
Decreased travel time.
Increased residential and public space per person.
Decreased housing prices and flexibility in changing residences.
Decreased noise pollution with electric vehicles.
Decreased dependence on foreign oil.
Feed everyone using hydroponics.
Electric cars outperform gasoline cars in all ways except range and are ideal for compact city cars. Electric motors can also be put on anything, such as a bike, a kick scooter, or rollerblades.
Battery technology is now prime time and and is capable of powering a flying car for 30 minutes.
Prefabricated homes can cost as little as $5000, are transportable, and can be assembled like legos into larger structures. A city can be built from scratch in a short time using prefabricated homes.
Hydroponics yield is 100 times larger than soil yield and 40 square meters of hydroponics is sufficient to sustain a person.
In the sections below we expand on each of these points.
Electric vehicles outperform gasoline vehicles in all regards except range, and if you splurge on the battery you can have the range. Electric vehicles are more powerful, quieter, simpler, more flexible, and cheaper than gasoline cars, and you can put an electric motor on anything, even a rollerblade. Electric power is ideal for compact and cheap city car.
Air drag determines a vehicle's top speed and energy usage, and this determines the battery size.
Air density = D = 1.22 kg/meter^{3} Air drag area = A Speed = V Air drag force = F = ½ A D V^{2} Air drag power = P = ½ A D V^{3} Range = X Energy used = E = F X Battery mass = M Battery cost = S Battery energy/mass= e = E/M = .8 MJoules/kg Battery power/mass = p = P/M = 1600 Watts/kg Battery energy/$ = s = S/M = .010 MJoules/$A compact car designed for city speeds doesn't need much power. Example values for various electric vehicles:
Speed Power Force Force/prsn People Range Drag area m/s kWatt Newton Newton km m^{2} Skate 10 .18 18 18 1 5 .3 Kick scooter 10 .18 18 18 1 5 .3 Bike 15 .82 55 55 1 8 .4 Car, small, city speed 20 4.9 244 244 1 10 1 Car, large, freeway speed 30 33 1100 1100 1 15 2 Bus, freeway speed 30 99 3290 46 72 15 6 Train car, freeway speed 30 99 3290 27 120 15 6 Airbus A380 251 251000 1000000 1840 544 10000 160 1 Horsepower = 746 WattsEnergy usage is proportional to the drag force per person. If a bus is full it is 5 times more efficient than a compact car, but buses are rarely full and usually slow.
Buses and trains are substantially more efficient than planes and they should be favored over short flights.
"Power" is the minimum power required for the given speed.
We assume a minimalist battery  the smallest battery that can provide the given power. We then calculate the energy for this battery using the battery parameters and we caculate a range using this energy. Larger range can be achieved with a larger battery. Since a minimalist battery is cheap, a larger battery is usually feasible.
The drag parameter is obtained from an analysis of commercial vehicles. Data
Battery cost as a function of power is 20 Watts/$. A 1 kWatt bike battery costs $50, a 10 kWatt city car battery costs $500, and a 100 kWatt freeway car battery costs $5000. For city vehicles the battery is a small fraction of the vehicle cost and for freeway vehicles it's a significant cost.
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) (km^{2}) 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 Pasadena 24 .140 59.5 10 Car Beverly Hills 23 .347 14.8 10 Car Iowa City 10 .068 64.8 10 Walk, bike Isla Vista 48 .023 4.8 5 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 contrasting city designs:
Design 1) Everyone has a yard adjacent to a park and no upstairs neighbors.
The house has a garage with a electric driverless car.
Design 2) Everyone lives in skycrapers
Lawns and parks are good for social interaction, especially for families with children. Skyscrapers are poor in this regard.
Being able to drive an electric car right up to your residence dramatically reduces travel time.
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/km^{2}.
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/km^{2} = 1 person every 10 meters^{2} City population = P = πDR^{2}=280000 peopleIt helps to centralize. 4 points of focus of a city are the college, the pub district, the shopping district, and the K12 school. These can be placed in the city center and the residences and businesses radiate out from the center.
Hydroponics is the technique of growing plants in water rather than soil, where the water is fertilized with nutrients. THis substantiall increases the yield.
The principal technical challenge for a hydroponics system is to supply the roots with oxygen, which requires a water flow system. These are called "grow kits".
Data for this chapter come from from Wikipedia and from Christopher Willis' article on hydroponics.
