Voder-Vocoder

“The Deliverator’s car has enough potential energy packed into its batteries to fire a pound of bacon into the Asteroid Belt.”

I did the calculation just now. My 20 gallon gas tank has enough potential energy to put 9 pounds of bacon into the Asteroid Belt.

131 megajoules * 20 / G / ( (mass of sun / 414,703,838 km) - (mass of sun/ 149,597,887.5 km) - (mass of earth / radius of earth)) in pounds

A galactic system of measures used be several species to communicate with each other in a SF universe in my head. This is an explicitly _designed_ system of units. Base 16 is used because of the importance of binary. Aliens might find caesium-133 as easy to use as humans do. I don’t use multiples of the plank length—which might seem like the natural thing to do—because measuring the constant of gravitation accurately is harder than measuring the elementary charge, speed of light in vacuum, Planck’s constant, or Boltzmann’s constant. But my unit of electrical charge is sqrt(2)*16^15 times the Planck charge.

* * *

L = length unit = wavelength of radiation from the transition between hyperfine ground states of caesium-133 atoms at absolute zero, as that radiation passes through a perfect vacuum = 3.26122557 centimeters = 0.0326122557 meters. (The length unit is exactly 299792458/9192631770 meters.)

T = time unit = 16^8 * (Length unit / speed of light in a vacuum) = 0.467218464 seconds. Or the duration of 16^8 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom at rest at a temperature of 0 K. (The time unit is exactly 4294967296/9192631770 seconds.)

M = unit of mass = 16^32 * Planck’s constant / (speed of light * length unit) = 0.0230618313 kg, which makes plank’s constant 16^-24. [I’m not sure of a nice way to state this definition.] (This unit is only as good as our measurement of Planck’s constant, currently with an uncertainty of around 5×10^-8. But we’re still arguing about how to define the kilogram.) [In the galaxy, the simplest way to realize this definition is to ask the most scientifically advanced species you can find to make a measurement of Planck’s constant with minimal uncertainty and manufacture a few 1-unit-of-mass artifacts.]

C = unit of current = 52.3615416 amperes. The Current Unit is a constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross section, and placed 1 Length Unit apart in a vacuum, would produce between these conductors a force per length equal to 1/(2*Pi) M*L/T^2/L.

E = unit of energy = M*L^2/T^2 = 0.000112360968 joules

P = unit of temPerature = 7.05881935 Kelvins, which makes Boltzmann’s constant 16^-16. One defines temperature in terms of the ideal-gas-law behavior of an ideal gas: the temperature of an ideal gas is defined to equal (16^16)(pressure)(volume)/(number of particles).

* * *

Therefore,

speed of light = 16^8 L/T (by definition)

Planck’s constant 16^-24 = M*L^2/T (by definition)

elementary charge = 16^-16 * sqrt(2 * the fine-structure constant) C*T (measured)

Newtonian constant of gravitation = 9.6853 × 10^-9 L^3/M/T^2 (measured)

electric constant = vacuum permittivity = 16^-16 T^4*C^2/L^3/M (by definition)

magnetic constant = vacuum permeability = 1 M*L/T^2/C^2 (by definition)

Boltzmann’s constant = 16^-16 M*L^2/T^2/P (by definition)

* * *

What is the tension in a spinning ring, for example Bank’s orbitals or a Niven Ring?

Let us brake the ring into N sections. The angle (in radians) subtended by each section, dθ, is 2π / N. Suppose the radius of the ring is R and the mass-per-unit-length of the ring is λ; then the mass of a section is λRdθ and the mass of the whole ring M = 2πRλ.

Ignoring gravity, there are two forces pulling on each small section: tension pulling to the left and tension pulling to the right. Because the ring is circularly symmetric, the magnitude of the two tensions are equal. The directions of the two forces are dθ from being opposite.

If at some moment in time, the left tension is pointing in the direction, then the right tension will be

where T is the magnatude of either tension.

As N gets large and dθ gets small, and . So:

Consequently, the centripital force on the small section is Tdθ. From Newton’s second law:

Tdθ = (λRdθ)a

where a is the centripetal acceleration.

T = λRa

Part B: Plug in some numbers.

Let P be the period of revolution. P = 2π√(R/a).

If the ring is made of solid steel, T / λ = 154000 N·m/kg. Setting our centripetal acceleration to an earthly 10 m/s², we find that the maximum radius for a ring of steel is 15 kilometers. Period of revolution = 243 seconds = 4 minutes. If you assume that half of the mass of your ring is structural material and the other half is nonstructural, then you get a diameter of 15 km. Multiply the period by 1/√2.

Carbon nanotubes: maximum size of 4800 kilometers. Period of revolution = 4353 seconds = 1.2 hours

The period of revolution for a Culture Orbital is a convenient 24 hours. The radius of a Niven Ring is 1 AU. Neither of these is feasible with today’s understanding of physics.

On the other hand, a Stanford Torus with a radius of 893 meters and an orbital period of 60 seconds would need to have an average specific strength of 8745 N·m/kg, so at least 6% of the mass would need to be steel structure. (You would probably want a 4x fudge factor. Say 25% structural steel. Then sections of the ring could be replaced if they show signs of wear.)

graphic and
article

For anyone interested in technology.

—Dirac, by way of the Feynman Lectures

| is the identity matrix. SUM <i|i> = 1 while SUM |i><i| = I.

Protoscience

When the poets take over, top and bottom will become truth and beauty again.