clearly see that they are using Buck's parameters, which might actually make the resulting equation they give not only empirical, but also incorrect. Though, it's probably within error bars, anyways.

In order for formula to be anything but empirical, and for the constants within to have meaning, it has to be derived from first principles, with only numbers present being either fundamental constants or unit conversions. For example, the ideal gas constant is just Boltzman constant per mole. Both of these are just unit conversions, and basically relate temperature to kinetic energy of a mole of gas. In natural units, R = 1. That makes Ideal Gas Law an actual first principles equation.

If you take observational data, fit it to an arbitrary formula, and get the parameters that way, no matter how much derivation and manipulation you do afterwards, it's just an empirical formula. And the parameters in it are just as arbitrary as the initial fitting parameters were. There is no hidden meaning behind any of them.

Empirical formulas are useful. I don't mean to knock them. But when somebody asks what the numbers in the formula mean, the answer is nothing. They are just fitting parameters to make the observation data fit the equation. No matter how much additional massaging of them you've done to fit your particular use case.

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10 hours ago, K^2 said:

Firework rockets and most hobby model rocket engines are based on gunpowder or something similar, and have exhaust velocity around the speed of sound. You'll notice that they have no bell on their nozzle, because the later only makes sense with supersonic exhaust. Exhaust from SRB is 5-6 times faster, which also means they operate with way higher pressure. Outside of both being solid fuel motors, they are actually very, very different rockets. You can launch an SRB into space. You cannot launch a firework rocket into space, no matter how big you make it.

Randal Monroe did the calculations based on Estes E9-4 model rocket engines and determined that a 30 stage rocket the size of a tow truck could deliver a squirrel into space (i.e. suborbital).  Going into orbit was roughly impossible.

I'd claim that as long as you limited yourself to "gunpowder fuels contained by cardboard-based tubes", you could get rid of most of the stages with much larger rockets (you'd still have issues with the Isp of gunpowder and the thrust limits of your cardboard) and get rid of most (but still leave plenty) of the engineering nightmare with such larger rockets.  I also suspect that the remaining engineering effort involved would be higher than a putting a "real rocket" payload into orbit.

https://what-if.xkcd.com/24/

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Yeah, I should have clarified that by "launch into space," I mean establishing an orbit. Thank you for that correction.

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Appliance question: We received this Sunbeam "Teadrop" tea-maker (now discontinued) for our wedding over 13 years ago, and the hotplate on it finally quit. I believe I've narrowed it down to this component circled in red:

RvFhpdM.jpg

Using my circuit tester set to measure resistance (as a continuity test), the leads on either side each make a complete circuit to their respective blades on the wall plug (power switch on, of course), but there is no circuit between the two leads themselves. It is mounted to the heating element. It's my assumption that inside that bit of white plastic is a thermostat, to keep the element from overheating, and therefore it would be dangerous to bypass it. I have removed it, and if the white kinda powdery goop between the piece and the bracket is some sort of thermal paste as I suspect (same stuff between the element and the bottom of the hot plate), then that should confirm my theory that it is some sort of thermostat.

Just typing out this post and preparing to ask for advice jogged my brain to remove the thing and do some googling. I may be able to find a replacement "thermodisk" tomorrow (stat holiday today). I hope so, anyways. We've located some used Teadrops for sale, but they're not nearby. There's one  on Amazon asking almost $300, rofl. That should tell Sunbeam that discontinuing this product was a mistake, because those who use these machines love them.

So yeah, I had a question, but I've answered it myself, I think. But feel free to confirm I'm on the right track!

Edited by StrandedonEarth

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4 hours ago, StrandedonEarth said:

Appliance question: We received this Sunbeam "Teadrop" tea-maker (now discontinued) for our wedding over 13 years ago, and the hotplate on it finally quit. I believe I've narrowed it down to this component circled in red:

RvFhpdM.jpg

Using my circuit tester set to measure resistance (as a continuity test), the leads on either side each make a complete circuit to their respective blades on the wall plug (power switch on, of course), but there is no circuit between the two leads themselves. It is mounted to the heating element. It's my assumption that inside that bit of white plastic is a thermostat, to keep the element from overheating, and therefore it would be dangerous to bypass it. I have removed it, and if the white kinda powdery goop between the piece and the bracket is some sort of thermal paste as I suspect (same stuff between the element and the bottom of the hot plate), then that should confirm my theory that it is some sort of thermostat.

Just typing out this post and preparing to ask for advice jogged my brain to remove the thing and do some googling. I may be able to find a replacement "thermodisk" tomorrow (stat holiday today). I hope so, anyways. We've located some used Teadrops for sale, but they're not nearby. There's one  on Amazon asking almost $300, rofl. That should tell Sunbeam that discontinuing this product was a mistake, because those who use these machines love them.

So yeah, I had a question, but I've answered it myself, I think. But feel free to confirm I'm on the right track!

Yup. Looks like a thermostat. The replacement part (or equiv.) should be less than $10 even at retail pricing.

Edited by mikegarrison

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