An example hydroponic system consists of:
$ Amazon link Grow kit, 90 sites 160 * LED grow light, 1000 Watts 140 * Fertilizer, 10 kg 130 * Mirror film, 400 square feet 24 * Greenhouse 120 * Total 600
Yield Yield Energy kCal/m^{2}/yr kg/m^{2}/yr Cal/kg Potato 48 52 923 Onion 20 50 400 Tomato cherry 17.2 98 176 Blueberry 13.8 24 573 Cucumber 12.6 82 154 Tomato 12.4 50 249 Lettuce 7.0 74 95
We calculate the price for food for 1 year. We assume 2600 calories/day.
Energy Price Efficiency Cal/kg $/kg Cal/$ Rice (dry) 3330 2.86 1160 Peanut 6000 6.60 910 Sunflower seed 5710 10.00 571 Chicken 2762 5.00 550 Milk 422 .80 530 Mountain Dew 440 1.00 440 Turkey 2429 6.00 404 Cheddar 4040 10.00 404 Beef 3380 9.00 375 Watermellon 300 .83 361 Egg 1400 4.00 350 Potato 930 2.84 327 Mozarella 2780 8.80 315 Palm oil 7353 24.00 306 Corn 860 4.40 195 Apple 579 5.00 115 Cucumber 154 2.00 77 Tomato 249 4.41 56 Lettuce 95 5.57 17 Cherry tomato 176 11.76 14Rice is the cheapest source of calories and peanuts are the cheapest source of macronutrients. You can feed a person for 2.5 $/day with rice, peanuts, and a vitamin pill.
A vitamin pill covers all micronutrients. The macronutrients are:
Requirement Centrum g/day g Protein 50 0 Potassium 3.5 .08 Calcium 1.0 .2 Phosphorus 1.0 .02 Magnesium .35 .05Foods with high macronutrient density. Numbers in parts per thousand.
Phosphorus Potassium Calcium Magnesium Protein Sunflower seed 6.6 6.4 .8 3.3 179 Cheddar 5.1 1.0 7.2 .28 283 Peanut 3.8 7.1 .9 1.7 267 Beef 3.0 2.4 .12 .19 247 Turkey 2.1 3.0 .1 .21 293 Egg 1.9 1.3 .53 .12 120 Milk .9 1.4 1.1 .10 33 Potato .7 5.4 .15 .28 13 Rice .7 .8 .11 .23 52 Avocado .5 4.8 .1 .29 13The cheapest source of macronutrients is cheese and peanuts.
Hydroponics offers gains over field agriculture in many categories. The following table shows the amplification for each category in terms of hydroponic yield over field yield. The total amplification is the product of the amplification from each category.
Plant density 8 In terms of plants/meter^{2} Crops per year 4 Crop variety 2 Temperature contro l 2 LED lighting 2 Carbon dioxide enhancement 1.5
Soil mass yield = 1 grams/meter^{2}/day Data Hydroponic mass yield = 100 grams/meter^{2}/day Data Typical food energy density =1000 Calorie/kg (Potato = 930 Cal/kg) Hydroponic calorie yield = 100 Calorie/meter^{2}/day Calorie requirement per day =2600 Calorie/day Hydroponic area/person = 26 meters^{2} (Area required to sustain one person) Hydroponic yield/growsite = 4 kg Electricity cost = 30 MJoules/$ Minimum water flow rate = .5 Litre/minute Optimal water flow rate = 1 Litre/minute Maximum water flow rate = 2 Litre/minute Maximum pipe length = 10 meters (If longer, nitrogen becomes depleted) Grow kit cost = 2 $/growsite Largest kit size = 72 growsites Nutrient solution cost = 13 $/kg (solid form) Water requirement = 500 kg of water per kg of solid nutrient fertilizer LED lamp cost = 7 Watts/$ Mirror film cost = 1.5 meter^{2}/$ Transparent acrylic sheets = 32 $/meter^{2} Greenhouse cost (sturdy) =.016 meters^{3}/$ (Plexiglass. Survives high wind) Greenhouse cost (unsturdy) =.18 meters^{3}/$ (Plastic. Cannot survive high wind) O2 solubility in H2O, 10 C =11.2 mg/Litre O2 solubility in H2O, 20 C = 9.1 mg/Litre O2 solubility in H2O, 30 C = 7.2 mg/Litre O2 density in the atmosphere= 280 mg/LitreThe water pipes should exclude light to prevent algae growth.
