Kerbal atmosphere Mach chart.

[Kerbal01]

is there a chart for determining the Mach number of a given speed in kerbins stock atmosphere? I know that Mach 1 is about 200 m/s. you would think that some thing like this would exist.

[Newt]

The stock atmosphere as far as I know really ignores the concept of the speed of sound; there are no Mach effects simulated. You could calculate based on the pressure/temperature by altitude, but I am unaware of any such tables, and it would have no bearing on gameplay (unless it is modified with the rest of the aerodynamics...).

[Zuqq]

I'm not positive but after a quick google search I came up with a few answers.

1) Rough mach can be calculated by dividing your m/s by ~340 (which is an earth-based number, so very rough conversion)

2) Until the atmospheric upgrades from KSP, due to the way the atmosphere behaves there isn't really a way to calculate mach number (since mach is based on variables not in the current stock calculations)

[OhioBob]

Based on Kerbin's sea level temperature, pressure and density, and assuming a specific ratio ratio of 1.40, the speed of sound is 340.56 m/s. Since the atmospheric model assumes a constant scale height, the speed of sound is also constant. (I can show the math if anyone is interested.)

Edited January 25, 2015 by OhioBob

[GoSlash27]

DarthVader,

It's not at all surprising that there wouldn't be a chart for it. 1) Mach is meaningless in KSP and 2) it's a constant in KSP because temperature is constant.

What were you planning on using the chart for?

Curious,

-Slashy

[SaturnV]

Based on the delay of distant explosion sound, the sound speed of Kerbin is about 299,792,458 m/s.

FYI.

[GoSlash27]

Based on the delay of distant explosion sound, the sound speed of Kerbin is about 299,792,458 m/s.

FYI.

Funny, I was just pondering how to test that, and I was thinking way too hard.

Also, sound travels in a vacuum in KSP.

Best,

-Slashy

[zekes]

Mach 1 is about 363 m/s at sea level, I assume it lowers from there.

[OhioBob]

Mach 1 is about 363 m/s at sea level

How did you get that number? I've used two methods to calculate the speed of sound and, unfortunately, they yield inconsistent results.

The first method uses the given sea level values of density, pressure and temperature.

ÃÂ = 1.2230948554874 kg/m²

P = 101325 Pa

T = 293.15 K

From ideal gas law the average molecular weight is

M = ÃÂRT/P = 1.2230948554874 * 8314.4621 * 293.15 / 101325 = 29.422 kg/kmol

where R is the universal gas constant.

Given this molecular weight the atmosphere is almost certainly nitrogen-oxygen, giving us a specific heat ratio of 1.40. Therefore the speed of sound is

C = (γRT/M)^1/2 = (1.40 * 8314.4621 * 293.15 / 29.422)^1/2 = 340.56 m/s

The second method uses the scale height of the atmosphere, which for Kerbin is 5000 m. Scale height is given by the equation

H = RT/(Mg)

Therefore, by substitution we get

C = (γHg)^1/2

Again assuming γ = 1.40, we obtain a speed of sound at sea level of

C = (1.40 * 5000 * 9.81)^1/2 = 262.05 m/s

Clearly the numbers we are given are inconsistent and could not exist together in real life. If we are to believe the sea level values of P, T and ÃÂ, then Kerbin's sea level scale height would have to be 8445 meters.

I assume it lowers from there.

The incompatibility of the numbers we see in KSP makes this really impossible to determine. If we use C = (γRT/M)^1/2 and assume a homogenous atmosphere, i.e. M = constant, then we'd expect speed of sound to vary with temperature (as it does on Earth). However, if we use C = (γHg)^1/2, and knowing that KSP assumes a constant scale height, then we'd expect the speed of sound to vary with gravity. In the real world everything is internally consistent and these two equations yield the same answer, in KSP, however, they do not.

Edited January 26, 2015 by OhioBob