The left column is the change in decibel level provided by soundproofing.
Decibels 25 Normal speech can be understood quite easily and distinctly through wall 30 Loud speech can be understood fairly well, normal speech heard but not understood 35 Loud speech audible but not intelligible 45 Loud speech not audible 50 Very loud sounds such as musical instruments or a stereo can be faintly heard; 60 Most sounds inaudibleTable for the reduction in intensity of sound for various kinds of walls. Values in decibels.
33 Typical interior wall 46 6 inch hollow concrete masonry 50 10 inch hollow concrete masonry
Sound transmission through the wall depends on the thickness of the wall.
L = Thickness of a wall Dair = Density of air Dwall = Density of wall material P = Characteristic pressure fluctuation of a sound wave striking the wall V = Characterstic velocity fluctuation of a sound wave striking the wall T = Wave period F = Wave frequency = 1/T Vwall = Characteristic recoil velocity of a wall upon being struck by a sound wave V^2 ~ P / DairThe impulse per area delivered to the wall is
Impulse / Area ~ P T ~ Dair T V^2The impulse per area is equal to the momentum per area delivered to the wall
Dair T V^2 ~ Dwall L Vwall Vwall ~ (Dair/Dwall) V^2 / (LF)The wall recoil generates a sound wave on the other side of the wall with a characteristic fluctuation magnitude of Vwall. The decibel level is proportional to the logarithm of the velocity.
log(Vwall) = Constant - log(L) - log(F)The change in decibel level is proportional to the logarithm of the wall thickness. It's better to divide a wall into many layers rather than having one solid wall.
The change in decibel level is proportional to the logarithm of the frequency. Low-frequency waves are difficult to block.
It's better to have multiple thin walls than one thick wall.
If a sound wave strikes a wall then only a small fraction of the energy is transmitted through the wall. If an object strikes the wall then a substantial amount of energy is transmitted through the wall. Carpets are a big help for soundproofing.
Noise is often characterized with a power spectrum because the properties of soundproofing depend on frequency. It is easier to stop high-frequency noise than low-frequency noise.
The walls of an anechoic chamber absorb all sound.
The absorbers are pointy to minimize the reflection of sound.
The information rate for sound is kilobytes/second and the rate for vision is megabytes/second.
The quality of a city depends on things such as
*) The average travel time
*) The amount of residential and yard space per person
*) The amount of public park space
Most cities are poorly designed in this regard and hence new cities may emerge that are built from scratch. These cities will take advantage of possibilities offered by electric driverless cars prefabricated housing, and factories where you can manufacture things for yourself.
Population Population Area Travel Travel density (millions) (km2) time means (people/ha) (mins) Manila 430 1.65 38.6 30 Taxi Delhi 255 11.0 431 30 Bus Paris 215 2.27 105 30 Subway Seoul 130 10.4 605 30 Subway New York City 104 8.18 784 30 Subway San Francisco 67 .81 121 30 Subway Boston 51 .65 125 30 Subway Isla Vista 48 .023 4.8 5 Walk, bike Pasadena 24 .140 59.5 10 Car Beverly Hills 23 .347 14.8 10 Car Iowa City 10 .068 64.8 10 Walk, bikeElectic cars outperform public transportation for travel time and energy use. New York City is a catastrophic case that illustrates the weaknesses of public transportation. To get anywhere you have to:
This often takes more than 30 minutes, plus the subway routes are awkwardly designed.
Consider two constrating city designes
Design 1) Everyone has a yard adjacent to a park and no upstairs neighbors. The house has a garage with an electric car.
Design 2) Everyone lives in skycrapers
Being able to drive an electric car right up to your residence dramatically reduces travel time.
Lawns and parks are good for social interaction, especially for families with children. Skyscrapers are poor in this regard.
A high population density can be achieved even if everyone has a yard.
For example, suppose a citizen has on average:
*) A residence of 30 square meters.
*) A yard of 20 square meters.
*) The residence is adjacent to a park with 30 square meters per person.
*) Road space of 20 square meters per person.
These residences are larger than typical New York City apartments and they achieve a respectable population density of 10000 people/km2.
