My math-fu is weak

[shadowdragon]

while looking at c/g lifters and trying to get a handle on what to tell my players when the c/g isnt doing exactly what they expected, i decided it would be a good idea to be able to tell them at what altitude they are hovering with c/g at full power, based on gravity and atmospheric density modified by ship mass and altitude, just in case they asked. now i know full well that once i figure this out, they will NEVER ask me, but if i dont, they will ask at every inopportune moment. so- HALP HALP HALP!!!!

i need an Excel equation to calculate mean change based on a reduction of 63.2% per 7640 units.. i know that no one here is a math wiz or anything like that :devil: but any help would be appreciated..........

(and that is a mean density change of -63.2% per 7.64 km at 1g with average atmo density of 1.292 at sea level)


tank you

next we tackle barometric changes!!!

 

[aramis]

Here's a link to a page with calculations for hot air balloons...
http://www.overflite.com/thermo.html


1.251kg/kl @ D=1 and T=282°K

So...
some rought
mass displaced = V * D * 0.353/T
where V is volume, D is base density in atmospheres at present location and T is in degrees kelvin, and mass is in tons.

You need a mass displaced equal to mass * (1-CGfactor. )

 

[shadowdragon]

so would it be bad form for me to just use the average temp of the planet for a quick and dirty result?

edit: on second thought- this helps with sea level density changes due to temperature (which i can have LOTS of fun with) but it doesnt address the density according to altitude which is the crux of my problem. i have two different formula to base calculations on, i just cannot figure out the formula- 50% drop in density every 5.6km (50% atmosphere mass) and 63.2% drop in density every 7.6km (average scale height of earths atmosphere below 70km).....*sigh*

my math-fu is weak. i cannot brain- i have the dumb


and a second question- would the night time temperature drop be higher for planets with a longer rotation than 24hrs? would it scale or be another damn exponential function?

 

[Captain Midnight]

Don't worry about the details; if the CG unit is providing an upward force equal to or higher than their weight, they'll stay aloft, although there may not be a lot of force left over to provide forward acceleration. The equations for lift will only make a difference if you're counting on a buoyant force to lift you (e.g., a hot-air balloon), or if you're counting on lift generated by the passage of air over the surface area of a wing.

Buoyant force is equal to the weight of the displaced fluid, so a 200-dton ship (just to use an example) gets a buoyant force equal to (200 dton) * (500 ft^3 / dton) * (0.075 pounds-force/ft^3) = 7500 pounds of force at sea level; reduce that as you go higher, and it quickly becomes clear that buoyant forces are unlikely to matter for any flying body in a Traveller setting. (There might be a division by 32.2 in there to account for converting pounds-mass to pounds-force, but after a hard day at work and two glasses of wine, I can't be bothered to check. Sorry.)

Lifting force depends on the square of velocity WRT the fluid, so if they're hovering, that will be zero by definition.

In other words, the lift generated by their CG unit is going to be what really decides whether they fly or they fall. Wings or some other control surfaces might allow a controlled descent, but without a significant source of lift, gravity will exert its will upon them in a manner most definite.

 

[aramis]

Midnight: CG doesn't provide thrust; given the term, it implies either TNE or T4 rules, in which case, it eliminates 98% of the weight (by reducing gravity binding). Bouyancy is a real issue then.

Simple method, not as accurate as accounting for temperature:

1.25kg lift per cubic meter per Atm. 16.5kg per Td.

With 98% gravity disconnect, that's Atm*825kg/Td
So at 1.2atm, 990Kg/Td. They simply do not float, given the typical baseline mass of about 1500-2000kg/Td.

 

[far-trader]

Just goofing around and wondering aloud...

Could it not be simplified...

CG negates enough gravity that:

1. Dense atmospheres result in neutral buoyancy for heavy vessels, positive buoyancy for medium and light vessels.
2. Standard atmospheres result in neutral buoyancy for medium vessels, positive buoyancy for light vessels.
3. Thin atmospheres result in neutral buoyancy for light vessels.

Heavy vessels are loaded armored vessels.

Medium vessels are loaded unarmored vessels, or unloaded armored vessels.

Light vessels are unloaded unarmored vessels.