1 kg of nutrient powder is mixed with ton of water. The composition of a typical nutrient solution is
Parts per million Potassium 160 Nitrogen 150 Calcium 100 Phosphorus 40 Sulfur 40 Magnesium 30 Iron 2 Manganese .5 Zinc .3 Boron .2 Copper .1 Molybdenum .075Source
Arizona solar intensity, peak =1000 Watts/meter^{2} (Noon in midsummer) Arizona solar intensity, ave. = 250 Watts/meter^{2} (Averaged over day and night) Manhattan solar intensity, ave.= 155 Watts/meter^{2} Electricity cost per Joule = 36 MJoules/$ Energy in one day =13.4 MJoules/day/meter^{2} Cost for one day = .37 $/day/meter^{2}
A greenhouse can be cooled by evaporating water.
Melting energy of water at 0 Celsius = 334 kJ/kg Vaporization energy of water at 100 Celsius = 2257 kJ/kg Energy to raise water from 0 to 30 Celsius = 126 kJ/kg Total energy for melting ice = 2717 kJ/kg
1 Calorie = 4184 Joules Daily requirement for men = 2600 Calories Daily requirement for women = 2000 Calories
Prefabricated homes can be made from shipping containers, which are abundant, cheap, and easily delivered.
$ Length Width Height Mass ft ft ft kg 10foot shipping container 1000 10 8 8.5 1300 20foot shipping container 1200 20 8 8.5 2200 40foot shipping container 1500 40 8 8.5 3800 Typical mobile home 90 18
The deformation of a solid is characterized by shear strain, tensile strain, and bulk compression.
Tensile strength relates to the strength of wires.
Shear strength relates to the strength of beams and columns.
The maximum force on a beam is determined by the shear strength.
F = Maximum force applied to the center of a beam before it breaks X = Beam length Y = Beam thickness Z = Beam height x = Deflection of the beam at the center when under force "F" ShearStrength = 3 F X / (2 Y Z^{2})If a column is short then it squashes before it buckles and if it is long then it buckles before it squashes.
A column's resistance to squashing is determined by the Bulk strength.
A = Area of the column B = Bulk strength of the column F = Force required to squash a column = B AA column's resistance to buckling is determined by the Young's modulus. Suppose a column is a hollow cylinder.
L = Length of the column R = Outer radius of the column r = Inner radius of the column (r=0 if the cylinder is not hollow) Y = Young's modulus Q = Dimensionless effective length of the column = .5 if both ends are fixed = 2 if one end is fixed and the other end is free to move laterally = 1 if both ends are pinned (hinged and free to rotate) = .699 if one end is fixed and the other is pinned F = Force required to buckle the column = ½ π^{3} Y (R^{4}r^{4}) / (Q L)^{2}If a column's buckling limit is equal to its squashing limit then (assume r=0)
R/L = (Q/π) * (2B/Y)^{1/2}
The figure of merit for materials for beams and columns is:
Tensile strength = y Pressure required to break the material Young's modulus = Y A measure of a material's rigidity Density = D Beam quality = y D^{2} Column quality = Y D^{2} Density Tensile Young's Beam Column Compression strength modulus quality quality strength g/cm^3 GPa GPa GPa Balsa .12 .020 3.7 1.39 257 Cedar .34 .054 8.2 .47 71 Pine .37 .063 9.0 .46 66 Mahogany .67 .124 10.8 .28 24 Spruce, red .41 .072 10.7 .43 64 Walnut, black .56 .104 11.8 .33 38 Oak, swamp .79 .124 14.5 .20 23 Hickory .81 .144 15.2 .22 23 Bamboo .85 .169 20 .23 28 Ironwood 1.1 .181 21 .15 17 Magnesium alloy 1.8 .25 45 .077 13.9 Aluminum + Be 2.27 .41 70 .080 13.6 Aluminum alloy 2.8 .40 70 .051 8.9 Titanium alloy 4.6 1.20 120 .057 5.7 Steel + CoNi 8.6 2.07 211 .028 2.9 Moly + WHa 14.3 1.8 330 .009 1.6 Polyamide 1.14 .11 4.5 .085 3.5 Polyimide 1.42 .085 2.5 .042 1.2 Acrylic 1.18 .07 3.2 .050 2.3 Polycarbonate 1.21 .07 2.6 .048 1.8 Carbon fiber 1.75 3.0 Quartzite .025 Granite 2.7 .020 .13 Basalt 2.9 .020 Marble .015 Limestone 2.7 .015 .06 Gneiss .015 Shale 2.5 .007 Cement .0035 .02 Slate .0035 .095 Concrete .003 .015 Brick .003 .08 Sandstone 2.3 .002 .06Wood is better than metal because of its lower density, but metal is easier to make into hollow tubes.
