. | Economics for Electric Take-Off to 10,000m Altitude | You can use this spreadsheet to experiment with the parameters for an electric-takeoff system. | |||

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. | Electricity Cost Estimates | Value | Unit | Notes | |

. | Electricity Cost | 80 | $/MWh | ||

. | Tow Aircraft Power Required | 13.3876190674319 | MW | See power calculation below | |

. | Hourly Cost | 1071.00952539455 | $/h | ||

. | Weight of electric tow aircraft | 10000 | KG | Assume no seats, no aviation fuel, retrofitted electric engines | |

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. | Drag from Power Cable | ||||

. | Width of cable (w) | 0.05 | m | HMPE rope and aluminium conductor. Assume aluminium and HMPE are packaged in aerodynamic sheath. | |

. | Length of electric cable (xmax) | 10770.329614269 | m | Assume 10km altitude, 4km radius for tow plane | |

. | Area of cable | 1538.51648071345 | m2 | ||

. | Coefficent of drag for cable with aerodynamic sheath/fairing | 0.02 | http://en.wikipedia.org/wiki/Drag_coefficient#Aircraft | ||

. | Air density (10000m altitude) | 0.4135 | kg/m3 | http://www.aerospaceweb.org/design/scripts/atmosphere/ | |

. | Velocity | 450 | kmh | Fastest point of cable | |

. | Max Cable Velocity (m/s) (Vmax) | 125 | m/s | ||

. | Cable Velocity at point x on cable: Vx = Vmax * x / xmax | Velocity on cable is proportional to radius of circle (i.e. distance x from center of circle) | |||

. | Substitute Cable Velocity equation into drag equation | Drag(x) = 1/2 * rho * (Vmax * x / xmax)^2 * cD * w | |||

. | Integrate from x=0 to x=xmax to get total drag | 11597.7377486985 | Total drag = 1/2 * rho * 1/3 x^3 * Vmax^2 / xmax ^2 * cD * w | ||

. | Cable drag | 11597.7377486985 | N | http://en.wikipedia.org/wiki/Drag_equation | |

. | Cable drag for tow cable + two pulley cables | 34793.2132460956 | N | ||

. | Aluminum weight (1km) | 150 | KG/km | ||

. | HMPE cable weight (1km) (184 MT breaking load) | 1340 | kg/km | http://www.samsonrope.com/offshore-pdf/ofs-neutron-8-specs.pdf | |

. | Aluminum total weight | 3,231 | KG | Two conductors to tow height for high voltage direct current power (HVDC) | |

. | HMPE + aluminum cable total weight | 43431.0988842807 | KG | Assume three tethers to tow plane height | |

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. | Freight Cost per Tonne-Mile | ||||

. | Payload (max. weight) - includes aircraft and cargo | 35,092 | KG | Note payload weight is halved to account for dual downward forces on the pulley (winch and payload) | |

. | Cargo weight | 17545.9441883686 | KG | Assume 50% cargo, 50% aircraft weight. | |

. | Lift duration | 3 | min | ||

. | Lifts per hour | 20 | Assumes continuous operation | ||

. | Cargo per hour (weight) | 350,919 | KG | ||

. | Energy Cost per 1000KG payload (fixed) | $3.05 | $/1000KG | Assumes continuous operation | |

. | Winch Lifting Velocity | 250 | kmh | ||

. | Lifting Velocity (m/s) | 69.44 | m/s | ||

. | Lifting Power at max payload | 23.8819795897239 | MW | Vertical distance per second multiplied by weight * 9.8 (gravity). Ignores friction of pulley and winch motor. | |

. | Lifting Power Cost per 1000KG (gravitational potential energy) | $5.44 | $/1000KG | ||

. | Lift distance | 10,000 | m | ||

. | Lift distance (feet) | 33,333 | feet | ||

. | Glide distance | 300000 | m | ||

. | Total cost per 1000KG (Tonne) | $8.50 | $/1000KG | ||

. | Fuel cost (Electric Air Freight) | $0.05 | tonne-mile | Multiply electric ascent height by glide ratio to calculate glide distance. Assumes insignificant landing or taxi fuel cost. Assume freight aircraft stops at intermittent airports after each glide for electric ascent. | |

. | Freight revenue (Conventional Trucking) | $0.27 | tonne-mile | http://www.bts.gov/publications/national_transportation_statistics/html/table_03_17.html | |

. | Freight revenue (Conventional Air Freight) | $0.82 | tonne-mile | see above | |

. | Freight revenue (Rail) | $0.03 | tonne-mile | see above | |

. | Freight cost per ton - kg | $0.03 | ton - km | ||

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. | Lift Calculation | ||||

. | Angle of Attack | 15 | Optimized for maximum lift (see diagram on right) | ||

. | Lift Coefficient (CL) | 1.5 | http://www.aerospaceweb.org/question/aerodynamics/q0015b.shtml | ||

. | Air density (10000m altitude) (p) | 0.4135 | KG/m3 | http://www.aerospaceweb.org/design/scripts/atmosphere/ | |

. | Wing area (A) | 250 | m2 | Multiple tow planes may be used or a single tow plane with large wing area. Boeing 737 has 125 m2 wing area for comparison. See http://www.airliners.net/aircraft-data/stats.main?id=96 | |

. | Speed | 450 | kmh | ||

. | Speed (m/s) | 125 | m/s | ||

. | Lift = 1/2 p V^2 A CL | 1211425.78125 | N | ||

. | Lift (KG) | 123614.875637755 | KG | http://www.aerospaceweb.org/question/aerodynamics/q0015b.shtml | |

. | Glide Distance Calculation | ||||

. | Glide ratio for freight aircraft | 30 | Note aircraft designed for glide may achieve a ratio of 30 or more. | http://en.wikipedia.org/wiki/Gliding_%28flight%29#Glide_ratio | |

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. | Lift to Drag ratio of tow aircraft | 20 | |||

. | Induced drag of tow aircraft | 60571.2890625 | N | ||

. | Drag from cable | 34793.2132460956 | N | ||

. | Parasitic drag of tow aircraft (guess) | 2000 | N | ||

. | Total drag = thrust required | 97364.5023085956 | N | ||

. | Tow aircraft power | 12.1705627885744 | MW | http://en.wikipedia.org/wiki/Thrust#Thrust_to_power | |

. | Electrical transmission losses (10%) | 1.21705627885744 | MW | ||

. | Total tow aircraft power | 13.3876190674319 | MW |