Atmosphere drops one category for each 1km x Size (so Earth, a size 8 world with standard atmosphere is treated as thin atmosphere at 8km altitude, and negligible at 16km)

Airframe allows gliding if neutral buoyancy.

Streamlined allows gliding if positive buoyancy.

Unstreamlined allows no gliding.

 

[aramis]

Dan:
Given the TNE FF&S definitions, no, it really can't.
Until you hit about 2atm, you're not going to float a starship with 98%.
At 99%, you can float an empty cargo ship... but not a warship... in 1atm...

Essentially, TNE/T4 Contragravity is a way to escape with much less fuel (since you are not having to overcome the full gravity); you still need significant thrust to counteract the rest, but you're only needing a fraction of a G to counter the downward accelleration of gravity.

MT and T20 gravitics tend to be thrusters, using some form of gravitics. Essentially, reaction drives using the planet as reaction mass. T4 has these available as well. Which is why a T4 design can be totally gravitic... CG makes the frightful T4 gravitic thrusters sufficient for use on world.

 

[shadowdragon]

thanks captain and dan- when quik and simple will do i will keep those answers in mind. unfortunately, i am smart enough to see the problem with the general statements "contra-grav negates the gravitational force of over 99% of the ships weight" and "it will allow hovering due to bouyant force" (paraphrased). what altitude? what is "sufficiently dense"? yada yada yada.
even more unfortunatly i am dumb enough to try and figure it out. blech
the answer i came up with is to stick with the 50% drop in density at each 5600m altitude idea, and for the general density at x altitude, i divide x by 5600 (lets call that number z) and then multiply the standard density at sea level by 0.5^z. it seems to work ok enough for me....i can also figure the rough density of the vehicle and get an approximate hover altitude based on atmo density. if anyone is interested i can post those calculations....

now for the fun part
gravity and atmo pressure
how do these two data points effect density?

i use astrosynthesis imtu and i have gravity and atmo pressure, but i dont think it translates straight across to density (it only would if i wasnt trying to figure this out).

 

[Captain Midnight]

now for the fun part
gravity and atmo pressure
how do these two data points effect density?

Check out this article on scale height for the answer. In short, it's an exponential relationship, with some dependence on local temperature and gravity, atmospheric composition, and atmospheric pressure at "sea level". If "g" is larger, pressure will drop off faster as you gain altitude.

Remember your ideal gas laws, too; pressure, density, and temperature are all related.

 

[shadowdragon]

thanks captain but i have one last question for you....

which part of "my math-fu is weak" eluded you?:rofl:

ideal gas laws...yeah
i looked at em. lots of letters

 

[overflite]

Thermo Gas & Elevation

overflite/thermo altitude adjustment formula for earth ...

Pressure Change = 1 - ( ( Altitude - in K-feet ) / ( 27 + ( Altitude - in K-feet / 2 ) ) )

Increasing 27 by +1 in a regular fashion corrects the formula for higher elevations. To 50k+ feet and presumably even higher. Hence avoiding more complex reckonings. While staying close to reality.

For other planets figure out why 27,000 feet is the factor that works for earth and adjust. Presumably it is some even multiplier of sea level pressure. Where the math just happens to work out right.

For temperature (Charles Law) ... consider that air at 175 F (635 Absolute F) weighs exactly one ounce per cubic foot. Similarly any gas at some temperature also equals an exact weight per cubic foot.

That temperature is the so-called Factor. Divide by the ambient temperature to get the weight per cubic foot.

This system avoids having to include gravity and acceleration and metric and other complexities.

 

[Captain Midnight]

Truthfully, if you're not up for solving exponentials (and that's perhaps more work than you may want to do for something this offhand), then you need to come up with a quick-and-dirty rule of thumb. For this one, buoyancy isn't going to cut it in anything resembling a Terran atmosphere; it might allow you to descend at something less than terminal velocity if your vessel is very light and you're not very high up when the CG craps out (as in a few hundred meters, maybe). However, a very light vessel probably won't have the structural strength needed to survive a significant impact with the ground, so the point is basically moot.