A city with sensible traffic flow can achieve a large population and a small travel time. For example,
City radius = R = 3 km Average travel speed = V = 15 meters/second Average travel time = T = R/V = 3.3 minutes City population density = D = 10000 people/km2 = 1 person every 10 meters2 City population = P = πDR2=280000 peopleIt helps to centralize. 4 points of focus of a city are the college, the pub district, the shopping district, and the K-12 school. These can be placed in the city center and the residences and businesses radiate out from the center.
Prefabricated homes can be made from shipping containers, which are abundant, cheap, and easily delivered.
$ Length Width Height Mass ft ft ft kg 10-foot shipping container 1000 10 8 8.5 1300 20-foot shipping container 1200 20 8 8.5 2200 40-foot shipping container 1500 40 8 8.5 3800 Typical mobile home 90 18
For a 1-level prefabricated square bamboo house,
Side length = 8 meters Wall height = 3 meters Floor area = 64 meters2 Wall area = 24 meters2 Interior walls = 24 meters2 Total wall area = 248 meters2 Floor, ceiling, 4 walls, and interior walls Wall thickness = .05 meters Wall volume = 12.4 meters3 Bamboo density = 350 kg/meter2 Bamboo mass = 4.3 tons Carbon mass = 2.2 tons Bamboo carbon frac= .5 House mass = 7.0 tonsA helicopter can carry 12 tons. A prefabricated house can be placed anywhere in the wilderness and multiple modules can be assembled on site.
Prefabricated houses can be helicoptered to wilderness locations and flying cars can be used to reach them.
Electric cars outperform gasoline cars in all regards except range. They're simpler, more powerful, quieter, and more flexible than gasoline cars.
The range and power of an electric car depends on the properties of batteries.
Battery energy/mass = e = .80 MJoules/kg Battery power/mass = p = 1600 Watts/kg Battery energy/$ = s = .010 MJoules/$The range depends on the battery energy and the drag force. For a typical car,
Drag force = F = 120 Newtons (At a city speed of 15 m/s) Range = X meters Battery energy = E = F X JoulesFor a typical car, the range per battery dollar is:
Battery mass = M = 100 kg Battery energy = E = M e = 80 MJoules Battery cost = S = E / s = 8000 $ Range = X = E / F = 670 km At a city speed of 15 m/s Range/$ = x = X / S = .084 km/$At a highway speed of 30 m/s the drag force is 3 times larger than at 15 m/s and the range is 3 times less.
We compare the transport cost per person for various vehicles.
Drag force = F Distance = X Energy expended = E Number of people = N Energy/distance/person = Z = E/X/N = F/N Force/person Force/person Mass Cr Area Cd Drag speed People at 15 m/s at 30 m/s Newtons Newtons kg m2 m/s Electric bike 99 387 20 .004 .7 1.0 2.6 1 Electric car 105 269 600 .0075 2.0 .3 14.3 1 Bus 23.1 56 10000 .005 8.0 .6 15.7 60 Subway car 9.7 34 34000 .00035 10.0 .6 6.3 100 18-wheel truck 2422 4400 36000 .005 8.0 .6 24.6 1The force/person for the 747 aircraft is for a cruising speed of Mach .9 and an altitude of 12 km.
We assume that each person adds 80 kg to the mass of the vehicle.
Buses use 5 times less energy as cars but only if they are full
Within cities, cars have faster travel times than buses, especially if parking is abundant or the cars are self-driving. Buses are more suited to inter-city transport.
Trains use 2 times less energy than buses but they are highly inflexible.
The performance of a car depends on its power source. Lithium batteries have a substantially lower value for energy/mass than gasoline.
Energy/Mass Power/mass Energy/$ Recharge Max MJoule/kg kWatt/kg MJoule/$ time charges Diesel fuel 48 - 41 - Lithium battery .60 .75 .007 hour 104 Supercapacitor .016 8 .00005 seconds 106 Aluminum electrolyte capacitor .010 10 .0001 seconds ∞Electric motors can reach a power/mass of 10 kWatts/kg.
Electric motors and gasoline motors have a similar power/mass.
MJ/kg kWatt/kg kWatts kg Supercapacitor, Li-ion .054 15 Electric motor, maximum - 10 200 19.9 EMRAX268 Brushless AC Turbofan jet engine - 10.0 83.2 8.32 GE90-115B Brayton Electric motor, DC - 7.8 1.04 .133 ElectriFly GPMG5220 brushless DC Gasoline engine (BMW) 7.5 690 BMV V10 3L P84/5 2005 Model aircraft engine - 2.8 Battery, lithium-ion .75 1.5 Fuel cell, Honda - 1.0 Typical diesel V8 turbo - .65 Solar cell, space station - .077
An electric aircraft uses 7 times more energy than an electric car in terms of energy/distance/mass. Electric aircraft have a cruising speed of 50 m/s and electric cars in cities move at around 15 m/s.
