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Equation 1 · Part 10 · Flight at the Energy Floor: Transport Selection to 2100

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R=aMg cT⋅LD⋅ln⁡ ⁣(W1W2)R = \frac{aM}{g\,c_T}\cdot\frac{L}{D}\cdot\ln\!\left(\frac{W_1}{W_2}\right)
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What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

Aircraft range is not a free parameter; it is fixed by a single classical relation once cruise speed, aerodynamic efficiency, and fuel fraction are set. In its standard Mach-number form, the range an aircraft can fly in cruise is: R=aMg cT⋅LD⋅ln⁡ ⁣(W1W2)R = \frac{aM}{g\,c_T}\cdot\frac{L}{D}\cdot\ln\!\left(\frac{W_1}{W_2}\right). 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…

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the surrounding passage

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