 

[shadowdragon]

i forgot something--- when landing on a planet with a CO2 30%/O2 5%/NO 60%/HE 5% atmo, how do i figure the density out? if i need to figure out the mol density of the atmo, how da heck does that work? for some reason i cannot wrap my tiny brain around mol and how it relates to anything else, but i know you can use it to figure g/ml density and such. that one thing right there makes me feel stupid... i KNOW i should be able to understand it but i have never seen an example that would make sense to me- its all greek

 

[aramis]

weighted average of the relative specific gravities of the relevant gasses.

relative densities
absolute mass by volume at STP

BTW, Overflight, I converted the method to metric, since it works mathematically the same, AND is thus consistent with the volumes and masses used in the Traveller line.

 

[dean]

i forgot something--- when landing on a planet with a CO2 30%/O2 5%/NO 60%/HE 5% atmo, how do i figure the density out? if i need to figure out the mol density of the atmo, how da heck does that work? for some reason i cannot wrap my tiny brain around mol and how it relates to anything else, but i know you can use it to figure g/ml density and such. that one thing right there makes me feel stupid... i KNOW i should be able to understand it but i have never seen an example that would make sense to me- its all greek

A very simple level explaination:

The ideal gas law: PV = nRT

(P) Pressure in Pascals * (V) Volume (liters) = number of moles (chemistry) of the gas * (R) the ideal gas constant (8.314472 J/mol/deg K) * (T) Temperature (in Kelvin)

In terms of an atmosphere, the volume is effectively fixed, the number of moles is effectively fixed, and the gas constant is fixed. The pressure is dependent on the size and density of the planet, which determines the gravity acting upon the atmosphere, and the depth of the atmosphere, which determines the amount of mass of the atmosphere that is acting upon (putting pressure on) the person/object on the surface. The the temperature is dependent on a host of factors, determined by the placement of the planet, exposure to sunlight, the atmosphere itself, etc.

The density of the atmosphere in this case is pretty much wholly determined by the Pressure and Temperature.

Density is the mass of something per unit volume.

The density of air, ρ (Greek: rho) (air density), is the mass per unit volume of Earth's atmosphere, and is a useful value in aeronautics. Air density decreases with increasing altitude, as does air pressure. It also decreases with increasing temperature. At sea level and at 20 °C, air has a density of approximately 1.2 kg/m3.

Here's a list of properties of "air"

The basic assumptions made for the 1962 version were:[1]

* air is a clean, dry, perfect gas mixture (cp/cv = 1.40)
* molecular weight to 90 km of 28.9644 (C-12 scale)
* principal sea-level constituents are assumed to be:
o N2–78.084%
o O2–20.9476%
o Ar–0.934%
o CO2–0.0314%
o Ne–0.001818%
o He–0.000524%
o CH4–0.0002%.

* assigned mean conditions at sea level are as follows :
o P = 0.1013250 MN/m2 = 2116.22 psf = 14.696 psi
o T = 288.15 K = 15 °C = 59 °F
o ρ = 1.225 0 kg/m3 = 0.076474 lb/ft3
o g = 9.80655 m/s2 = 32.174 1 ft/s2
o R = 8.31432 J/mol-K = 1545.31 ft lb/lbmol-°R.

If you really want you could calculate the molecular weight of a given volume of atmosphere (say Kg/m3), determine the gravity (force) acting on the atmosphere at a given altitude, and depth of the atmosphere above the given altitude, and then calculate the effect of temperature of the gas at various index depths, but why?

I don't think anybody's Traveller needs to be this "crunchy".

 

[far-trader]

...I don't think anybody's Traveller needs to be this "crunchy".

Quite.

...but it sounds like Shadowdragon has one of "those" players Like my friend who told us the casting time for Featherfall spells (in old AD&D) was too long to save you once you were falling (and this from a couple hundred feet). Obviously not the intent in the game, but factually correct. The intent seemed (to most of us anyway) to be "if you find yourself falling cast this spell and you live".

Same should be good enough for Traveller. Something along the lines of if you have CG and no other lift you sink slowly to the ground in most cases. If your CG fails you crash (and the ref will say how hard to keep the game going, i.e. you live but the ship is a (right-off/scrap salvage/repairable).