For metal, wood, and plastic, the tensile strength is similar to the compression stength. For rock the tensile strength is much less than the tensile strength.
The larger the propeller radius, the less power that is required to fly. One hence makes the propeller as large as possible, subject to the constraint that if the propeller is too large, the mass is too large.
The most efficient copter has one large rotor for lift plus a small rotor for stability (a "monocopter"). If we increase the number of lift rotors while preserving the total rotor mass then the radius of each rotor is smaller and it takes more power to fly.
Increasing the rotor number increases stability and redundancy. Most drones use 4, 6, or 8 rotors. We construct a design for a flying car using 2 large rotors and 2 small rotors. The large rotors carry most of the weight and the small rotors add stability and failsafe.
The large propellers are mounted forward and aft and the foward propeller tilts forward for horizontal flight. The small propellers are to the right and left.
We assume the total vehicle mass is 400 kg and we use the properties of propellers to calculate the power required to hover. We use a peak power that is comfortably larger than the hover power. The battery mass required to supply this power is 1/4 the total vehicle mass.
Total aircraft mass = M = 400 kg (Includes passenger) # of large rotors = N = 2 Rotor radius = R = 1.5 meters Gravity constant = g = 9.8 meters/second^{2} Rotor force = F = Mg/N =1960 Newtons Rotor quality = q = 1.02 Air density = D = 1.22 kg/meter^{3} Rotor power = P_{r}=(qDR)^{1}F^{3/2}= 46.2 kWatts Hover power = P_{h}= N P_{r} = 92.4 kWatts Peak power = P = 150 kWatts Battery power/mass = p =1600 Watts/kg Battery energy/mass = e = .8 MJoules/kg Battery mass = m = P/p = 94 kg Battery energy = E = e m = 75 MJoules Hover time = T = E/P_{h} = 812 seconds = 14 minutesThe properties of propellers are discussed in the propeller section. The rotor tip speed is
Rotor lift/drag = Q = 5.5 Rotor tip speed = V = P Q / F = 130 m/sThe maximum horizontal speed is around 1/3 of the rotor tip speed. If we assume a horizontal speed of 40 meters/second then the range is 32 km.
For the large propellers,
Propeller radius = R = 1.5 meters Propeller mass parameter = C = 5 kg/meter^{3} Propeller mass = M = C R^{3} = 17 kgFor the motors on the large propellers,
Motor power = 60 kWatts Motor power/mass = 8 kWatts/kg Motor mass =7.5 kgThe masses of the components in kg is
2 large 1.5 meter rotors 32 2 small 1.0 meter rotors 10 2 motors fo rthe large rotors 16 2 motors for the small rotors 10 Battery 100 Cabin 50 Fuselage 50 Pilot 80 Cargo 20 Total 380
The flight time of a drone is determined by:
*) The battery energy/mass.
*) The power/mass required to hover.
*) The ratio of the battery mass to the drone mass.
Typical parameters for a drone are:
Drone mass = M = 1.0 kg Battery mass = M_{bat} = .5 kg (The battery is the most vital component) Battery energy = E = .38 MJoules Battery energy/mass= e_{bat}= E/M_{bat}= .75 MJoules/kg (Upper range for lithium batteries) Drone energy/mass = e = E/M = .38 MJoules/kg Drone power/mass = p = P/M = 60 Watts/kg (Practical minimum to hover. Independent of mass) Drone power = P = p M = 60 Watts (Power required to hover) Flight time = T = E/P = 6250 seconds = 104 minutesThe flight time in terms of component parameters is
T = (e_{bat}/p) * (M_{bat}/M)
Electric bikes are easy to make. All you have to do is replace a conventional wheel with an electric wheel and attach a battery pack. Electric wheels come in kits and you can make the battery pack yourself. Example configurations for various motor powers:
Power Max Range Motor Battery Battery speed cost cost energy kWatt mph miles $ $ MJoule .75 30 10 160 40 .5 1.5 35 20 240 60 1.2 3 45 40 570 100 1.8 6 55 80 1150 200 3.6The bikes have one electric wheel and one conventional wheel except for 6 kWatt bike, which has 2 electric wheels with 3 kWatt each.
Electric wheel prices are from Amazon.com.
Speed Power License mph kWatt required? Connecticut 30 1.5 Yes California 28 .75 No Massachusetts 25 .75 Yes Oregon 20 1.0 No Washington 20 1.0 No Pennsylvania 20 .75 No Delaware 20 .75 No Maryland 20 .5 No DC 20 ? No
Not all benches are created equal. Care must be taken in designing a bench that is comfortable.
