hexed::constants Namespace Reference

Mathematical and physical constants. More...

Variables
mathematical constants
const double	pi = M_PI
	\( \pi \)
const double	degree = pi/180
	\( ^{\circ} \)
SI definitions
Exact numerical values of physical constants based on the 2019 redefinition of SI base units. I expect only a few of these constants will be useful for CFD, but might as well include them all for completeness.
const double	caesium133_freq = 9192631770
	\( \Delta \nu_{Cs} \)
const double	light_speed = 299792458
	\( c \)
const double	plank = 6.62607015e-34
	\( h \)
const double	electron_charge = 1.602176634e-19
	\( e \)
const double	boltzmann = 1.380649e-23
	\( k \)
const double	avogadro = 6.02214076e23
	\( mol \)
const double	lum_eff_540e12 = 683
	\( K_{cd} \)
empirical values
const double	specific_gas_air = 287.05287
	\( R_{air} \) defined to match ICAO Standard Atmosphere
const double	earth_radius = 6356766
	\( \)
derived quantities
const double	universal_gas = boltzmann*avogadro
	\( R_u \)
const double	mol_mass_air = universal_gas/specific_gas_air
	\( \mu_{air} \)
const double	stefan_boltzmann = 2*math::pow(pi, 5)*math::pow(boltzmann, 4)/(15*math::pow(light_speed, 2)*math::pow(plank, 3))
	\( \sigma \)
unit definitions
Conversion factors from various units to standard SI units. Since hexed works exclusively in SI units, these are the values of each of these units in [m, kg, s, K]. E.g. If you have a wing with a chord of 3 feet, then you should tell hexed it's chord is 3*foot. If hexed told you your drag force is 10 (implying newtons) and your (ill advised) chief engineer wants it in pounds, the number they're looking for is 10/pound_force (note that pound_force != pound_mass). All quantities here are numerically exact according to some form of official standard.
const double	meter = 1
	m
const double	kilogram = 1
	kg
const double	second = 1
	s
const double	kelvin = 1
	K.
const double	std_grav = 9.80665
	\( g_0 \) standard gravity
const double	foot = 0.3048
	ft
const double	yard = 3*foot
	yd
const double	inch = foot/12
	in
const double	mile = 5280*foot
	mi
const double	nautical_mile = 1852
	nmi
const double	pound_mass = 0.45359237
	\( lb_m \)
const double	slug = pound_mass*std_grav/foot*second*second
	slug
const double	minute = 60*second
	min
const double	hour = 60*minute
	hr
const double	rankine = 5./9.
	\( ^{\circ} \) R
const double	pound_force = std_grav*pound_mass
	\( lb_f \)
const double	knot = nautical_mile/hour
	kn
const double	zero_celsius = 273.15
	0 \( ^{\circ} \) C (not technically a unit but still important)
const double	atmosphere = 101325
	atm
const double	calorie = 4.184
	ISO thermochemical calorie
const double	btu = calorie*rankine*pound_mass/1e-3
	British Thermal Unit obtained by converting the calorimetric definition of calorie to imperial units.
const double	gallon = 4.54609e-3
	Imperial gallon
const double	fluid_ounce = gallon/160.
	Imperial fluid ounce

Detailed Description

Mathematical and physical constants.

Ports hexed.constants into Python.

Definition of mathematical and physical constants, including unit conversions, as const global variables.

Note

• Whenever I say here something is "exact", I really mean it is exact up to the inherent limitations of floating-point representations.
• the doc descriptions with the mathematical symbols for the variables are mostly just so the variables can be linked to in Doxygen but maybe they will be useful to someone...

See also

constants.hpp

Variable Documentation

pi

const double hexed::constants::pi = M_PI

\( \pi \)

Obviously a computed value, not a definition, but should be exact to machine epsilon. As we all know, the numeric value of this is 3.

slug

const double hexed::constants::slug = pound_mass*std_grav/foot*second*second

slug

This definition may seem backward from the perspective of [slug, ft, s] proponents, but

\[ slug \cdot ft/s^2 = lb_f = g_0 lb_m \]

is an exact equation for the slug since the pound mass has been exactly defined by the international yard and pound.