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ln⁡(W1/W2)\ln(W_1/W_2)

Why this formula appears here

where a is the local speed of sound, M is cruise Mach number, g is standard gravity, cTc_T is thrust-specific fuel consumption, L/D is the lift-to-drag ratio, and W1W_1 and W2W_2 are the aircraft’s weight at the start and end of the cruise segment [ 1 ] . Three of those four factors — speed, engine efficiency, and aerodynamic efficiency — are where a century of aeronautical engineering has already done most of its work and where further gains now come in single-digit percentages per generation, the flattened tail of aviation’s S-curve. The fourth factor, the mass-ratio term ln⁡(W1/W2)\ln(W_1/W_2) , is where the aviation lineage’s entire battery-versus-kerosene argument actually lives, because W1W_1/W2W_2 is set…

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W1W_1

Symbol W_1

W1W_1 is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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W2W_2

Symbol W_2

W2W_2 is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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Published contexts (3)

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ln⁡(W1/W2)\ln(W_1/W_2)

Equation 9 · Technological Evolution

Flight at the Energy Floor: Transport Selection to 2100

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

where a is the local speed of sound, M is cruise Mach number, g is standard gravity, cTc_T is thrust-specific fuel consumption, L/D is the lift-to-drag ratio, and W1W_1 and W2W_2 are the aircraft’s weight at the start and end of the cruise segment [ 1 ] . Three of those four factors — speed, engine efficiency, and aerodynamic efficiency — are where a century of aeronautical engineering has already done most of its work and where further gains now come in single-digit percentages per generation, the flattened tail of aviation’s S-curve. The fourth factor, the mass-ratio term ln⁡(W1/W2)\ln(W_1/W_2) , is where the aviation lineage’s entire battery-versus-kerosene argument actually lives, because W1W_1/W2W_2 is set…

Equation guide → · Article →
ln⁡(W1/W2)\ln(W_1/W_2)

Equation 11 · Technological Evolution

Flight at the Energy Floor: Transport Selection to 2100

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

where a is the local speed of sound, M is cruise Mach number, g is standard gravity, cTc_T is thrust-specific fuel consumption, L/D is the lift-to-drag ratio, and W1W_1 and W2W_2 are the aircraft’s weight at the start and end of the cruise segment [ 1 ] . Three of those four factors — speed, engine efficiency, and aerodynamic efficiency — are where a century of aeronautical engineering has already done most of its work and where further gains now come in single-digit percentages per generation, the flattened tail of aviation’s S-curve. The fourth factor, the mass-ratio term ln⁡(W1/W2)\ln(W_1/W_2) , is where the aviation lineage’s entire battery-versus-kerosene argument actually lives, because W1W_1/W2W_2 is set…

Equation guide → · Article →
ln⁡(W1/W2)\ln(W_1/W_2)

Equation 12 · Technological Evolution

Flight at the Energy Floor: Transport Selection to 2100

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

Jet fuel carries about 43 megajoules of chemical energy per kilogram, or roughly 11,944 watt-hours per kilogram [ 2 ] . A modern commercial lithium-ion cell, by contrast, runs 160 to 300 watt-hours per kilogram at the cell level, with specialty laboratory cells using silicon-anode and graphene-enhanced chemistries reaching a record of roughly 450 watt-hours per kilogram [ 3 ] — figures that describe a bare cell, not a certified aircraft pack, which must add cooling, structure, wiring, and safety margin on top. A widely cited 2018 estimate for a packaged aviation battery, including that overhead, put usable specific energy at around 160 watt-hours per kilogram, or about two percent of…

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