The higher the back of the bench, the better. Best of all is if the bench can
support the back of your head.
Benches with curvature are more comfortable than flat benches.
There should be space underneath the bench for your feet.
There should be a canopy for rain, with side walls to shield against wind.
There should be benches in the sun for cold weather and benches in the shade for hot weather.
Benches should have arm rests.
We give thanks to Broadway Presbyterian Church, Starbucks, and Morning 2 Midnight.
The properties of the best commercial lithium ion batteries are:
Energy/Mass = .8 Joule/kg Power/Mass = 1.6 kWatt/kg Energy/$ = .01 MJoule/kg Density = 3.5 gram/cm^{3} Recharges =1000 Shelf life = 1.0 year Voltage = 3.7 Volt Max temperature = 60 Celsius Min temperature = 20 CelsiusEnergy/Mass and Power/Mass are an engineering tradeoff. One can be increased at the expense of the other.
Energies and powers are for lithium batteries, which have a voltage of 3.7 Volts. The "ID #" is often used instead of cell size.
Cell Energy Power Current Mass Diameter Length Charge Price ID # size kJoule Watt Ampere gram mm mm AmpHour $ D 107 220 60 138 32 67 8.0 13 32650 C 67 220 60 92 26 50 5.0 8 26650, 25500 B 58 160 45 72 22 60 4.5 5 21700, 20700 A 47 110 30 49 18 50 3.5 3 18650 AA 9 22 6 15 14 53 .70 1 14500 AAA 4.7 11 3 7.6 10 44 .35 .5 10440 AAAA 2.3 6 1.5 3.8 8 42 .17 .25 75400
A single battery is a "cell" and a set of cells is a "pack". Packs are used to multiply the energy and power of cells.
Battery packs are notorous for catching fire, but cell technology has reached the point where it's now possible to make safe battery packs, and the design is simple enough so that anyone can construct their own packs.
Cells can be combined in series and/or parallel. Connecting in series multiples voltage, and voltage is helpful for achieving high power in a motor.
Connecting in series is easier than in parallel. If it's possible to achieve the required power without parallelization then one should do so, and this is usually possible with modern cells.
Series packs have the advantage that the cells can easily be extracted and charged individually, and cells can be interchanged between packs. One can also construct a set of series packs and swap them in like gun clips.
High power electric bikes use a voltage of 72 Volts. If we use one series array of C cells then a pack provides 4440 Watts and 1.2 MJoules. Any electric device requiring less than this much power can be powered by a series pack.
The properties of a modern highpower cell are:
Type = "C" Voltage = 3.7 Volts Energy = 60 kJoules Power = 155 Watts Mass = 92 grams Energy/mass = 650 kJoules/kg Power/mass =1680 Watts/kg Current = 42 Amperes Manufacturer = "Basen"When the cells are connected in series the values for voltage and power are:
Cells Voltage Power Volts kWatts 1 3.7 .15 2 7.4 .30 3 11 .45 Electric kick scooter 4 15 .60 6 24 .90 Electric bike 10 36 1.5 20 72 3.0 Compact electric car 96 356 15.0 Large electric car
Electric bike motors use either 36, 48, or 72 Volts. The following table shows how to build a battery pack for each motor power.
Power Volts Cells Series Parallel Current Cell Cell Cell Cell Cell kWatt Amperes Amperes Amphours $ type ID# .5 36 10 .75 36 10 10 1 21 25 2.1 4 A LG HD4 1.5 48 13 13 1 31 30 2.0 4.5 A Sony VTC4 3 72 20 20 1 42 60 4.5 4.5 C Basen 6 72 40 20 2 83 120 4.5 4.5 C Basen 12 72 80 20 3 167 180 4.5 4.5 C Basen Cells Total number of cells, equal to the number of cells connected in series times the number of cells connected in parallel. Series Number of cells connected in series. For example, 20 batteries with 3.6 volts each connected in series produces a voltage of 72 Volts. Parallel Number of cells connected in parallel. Current Current required to provide given power Cell Maximum current of a cell
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 order 50 m/s.