Anyway, to those interested please do continue with the detailing, I'm enjoying the reading

 

[shadowdragon]

again with the math:rofl:

ok lets see if i can clean this up a little......lets say the players land on the following planet

planet x

diameter- 5866km
atm 1.64 std (CO2 45%, NO 20%, SO2 18%, He 10%, H2 4%, Trace 3%)
grav 1.23 std
mean temp 145 K
Water/Ice Index 30.23 (% of surface covered by H2O either liquid or solid)
Rotation: 255 hrs

(standard = earth norm)

so. they decide to have the ship hover on c/g to act as a com relay for the various exploration parties, how do i figure, based on atmo composition, gravity and temp, what will be the hover altitude at full c/g, or if it is even possible. on earth the number i am using to calulate mean density at altitude is 5600m, so i need to be able to adjust this based on gravity and possibly atmo composition(?) and mean pressure at sea level.
what temperature variance will i have throughout the day and night based on rotation, which will in turn affect the atmo density.

so i need to figure out the density of the atmo based on the constituant parts, and therefore i am compiling a table of the different elements and chemicals for reference, but i dont know how to use it...yet

yes i know this is more crunchy than most peeps are willing to get, but once i figure on some SIMPLEpyeah right!) formulae for figuring this out it will all be loaded into excel for me to punch in some numbers and get an answer....

and since i have players who are interested in the crunchy side of things this allows me to counter their silly ideas to survive my game. when pc's get devious i have more fun killing them.:devil:

the formulae i am currently using are:
density at altitude:
D=D(sea level) x 0.5^(alt/5600)

mean density at sea level:
mass=1000*(std density?)*.3725/T(kelvins, i use mean temp) giving me the density of 1m^3 of air.

my research gave me a number for mean density on earth of 1.292kg.m^3, so i changed the original .353 in the formula to the .3725 to make it work with my numbers whereas i have all of you citing 1.225kg/m^3, should i use that instead?

 

[aramis]

Weighted average method...
CO2 45%, 45x1.59=71.55
NO 20%, 20*1.037=20.74
SO2 18%, 18*2.264=40.75
He 10%, 10*0.138=1.38
H2 4%, 4*0.0696=0.2784
Trace 3%, 3*? (~1)=0.03

total weight 134.73039999999997
divide by 100 = 1.347 relative mass... roughly... +.03 or so..
about 1.7417227199999998 kg/m³ or 24kg/td; it will bouy (at 273.15°K and 1atm) about 1.2TonsMetric per Ton Displacement with Contragrav disconnect. Assuming a size 8 world like earth, it will lift about 1.5 tons per TD at surface....

 

[ThunderChilde]

I have nothing useful to offer other than a few questions and an observation.
1. What system? There seems to a general unstated understanding of what everyone is talking about, I really haven't a clue.
2. Is this really that important? Seems to be an awful lot of work for little gain, unless this is an excersise in improving your Math-Fu.
3. Um, if they are leaving the ship on CG this way, why can't the drives handle any fractional thrust needed for station keeping?

I am really at a loss on the whole discussion of floating and loss of lift at altitude thing, and what possible impact density has on a ships that probably masses 1200 displacement tons or more if it were a sea going ship. This is really obtuse to me. It hovers or it falls, it works or it won't, it's an if then statement, a binary solution.

This is a game fer gosh sakes, just make a call and stand by it as the ref.

 

[shadowdragon]

[FONT=arial,helvetica][/FONT]
aramis- where did you come up with those numbers btw? they dont match anything i have found so far......

1. the system is a bastardized version of t20 but all forms of traveller can be used as a base,

2. i use astrosynthesis for mtu and while it is not critical information to know for general gameplay, i also use excel for a lot of data tracking so it isnt all that complicated to figure out, once i have the formulas. i never took physics or chemistry or anything else that would have taught me this or even the fundamentals leading up to it. it is not important per se, but i like the little details. as for improving my math-fu- life is a lesson to be learned. when i stop learning new things, it will be time to burn me..

3. yes m-drives can be used for that, except not all ships imtu use m-drives (only by pure luck (gm fiat) are they in a tl10 starship (prototype), the actual everyday average is late tl8-early tl9). the ship they will be in later (they dont get to keep this one) uses Heplar thrusters..

it is not an if then statement, nor is it a binary argument. i prefer not to run my games by fiat, as it bugs the hell out of me to play in games that are. so, since as i said before i have gearhead players, and i am a tad of a gearhead myself, its something to learn, and i dont mind being that crunchy, and if i dont figure it out i am guarenteed to have to make a fiat descision that someone will remember when i do it different the second time..