Typical values for electric aircraft and cars are:
Electric aircraft speed = 50 m/s Electric aircraft power/mass = 50 Watts/kg Electric aircraft energy/distance/mass= eair= 1.0 Joules/m/kg Electric aircraft flying time = T =3600 seconds Electric aircraft range = X = 180 km Gravity constant = g = 9.8 m/s2 Electric car mass = M Electric car rolling drag coefficient = Cr = .0075 Electric car rolling drag = Fr = Cr M g Electric car total drag = F = 2 Fr (Assume rolling drag = air drag) Electric car energy/distance/mass = ecar= 2 Cr g = .147 Joules/m/kg Aircraft energy / Car energy = eair / ecar = 6.8
For a typical car,
Car mass = M = 1200 kg Gravity constant = g = 9.8 m/s2 Tire rolling drag coeff = Cr =.0075 Rolling drag force = Fr = Cr M g = 88 Newtons Air drag coefficient = Ca = .25 Air density = D = 1.22 kg/meter3 Air drag cross-section = A = 2.0 m2 Car velocity = V = 17 m/s (City speed. 38 mph) Air drag force = Fa = ½CaADV2 = 88 Newtons Total drag force = F = Fr + Fa = 176 Newtons Drag speed = Vd = 17 m/s Speed for which air drag equals rolling drag Car electrical efficiency = Q = .80 Battery energy = E = 60 MJoules Work done from drag = EQ = F X = Cr M g [1 + (V/Vd)2] X Range = X = EQ/(CrMg)/[1+(V/Vd)2] = 272 kmThe range is determined by equating the work from drag with the energy delivered by the battery.   E Q = F X.
The drag speed Vd is determined by setting Fr = Fa.
Drag speed = Vd = [Cr M g / (½ Ca D A)]½ = 4.01 [Cr M /(Ca A)]½ = 17.0 meters/second
Acceleration depends on the size of the battery, and supercapacitors can add an extra boost. For a typical car that accelerates from 0 to 100 km/h (37.8 m/s) in 8 seconds, the size of the battery required is:
Car mass = M = 1200 kg Target speed = V = 27.8 m/s (100 km/h. Speed at end of acceleration) Kinetic energy = E = ½ M V2 = 464000 Joules Time = T = 8 seconds (Time to accelerate from rest to speed V) Engine efficiency = Q = .8 Power = P = E/T = 58000 Watts Battey power/mass = p = 750 Watts/kg Battery mass = MB = P / (Q p) = 112 kg Battery cost/mass = c = 86 $/kg Battery cost = C = 9600 $
Supercapacitors are ideal for recovering breaking energy because they can be charged/discharged more times than batteries. To capture the energy from breaking from freeway speed, on order of 27 kg of supercapacotors are required.
Car mass = M = 1200 kg Car velocity = V = 27.8 m/s Car kinetic energy = E =464000 Joules Supercapacitor energy/mass = e = 16000 Joules/kg Supercapacitor mass = E/e = 29 kg
The principal challenge for flying cars is noise. There is no such thing as a quiet flying car.
Fixed wing flight is at least 6 times more efficient than helicopter flight.
The larger the propeller the less noise. The sound power of a propeller scales as the 5th power of tip speed. A flying car should have a propeller as large as possible. A single large propeller is better than multiple small propellers.
A ducted (shielded) propeller is substantially quieter than an unshielded propeller, and is more efficient in producing thrust.
Electric aircraft are substantially simpler and safer than gasoline aircraft.
Nominal configuration for a quiet flying car:
A single large ducted fan mounted on the rear
50 kWatt engine
Gyrofans and gyroscopes for stability
Wings that fold for driving
Telescoping wing section within the main wing (wings should be as long as possible)
A cockpit with a low cross-section, like a velobike. The passengers sit behind the pilot
Thin tires for a low cross section
A 10 kg vehicle parachute for emergency landing
2 kg parachutes for passengers
A total mass in the range of 500 kg