Typical values for electric cars and aircraft are:
Electric aircraft speed = 50 m/s Electric aircraft power/mass = 50 Watts/kg Electric aircraft energy/distance/mass= e_{air}= 1.0 Joules/m/kg Electric aircraft flying time = T =3600 seconds Electric aircraft range = X = 180 km Gravity constant = g = 9.8 m/s^{2} Electric car mass = M Electric car rolling drag coefficient = C_{r} = .0075 Electric car rolling drag = F_{r} = C_{r} M g Electric car total drag = F = 2 F_{r} (Assume rolling drag = air drag) Electric car energy/distance/mass = e_{car}= 2 C_{r} g = .147 Joules/m/kg Aircraft energy / Car energy = e_{air} / e_{car} = 6.8
The drag force on an object moving through a fluid is
Velocity = V Fluid density = D = 1.22 kg/m^{2} (Air at sea level) Crosssectional area = A Drag coefficient = C Drag force = F = ½ C A D V^{2} Drag power = P = ½ C A D V^{3} = F V Drag parameter = K = C A"Terminal velocity" occurs when the drag force equals the gravitational force.
M g = ½ C D A V^{2}Suppose we want to estimate the parachute size required for a soft landing. Let a "soft landing" be the speed reached if you jump from a height of 2 meters, which is V_{t} = 6 m/s. If a skydiver has a mass of 100 kg then the area of the parachute required for this velocity is 46 meters^{2}, which corresponds to a parachute radius of 3.8 meters.
Drag coefficient Bicycle car .076 Velomobile Tesla Model 3 .21 2017 Toyota Prius .24 2016 Bullet .30 Typical car .33 Cars range from 1/4 to 1/2 Sphere .47 Typical truck .6 Formula1 car .9 The drag coeffient is high to give it downforce Bicycle + rider 1.0 Skier 1.0 Wire 1.2
Force of the wheel normal to ground = F_{normal} Rolling friction coefficient = C_{roll} Rolling friction force = F_{roll} = C_{roll} F_{normal }Typical car tires have a rolling drag coefficient of .01 and specialized tires can achieve lower values.
C_{roll} Railroad .00035 Steel wheels on steel rails Steel ball bearings on steel .00125 Racing bicycle tires .0025 8 bars of pressure Typical bicycle tires .004 18wheeler truck tires .005 Best car tires .0075 Typical car tires .01 Car tires on sand .3
Wheel diameter = D Wheel sinkage depth = Z Rolling coefficient = C_{roll} ≈ (Z/D)^{½}
Energy = E Joules Time = T seconds Power = P = E/T Watts Mass = M kilograms Energy/Mass = e = E/M Joules/kilogram Power/Mass = p = P/M Watts/kilogram
The energy sources that can be used by vehicles are:
Energy/Mass Power/mass Energy/$ Rechargeable Charge Maximum charging MJoule/kg Watt/kg MJoule/$ time cycles Gasoline 45 60 Battery, aluminum 4.6 130 No Battery, lithium .8 1600 .010 Yes 1 hour 1000 Supercapacitor .016 8000 .00005 Yes Instant Infinite Aluminum capacitor .010 10000 .0001 Yes Instant Infinite
Speed Power Force Force Force Mass Drag Drag Area Drag Roll Year 100kph (total) (fluid) (roll) (data) (specs) coef coef time m/s kWatt kN kN kN ton m^{2} m^{2} m^{2} s eSkate 5.3 .11 .021 .013 .008 .08 .76 1.0 .01 eScooter Zoomair 7.2 .25 .035 .027 .008 .08 .85 1.0 .01 Bike 10 .30 .035 .030 .005 .10 .49 1.0 .005 Bike 18 1.78 .103 .098 .005 .10 .50 1.0 .005 eBike 250 Watt 8.9 .25 .028 .023 .005 .10 .48 1.0 .005 eBike 750 Watt 10.6 .75 .071 .066 .005 .10 .96 1.0 .005 eBike 1 kWatt 12.5 1.0 .080 .075 .005 .10 .79 1.0 .005 eBike 1.5 kWatt 15.3 1.5 .098 .093 .005 .10 .65 1.0 .005 eBike 3 kWatt 16.7 3.0 .180 .175 .005 .10 1.03 1.0 .005 eBike Stealth H 22.2 5.2 .234 .228 .006 .12 .76 1.0 .005 eBike Wolverine 29.2 7.0 .240 .234 .006 .12 .45 1.0 .005 Bike, record 22.9 3.66 .160 .155 .005 .10 .48 1.0 .005 Bike, steamline 38.7 3.66 .095 .090 .005 .10 .099 .11 .005 Loremo 27.8 45 1.62 1.58 .035 .47 3.39 .25 1.25 .20 .0075 2009 Mitsubishi MiEV 36.1 47 1.30 1.22 .081 1.08 1.53 .35 .0075 2011 Aptera 2 38.1 82 2.15 2.09 .062 .82 2.36 .19 1.27 .15 .0075 2011 Nissan Leaf SL 41.7 80 1.92 1.81 .114 1.52 1.71 .72 2.50 .29 .0075 2012 10.1 Volkswagen XL1 43.9* 55 1.25 1.19 .060 .80 1.01 .28 1.47 .19 .0075 2013 11.9 Chevrolet Volt 45.3 210 4.64 4.52 .121 1.61 3.61 .62 2.21 .28 .0075 2014 7.3 Saab 900 58.3 137 2.35 2.25 .100 1.34 1.09 .66 1.94 .34 .0075 1995 7.7 Tesla S P85 249+ 69.2* 568 8.21 8.06 .150 2.00 2.76 .58 2.40 .24 .0075 2012 3.0 BMW i8 69.4* 260 3.75 3.63 .116 1.54 1.24 .55 2.11 .26 .0075 2015 4.4 Nissan GTR 87.2 357 4.09 3.96 .130 1.74 .85 .56 2.09 .27 .0075 2008 3.4 Lamborghini Dia 90.3 362 4.01 3.89 .118 1.58 .78 .57 1.85 .31 .0075 1995 Porsche 918 94.4 661 7.00 6.88 .124 1.66 1.27 .29 .0075 LaFerrari 96.9 708 7.31 7.19 .119 1.58 1.26 .0075 Lamborghini SV 97.2 559 5.75 5.62 .130 1.73 .98 .0075 Bugatti Veyron 119.7 883 7.38 7.24 .142 1.89 .83 .74 .0075 2005 Hummer H2 242 .218 2.90 2.46 4.32 .57 .0075 2003 Formula 1 .053 .702 .9 .0075 2017 Bus (2 decks) 138 12.6 .005 2012 Subway (R160) 24.7 448 38.6 .0004 2006 Airbus A380 320 435200 1360 1360 21.8 F22 Raptor 740 231000 312 312 .93 Blackbird SR71 1100 332000 302 302 .41 Skydive, min 40 30 .75 .75 0 .075 .77 1.0 0 Skydive, max 124 101 .75 .75 0 .075 .080 1.0 0 Sub, human power 4.1 1.78 .434 .051 Blue Whale 13.9 3750 270 2.74 Sub, nuke 17.4 30000 1724 11.2 Virginia Class *: The top speed is electronically limited Drag (data) Drag parameter obtained from the power and top speed Data (specs) Drag parameter from Wikipedia Force (total) Total drag force = Fluid drag force + Roll drag force Force (fluid) Fluid drag force Force (roll) Roll drag force Area Cross section from Wikipedia Drag coef Drag coefficient from Wikipedia Roll coef Roll coefficient. Assume .0075 for cars and .005 for bikes. 100kph time Time to accelerate to 100 kphFor the skydiver, the minimum speed is for a maximum cross section (spread eagled) and the maximum speed is for a minimum cross section (dive).
Wiki: Energy efficiency in transportation
For a typical car,
Car mass = M = 1200 kg Gravity constant = g = 9.8 m/s^{2} Tire rolling drag coeff = C_{r} =.0075 Rolling drag force = F_{r} = C_{r} M g = 88 Newtons Air drag coefficient = C_{a} = .25 Air density = D = 1.22 kg/meter^{3} Air drag crosssection = A = 2.0 m^{2} Car velocity = V = 17 m/s (City speed. 38 mph) Air drag force = F_{a} = ½C_{a}ADV^{2} = 88 Newtons Total drag force = F = F_{r} + F_{a} = 176 Newtons Drag speed = V_{d} = 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 = C_{r} M g [1 + (V/V_{d})^{2}] X Range = X = EQ/(C_{r}Mg)/[1+(V/V_{d})^{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 V_{d} is determined by setting F_{r} = F_{a}.
Drag speed = V_{d} = [C_{r} M g / (½ C_{a} D A)]^{½} = 4.01 [C_{r} M /(C_{a} A)]^{½} = 17.0 meters/second
Electric car engine .80 Gasoline engine .15 Diesel engine .20 Human muscles .22 Biomass plant .25 Natural gas plant .35 Solar cell .20 Crystalline type Solar cell .40 Multilayer type Turboprop, Mach .4 .80 Turboprops work up to Mach .5 Turbojet, Mach .4 .40 Turbofan, Mach .4 .68 Turbojet, Mach .9 .77 Turbofan, Mach .9 .90For an electric vehicle the overall efficiency is similar to that of a diesel engine.
