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Equation 1 · Part 14 · Flight at the Energy Floor: Transport Selection to 2100

Numerator: aM

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)
aMaM

What this part means

The complete quantity above the fraction bar.

Its job in the formula

aM occurs above the fraction bar. The numerator is divided by the entire denominator below it.

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

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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Sources cited in the surrounding passage

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