Starship Speed In Atmosphere

[Ishmael]

Last is Cd

The drag coefficient is based on standardized shapes' drag.
I use flat plate for un-streamlined
hemisphere for partially streamlined
sphere for streamlined.
I consider 'airframe' to only allow aero controls and aero lift, but not a level os streamlining.
Compare a WW1 Voisin bomber to a teardrop shape; the teardrop shape is certainly more streamlined than the antique bomber, but the bomber has aero controls and lift.

For simplicity, the base Cd for
un-streamlined = .9
partial streamline = .4
streamline = .1

the final Cd value is modified by the fineness ratio involving length. More specifically, by divided the base Cd by the square root of fineness. The fineness ratio is chosen by the designer when creating the hull/fuselage as in the previous post. Use the best ratio using length.

Cd = base_Cd / sqrt ( fineness )

From the previous post, the example ship had a fineness ratio of 5:1
Partial streamlined, the example hull has a Cd = ~ .4 / sqrt ( 5 ) = ~ .178

Had it been streamlined, it'd have a Cd = ~ .045

--------------------------------------------

Now we have density, frontal area and Cd.
Thrust is simply G's acceleration * ship mass.
Ship mass is taken either from a prefered design ruleset, or by using a common convention that 1 dton mass 10 tonnes ( dton displacement * 10 )

So that's everything we need to fill in the equations for top speed in an atmosphere using the standard drag equation rearranged to solve for velocity.
v = sqrt ( (2*Fd) / (p*Cd*A) )

--------------------------------------------------
whew...
hope that didn't scare anyone off
its much easier in a spreadsheet even though its simple enough for a calculator, pencil and paper

 

[Wil Mireu]

Thanks for posting that - could come in very handy!

What follows is so that people can have some numbers to refer to....

M is the molar mass of the atmosphere and can change depending on composition, so this method will work for any world, from Venus to Mars and even Gas Giants. Traveller's UWP usually assumes that the atmosphere is an oxygen-nitrogen mix. For Earth, 29 can be used. this is pretty close to 79% N2 and 21% O2 ( .79 * 28 + .21 * 32 = 28.84 ). Other worlds will have different numbers, but always less that the minimum molecular weight retained ( Jean's Escape ).

Venus' M is about 43, Earth is about 29, Mars is also about 43 (it's mostly CO2, like Venus. There's just a lot less of it), Jupiter is 2.2, Saturn is 2.07, Uranus is 2.64 and Neptune is about 2.6. (from http://nssdc.gsfc.nasa.gov/planetary/planetfact.html )

So M for gas giants will generally be around 2. Earthlike N2/O2 mixes will be around 29-30. Exotic atmospheres will be around 42-44, if they're full of CO2 - if they're all N2 then it'll be closer to 28-30. That's in grams/mol - for kg/mol, divide that number by 1000.

P is pressure. Surface pressure of the world is a good start, but Mongoose doesn't produce that.

According to the old World Builders Handbook for MT, the pressures break down as follows - pick a number in the appropriate range:

Trace (atm 1) - 0.01 to 0.09 atm
Very Thin (2,3) - 0.1 atm to 0.40 atm
Thin (4,5,E) - 0.43 to 0.75 atm
Standard (6,7) - 0.76 to 1.4 atm
Dense (8,9) - 1.5 to 2.4 atm
Very Dense (C,D) - 2.5 to 750 atm. (atm A and B can have any pressure)

T is Temperature in Kelvin. Again, Mongoose doesn't produce this, but there are a number of methods from world-building that can generate this.

Actually MGT worldgen does produce Temperature - it's on p171 of the MGT corebook (it's not listed in the UWP though). Add 273 to the provided temperature in °C to get the temperature in Kelvin.

 

[Ishmael]

I forgot to include a way of calculating the speed of sound.

for an ideal gas;

speed of sound = sqrt ( 1.4 * 8.3144 * T * 1000 / M )

1.4 is the adiabatic index for diatomic molecules ( that's over my head )
8.3144 is the gas constant
T is temperature in kelvin
M is molar mass in g/mol

for Earth,
Vs = sqrt ( 1.4 * 8.3144 * 288 / 29 ) = ~339 m/s

ship velocity / Vs = mach number


again, to "1000" in the equation is to convert g/mol to Kg/mol

 

[spidersrepublic]

Great work ishmael! your equations will help me out heaps, and also blow my players minds with detail!