Overall efficiency = Power plant efficiency * Vehicle efficiency = .35 * .80 = .28
Speed l/km l/km/ Passengers m/s person Walk 1.4 .0065 .0065 1 60 Watts Run .009 .009 1 Bike 4.4 .0032 .0032 1 Bike, aerodynamic 13.9 .0005 .0005 1 Car, solar power .067 .067 1 Car, electric, Tesla .015 .004 4 Car, electric, GEM NER 10.8 .012 .003 4 Car, electric, GE EV1 .026 .006 4 Car, electric, Volt .026 .006 4 Car, VW Bluemotion .038 .010 4 Car, Honda Insight .049 .012 4 Car, Toyota Prius .051 .013 4 Car, Cadillac Wagon .17 .028 6 6.2L engine Car, Bugatti Veyron .24 .12 2 Train, Switzerland .17 .0026 65 Train, Japan .65 .011 59 Plane, Dieselis 44.4 .019 .010 2 Plane, Pipistrel Sinus 62.5 .048 .024 2 Plane, Tecnam Sierra 65.8 .072 .036 2 Plane, DynAero MCR4S 61.1 .088 .022 4 100 hp Plane, Boeing 747400 3.1 660 Plane, Concorde 16.6 128 Plane, Airbus A380 3.0 835 Ship, Queen Elizabeth 300 .17 1777 Ship, Cargo 12.8 1070   Emma Maersk. 170000 tons Helicopter, Sikorsky 72.2 1.43 .12 12 Model S761 litre gasoline = 31.7 MJoules
MJ/km/ Passengers person per vehicle Train, Switzerland .085 65 Train, Japan .35 59 Car, electric 1.2 1.5 Train, city 1.60 30.9 Train, intercity 1.65 24.5 Motorcycle 1.61 1.16 Air 1.85 99.3 Car, gasoline 2.32 1.55 Bus 2.78 9.2 Taxi 10.3 1.55
MJ/km/ton Ship, U.S. local .16 Ship, ocean cargo .22 Emma Maersk. 170000 tons Train .21 Truck 2.43 Air 6.9
For a 1level prefabricated square bamboo house,
Side length = 8 meters Wall height = 3 meters Floor area = 64 meters^{2} Wall area = 24 meters^{2} Interior walls = 24 meters^{2} Total wall area = 248 meters^{2} Floor, ceiling, 4 walls, and interior walls Wall thickness = .05 meters Wall volume = 12.4 meters^{3} Bamboo density = 350 kg/meter^{2} 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.
Battery lithium content = .023 kg/MJoule Lithium price = 20 $/kg Battery lithium $/MJoule = .46 $/MJoule Battery total $/MJoule = 100 $/MJoule CO2 per MJoule = 42 kg/MJoules (to produce lithiumion batteries)
Cost of electricity = 30 MJoules/$ Crop time = 3 Mseconds = 40 days Lamp power =1000 Watts Lamp energy per crop = 3 GJoules/crop Lamp energy cost per crop = 100 $/crop
The following table shows the elemental composition of a typical hydroponic nutrient solution in parts per million.
Nitrogen 600 Calcium 400 Sulfur 400 Potassium 250 Magnesium 80 Phosphorus 80 Iron 4 Boron 2 Nickel 1 Manganese .8 Zinc .5 Copper .5 Molybdenum .01Hydroponic fertilizer can be purchased in solid form for $12/kg on Amazon.com. One kg of solid fertilizer supplies 500 kg of water.
The Gigafactory in Nevada has a production target for 2020 of:
Battery production = 200 TeraJoules/year Energy of one car = 310 MJoules (Tesla Model S) Cars supplied/year = .64 millionThe Solar City Factory produces solar panels.
Panel production = 1.0 GWatts/year Panel duty factor = .25 (Average solar intensity over peak solar intensity) Effective power production = .25 GWatts/yearce1.html 0;256;0c
Hydrogen White Carbon Black Nitrogen Blue Oxygen Red Sulfur Yellow
Scoville scale (relative capsaicin content) Ghost pepper 1000000 Trinidad 1000000 Trinidad moruga scorpion Naga Morich 1000000 Habanero 250000 Cayenne 40000 Tabasco 40000 Jalapeno 6000 Pimento 400 Molecule Relative hotness Rresiniferatoxin 16000 Tinyatoxin 5300 Capsaicin 16 Chili pepper Nonivamide 9.2 Chili pepper Shogaol .16 Ginger Piperine .1 Black pepper Gingerol .06 Ginger Capsiate .016 Chili pepper